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Track-to-Track Association for Intelligent Vehicles by Preserving Local Track Geometry

1 Key Laboratory of Intelligent Air-Ground Cooperative Control for Universities in Chongqing, College of Automation, Chongqing University of Posts and Telecommunications, Chongqing 400065, China; nc.ude.tpuqc@oahuhz (H.Z.); nc.ude.tpuqc@ufgnoyil (Y.L.)

Allan De Freitas

2 Department of Electrical, Electronic and Computer Engineering, University of Pretoria, Hatfield 0002, South Africa; [email protected]

Hamid Esmaeili Najafabadi

3 Department of Electrical and Computer Engineering, University of Calgary, Calgary, AB T2N 1N4, Canada; [email protected]

Track-to-track association (T2TA) is a challenging task in situational awareness in intelligent vehicles and surveillance systems. In this paper, the problem of track-to-track association with sensor bias (T2TASB) is considered. Traditional T2TASB algorithms only consider a statistical distance cost between local tracks from different sensors, without exploiting the geometric relationship between one track and its neighboring ones from each sensor. However, the relative geometry among neighboring local tracks is usually stable, at least for a while, and thus helpful in improving the T2TASB. In this paper, we propose a probabilistic method, called the local track geometry preservation (LTGP) algorithm, which takes advantage of the geometry of tracks. Assuming that the local tracks of one sensor are represented by Gaussian mixture model (GMM) centroids, the corresponding local tracks of the other sensor are fitted to those of the first sensor. In this regard, a geometrical descriptor connectivity matrix is constructed to exploit the relative geometry of these tracks. The track association problem is formulated as a maximum likelihood estimation problem with a local track geometry constraint, and an expectation–maximization (EM) algorithm is developed to find the solution. Simulation results demonstrate that the proposed methods offer better performance than the state-of-the-art methods.

1. Introduction

Reliable situational awareness plays an essential role in intelligent vehicles and surveillance systems [ 1 , 2 , 3 , 4 , 5 , 6 ]. Typical intelligent vehicles employ various types of sensors, such as radio detection and ranging (radar), light detection and ranging (lidar), and video. The radar sensor determines the relative location and the radial velocity of objects by emitting radio signals. Radar measurements often consist of false alarm detections in addition to detections from real objects or targets while missing some target-originated detections. The lidar sensor uses laser light to detect objects. Compared to radar, it provides more detailed measurements at an increased cost. Video sensors are feature-rich with a wide field-of-view, but they are more sensitive to different illumination and weather conditions [ 1 ]. Since these sensors have different sensing capabilities, features, and accuracies, the use of multiple heterogeneous sensors can result in more reliable and multi-modal environment perception systems. Therefore, pedestrians, vehicles, and obstacles are typically detected and tracked using a multi-sensor system in intelligent vehicles [ 7 , 8 , 9 ]. A multi-sensor multi-target tracking module jointly estimates the states and the number of targets from sensor measurements in intelligent vehicles, and it can be broadly categorized as centralized or distributed. The advantage of the distributed tracking systems is that they can provide a degree of scalability and robustness not achievable by traditional centralized tracking systems [ 1 ].

Track-to-track association (T2TA) is a crucial task in distributed tracking to find the correspondence between local tracks from different sensors. It is commonly applied to combine the local tracks of a sensor with those of another sensor to form the global tracklist. For automotive applications, radar, lidar, and video sensors in environmental perception systems for intelligent vehicles use different coordinate systems and sampling frequencies. Therefore, a spatio-temporal calibration should be performed to align the detections from different sensors [ 1 ]. In practice, detection from radar, lidar, and video sensors cannot always be calibrated or aligned accurately [ 10 ]. Each sensor may cover a different part of the surveillance region with a detection probability of less than one. As a result, some local tracks from a sensor may not correspond to those of other sensors. The range, azimuth, and elevation biases of a radar sensor may lead to errors in the local tracks from that sensor. The relationship between radar sensor bias and local tracks is presented in Figure 1 , where two radar sensors, A and B , and one target, T , are shown. The radar sensor bias leads to the reporting of the target T as tracks T A and T B by radar A and B , respectively. Note that if the biases in A and B radars are significant, the distance between T A and T B is correspondingly high. In this case, T A and T B is considered as originating from two different targets by the T2TA module. Therefore, T2TA in intelligent vehicles or surveillance systems suffers from many challenges, including missing detection and measurement bias. In this paper, the focus is on the problem of independent T2TA for each frame in the presence of missed detections and sensor bias.

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Relationship between sensor bias and local tracks.

To formulate the T2TA as an optimization problem, different statistical distances or metrics are proposed in literature [ 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 ]. In [ 11 ], a weighted statistical distance is proposed for T2TA with the assumption that the local estimation error of one sensor is independent of those of other sensors for the same target. In [ 13 ], the independence assumption is relaxed, and a modified statistical distance with dependent errors is developed for T2TA. In [ 19 ], three algorithms based on the squared Mahalanobis distance are investigated, and the nearest neighbor (NN) and global nearest neighbor (GNN) algorithms are applied to compute the distance between two tracks for T2TA. In [ 20 ], a likelihood function for T2TA from multiple sensors is derived, and the multidimensional assignment algorithm is employed to solve the optimal matching problem. State augmentation data, which combines the kinematic state information and the additional feature state information, is proposed to perform T2TA in [ 21 ]. In [ 25 ], a track association algorithm is proposed based on the permutation matrix to support the track-to-track multi-sensor data fusion for multiple targets in an autonomous driving system. It is worth noting that most T2TA algorithms in intelligent vehicles employ the conventional GNN algorithm [ 25 , 26 , 27 , 28 ].

Nevertheless, most of the above methods do not consider the presence of sensor bias. In reality, T2TA performance significantly degrades with sensor bias [ 29 ]. Literature addressing this problem can be roughly divided into batch and online approaches. The batch approach is an offline implementation that estimates the track association and sensor bias using all local tracks [ 30 , 31 , 32 ]. A joint sensor registration and track-to-track fusion method is derived using an equivalent measurement method in [ 30 ], while a pseudo-measurement approach is adopted to handle registration and track fusion simultaneously in [ 31 ]. In [ 32 ], a joint registration, data association, and fusion method in a distributed sensor network is formulated as a maximum likelihood (ML) optimization problem. An expectation-maximization (EM) algorithm is then proposed to perform the ML optimization, joint association, and bias removal through following an iterative strategy. However, these methods are susceptible to being trapped in local minima and have high computational costs. The online approach is a real-time implementation to perform track association with sensor bias. In [ 33 ], relative position information among neighboring tracks is analyzed, and a reference topology feature is derived for the absolute position information. An optimal sub-pattern assignment (OSPA) metric is also proposed to construct the association cost for T2TASB. In [ 34 ], the OSPA metric is modified by compensating for the relative azimuth bias. In [ 35 ], the T2TASB is formulated as a point set registration problem, and a coherent point drift (CPD) algorithm is proposed to perform T2TASB. In the CPD algorithm, local tracks of one sensor are represented by Gaussian mixture model (GMM) centroids [ 4 , 36 ], where local tracks of all sensors are fitted to those of a reference sensor. Still, the CPD algorithm only exploits the relationship among local tracks from different sensors, i.e., it does not utilize the relative geometric relationship between a local track and its neighbors from each sensor. The geometry among neighboring local tracks is usually stable at least for a while and thus helpful in improving the T2TASB. Here, the geometry is inspired by the idea that the relationship between a local track and its neighbors from different sensors could be preserved after the transformation. Hence, the geometry among neighboring local tracks is usually stable at least for a while and thus helpful in improving the T2TASB.

In this paper, the problem of independent T2TA for each frame in the presence of missed detections and sensor bias is considered. A probabilistic method, called the local track geometry preservation (LTGP) algorithm, is proposed to handle T2TASB. In the proposed method, the local tracks of one sensor are represented by GMM centroids, and the local tracks of the other sensor are fitted to those of the first using a nonlinear transformation function. The local track geometry with k -connected neighborhood is developed, and the T2TASB is formulated as an ML optimization problem with an EM algorithm being proposed to address it.

