Keywords

Multitarget tracking; Multisensor fusion; Bayesian filtering; Clutter estimation; Tracklet; Data association

3.15.1 Introduction

Multisensor-multitarget tracking is an emerging technology in which measurements from several sensors are combined such that resulting tracks are significantly better than that obtained when these devices operate individually. Recent advances in sensor technologies, signal processing techniques and improved processor capabilities make it possible for large amounts of data to be fused in real-time. These technical advancements allow the use of many sophisticated algorithms and robust mathematical techniques in multisensor-multitarget tracking. Furthermore, multisensor-multitarget tracking has received significant attention for military applications. Such applications involve a wide range of expertise including filtering, tracking initialization and maintenance, data association, and performance evaluation.

Three major types of architecture, namely, centralized, distributed and decentralized, are commonly used in multisensor-multitarget tracking applications [9,62,92,126]. In the centralized architecture, there are several sensors monitoring the region of interest with only one fusion center. All sensors report their measurements to the fusion center. It is the fusion center’s responsibility to process all acquired measurements and update the tracks. The single sensor-multitarget tracking problem can be considered as a special case of the centralized architecture, where only one sensor is deployed to observe the region of interest. In the distributed multisensor-multitarget tracking architecture, there are several fusion centers. One of them is the Central Fusion Center (CFC) and the remaining ones are Local Fusion Centers (LFCs). Measurements generated by the sensors are first processed by the LFCs and local tracks are updated inside each LFC. Then, local tracks from each LFC are reported to the CFC and the track-to-track fusion is accomplished by the CFC to form the global track set. In decentralized tracking architecture, each fusion center (FC) can be considered as a combination of LFC and CFC. Each FC is connected with several sensors and measurements reported by those sensors are used to update the track state inside the FC. Furthermore, each FC will also do track-to-track fusion whenever it receives additional information from its neighboring FCs. Usually, without a major modification, the algorithms developed for the distributed tracking architecture can be used to handle the decentralized tracking architecture. Regardless whether the sensor measurements are processed in the centralized or the distributed architecture, the data of each sensor has to be converted to a common coordinate system before multisensor-multitarget tracking, i.e., sensor registration and data alignment [39,54,74].

Filtering plays a vital role in multitarget tracking by obtaining the state estimate from the measurements received from one or more sensors. Tracking filters [10,31] can be broadly categorized as either linear or nonlinear. The Kalman filter [10,53] is a widely known recursive filter that is most suited for linear Gaussian systems. However, most systems are inherently nonlinear. The extensions of Kalman filter, such as extended Kalman filter (EKF) [10] and unscented Kalman filter (UKF) [52,105,128] are applicable to nonlinear systems. Both EKF and UKF are restricted in that the resulting probability densities are approximated as Gaussian. When the system is nonlinear and non-Gaussian, particle filters (or sequential Monte Carlo methods) [3,33,38,100] provide better estimates than many other filtering algorithms. In general, a tracking filter requires a model for target dynamics, and a model mismatch would diminish the performance of the filter. Thus, different models may be required to describe the target dynamics accurately at different times, especially in the case of maneuvering targets, whose kinematic models may evolve in a time-varying manner. Multiple model tracking algorithms such as the Interacting Multiple Model (IMM) [1,10,14–16,18] estimator, which contains a bank of models matched to different modes of possible target dynamics, would perform better in such situations.

Data association [9,13,113] is an essential component in multisensor-multitarget tracking due to the uncertainty in the data origin. Data association refers to the methodology of correctly associating the measurements to tracks, measurements to measurements [58,106] or tracks to tracks [2,6,8,9,19,22,127], depending on the fusion architecture. To address data association, a number of techniques have been developed and two widely used are single-frame assignment algorithm [11,95] and the multi-frame assignment algorithm [11,17,27,32,59,63,95].

Many algorithms have been proposed for the single sensor-multitarget tracking problem, such as the Probability Data Association (PDA) algorithm and the Joint Probability Data Association (JPDA) algorithm [9], the Multiple Hypotheses Tracking (MHT) algorithm [12], and the Probability Hypothesis Density (PHD) filter [78]. In PDA and JPDA algorithms, for each scan the track-to-measurement association events are enumerated and combined probabilistically, while in the MHT algorithm the track-to-measurement association history over several scans are enumerated and updated. In PHD filter, the track-to-measurement association events are not explicitly constructed. Although these algorithms are originally proposed to handle the single sensor-multitarget tracking problem, they are also widely used as the backbone for the multisensor-multitarget tracking.

