This paper studies the RaoBlackwellized Monte Carlo data association (RBMCDA) filter for multiple target tracking. The elliptical gating strategies are redesigned and incorporated into the framework of the RBMCDA filter. The obvious benefit is the reduction of the time cost because the data association procedure can be carried out with less validated measurements. In addition, the overlapped parts of the neighboring validation regions are divided into several separated subregions according to the possible origins of the validated measurements. In these subregions, the measurement uncertainties can be taken into account more reasonably than those of the simple elliptical gate. This would help to achieve higher tracking ability of the RBMCDA algorithm by a better association prior approximation. Simulation results are provided to show the effectiveness of the proposed gating techniques.
Data association plays an important role in filtering methods for multitarget tracking in cluttered (or false alarm) environment. Many approaches have been developed to solve this problem [
In traditional tracking algorithms, a gate (validation region) can be used to guarantee that the target originated measurement falls into it with high (gate) probability [
The remainder of this paper is organized as follows. Section
Consider the following timevarying system:
In [
A gate is set up for selecting the measurement originated from the target in high probability, and gate can also be called gating region or validation region. In practical tracking algorithms, validation region is often used to reduce the cardinality of measurement set. Measurements outside the validation region can be ignored reasonably because the probabilities of them being from the corresponding targets are quite low according to the statistical characterization. Data association method often incorporates an elliptical validation region [
Figure
Examples of measurement validation region: (a) for a single target, (b) for two targets.
Figure
In the original RBMCDA approaches [
In this section, three different gating techniques are presented applicable to the framework of the RBMCDA filter, and the required
To reduce the cardinality of the validated measurement set, we can define a union which consists of all the elliptical validation regions (see Figure
Regulations of measurement validation regions, (a) as a union, (b) in separated forms.
In fact, the joint validation region can be seen as consisting of several subvalidationregions (SVRs) according to the possible origins of the validated measurements, and the
In a SVR with identifier
In this process, the possible events can be constructed in a similar way as JPDA does [
To develop a practical suboptimal JRBMCDA method with less time cost, we present a simplified joint events (SJ) based gating technique. In JRBMCDA, the numbers of validated measurements in the SVRs play the key roles to calculate the target existent probability or even determine the results. In fact, they represent the relative importance of these subregions, or the gate weights of the SVRs. So we can use the normalized weights and the target detection probability
This simplified joint events based RBMCDA (SJRBMCDA) can be seen as a very simple form of the JRBMCDA with the joint events being broken up into several isolated events. The significant difference is that, in SJRBMCDA, the procedure of enumerating the possible association events is replaced by a simple nonparametric method. Therefore, the required
It should be pointed out that the JRBMCDA and SJRBMCDA algorithms may provide more weights to the right SVRs if the tracker can get the correct target estimates. Like all other gating based algorithms, however, the performance of the proposed gating based RBMCDA algorithms will also be degraded in the cases that the tracker provides incorrect target estimates. Another problem is that, for both JRBMCDA and SJRBMCDA, the number of SVRs seems to increase dramatically with the number of targets to be tracked. Figure
An example of measurement validation regions for a large number of targets.
The gating technique based RBMCDA algorithm is presented in Algorithm
Calculate the target state vectors
In some extreme cases (such as that all elliptical validation regions are separated, or coincide exactly), the
This section just concerns with the general cases. Since
As shown in Figure
The
( 





O  1/1/—/—  1/1/—/—  1/1/—/—  1/0.5/—/— 
U  1/—/1/—  1/—/1/—  1/—/1/—  1/—/0.5/— 
J  —/1/1/1  —/1/1/1  —/0/1/1  —/0.5/1/1 
SJ  —/1/1/1  —/1/1/1  —/1/0/1  —/1/0.5/1 
All possible hypotheses for measurements that fall inside two validation regions on condition that
In cluttered environment (see Figure
The
( 





U  1/1  1/1  1/1  1/1 
J  0.3077/0.1220  0.3077/0.2195  0.6923/0.8780  0.6923/0.7805 
SJ  0.25/0.1111  0.25/0.2  0.75/0.8889  0.75/0.8 
In Figure
The
( 











J  0.61  0.42  0.55  0.21  0.25  0.12  0.16  0.18  0.21  0.29 
SJ  0.56  0.38  0.5  0.22  0.25  0.13  0.17  0.22  0.25  0.33 
Example of measurement validation regions for tracking three targets.
In the simulations, we model each target with constant velocity model in
Example of tracking two crossing targets.
The average position estimation errors for target 1.
The average position estimation errors for target 2.
The simulation results show that the tracking process can be divided into two stages: before and after the happening of target crossing. In the first stage, the RMSE curves by all the algorithms have the similar values. It indicates that the proposed gating methods do not have an impact on the performance of the RBMCDA algorithm for tracking separated targets. In the second half of the tracking process, the significant arising of the RMSE curves by “O" and “U" algorithms indicates that, when target crossing happens, the “O" and “U" algorithms have more times of tracking failures (or mistracking) than “S" and “SJ" algorithms. This is because “S" and “SJ" can provide more accurate targets’ origins than the “O" and “U" algorithms. In this example, the performance of “SJ" is approximate to that of the “J." This also supports the results obtained in the previous numerical examples.
In the second example, we consider a threetargetcrossing situation (as shown in Figure
Computational time (sec) using different numbers of particles.
Numbers of particles  20  40  60  80  100 

O  12.1373  18.2593  25.3149  31.7860  38.4171 
U  1.1085  2.2064  3.3344  4.4614  5.6046 
J  1.2446  2.5641  4.0014  5.3252  6.5214 
SJ  1.1248  2.3910  3.6465  4.8110  5.8696 
Computational time (sec) in different clutter rates.
Clutter rates ( 
20  40  60  80  100 

O  12.0975  17.5701  22.9209  28.4144  34.0663 
U  1.0522  1.1306  1.2546  1.3155  1.3967 
J  1.1965  1.2832  1.4081  1.4914  1.6091 
SJ  1.0925  1.2024  1.3330  1.4350  1.5127 
Example of tracking three crossing targets.
In Table
In both Tables
This paper has studied the gating techniques in the application of the RBMCDA filter to multitarget tracking. Three different gating methods are presented and compared by computing both the tracking errors and time cost. “U" incorporates a very simple gate into the framework of the RBMCDA approach. “J" can take the measurement uncertainties into account reasonably by calculating the joint events. As a simplification of “J," “SJ" is more efficient than “J" and the tracking performance loss incurred is not significant in the experimental examples. Therefore, “SJ" can be a timesaving choice for practical applications. It should be pointed out that the gating techniques discussed in this paper may eliminate all measurements outside the validation regions of the targets that have already been detected, which will make it difficult to detect newly appearing targets. To address this, the proposed gating techniques could be started after the initialization periods of the RBMCDA filter to avoid impairing the tracks initiation.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors would like to thank the editors and the anonymous reviewers for their valuable comments and suggestions.