Different from other literature, the main contributions of this paper are as follows:

  • The mathematical formulation for T2TASB is presented. Moreover, the local track geometry with k -connected neighborhood is derived to improve the robustness and accuracy of T2TASB. The proposed method extends the CPD method by considering the geometric relationship between neighboring tracks.
  • An EM algorithm is proposed for T2TASB. The optimal T2TASB correspondence matrix and transformation function between local tracks are estimated simultaneously.
  • The performance of the proposed method is validated by the experiments and computer simulations using the KITTI dataset.

This paper is organized as follows. The formulation of T2TASB is presented in Section 2 . In Section 3 , the EM algorithm is used to estimate the parameters in the proposed method. The performance of the proposed approach is evaluated using computer simulations and experiments on the KITTI dataset in Section 4 and Section 5 , respectively. Finally, conclusions and future work are discussed in Section 6 .

2. A New Method for T2TASB

In this section, the T2TASB problem is formulated and a new solution is proposed. Let X k s denote the local tracks from sensor s at time k , where X k s = x 1 , k s T , x 2 , k s T … , x N k s , k s T T . The  x i , k s denotes the i -th track state estimate and the corresponding covariance from sensor s at time k , where k = 1 , 2 , … K , i = 1 , 2 … , N k s with K and N k s being the total number of discrete time steps and the number of tracks at time k by sensor s , respectively. Here, two sensors are applied to find the global track states, i.e., s = 1 , 2 . The objective of the T2TASB algorithm is to find the correspondence between X k 1 and X k 2 .

In [ 35 ], T2TASB is considered as a probability density estimation problem. In this paper, the relative geometry among neighboring local tracks from each sensor is proposed to formulate a maximum likelihood estimation problem with a local track geometrical constraint. Assuming that the local tracks of one sensor are represented by GMM centroids, the corresponding local tracks of the other sensor are fitted to those of the first sensor. Let x t , k 1 be the t -th data and x l , k 2 be the centroid of the l -th component. That is,

where N denotes the Gaussian distribution; σ k 2 denotes the equal isotropic covariance at time k ; f denotes the nonrigid transformation; I is the identity matrix; D is the size of a local track vector, and π t , l k is the mixing coefficient at time k with ∑ l π t , l k = 1 . We introduce an indicator Z k = [ z 1 k , z 2 k , … z N k 1 k ] , where z t k is a 1 × N k 1 binary vector with elements z t , l k for l = 1 , 2 , … N k 2 . The  z t , l k satisfy z t , l k ∈ { 0 , 1 } and ∑ l z t , l k = 1 conditions. That is, only one element in vector z t k is 1 while all other elements are 0. We have

where π k = { π t , l k } t = 1 , 2 , … N k 1 l = 1 , 2 , … N k 2 . Here, a distribution 1 N k 1 with weight w is employed to represents the component of a target detected by sensor 1, but not detected by sensor 2. The relationship between the local track lists x t , k 1 and x l , k 2 can be given by

The nonrigid transformation f aligns the local tracks, while some nonlinear functions might be employed to approximate it as well. More detail of the nonrigid transformation is given in Appendix A . Here, the displacement function is adopted as [ 35 ]

where W k is an N k 2 × D dimensional weight matrix of the Gaussian kernel; G k denotes an N k 2 × N k 2 Gaussian kernel matrix with elements g i j = e − 1 2 β ( x i , k 2 − x j , k 2 ) T ( x i , k 2 − x j , k 2 ) ; and, β denotes the width parameter in the smoothing Gaussian filter. To enforce the smoothness of transformation f , the constraint on the weight matrix W k can be given by [ 35 , 37 ]:

where Tr ( . ) denotes the trace of a matrix and superscript T denotes transposition. By ignoring the constants independent of { σ k 2 } and { W k } , the objective function of T2TASB can be written as

where α controls the trade-off parameter and q ( z t , l k ) is used to denote p ( z t , l k = 1 X k 1 , X k 2 ) .

Consider the membership probability π t , l k in ( 2 ), which is assumed to be the same for all components [ 35 ]. Here, π t , l k is initialized using the traditional nearest neighbor (NN) method [ 38 ] as follows:

(1) If track t from sensor 1 is associated with track l from sensor 2 at time k using NN assignment, we have

where 0 ≤ τ ≤ 1 is the confidence in association with the NN method.

(2) If track t from sensor 1 is not associated with any track from sensor 2 at time k using NN assignment, then the uniform membership probability is applied:

The transformation f uses the relationship between local tracks from different sensors, but does not consider the relative geometry between one track and its neighbors from each sensor. The geometry is inspired by the idea that the relationship between a local track and its neighbors from different sensors could be preserved after the transformation, as depicted in Figure 2 . To ensure an accurate T2TA, a geometrical constraint on the local tracks is proposed in this paper. A schematic illustration of the geometrical constraint is given in Figure 2 .

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Schematic illustration of the geometrical constraint. ( a ) with local tracks from sensor 1 and 2, assign neighbors to each local track from its sensor, e.g., the four local tracks around x i 2 ( b ) compute the weights L ( c ) perform the transformation f with the constraint that each local track x i 2 be reconstructed by its neighbors with weights L after the transformation ( d ) align the Local tracks from sensor 1 and 2 after transformation f by maximizing the objective function.

We desire to preserve the geometry of tracks X k 2 after the nonrigid transformation f . Based on the Euclidean distance between each local track and its neighbors in X k 2 , the M nearest neighbors of each local track in X k 2 are obtained. Then, each point in X k 2 is represented as a weighted linear combination of its M nearest neighbors. Let L = { L l j } l = 1 : N k 2 j = 1 : N k 2 be an N k 2 × N k 2 weighted matrix. If track state x j , k 2 does not belong to the M nearest neighbors of track state x l , k 2 , then L l j is set to 0. Here, matrix L is obtained by minimizing the following cost function:

where the sum of each row of L is equal to 1. After the nonrigid transformation, the local track geometry can be preserved by minimizing the transformed cost function:

where G k ( i , . ) is the i -th row of G k . The objective function of T2TA with sensor bias in ( 7 ) is given by

where γ controls the trade-off between Q and E ( L ) .

3. EM Solution for the Proposed Method

Let Θ = { Z k } , { σ k 2 } , { W k } be the unknown parameters. To obtain an ML estimate of Θ , the EM algorithm is applied here. There are two steps in the EM algorithm:

  • 1). E -step: E L ( Θ , Θ ( m ) ) = Q 1
  • 2). M -step: Θ ( m + 1 ) = max E L ( Θ , Θ ( m ) ) ,

where m is the iteration number of the algorithm. The  E -step calculates the conditional expectation using the current estimate Θ ( m ) , whereas the M -step provides an updated estimation, Θ ( m + 1 ) . The estimate of Θ is updated by iterating through these two steps while the complete data likelihood function is maximized.

3.1. E-Step

First, q ( z t , l k ) can be found using Bayes’ theorem as

3.2. M-Step

Then, E L ( Θ , Θ ( m ) ) is rewritten as

where d i a g ( . ) indicates diagonal matrix; R k is an N k 1 × N k 2 matrix with elements q ( z t , l k ) for t = 1 , 2 , ⋯ N k 1 , l = 1 , 2 , ⋯ N k 2 + 1 ; B k = I − L T d i a g ( R k T 1 ) I − L ; 1 represents the all-one column vector of corresponding length; and, I means the identity matrix.