In many scenarios, after the signal detection process, clutter points provided by the sensor (e.g., sonar, infrared sensor, radar) are not distributed uniformly in the surveillance region as assumed by most tracking algorithms. On the other hand, in order to obtain accurate results, the target tracking filter requires information about clutter’s spatial intensity. Thus, nonhomogeneous clutter spatial intensity has to be estimated from the measurement set and the tracking filter’s output. Also, in order to take advantage of existing tracking algorithms, it is desirable for the clutter estimation method to be integrated into the tracker itself.

Performance evaluation is very important for multisensor-multitarget tracking problem, especially when the performance of different tracking algorithms needs to be compared. Many measures of performance have been proposed in multisensor-multitarget tracking literatures. These measures can be divided into two different classes: sensor-related measures and tracker-related measures [40]. Sensor-related measures are independent of the tracking algorithm, therefore, most of them are not useful for the performance evaluation of multiple trackers. One exception is the Posterior Cramér-Rao Lower Bound (PCRLB) of tracking [10,44,46], which provides a minimum bound of any tracking estimation. On the other hand, tracker-related measures have been widely used in the tracker performance evaluation. For general multitarget tracking problem, tracker-related measures have been defined in terms of cardinality, time and accuracy measures [66,103]. To evaluate a general multitarget tracking problem, a combination of tracker-related measures should be used, because as shown in [29], it has been observed that the tracker may have provided inaccurate results while some measures show correct and satisfactory performances.

In this chapter, various multisensor-multitarget tracking architectures, estimators for spatial clutter intensity, filters for linear and nonlinear systems, algorithms for data associations and multitarget tracking, techniques used in centralized and distributed track-to-track fusion are discussed in detail. In addition, their quantitative and qualitative merits are discussed. Various combinations of these algorithms will provide a complete tracking framework for multisensor networks with application to civilian as well as military problems. For example, the tracking and fusion techniques discussed here are applicable to fields like air traffic control, air/ground/maritime surveillance, mobile communication, transportation, video monitoring and biomedical imaging/signal processing. The tracker performance evaluation, including its guiding principle and several measures of performance, is also discussed in this chapter. A challenging scenario with many closely-spaced targets is used to compare several multitarget tracking algorithms.

3.15.2 Formulation of multisensor-multitarget tracking problems

In a multisensor surveillance systems, several sensors such as radar, infrared (IR), and sonar, report their measurements to the tracker at regular intervals of time (scans or data frames). However, not all measurements are originated from the targets of interest; some measurements may come from physical background objects such as clutter, and others may be generated by thermal noise. In other words, there is a measurement origin ambiguity. Furthermore, in some scans, the target of interest does not produce any measurements at all (i.e., the probability of detection is less than unity). The objective of a typical multisensor-multitarget tracking system is to first partition all sensors’ measurements into sets, such that all observations in one set are produced by the same object (i.e., data-association process); then the measurements corresponding to the same object are processed in order to estimate the state of the object (i.e., filtering process) [9,12].

To handle the multisensor-multitarget tracking problem, usually the Bayesian approach is applied. In the Bayesian approach, the final goal is to construct the posterior probability density function (pdf) of the multitarget state given all the received measurements so far. Since this pdf contains all available statistical information, it is the complete solution to the multisensor-multitarget tracking problem. In principle, given a cost function, it is always possible to obtain the optimal estimate under the given cost function from the posterior probability. Note that, the state of the multitarget system should be a combination of the number of the targets and the state of each target, because in a real scenario both of them are random and unknown [78,120].

To distinguish the target-originated measurements from the clutter and estimate the state of the multitarget system, the following three models, namely, the target dynamic model, the sensor model, and the clutter model are crucial for all multisensor-multitarget tracking systems.

3.15.3 Filters

Filtering is the estimation of the state of a dynamic system from noisy data, based on the predefined target dynamic model and the sensor model. In recursive filtering, the received measurements are processed sequentially rather than as a batch so that it is neither necessary to store the complete measurement set nor to reprocess existing measurement if a new measurement becomes available. The Bayesian recursive filter is widely used in the multisensor-multitarget tracking area and such a filter consists of two stages: prediction and update.

The prediction stage uses the system model to predict the state pdf forward from one measurement time to the next. Suppose that the required pdf at measurement time is available, where . The prediction stage involves using the system model (15.1) to obtain the prior pdf of the state at measurement time

(15.31)

The update stage uses the latest measurement to update the prior via Bayes’ formula

(15.32)

The above recursive propagation of the posterior density is only a conceptual solution. Analytical formulas of the posterior density exist only in a restrictive set of cases.

3.15.4 Filter initialization

Track initiation is an essential component of all tracking algorithms. Two major types of initialization techniques, namely, the Single-Point (SP) method and the Two-Point-Difference (TPD) method, are commonly used in multisensor-multitarget tracking applications [9,10,84].

3.15.5 Data association

In Section 3.15.3, it has been implicitly assumed that there is no measurement origin ambiguity. However, the crux of the multitarget problem is to carry out the association process for measurements whose origins are uncertain due to

Furthermore, the probability of obtaining a measurement from a target—the target detection probability—is usually less than unity.

Data association problems may be categorized according to the pairs of information that are associated together:

In this subsection, measurement-to-track association and measurement-to-measurement association techniques are discussed. The track-to-track association is discussed in Section 3.15.9.

3.15.6 Multitarget tracking algorithms

Three widely used multitarget tracking algorithms, namely, the Probabilistic Data Association (PDA) and Joint Probabilistic Data Association (JPDA) algorithm, the Multiple Hypothesis Tracker (MHT) algorithm, and the Probability Hypothesis Density (PHD) algorithm, are discussed in this section.

3.15.7 Architectures of multisensor-multitarget tracking

Three major types of architecture, namely, centralized, distributed, and decentralized, are commonly used in multisensor-multitarget tracking applications [9,62,126]. Here, it is assumed that the data of each sensor has already been converted to a common coordinate system, regardless whether the sensor measurements are processed in the centralized or the distributed architecture.

Centralized Tracking: In the centralized architecture, Figure 15.2a, several sensors are monitoring the region of interest to detect and track the targets therein. All sensors generate measurements at each revisit time and report those measurements to the Central Fusion Center (CFC). It in turn fuses all the acquired measurements and updates the tracks. This is the optimal architecture in terms of tracking performance. However, in a large surveillance region with many sensors, this architecture may not be feasible because of limited resources, e.g., communication bandwidth and computation power. To further improve the reliability and the performance of the centralized architecture, one can use the replicated centralized architecture [24]. In the replicated centralized architecture, there are multiple CFCs operating independently and each sensor reports its measurements to all CFCs. In other words, each CFC processes data from all sensors and there is no communication among CFCs. This architecture has high performance and reliability because the multiple CFCs process the same data. However, it also has higher communication and processing costs.

Two well known schemes used by the CFC to incorporate measurements from multiple sensors are sequential updating and parallel updating:

In the two schemes mentioned above, usually it has been assumed that the sensors are synchronized. In real scenarios, the sensors are seldom perfectly synchronized and too many asynchronous sensors will reduce the optimality of the centralized tracking architecture.

Distributed Tracking: In order to avoid the heavy communication and computational requirement of centralized fusion, distributed or hierarchical architecture, shown in Figure 15.2b, is used alternatively [126]. In this architecture, sensors are connected to Local Fusion Centers (LFCs) and LFCs are in turn connected to a CFC. Each LFC updates its local tracks based on the measurements obtained from the local sensors and sends its tracks state information to CFC. Then, the CFC performs the track-to-track fusion and may send back the updated tracks to the LFCs, if the feedback path is available.

There are two crucial questions in this type of architecture. The CFC needs to decide whether local tracks from different LFCs represent the same target, i.e., the problem of track-to-track association. Furthermore, because of the common process noise or the common prior, the local state estimates for the same target from different LFCs are not independent anymore. Thus, the dependency between the local tracks for the same target from different LFCs has to be handled optimally in the track-track fusion. First, the cross-covariance between the local tracks has to be estimated and then the covariance of the fused track has to be increased correspondingly. Note that, even the above two questions are solved optimally, the distributed tracking architecture is still suboptimal compared to the centralized architecture, because the optimal fusion of the state estimates of local tracks can not provide the same performance as the optimal fusion of the entire data set [9].