The estimates of σ k 2 and W k are iteratively updated by solving the corresponding partial derivative of the expected log likelihood to zero. That is,

This results in

Thus, W k can be obtained by solving

Here, C k is used to denote the cost matrix of T2TASB at time k as an N k 1 × ( N k 2 + 1 ) matrix with ( t , l ) element C k ( t , l ) for t = 1 , 2 , ⋯ N k 1 , l = 1 , 2 , ⋯ N k 2 + 1 given by

where C k ( t , N k 2 + 1 ) represents the cost of not making an assignment. The assignment of track t from sensor 1 to track l from sensor 2 can occur only if C k ( t , l ) < C k ( t , N k 2 + 1 ) for t = 1 , 2 , ⋯ N k 1 , l = 1 , 2 , ⋯ N k 2 with C k ( t , N k 2 + 1 ) being a gate. If that gate is violated, no assignment option is selected. The solution for the above assignment problem is computed using the Hungarian algorithm [ 39 ].

The proposed LTGP method for T2TASB is summarized in Algorithm 1.

4. Computer Simulations

In this section, the performance of the proposed methods is evaluated using simulated data. Thirty targets following a discretized nearly constant velocity motion model [ 40 ] are tracked by multiple radar sensors. The initial target positions are randomly generated in the region − 100 km , 100 km × − 100 km , 100 km . The initial velocities of these targets are chosen as [ 0.5 km / s , 0.2 km / s ] . The covariances of the process and measurement noise components are respectively set to diag ( 10 − 4 k m 2 , 10 − 4 k m 2 / s 2 , 10 − 4 k m 2 , 10 − 4 k m 2 / s 2 ) , and diag(10 −4 km 2 , 10 −5 rad 2 ), where the cross-covariance terms have been ignored in the former [ 40 ]. The clutter is generated uniformly over the surveillance region using a Poisson random variable with a mean of 30 at each time step. The sampling period of the measurements is 1s. The number of time steps is 100.

Two radar sensors are considered in the distributed sensor network. The biases in the two sensors are set to η 1 = [ 1 km , − 0.017 rad ] T , and η 2 = [ − 2 km , 0.034 rad ] T . The detection probabilities P d of both radars are chosen as 0.95. Measurement-to-track association is performed at each sensor without considering the sensor bias. The local tracks from sensor 1 and sensor 2 are illustrated in Figure 3 .

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( a ) Local tracks from sensor 1 ( b ) Local tracks from sensor 2.

Parameter τ denotes the confidence in the association by the NN method. Parameter w denotes the initial assumption on the number of false targets detected by sensor 1, but not detected by sensor 2. Parameter β represents the width of the smoothing Gaussian filter in the nonlinear transformation function. Parameter M represents the number of nearest neighbors used in linear reconstruction to preserve the local track structure, while ρ is the parameter in the cross-covariance fusion. We set τ = 0.5, w = 0.2, β = 0.1, M = 10, and ρ = 0.4 throughout this paper.

Parameters α and γ represent the trade-off regularization terms. The ranges of these parameters were determined experimentally. The correct association probability P c defined as the ratio of the correctly assigned tracks over the total number of tracks is employed as the primary metric for performance evaluation. The variation of P c with regularization parameters α and γ at time step k = 50 is shown in Figure 4 . It is observed that the proposed method performs best when α ∈ [ 5 , 7 ] and γ ∈ [ 10 , 20 ] . Here, we set α = 6, and γ = 15.

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Model selection of the regularization parameters α and γ . ( a ) α ∈ [ 0.5 , 50 ] and γ ∈ [ 5 , 100 ] , ( b ) α ∈ [ 2 , 10 ] and γ ∈ [ 5 , 50 ] .

The proposed LTGP algorithm is used for T2TASB, and the results at time step k = 50 are given in Figure 5 , which illustrates that the local tracks from the two sensors are associated correctly by the proposed LTGP method.

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( a ) Local tracks at time step k = 50 ( b ) Local tracks at time step k = 50 after transformation with proposed method.

The performance of the proposed method is demonstrated next relative to those of GNN without registration, the reference pattern-based algorithm [ 33 ], and the CPD algorithm [ 35 ]. All results are averaged over 50 Monte Carlo runs. The proposed method achieves the best performance, as illustrated in Figure 6 . Compared to the reference pattern-based algorithm, the CPD algorithm improves the P c by about 8%. The P c of the proposed method has improved by 5% as compared with the CPD algorithm. Furthermore, the results for a scenario with varying detection probabilities and different numbers of targets are respectively illustrated in Figure 7 and Figure 8 . It is observed that the proposed algorithm outperforms the other three benchmark algorithms. From Figure 7 , the performance of GNN without registration, reference pattern-based algorithm, and CPD algorithm degrade rapidly with a decreased detection probability. From Figure 8 , the performance of the proposed method is almost constant while increasing the number of targets. Moreover, the average P c of the proposed method is improved by approximately 9% as compared with the CPD algorithm.

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Correct association probabilities of GNN without registration, reference pattern-based algorithm, CPD algorithm and the proposed method.

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Correct association probabilities of GNN without registration, reference pattern-based algorithm, CPD algorithm and the proposed method for different detection probabilities.

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Correct association probabilities of GNN without registration, reference pattern-based algorithm, correlation-based algorithm and the proposed method for a detection probabilities of P d = 0.9 when target cardinality changes within a fixed surveillance region.

The computational complexities of the proposed LTGP algorithm are analyzed next. For simplicity, the same number of local tracks N for each sensor every time is considered. At each time step in the LTGP algorithm, the computational complexity to search the M nearest neighbors for each local track in X k 2 is O ( ( M + N ) log N ) , using the k -d tree [ 41 ]; the computational complexity to obtain matrix L is O ( M 3 N ) ; and, the complexity of the EM algorithm is almost O ( N 3 ) [ 42 ]. The computational complexity at each time step in the LTGP algorithm is O ( N 3 ) . Therefore, the total computational complexity of the proposed LTGP algorithm is O ( N 3 K ) , where K is the total number of measurement samples.

5. Experiments on KITTI Dataset

In this section, we evaluate the proposed algorithm using the KITTI dataset. Here, the KITTI multi-object tracking dataset [ 43 ] is applied to evaluate the proposed data association method. The vehicle tracking test sequences 01 and 20, and pedestrian tracking test sequences 16 and 17 are used. Each sequence consists of 30 frames. Figure 9 depicts the starting frames of left and right cameras for each sequence along with the results of object detection. For the left camera, the detection results of vehicle or pedestrian are provided by the ground truth. Meanwhile, the deformable part model detector method [ 44 ] is proposed to detect vehicle or pedestrian for images of rthe ight camera.

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Typical frames of the KITTI dataset [ 43 ]. ( a ) Sequence 01 starting frame #34. ( b ) Sequence 20 starting frame #31. ( c ) Sequence 16 starting frame #63. ( d ) Sequence 17 starting frame #23.

The ground truth matching between the left and right images in each frame is confirmed by manual annotation. The GNN without registration, the reference pattern-based algorithm, the CPD algorithm, and the proposed method are employed to associate the local tracks. The average T2TA matching accuracy performances of different T2TA methods are depicted in Figure 10 . It is confirmed that the performance of the proposed method is substantially better than those of GNN without registration, the reference pattern-based algorithm, and the CPD algorithm. Compared with the CPD algorithm, the average performance of the proposed method is improved by about 7.8%. In addition, since the KITTI sequence 17 contains large pedestrian occlusion while the motion is more than the other sequences, the performance gap between this and other sequences is more evident. The proposed LTGP method has better performance compared to three benchmark algorithms in the KITTI sequence 17. It is because the proposed method preserves the geometry of local tracks in the data association. The average run-times of these algorithms are given in Table 1 , which reveals that the proposed LTGP method has higher computational complexity compared to the GNN without registration, reference pattern-based, and CPD methods.

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Track-to-track association matching accuracy of the GNN without registration, reference pattern-based algorithm, CPD algorithm and proposed LTGP method under different sequences of KITTI dataset.