To optimally handle the dependency between the local tracks for the same target, the computational cost may be large and the required information may take up too much communication bandwidth, especially when there are many LFCs. Thus, several suboptimal methods are proposed to handle the dependency between the local tracks for the same target. One suboptimal way is using the corresponding tracklets of the local tracks in the CFC for the track-track fusion. A tracklet is a track specially calculated from the local track such that its errors are not cross-correlated with the errors of any other data in the system for the same target [34,35]. Another suboptimal methods is the covariance intersection technique, which takes a convex combination of the estimate of the mean and the information matrix (i.e., the inverse of the covariance matrix) of the local tracks. The covariance intersection method actually provides an estimate of the upper bound of the covariance matrix of the optimally fused track [25,51].

Decentralized tracking: When there is no CFC that can communicate with all LFCs in a large surveillance region, neither centralized nor distributed tracking is possible. In such cases, an alternative called decentralized architecture, shown in Figure 15.2c, is used. Decentralized architecture is composed of multiple Fusion Centers (FCs) and no CFC [126]. Here, each FC gets the measurements from one or more sensors that are connected to it, and uses those measurements to update its tracks. In addition, tracks are also updated whenever an FC gets additional information from its neighbors. Note that even though many FCs are available, each FC can communicate only with its neighbors; the FCs within the communication distance every few measurement time steps. There is no common communication facility in decentralized tracking network, i.e., FC cannot broadcast results and communication must be kept on a strictly neighbor-to-neighbor basis [36]. In decentralized tracking architecture, each FC can be considered as a combination of LFC and CFC, because it updates the track state using measurements from connected sensors and it also does track-track fusion whenever neighboring FCs report their track states. Usually, the algorithms developed for the distributed tracking architecture can be used here without any major modification.

Sensor Registration: The benefits afforded by the integration of data from multiple sensors are greatly diminished if sensor biases are present. In practical systems, sensor states are not precisely specified with respect to some common coordinate system and measurements may be subjected to pointing errors, calibration errors or computational errors. As a result, knowledge about sensor location or attitude may not be accurate. Without this knowledge, there may be severe degradation in the performance of data association, filtering and fusion, leading to eventual loss of track quality. Thus, sensor registration and data alignment is the first step in the fusion process. In sensor registration [5], the bias is estimated and the resulting values are used to debias measurements prior to fusion. Assume that local tracks for the same target from different sensors have already been associated, then to estimate the bias vector, the classical approach is to augment the system state to include the bias vector as part of the state and implement an augmented state Kalman filter (ASKF) [39,54,74]. However, under some circumstances, the prior track-to-track association may be unnecessary for the sensor registration process [64].

3.15.8 Centralized tracking

It is assumed that there are sensors. The measurement from sensor at time is

(15.97)

The measurement noise sequences are zero mean, white, independent of the process noise and independent from sensor to sensor with covariances . If , the above problem becomes a single sensor-multitarget tracking problem. Two widely used techniques to incorporate multiple sensors are sequential updating technique and parallel updating technique.

3.15.9 Distributed tracking

In a distributed or decentralized configuration, each fusion center has a number of tracks. One crucial question is how to handle the dependency between different local tracks generated by the same target.

There are three sources for the cross correlation between any track pairs for the same target [35]:

Thus, if the target is strictly moving with a constant velocity, no process noise is used in LFCs and CFC, each LFC form its tracks strictly based on its own measurement sets (i.e., no feedback from the CFC to the LFC), and the CFC is restarted whenever a new or updated local track was available (i.e., memoryless fusion center), then there will not be any cross-correlation between any track pairs for the same target.

One useful tool to explain and analyze the information dependence due to communication is information graph [26,62]. Information events, such as observation by a sensor at a given time or fusion by a FC at a specific time, are represented by the nodes of the graph. The flow of information is represented by a directed link between the nodes. Thus, a node that is a common predecessor to two nodes contains the common information of those two nodes and the common information of any two or more nodes can be found out by identifying their common predecessors. Information graph is especially useful when the communication structure among FCs is complicated since in this case the identification of common information may not be easy.

3.15.10 Performance evaluation

In this section, the Posterior Cramér-Rao Lower Bound (PCRLB) of tracking [10,44,46,47,115], which provides a minimum bound of any tracking estimation, and several tracker-related metrics, which measure the performance of multitarget trackers in cardinality, time and accuracy [40,66,103], are discussed.

3.15.11 Simulations—a multiple closely-spaced target scenario

In this subsection, several tracker-related measures of performance are applied to a simulated scenario in order to demonstrate the application of several multitarget tracking algorithms [40]. The following tracking algorithms are applied in this subsection:

Parameters of every tracker are adjusted according to the scenario used for the simulation. An EKF algorithm is used in the filtering stage of all algorithms. Three different types of motion models are used for the IMM filter: the Constant Velocity (CV) model, the Constant Acceleration (CA) model and the Constant Turn (CT) [10] model. Although it is possible that every tracker uses its own selection of motion models, in order to provide a good comparison here the same models are used as IMM modes in every trackers. In order to deal with time varying number of targets, logic and track quality methods are used to initialize new-born targets and delete dead ones [4]. The values of and depend on the scenario and tracking algorithm. Except JIPDA algorithm and PHD filters that utilize quality-based method for track management, other methods use logic. Once the estimated tracks are obtained, the tracking results as well as the truths are both used to calculate performance metrics. For the PHD and the CPHD filter, unique tag is attached to each Gaussian component and a JIPDA type algorithm is used for the track management. For the TOMHT, an enumeration based algorithm is used to approximately search the best global hypothesis. Table 15.1 summarizes the general parameters that are common among all scenarios.

A challenging multiple target scenario is used in this section in order to evaluate the performance of trackers in dealing with closely-spaced targets [55].

Parameters of the simulated scenario are described as follows:

The tracking results as well as available truths are used to calculate performance metrics. Figure 15.4 shows the performance evaluator, which is designed by the ETF Lab, ECE Department, McMaster University, and this performance evaluator is used in the chapter to calculate and present metrics. Metrics have been classified into time, cardinality and accuracy measures.

For graphical interpretations, the results of three metrics are shown in Figures 15.5–15.7. For the precise definition of each metric, please refer to [40]. Also, the average results are presented in Tables 15.4–15.6 for the analysis over every individual tracker. In all tables, T1 to T6 stand for IMM-SD, IMM-JIPDA, IMM-HOMHT, IMM-TOMHT, IMM-GM-PHD, IMM-GM-CPHD, respectively. It can be seen that all trackers achieve, relatively the same detection performance in terms of track probability of detection. From Figure 15.6, it can be concluded that all targets have been well detected by trackers because measure of completeness shows a value very close to one for all trackers. Note that, there is no dense clutter area in this scenario. Therefore, the average number of false tracks shows a small value for all trackers. Nevertheless, the main difficulty of this scenario is the presence of crossing and closely-spaced targets that may affect the continuity measure and number of breaks and swaps. As the Table 15.4 shows, MHT trackers provide the lowest measure of continuity. It can be seen that IMM-HOMHT generates the most number of breaks in tracks leading to the lowest continuity measure. IMM-JIPDA tracker provides results with acceptable number of breaks even though there are many swaps in the estimated tracks that results in representing IMM-JIPDA as the third-worst tracker in terms of the continuity measure. These results show that, when using the parameters listed in Table 15.3, MHT and JIPDA trackers cannot provide satisfactory results compared to SD and PHD trackers, becuase the probability of breaks and swaps gets higher due to the presence of closely-spaced targets. Also, the tables show the superiority of IMM-SD tracker in terms of the majority of metrics over other trackers.

As a conclusion, it can be observed that, with parameters listed in Table 15.3, IMM-SD tracker has been able to provide the most accurate results with the least number of breaks and swaps in the tested tracks. MHT and JIPDA cannot track available targets continually although the detection capability of trackers are still comparable with other trackers. PHD filters stand between the best tracker and MHT and JIPDA trackers with satisfactory detection and continuity measures. It should be noted that theoretically the IMM-SD tracker can be considered as an implementation of IMM-TOMHT and both two trackers should provide the same performance. However, the simulation results show that the IMM-SD tracker works better than the IMM-TOMHT. One explanation is that the global optimal hypothesis is obtained thorough the enumeration in the current IMM-TOMHT tracker, so there is no guarantee that the hypothesis found by the current IMM-TOMHT is the real optimal one. On the other hand, in IMM-SD tracker, Lagrange Relaxation method is used to get an approximated optimal global hypothesis.

3.15.12 Summary

In this chapter, various filters, data-association techniques, multitarget tracking algorithms, multisensor-multitarget architectures and measures of performance were discussed in detail for the multisensor-multitarget tracking problem. Various combinations of these algorithms provide a complete tracking and fusion framework for multisensor networks with application to civilian as well as military problems. For example, the tracking and fusion techniques discussed here are applicable to fields like air traffic control, air/ground/maritime surveillance, mobile communication, transportation, video monitoring and biomedical imaging/signal processing. Using a scenario with many closely-spaced targets, it was also shown that the algorithms discussed here are all capable of handling the challenging multitarget tracking problem.