The average run-times of these algorithms in four KITTI sequences

6. Conclusions

A probabilistic method for the track-to-track association, namely, LTGP, was proposed in this paper. In the LTGP method, one local track was transformed into another local track using a nonlinear function. We utilized k -connected neighbors to preserve the relative local track geometry. The T2TASB problem was formulated as a probability density estimation problem. The EM algorithm was used to fuse biased tracks from two sensors. To illustrate the advantages of the proposed method, some experiments of computer simulation and KITTI dataset were performed and the result is compared with GNN without registration, reference pattern-based algorithm, and CPD algorithm. Experiments on computer simulation involve varying detection probabilities and different numbers of targets, the proposed method has better performance than other algorithms for all detection probabilities and numbers of targets, but it has higher computational complexity. In the KITTI dataset, the proposed LTGP method has better performance than other methods. The T2TA matching accuracy of the proposed LTGP method was improved by about 7.8% as compared with the CPD method. From the experimental results of computer simulation and KITTI dataset, it can be concluded that the proposed LTGP method outperforms the GNN without registration algorithm, the reference pattern-based algorithm, and the CPD algorithm, but it has a higher computational load.

In the future, the proposed method is not restricted to the considered application but can be extended to other tasks, such as multi-sensor T2TASB for the connected vehicle. For the multi-sensor T2TASB scenario, the LTGP method can be extended using sequential processing.

Acknowledgments

The authors gratefully acknowledge the Autonomous Vision Group for providing the KITTI dataset. The authors also would like to thank the editors and referees for the valuable comments and suggestions.

Abbreviations

Appendix a. the relationship of two local tracks.

Assume that a target is detected by two sensors and that the two sensors are located at the coordinate origins. Due to the sensor bias, the target ( x , y ) is reported as x t , k 1 = [ x t , k 1 , y t , k 1 ] and x j , k 2 = [ x j , k 2 , y j , k 2 ] by the two sensors, respectively. By ignoring the random noises, we have [ 35 ]

where Υ i , k s and θ i , k s denote the real range and angle measurement of target i for sensor s , respectively. The Δ Υ s and Δ θ s represent the range bias and angle bias, respectively. Therefore,

From ( A5 )–( A8 ), we get

where θ 12 = Δ θ 1 − Δ θ 2 . Equation ( A9 ) gives the relationship between the local tracks x t , k 1 and x j , k 2 . In this paper, a non-rigid transformation as ( 5 ) is proposed to approximate the relationship from one local tracks to other local tracks.

Author Contributions

Major framework for the review, K.Z., H.Z. and Y.L.; software, K.Z.; writing–original draft preparation, K.Z. and H.Z.; writing–review and editing, A.D.F.; supervision, H.E.N. All authors have read and agreed to the published version of the manuscript.

This work is jointly supported by the Research Funds of Chongqing Science and Technology Commission (Grant No. cstc2017jcyjAX0293, No. CSTC2017JCYJBX0018, and No. CX2017044), by the National Natural Science Foundation of China (Grant No. 61773082), by the Key Project of Crossing and Emerging Area of CQUPT (Grant No. A2018-02), by the Research Fund of young-backbone university teacher in Chongqing province, by Chongqing Overseas Scholars Innovation Program, by Wenfeng Talents of Chongqing University of Posts and Telecommunications, by Innovation Team Project of Chongqing Education Committee (Grant No. CXTDX201601019), by the National Key Research and Development Program (Grant No. 2016YFB0100906), by the Research and Innovation of Chongqing Postgraduate Project (Grant No. {"type":"entrez-protein","attrs":{"text":"CYS19274","term_id":"993785037","term_text":"CYS19274"}} CYS19274 ), by the Lilong Innovation and Entrepreneurship Fund of Chongqing University of Posts and Telecommunications (Grant No. 2019-1-01).

Conflicts of Interest

The authors declare no conflict of interest.

Multisensor track-to-track association for tracks with dependent errors

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Book cover

Optimization and Cooperative Control Strategies pp 319–354 Cite as

Robust Track Association and Fusion with Extended Feature Matching

  • Huimin Chen 4 ,
  • Genshe Chen 5 ,
  • Erik P. Blasch 6 &
  • Tod M. Schuck 7  
  • Conference paper

1747 Accesses

6 Citations

Part of the Lecture Notes in Control and Information Sciences book series (LNCIS,volume 381)

In this work, we propose a new data processing architecture as well as track association and fusion algorithms to improve target classification and tracking accuracy using distributed and, possibly, legacy-sensor platforms. We present a robust data fusion algorithm that can incorporate target classes/types at the fusion center when receiving sensor reports and/or local tracks. We aim to tackle the following technical challenges in feature aided tracking.

Unknown number of targets: When the fusion center does not have any prior knowledge on the number of targets in the surveillance area, track fusion becomes extremely difficult especially when targets are closely spaced.

Measurement origin uncertainty: The local tracker does not know which measurement comes from which target and each local tracker may provide false tracks or incorrect target types. Consequently, the fusion center does not know which local tracks are from the same target and fusion has to be made based on imperfect data association.

Tracks from legacy sensor systems: Existing trackers often have very different filter designs. Some may be based on the state-of-the-art multiple model algorithm while some on the fixed gain Kalman filter. Thus some trackers can report both target state estimate and the associated covariance to the fusion center, but others may only provide target state estimate without the covariance information. Those legacy sensor systems require special treatment in the development of fusion algorithms.

Our track association framework can also incorporate tracks with extended feature points and kinematic constraints, which improves both data association and tracking accuracy.

  • Root Mean Square
  • Fusion Center
  • Fusion Algorithm
  • Local Track
  • Surveillance Region

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Chen, H., Chen, G., Blasch, E.P., Schuck, T.M. (2009). Robust Track Association and Fusion with Extended Feature Matching. In: Hirsch, M.J., Commander, C.W., Pardalos, P.M., Murphey, R. (eds) Optimization and Cooperative Control Strategies. Lecture Notes in Control and Information Sciences, vol 381. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88063-9_19

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The problem of track-to-track association has been considered until recently in the literature only for pairwise associations. In view of the extensive recent interest in multisensor data fusion, the need to associate simultaneously multiple tracks has arisen. This is due primarily to bandwidth constraints in real systems, where it is not feasible to transmit detailed measurement information to a fusion center but, in many cases, only local tracks. As it has been known in the literature, tracks of the same target obtained from independent sensors are still dependent due to the common process noise [2]. This paper derives the exact likelihood function for the track-to-track association problem from multiple sources, which forms the basis for the cost function used in a multidimensional assignment algorithm that can solve such a large scale problem where many sensors track many targets. While a recent work [14] derived the likelihood function under the assumption that the track errors are independent, the present paper incorporates the (unavoidable) dependence of these errors.

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Global Nearest Neighbor Multi Object Tracker

Multi-sensor, multi-object tracker using GNN assignment

Since R2019b

Global Nearest Neighbor Multi Object Tracker block

Libraries: Sensor Fusion and Tracking Toolbox / Multi-Object Tracking Algorithms

Description

The Global Nearest Neighbor Multi Object Tracker block is capable of processing detections of many targets from multiple sensors, much like the trackerGNN System object™. The tracker initializes, confirms, predicts, corrects, and deletes tracks based on a global nearest neighbor (GNN) assignment algorithm. The tracker estimates the state vector and state vector covariance matrix for each track. Each detection is assigned to at most one track. If the detection cannot be assigned to any track, the tracker initializes a new track.

Any new track starts in a tentative state. If enough detections are assigned to a tentative track, its status changes to confirmed. If the detection already has a known classification (the ObjectClassID field of the returned track is nonzero), that track is confirmed immediately. When a track is confirmed, the tracker considers the track to represent a physical object. If detections are not assigned to the track within a specifiable number of updates, the track is deleted.

Track Closely Spaced Targets Under Ambiguity in Simulink

Track objects in Simulink® with Sensor Fusion and Tracking Toolbox™ when the association of sensor detections to tracks is ambiguous. It closely follows the Tracking Closely Spaced Targets Under Ambiguity MATLAB® example.

Track Simulated Vehicles Using GNN and JPDA Trackers in Simulink

Track Simulated Vehicles Using GNN and JPDA Trackers in Simulink

Configure and utilize GNN and JPDA trackers in a simulated highway scenario in Simulink® with Sensor Fusion and Tracking Toolbox™. It closely follows the Sensor Fusion Using Synthetic Radar and Vision Data in Simulink (Automated Driving Toolbox). A main benefit of modeling the system in Simulink is the simplicity of performing "what-if" analysis and choosing a tracker that results in the best performance based on the requirements.

Detections — Detection list Simulink ® bus containing MATLAB ® structure

Detection list, specified as a Simulink bus containing a MATLAB structure. The structure has the form:

The fields of Detections are:

See objectDetection for more detailed explanations of these fields.

The object detection structure contains a Time field. The time tag of each object detection must be less than or equal to the time of the current invocation of the block. The time tag must also be greater than the update time specified in the previous invocation of the block.

Prediction Time — Track update time real scalar

Track update time, specified as a real scalar in seconds. The tracker updates all tracks to this time. The update time must always increase with each invocation of the block. Units are in seconds. The update time must be at least as large as the largest Time specified at the Detections input port.

If this port is not enabled, the simulation clock managed by Simulink determines the update time.

Dependencies

To enable this port, in the Port Setting tab, set Prediction time source to Input port .

Cost Matrix — Cost matrix real-valued N t -by- N d matrix

Cost matrix, specified as a real-valued N t -by- N d matrix, where N t is the number of existing tracks and N d is the number of current detections.

The rows of the cost matrix correspond to the existing tracks. The columns correspond to the detections. Tracks are ordered as they appear in the list of tracks at the All Tracks output port on the previous invocation of the block.

In the first update to the tracker, or if the track has no previous tracks, assign the cost matrix a size of [0, N d ]. The cost must be calculated so that lower costs indicate a higher likelihood that the tracker assigns a detection to a track. To prevent certain detections from being assigned to certain tracks, use Inf .

If this port is not enabled, the filter initialized by the Filter initialization function calculates the cost matrix using the distance method.

To enable this port, in the Port Setting tab, select Enable cost matrix input .

Detectable TrackIDs — Detectable track IDs real-valued M -by-1 vector | real-valued M -by-2 matrix

Detectable track IDs, specified as a real-valued M -by-1 vector or M -by-2 matrix. Detectable tracks are tracks that the sensors expect to detect. The first column of the matrix contains a list of track IDs that the sensors report as detectable. The second column contains the detection probability for the track. The detection probability is either reported by a sensor or, if not reported, obtained from the Probability of detection used for track score parameter.

Tracks whose identifiers are not included in Detectable TrackIDs are considered undetectable. The track deletion logic does not count the lack of detection as a "missed detection" for track deletion purposes.

If this port is not enabled, the tracker assumes all tracks to be detectable at each invocation of the block.

To enable this port, in the Port Setting tab, select Enable detectable track IDs Input .

State Parameters — Track state parameters Simulink bus containing MATLAB structure

Track state parameters, specified as a Simulink bus containing a MATLAB structure. The structure has the form:

The block uses the value of the Parameters field for the StateParameters field of the generated tracks. You can use these parameters to define the reference frame in which the track is reported or other desirable attributes of the generated tracks.

For example, you can use the following structure to define a rectangular reference frame whose origin position is at [10 10 0] meters and whose origin velocity is [2 -2 0] meters per second with respect to the scenario frame.

To enable this port, in the Tracker Configuration tab, select the Update track state parameters with time parameter.

Confirmed Tracks — Confirmed tracks Simulink bus containing MATLAB structure

Confirmed tracks, returned as a Simulink bus containing a MATLAB structure. The structure has the form:

The fields of the track structure are shown in Track Structure .

Depending on the track logic, a track is confirmed if:

History – A track receives at least M detections in the last N updates. M and N are specified in Confirmation threshold for the History logic.

Score – The track score is at least as high as the confirmation threshold specified in Confirmation threshold for the Score logic.

Tentative Tracks — Tentative tracks Simulink bus containing MATLAB structure

Tentative tracks, returned as a Simulink bus containing a MATLAB structure. A track is tentative before it is confirmed.

To enable this port, in the Port Setting tab, select Enable tentative tracks output .

All Tracks — Confirmed and Tentative tracks Simulink bus containing MATLAB structure

Combined list of confirmed and tentative tracks, returned as a Simulink bus containing a MATLAB structure.

To enable this port, in the Port Setting tab, select Enable all tracks output .

Info — Additional information for analyzing track updates Simulink bus containing MATLAB structure

Additional information for analyzing track updates, returned as a Simulink bus containing a MATLAB structure.

This table shows the fields of the info structure:

The OOSMHandling structure contains these fields:

To enable this port, in the Port Setting tab, select Enable information output .

Tracker identifier — Unique tracker identifier 0 (default) | nonnegative integer

Specify the unique tracker identifier as a nonnegative integer. This parameter is passed as the SourceIndex in the tracker outputs, and distinguishes tracks that come from different trackers in a multiple-tracker system. You must specify this property as a positive integer to use the track outputs as inputs to a Track-To-Track Fuser block.

Filter initialization function — Filter initialization function initcvekf (default) | function name

Filter initialization function, specified as the name of a valid filter initialization function. The tracker uses the filter initialization function when creating new tracks.

Sensor Fusion and Tracking Toolbox™ supplies many initialization functions that you can use:

You can also write your own initialization function. The function must have this syntax: filter = filterInitializationFcn(detection) The input to this function is a detection report like those created by objectDetection . The output of this function must be a filter object: trackingKF , trackingEKF , trackingUKF , trackingCKF , trackingPF , trackingMSCEKF , trackingGSF , trackingIMM , or trackingABF .

To guide you in writing this function, you can examine the details of the supplied functions from within MATLAB. For example:

type initcvekf

Maximum number of tracks — Maximum number of tracks 200 (default) | positive integer

Maximum number of tracks that the block can maintain, specified as a positive integer.

Maximum number of sensors — Maximum number of sensors 20 (default) | positive integer

Maximum number of sensors that the block can process, specified as a positive integer. This value should be greater than or equal to the highest SensorIndex value input at the Detections input port.

Out-of-sequence measurements handling — Out-of-sequence measurements handling Terminate (default) | Neglect | Retrodiction

Out-of-sequence measurements handling, specified as Terminate , Neglect , or Retrodiction . Each detection has an associated timestamp, t d , and the tracker block has it own timestamp, t t , which is updated in each invocation. The tracker block considers a measurement as an OOSM if t d < t t .

When you specify the parameter as:

Terminate — The block stops running when it encounters an out-of-sequence measurement.

Neglect — The block neglects any out-of-sequence measurements and continues to run.

Retrodiction — The block uses a retrodiction algorithm to update the tracker by either neglecting the OOSM, updating existing tracks, or creating new tracks using the OOSM. You must specify a filter initialization function that returns a trackingKF , trackingEKF , or trackingIMM object in the Filter initialization function parameter.

If you specify this parameter as Retrodiction , the tracker follows these steps to handle the OOSM:

If the OOSM timestamp is beyond the oldest correction timestamp (specified by the Maximum number of OOSM steps parameter) maintained in the tracker, the tracker discards the OOSMs.

If the OOSM timestamp is within the oldest correction timestamp by the tracker, the tracker first retrodicts all the existing tracks to the time of the OOSMs. Then, the tracker applies the joint probability data association algorithm to try to associate the OOSMs to the retrodicted tracks.

If the tracker successfully associates the OOSM to at least one retrodicted track, then the tracker updates the retrodicted tracks using the OOSMs by applying the retro-correction algorithm to obtain current, corrected tracks.