Relevant Theory: Signal Processing Theory and Machine Learning

References

1. Ackerson GA, Fu KS. On state estimation in switching environments. IEEE Trans Automat Control. 1970;15(1):10–17.

2. Alouani AT, Gray JE, McCabe DH. Theory of distributed estimation using multiple asynchronous sensors. IEEE Trans Aerosp Electron Syst. 2005;41(2):717–722.

3. Arulampalam MS, Maskell S, Gordon N, Clapp T. A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking. IEEE Trans Signal Process. 2002;50(2):174–188.

4. Bar-Shalom Y, Blair WD. Multitarget/Multisensor Tracking: Applications and Advances. Artech House October 2000.

5. Bar-Shalom Y. Airborne GMTI radar position bias estimation using static-rotator targets of opportunity. IEEE Trans Aerosp Electron Syst. 2001;37(2):695–699.

6. Bar-Shalom Y. Dimensionless score function for multiple hypothesis tracking. IEEE Trans Aerosp Electron Syst. 2007;43(1):392–400.

7. Bar-Shalom Y, Challa S, Blom HAP. IMM estimator versus optimal estimator for hybrid systems. IEEE Trans Aerosp Electron Syst. 2005;41(3):986–991.

8. Bar-Shalom Y, Chen H. Multisensor track-to-track association for tracks with dependent errors. J Adv Inform Fusion. 2006;1(1):3–14.

9. Bar-Shalom Y, Willett P, Tian X. Tracking and Data Fusion: A Handbook of Algorithm. Storrs, CT: YBS Publishing; 2011.

10. Bar-Shalom Y, Li XR, Kirubarajan T. Estimation with Applications to Tracking and Navigation. Wiley 2001.

11. Bar-Shalom Y, Kirubarajan T, Gokberk C. Tracking with classification-aided multiframe data association. IEEE Trans Aerosp Electron Syst. 2005;41(3):868–878.

12. Blackman SS. Multiple hypothesis tracking for multiple target tracking. IEEE Aerosp Electron Syst Mag. 2004;19(1, Part 2):5–18.

13. Blackman SS, Popoli R. Design and Analysis of Modern Tracking Systems. Artech House 1999.

14. Blair WD, Watson GA, Kirubarajan T, Bar-Shalom Y. Benchmark for radar resource allocation and tracking in the presence of ECM. IEEE Trans Aerosp Electron Syst. 1998;34(4):1097–1114.

15. Blom HAP. A sophisticated tracking algorithm for ATC surveillance data. In: Proceedings of the International Radar Conference, Paris. May 1984;393–398.

16. Blom HAP, Bar-Shalom Y. The interacting multiple model algorithm for systems with Markovian switching coefficients. IEEE Trans Automat Control. 1988;33(8):780–783.

17. Capponi A, De Waard HW. A mean track approach applied to the multidimensional assignment problem. IEEE Trans Aerosp Electron Syst. 2007;43(2):450–471.

18. Chang CB, Athans M. State estimation for discrete system with switching parameters. IEEE Trans Aerosp Electron Syst. 1978;14(3):418–425.

19. Chen H, Kirubarajan T, Bar-Shalom Y. Performance limits of track-to-track fusion versus centralized estimation: theory and application. IEEE Trans Aerosp Electron Syst. 2003;39(2):386–400.

20. Chang KC, Mori S, Chong CY. Evaluating a multiple-hypothesis multitarget tracking algorithm. IEEE Trans Aerosp Electron Syst. 1994;30(2):578–590.

21. Chang KC, Zhao X. A greedy assignment algorithm and its performance evaluation. In: Proceedings of American Control Conference, Seattle, USA. June 1995.

22. Chang KC, Saha RK, Bar-Shalom Y. On optimal track-to-track fusion. IEEE Trans Aerosp Electron Syst. 1997;33(4):1271–1276.

23. Chen X, Tharmarasa R, Pelletier M, Kirubarajan T. Integrated clutter estimation and target tracking using Poisson point processes. IEEE Trans Aerosp Electron Syst. 2012;48(2):1210–1235.

24. Chong CY. Distributed architectures for data fusion. In: Proceedings of the First International Conference on Information Fusion, Las Vegas, NV. August 1998.

25. Chong CY, Mori S. Convex combination and covariance intersection algorithms in distributed fusion. In: Proceedings of the Fourth International Conference on Information Fusion, Montreal, QC, Canada. August 2001.