If the tracker cannot associate an OOSM to any retrodicted track, then the tracker creates a new track based on the OOSM and predicts the track to the current time.

For more details on the retrodiction and retro-correction algorithms, see Retrodiction and Retro-Correction . To simulate out-of-sequence detections, use objectDetectionDelay .

When you select Retrodiction , you cannot use the Cost Matrix input.

Maximum number of OOSM steps — Maximum number of OOSM steps 3 (default) | positive integer

Maximum number of out-of-sequence measurement (OOSMs) steps, specified as a positive integer.

Increasing the value of this parameter requires more memory but allows you to call the tracker block with OOSMs that have a larger lag relative to the last timestamp when the block was updated. Also, as the lag increases, the impact of the OOSM on the current state of the track diminishes. The recommended value of this parameter is 3 .

To enable this parameter, set the Out-of-sequence measurements handling parameter to Retrodiction .

Track state parameters — Parameters of track state reference frame structure | structure array

Specify the parameters of the track state reference frame as a structure or a structure array. The block passes the value of this parameter to the StateParameters field of the generated tracks. You can use these parameters to define the reference frame in which the track is reported or other desirable attributes of the generated tracks.

You can update the track state parameters through the State Parameters input port by selecting the Update track state parameters with time parameter.

Data Types: struct

Update track state parameters with time — Update track state parameters with time off (default) | on

Select this parameter to enable the input port for track state parameters through the State Parameters input port.

Enable memory management — Enable memory management off (default) | on

Select this parameter to enable memory management using the Maximum number of detections per sensor parameter to specify the maximum number of detections that each sensor can pass to the tracker during one call of the tracker. Additionally, if the Cluster tracks and detections for assignment parameter is specified as on , you can use three more parameters to specify bounds for certain variable-sized arrays in the tracker as well as determine how the tracker handles cluster size violations:

Maximum number of detections per cluster

Maximum number of tracks per cluster

Handle run-time violation of cluster size

Specifying bounds for variable-sized arrays allows you to manage the memory footprint of the tracker in the generated C/C++ code.

Assignment algorithm name — Assignment algorithm name 'MatchPairs' (default) | 'Munkres' | 'Jonker-Volgenant' | 'Auction' | 'Custom'

Assignment algorithm, specified as 'MatchPairs' , 'Munkres' , 'Jonker-Volgenant' , 'Auction' , or 'Custom' . Munkres is the only assignment algorithm that guarantees an optimal solution, but it is also the slowest, especially for large numbers of detections and tracks. The other algorithms do not guarantee an optimal solution but can be faster for problems with 20 or more tracks and detections. Use 'Custom' to define your own assignment function and specify its name in the CustomAssignmentFcn property.

Name of 'Custom' assignment function — Custom assignment function name character vector

Custom assignment function name, specified as a character string. An assignment function must have this syntax: [assignment,unTrs,unDets] = f(cost,costNonAssignment) For an example of an assignment function and a description of its arguments, see assignmunkres .

Example: 'mycustomfcn'

To enable this property, set the Assignment algorithm name name to 'Custom' .

Threshold for assigning detections to tracks — Threshold for assigning detections to tracks 30*[1 Inf] (default) | positive scalar | 1-by-2 vector of positive values

Threshold for assigning detections to tracks (or gating threshold), specified as a positive scalar or an 1-by-2 vector of [ C 1 ,C 2 ], where C 1 ≤ C 2 . If specified as a scalar, the specified value, val , will be expanded to [ val , Inf ].

Initially, the tracker executes a coarse estimation for the normalized distance between all the tracks and detections. The tracker only calculates the accurate normalized distance for the combinations whose coarse normalized distance is less than C 2 . Also, the tracker can only assign a detection to a track if their accurate normalized distance is less than C 1 . See Algorithms for an explanation of the normalized distance.

Increase the value of C 2 if there are combinations of track and detection that should be calculated for assignment but are not. Decrease it if cost calculation takes too much time.

Increase the value of C 1 if there are detections that should be assigned to tracks but are not. Decrease it if there are detections that are assigned to tracks they should not be assigned to (too far away).

If the value of C 2 is finite, the state transition function and measurement function, specified in the tracking filter used in the tracker, must be able to take an M -by- N matrix of states as input and output N predicted states and N measurements, respectively. M is the size of the state. N , the number of states, is an arbitrary nonnegative integer.

Cluster tracks and detections for assignment — Cluster tracks and detections for assignment off (default) | on

Specify cluster tracks and detections for assignment as:

off — The tracker solves the global nearest neighbor assignment problem per sensor using a cost matrix. The number of columns in the cost matrix is equal to the number of detections by the sensor, and the number of rows is equal to the number of tracks maintained by the tracker. Forbidden assignments (assignments with a cost greater than the Threshold for assigning detections to tracks parameter) have an infinite cost of assignment.

on — The tracker creates a cluster after separating out the forbidden assignments (assignments with a cost greater than the Threshold for assigning detections to tracks parameter) and uses the forbidden assignments to form new clusters based one the Threshold for assigning detections to tracks parameter. A cluster is a collection of detections (per sensor) and tracks considered to be assigned to each other. In this case, the tracker solves the global nearest neighbor assignment problem per cluster.

When you both specify this property as on and select Enable memory management in the Tracker Management tab, you can use these three parameters to specify bounds for certain variable-sized arrays in the tracker as well as determine how the tracker handles cluster size violations:

Specifying bounds for variable-sized arrays enables you to manage the memory footprint of the tracker, especially in the generated C/C++ code.

Simulate using — Type of simulation to run Interpreted Execution (default) | Code Generation

Interpreted execution — Simulate the model using the MATLAB interpreter. This option shortens startup time. In Interpreted execution mode, you can debug the source code of the block.

Code generation — Simulate the model using generated C code. The first time you run a simulation, Simulink generates C code for the block. The C code is reused for subsequent simulations as long as the model does not change. This option requires additional startup time.

Type of track confirmation and deletion logic — Confirmation and deletion logic type History (default) | Score

Confirmation and deletion logic type, selected as History or Score .

History – Track confirmation and deletion is based on the number of times the track has been assigned to a detection in the latest tracker updates.

Score – Track confirmation and deletion is based on a log-likelihood track score. A high score means that the track is more likely to be valid. A low score means that the track is more likely to be a false alarm.

Confirmation threshold [M N] — Track confirmation threshold for history logic [2 3] (default) | real-valued 1-by-2 vector of positive integers

Track confirmation threshold for history logic, specified as a real-valued 1-by-2 vector of positive integers [M N] . A track is confirmed if it receives at least M detections in the last N updates.

To enable this parameter, set Type of track confirmation and deletion logic to History .

Deletion threshold [P Q] — Track deletion threshold for history logic [5 5] (default) | real-valued 1-by-2 vector of positive integers

Track deletion threshold for history logic, specified as a real-valued 1-by-2 vector of positive integers [P Q] . If a confirmed track is not assigned to any detection P times in the last Q tracker updates, then the track is deleted.

Confirmation threshold [positive scalar] — Track confirmation threshold for score logic 20 (default) | positive scalar

Track confirmation threshold for score logic, specified as a real-valued positive scalar. A track is confirmed if its score is at least as high as the confirmation threshold.

To enable this parameter, set Type of track confirmation and deletion logic to Score .

Deletion threshold [negative scalar] — Track deletion threshold for score logic -7 (default) | scalar | negative scalar

Track deletion threshold for score logic, specified as a negative scalar. A track is deleted if its score decreases by at least the threshold from the maximum track score.

Probability of detection used for track score — Probability of detection used for track score 0.9 (default) | scalar in (0,1)

Probability of detection used for track score, specified as a positive scalar in (0,1).

Example: 0.5

Rate of false positives used for track score — Probability of false alarm used for track score 1e-6 (default) | scalar in (0,1)

The probability of false alarm used for track score, specified as a scalar in (0,1).