26. Chong CY, Mori S. Distributed fusion and communication management for target identification. In: Proceedings of the Eighth International Conference on Information Fusion, Philadelphia, PA. July 2005.

27. Chummun MR, Kirubarajan T, Pattipati KR, Bar-Shalom Y. Fast data association using multidimensional assignment with clustering. IEEE Trans Aerosp Electron Syst. 2001;37(3):898–913.

28. Coman CI, Kreitmair T. Evaluation of the tracking process in ground surveillance applications. In: Proceedings of the Sixth European Radar Conference, Rome, Italy. September 2009.

29. Coraluppi S, Grimmett D, de Theije P. Benchmark evaluation of multistatic trackers. In: Proceedings of the Sixth International Conference on Information Fusion, Florance, Italy. July 2006.

30. Crouse DF, Willett P, Svensson L, Svensson D, Guerriero M. The set MHT. In: Proceedings of the 14th International Conference on Information Fusion, Chicago, IL. July 2011.

31. Daum F. Nonlinear filters: beyond the Kalman filter. IEEE Aerosp Electron Syst Mag. 2005;20(8, Part 2):57–69.

32. Deb S, Yeddanapudi M, Pattipati KR, Bar-Shalom Y. A generalized S-dimensional assignment for multisensor-multitarget state estimation. IEEE Trans Aerosp Electron Syst. 1997;33(2):523–538.

33. Doucet A, de Freitas N, Gordon N. Sequential Monte Carlo Methods in Practice. New York: Springer-Verlag; 2001.

34. Drummond OE. A hybrid sensor fusion algorithm architecture and tracklets. In: July 1997;485–502. Proceedings of SPIE Conference on Signal and Data Processing of Small Targets, San Diego, CA. vol. 3163.

35. Drummond OE. Track and tracklet fusion filtering using data from distributed sensors. In: Proceedings of Estimation, Tracking and Fusion: A Tribute to Yaakov Bar-Shalom, Monterey, CA. May 2001;167–186.

36. Durrant-Whyte H, Stevens M. Data fusion in decentralised sensing networks. In: Proceedings of the Fourth International Conference on Information Fusion, Montreal, QC, Canada. August 2001.

37. Fränken D, Hüpper A. Improved fast covariance intersection for distributed data fusion. In: Proceedings of the Seventh International Conference on Information Fusion, Stockholm, Sweden. July 2005.

38. Gordon NJ, Salmond DJ, Smith AFM. Novel approach to nonlinear/non-Gaussian Bayesian state estimation. IEE Proc Radar Signal Process. 1993;140(2):107–113.

39. Gordon NJ, Ristic B, Robinson M. Performance bounds for recursive sensor registration. In: Proceedings of the Sixth International Conference on Information Fusion, Cairns, Australia. July 2003.

40. Gorji AA, Tharmarasa R, Kirubarajan T. Performance measures for multiple target tracking problems. In: Proceedings of 14th International Conference on Information Fusion, Chicago, US. July 2011.

41. Grimmett D, Coraluppi S, La Cour BR, et al. MSTWG multistatic tracker evaluation using simulated scenario data sets. In: Proceedings of the 11th International Conference on Information Fusion, Cologne, Germany. September 2008.

42. Harishan K, Tharmarasa R, Kirubarajan T, Thayaparan T. Automatic track initialization and maintenance in heavy clutter using integrated JPDA and ML-PDA algorithms. In: September 2011; Proceedings of SPIE Conference on Signal and Data Processing of Small Targets, San Diego, CA. vol. 8137.

43. Hanselmann T, Mus̆icki D, Palaniswami M. Adaptive target tracking in slowly changing clutter. In: Proceedings of the Ninth International Conference on Information Fusion, Florence, Italy. July 2006.

44. Hernandez ML, Marrs AD, Gordon NJ, Maskell SR, Reed CM. Cramér-Rao bounds for non-linear filtering with measurement origin uncertainty. In: Proceedings of the Fifth International Conference on Information Fusion, Annapolis, USA. 2002.

45. Hernandez ML, Kirubarajan T, Bar-Shalom Y. Multisensor resource deployment using posterior Cramér-Rao bounds. IEEE Trans Aerosp Electron Syst. 2004;40(2):399–416.

46. Hernandez ML, Ristic B, Farina A, Timmoneri L. A comparison of two Cramér-Rao lower bounds for nonlinear filtering with . IEEE Trans Signal Process. 2004;52(9):2361–2370.