Example: 1e-5

Volume of the sensor's detection bin — Volume of sensor detection bin 1 (default) | positive scalar

The volume of a sensor detection bin, specified as a positive scalar. For example, if a radar produces a 4-D measurement, which includes azimuth, elevation, range, and range rate, the 4-D volume is defined by the radar angular beam width, the range bin width, and the range-rate bin width. Volume is used in calculating the track score when initializing and updating a track.

Example: 1.5

Rate of new tracks per unit volume — Rate of new tracks per unit volume 1 (default) | positive scalar

The rate of new tracks per unit volume, specified as a positive scalar. The rate of new tracks is used in calculating the track score during track initialization.

Example: 2.5

Prediction time source — Source of prediction time Auto (default) | Input port

Source for prediction time, specified as Input port or Auto . Select Input port to input an update time by using the Prediction Time input port. Otherwise, the simulation clock managed by Simulink determines the update time.

Enable cost matrix input — Enable input port for cost matrix off (default) | on

Select this check box to enable the input of a cost matrix by using the Cost Matrix input port.

Enable detectable track IDs input — Enable detectable track IDs input off (default) | on

Select this check box to enable the Detectable track IDs input port.

Enable tentative tracks output — Enable output port for tentative tracks off (default) | on

Select this check box to enable the output of tentative tracks through the Tentative Tracks output port.

Enable all tracks output — Enable output port for all tracks off (default) | on

Select this check box to enable the output of all the tracks through the All Tracks output port.

Enable information output — Enable output port for analysis information off (default) | on

Select this check box to enable the output port for analysis information through the Info output port.

Source of output bus name — Source of output track bus name Auto (default) | Property

Source of the output track bus name, specified as:

Auto — The block automatically creates an output track bus name.

Property — Specify the output track bus name by using the Specify an output bus name parameter.

Source of output info bus name — Source of output info bus name Auto (default) | Property

Source of the output info bus name, specified as one of these options:

Auto — The block automatically creates an output info bus name.

Property — Specify the output info bus name by using the Specify an output bus name parameter.

Maximum number of detections per sensor — Maximum number of detections per sensor 100 (default) | positive integer

Specify the maximum number of detections per sensor as a positive integer. This parameter determines the maximum number of detections that each sensor can pass to the tracker in each call of the tracker.

Set this parameter to a finite value if you want the tracker to establish efficient bounds on local variables for C/C++ code generation. Set this property to Inf if you do not want to bound the maximum number of detections per sensor.

To enable this parameter, select Enable Memory Management in the Tracker Management tab.

Maximum number of detections per cluster — Maximum number of detections per cluster 5 (default) | positive integer

Specify the maximum number of detections per cluster during the run-time of the tracker as a positive integer.

Setting this parameter to a finite value allows the tracker to bound cluster sizes and reduces the memory footprint of the tracker in generated C/C++ code. Set this property to Inf if you do not want to bound the maximum number of detections per cluster.

If during run-time, the number of detections in a cluster exceeds this parameter, the tracker reacts based on the Handle run-time violation of cluster size parameter.

To enable this parameter, specify the Cluster tracks and detections for assignment as on and select Enable Memory Management in the Tracker Management tab.

Maximum number of tracks per cluster — Maximum number of tracks per cluster 5 (default) | positive integer

Specify the maximum number of tracks per cluster during the run-time of the tracker as a positive integer.

If, during run-time, the number of tracks in a cluster exceeds this parameter, the tracker reacts based on the Handle run-time violation of cluster size parameter.

Handle run-time violation of cluster size — Handle run-time violation of cluster size Auto (default) | Property

Specify the handling of run-time violation of cluster size as one of these options:

Teminate — The tracker reports an error if, during run-time, any cluster violates the cluster bounds specified in the Maximum number of detections per cluster and Maximum number of tracks per cluster parameters.

Split and warn — The tracker splits the size-violating cluster into smaller clusters by using a suboptimal approach. The tracker also reports a warning to indicate the violation.

Split — The tracker splits the size-violating cluster into smaller clusters by using a suboptimal approach. The tracker does not report a warning.

In the suboptimal approach, the tracker separates out detections or tacks that have the smallest likelihoods of association to other tracks or detections until the cluster bounds are satisfied. These separated-out detections or tracks can form one or many new clusters depends on their association likelihoods with each other and the Threshold for assigning detections to tracks parameter.

Tracker Logic Flow

When a GNN tracker processes detections, track creation and management follow these steps:

The tracker divides detections by originating sensor.

For each sensor:

The tracker calculates the distances from detections to existing tracks and forms a cost matrix.

Based on the costs, the tracker performs global nearest neighbor assignment using the algorithm specified by the Assignment algorithm name parameter.

The assignment algorithm divides the detections and tracks into three groups:

Assigned one-to-one detection and track pairs

Unassigned detections

Unassigned tracks

Unassigned detections initialize new tracks. Using the unassigned detection, the tracker initializes a new track filter specified by the Filter initialization function parameter. The track logic for the new track is initialized as well.

The tracker checks if any of the unassigned detections from other sensors can be assigned to the new track. If so, the tracker updates the new track with the assigned detections from the other sensors. As a result, these detections no longer initialize new tracks.

The pairs of assigned tracks and detections are used to update each track. The track filter is updated using the correct method provided by the specified tracking filter. Also, the track logic is updated with a "hit". The tracker checks if the track meets the criteria for confirmation. If so, the tracker confirms the track and sets the IsCoasted field to false .

Unassigned tracks are updated with a "miss" and their IsCoasted field is set to true . The tracker checks if the track meets the criteria for deletion. If so, the tracker removes the track from the maintained track list.

All tracks are predicted to the latest time value (either the time provided by the Prediction Time input port, or the time determined by Simulink).

Track Structure

The fields of the track structure are:

Extended Capabilities

C/c++ code generation generate c and c++ code using simulink® coder™..

Usage notes and limitations:

The block supports strict single-precision code generation with these restrictions:

You must specify the assignment algorithm as 'Jonker-Volgenant' .

You must specify the filter initialization function to return a trackingEKF , trackingUKF , trackingCKF , or trackingIMM object configured with single-precision.

For details, see Generate Code with Strict Single-Precision and Non-Dynamic Memory Allocation .

The tracker supports non-dynamic memory allocation code generation with these restrictions:

You must specify the assignment algorithm as 'Jonker-Volgenant' or 'MatchPairs' .

You must specify the filter initialization function to return a trackingEKF , trackingUKF , trackingCKF , or trackingIMM object.

After enabling non-dynamic memory allocation code generation, consider using these parameters to set bounds on the local variables in the tracker:

Enable memory management

Cluster tracks and detections for assignment

Maximum number of detections per sensor

In code generation, if the detection inputs are specified in double precision, then the NumTracks field of the track outputs is returned as a double variable. If the detection inputs are specified in single precision, then the NumTracks field of the track outputs is returned as a uint32 variable.

Version History

R2023a: simulink buses do not show in workspace.

As of R2023a, the Simulink buses created by this block no longer show in MATLAB workspace.

  • Joint Probabilistic Data Association Multi Object Tracker
  • assignauction | assignjv | assignkbest | assignkbestsd | assignmunkres | assignsd | getTrackPositions | getTrackVelocities | fusecovint | fusecovunion | fusexcov
  • objectDetection | trackingKF | trackingEKF | trackingUKF | trackingABF | trackingCKF | trackingGSF | trackingIMM | trackingMSCEKF | trackingPF | trackHistoryLogic | trackScoreLogic | objectTrack | trackerJPDA | trackerTOMHT | trackerGNN
  • Track-Oriented Multi-Hypothesis Tracker | Track-To-Track Fuser | Joint Probabilistic Data Association Multi Object Tracker
  • Introduction to Multiple Target Tracking
  • Introduction to Assignment Methods in Tracking Systems
  • Create Nonvirtual Buses (Simulink)

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IMAGES

  1. (PDF) Assignment costs for multiple sensor track-to-track association

    assignment costs for multiple sensor track to track association

  2. Figure 1 from Assignment costs for multiple sensor track-to-track

    assignment costs for multiple sensor track to track association

  3. Figure 2 from Assignment costs for multiple sensor track-to-track

    assignment costs for multiple sensor track to track association

  4. Track accuracy and sensor costs for multiple target tracking

    assignment costs for multiple sensor track to track association

  5. Track accuracy and sensor costs for multiple target tracking

    assignment costs for multiple sensor track to track association

  6. Figure 1 from A practical new method for multi-sensor track-to-track

    assignment costs for multiple sensor track to track association

VIDEO

  1. Track association and state fusion

  2. Track Monitoring TRC & Tolerances#entranceexam #governmentexam #governmentjobs #indianrailway

  3. issue tracker project

  4. Track Sensor Solid👀

  5. AMM Digital Recording Class Countdown Track Assignment

  6. track management ###

COMMENTS

  1. Assignment costs for multiple sensor track-to-track association

    Assignment costs for multiple sensor track-to-track association Abstract: Successful track-to-track data association in a multisensor, multitarget scenario is predicated on a proper cost function. The cost function for associating two tracks is well established.

  2. Assignment costs for multiple sensor track-to-track association

    Assignment costs for multiple sensor track-to-track association Authors: Lance Kaplan Army Research Laboratory Yaakov bar-shalom University of Connecticut William D. Blair Abstract Successful...

  3. Assignment costs for multiple sensor track-to-track association

    The main goal of the proposed track-to-track association method is to link the histories of fused tracks over several frames and avoid track swapping at the fusion center level and to preserve the continuity of the fused tracks through their identities. 2 Excerpts Simulations studies of multisensor track association and fusion methods

  4. PDF Assignment Costs for Multiple Sensor Track-to-Track Association

    Assignment Costs for Multiple Sensor Track-to-Track Association Lance M. Kaplan Clark Atlanta University 223 J.P. Brawley Dr., SW Atlanta, GA 30314 USA [email protected] Abstract - Successful...

  5. Assignment costs for multiple sensor track-to-track association

    DOI: 10.1109/TAES.2008.4560213 Corpus ID: 14120195; Assignment costs for multiple sensor track-to-track association @article{Kaplan2008AssignmentCF, title={Assignment costs for multiple sensor track-to-track association}, author={Lance M. Kaplan and Yaakov Bar-Shalom and William Dale Blair}, journal={IEEE Transactions on Aerospace and Electronic Systems}, year={2008}, volume={44} }

  6. Assignment Costs for Multiple Sensor Track-to-Track Association Lance M

    ... Effective association result is crucial to the success of any data fusion system. Most existing methods formulate multisensor track association problem as a generalized S-D assignment...

  7. Track-to-Track Association for Intelligent Vehicles by Preserving Local

    Track-to-track association (T2TA) is a challenging task in situational awareness in intelligent vehicles and surveillance systems. In this paper, the problem of track-to-track association with sensor bias (T2TASB) is considered. Traditional T2TASB algorithms only consider a statistical distance cost between local tracks from different sensors ...

  8. Assignment costs for multiple sensor track-to-track association

    Assignment costs for multiple sensor track-to-track association Kaplan, Lance; Bar-Shalom, Yaakov; Blair, William; Abstract. Publication: IEEE Transactions on Aerospace Electronic Systems. Pub Date: April 2008 DOI: 10.1109/TAES.2008.4560213 Bibcode: 2008ITAES..44..655K full text sources ...

  9. Track-to-Track Association Based on Structural Similarity in the

    Thirdly, a two-dimensional (2D) assignment model is established to implement track-to-track association in the presence of sensor biases. Instead of using the absolute kinematic states only, the structural similarity between local tracks is adopted to measure the association cost and is evaluated by solving another 2D assignment subproblem.

  10. Asynchronous track-to-track association algorithm based on reference

    1 Introduction In multi-sensor multi-target tracking (MSMTT) systems, each target is represented by a track estimate. The tracks from individual sensors that belong to the same target are fused to form a single track, and this process is called track-to-track fusion (T2TF).

  11. Multisensor track-to-track association for tracks with dependent errors

    This paper derives the likelihood function for the track-to-track association problem from multiple sources, which forms the basis for the cost function used in a multidimensional assignment algorithm that can solve such a large scale problem where many sensors track many targets.

  12. Robust Track Association and Fusion with Extended Feature ...

    Kaplan, L., Blair, W.D.: Assignment costs for multiple sensor track-to-track association. In: Proc. 7th International Conference on Information Fusion, Stockholm, Sweden (2004) ... Chong, C.-Y.: Effects of unpaired objects and sensor biases on track-to-track association: problems and solutions. In: Proc. MSS National Symp. on Sensor and Data ...

  13. Machine Learning Methods for Data Association in Multi-Object Tracking

    Multisensor track-to-track association for tracks with dependent errors. In Proceedings of the 43rd IEEE Conference on Decision and Control (CDC'04), Vol. 3. ... Yaakov Bar-Shalom, and William D. Blair. 2008. Assignment costs for multiple sensor track-to-track association. IEEE Transactions on Aerospace and Electronic Systems 44, 2 (2008 ...

  14. Multisensor track-to-track association for tracks with dependent errors

    The likelihood function for the track-to-track association problem from multiple sources is derived, which forms the basis for the cost function used in a multidimensional assignment algorithm that can solve such a large scale problem where many sensors track many targets. Expand View on IEEE isif.org Save to Library Create Alert Cite Topics

  15. Assignment costs for multiple sensor track-to-track association

    Fig. 1: Probability of correct assignment versus target separation when using the sequential pairwise sum, SAPC and likelihood cost functions for the case of three sensors and two targets: (a) Isotropic measurement errors and (b) anisotropic measurement errors. - "Assignment costs for multiple sensor track-to-track association"

  16. Sensor Bias Estimation for Track to Track Association

    HE objective of multi-target tracking (MTT) is to jointly estimate the number of targets and their individual states from a sequence of measurements provided by sensing devices such as radar [1],...

  17. Multisensor Track-to-Track Association for Tracks with Dependent Errors

    This paper derives the exact likelihood function for the track-to-track association problem from multiple sources, which forms the basis for the cost function used in a multidimensional assignment algorithm that can solve such a large scale problem where many sensors track many targets. While a recent work [14] derived the likelihood function ...

  18. Simulations studies of multisensor track association and fusion methods

    The likelihood function for the track-to-track association problem from multiple sources is derived, which forms the basis for the cost function used in a multidimensional assignment algorithm that can solve such a large scale problem where many sensors track many targets. ... Assignment costs for multiple sensor track-to-track association ...

  19. An improved 2-D assignment algorithm for track-to-track association

    Assignment costs for multiple sensor track-to-track association. Article. Full-text available. May 2008; ... additional sensor(s), track-to-track association (T2TA) must be performed. In addition ...

  20. Multi-sensor, multi-object tracker using GNN assignment

    The tracker initializes, confirms, predicts, corrects, and deletes tracks based on a global nearest neighbor (GNN) assignment algorithm. The tracker estimates the state vector and state vector covariance matrix for each track. Each detection is assigned to at most one track. If the detection cannot be assigned to any track, the tracker ...

  21. A Survey on Track Fusion for Radar Target Tracking

    The likelihood function for the track-to-track association problem from multiple sources is derived, which forms the basis for the cost function used in a multidimensional assignment algorithm that can solve such a large scale problem where many sensors track many targets. ... Assignment costs for multiple sensor track-to-track association ...

  22. Multi-Sensor Track-to-Track Association and Spatial Registration

    A residual bias estimation registration (RBER) method based on maximum likelihood and the sequential m-best track association algorithm based on the new target density (SMBTANTD) that effectively solves the association problem in the scenarios where the numbers of targets measured by multiple sensors are inconsistent. Expand View on IEEE doi.org