47. Hernandez ML, Farina A, Ristic B. A PCRLB for tracking in cluttered environments: measurement sequence conditioning approach. IEEE Trans Aerosp Electron Syst. 2006;42(2):680–704.

48. Hernandez ML, Ristic B, Farina A, Sathyan T, Kirubarajan T. Performance measure for Markovian switching systems using best-fitting Gaussian distributions. IEEE Trans Aerosp Electron Syst. 2008;44(2):724–747.

49. Hue C, Le Cadre JP, Pérez P. Performance analysis of two sequential Monte Carlo methods and posterior Cramér-Rao bounds for multitarget tracking. In: July 2002;464–473. Proceedings of the Fifth International Conference on Information Fusion, Annapolis, MD. vol. 1.

50. Johnston LA, Krishnamurthy V. Performance evaluation of a dynamic programming track before detect algorithm. IEEE Trans Aerosp Electron Syst. 2002;38(1):228–242.

51. Julier SS, Uhlmann JK. A non-divergent estimation algorithm in the presence of unknown correlations. In: Proceedings of American Control Conference, Albuquerque, New Mexico. June 1997.

52. Julier SJ, Uhlmann JK. A new extension of the Kalman filter to nonlinear systems. In: April 1997;182–193. Proceedings of SPIE Conference on Signal Processing, Sensor Fusion and Target Recognition VI, Orlando, FL. vol. 3068.

53. Kalman RE. A new approach to linear filtering and prediction problems. Trans ASME—J Basic Eng. 1960;82:34–45.

54. Kastella K, Yeary B, Zadra T, Brouillard R, Frangione E. Bias modeling and estimation for GMTI applications. In: Proceedings of the Third International Conference on Information Fusion, Paris, France. July 2000.

55. Kirubarajan T, Bar-Shalom Y, McAllister R, Schutz R, Engelberg B. Multitarget tracking using an IMM estimator with debiased E-2C measurements for AEW systems. In: Proceedings of the Second International Conference on Information Fusion, Sunnyvale, CA. July 1999.

56. Kirubarajan T, Bar-Shalom Y. Kalman filter versus IMM estimator: when do we need the latter? IEEE Trans Aerosp Electron Syst. 2003;39(4):1452–1457.

57. Kirubarajan T, Bar-Shalom Y. Probabilistic data association techniques for target tracking in clutter. Proc IEEE. 2004;92(3):536–557.

58. Kirubarajan T, Bar-Shalom Y, Lerro D. Bearings-only tracking of maneuvering targets using a batch-recursive estimator. IEEE Trans Aerosp Electron Syst. 2001;37(3):770–780.

59. Kirubarajan T, Wang H, Bar-Shalom Y, Pattipati KR. Efficient multisensor fusion using multidimensional data association. IEEE Trans Aerosp Electron Syst. 2001;37(2):386–400.

60. Kreucher C, Kastella K, Hero III AO. Multitarget tracking using the joint multitarget probability density. IEEE Trans Aerosp Electron Syst. 2005;41(4):1396–1414.

61. Lefebvre T, Bruyninckx H, De Schutter J. Kalman filters for non-linear systems: a comparison of performance. Int J Control. 2004;77:639–653.

62. Liggins ME, Chong CY, Kadar I, Alford MG, Vannicola V, Thomopoulos S. Distributed fusion architectures and algorithms for target tracking. Proc IEEE. 1997;85(1):95–107.

63. Lin L, Bar-Shalom Y, Kirubarajan T. New assignment-based data association for tracking move-stop-move targets. IEEE Trans Aerosp Electron Syst. 2004;40(2):714–725.

64. Lin X, Kirubarajan T, Bar-Shalom Y. Multisensor bias estimation with local tracks without a priori association. In: August 2003; Proceedings of SPIE Conference on Signal and Data Processing of Small Targets, San Diego, CA. vol. 5204.

65. Li XR, Bar-shalom Y. Performance prediction of interacting multiple model algorithm. IEEE Trans Aerosp Electron Syst. 1993;29.

66. Li XR, Zhao Z. Evaluation of estimation algorithms Part I: Incomprehensive measures of performance. IEEE Trans Aerosp Electron Syst. 2006;42(5):1340–1358.

67. Li XR, Li N. Integrated real-time estimation of clutter density for tracking. IEEE Trans Signal Process. 2000;48(10):2797–2805.

68. Li N, Li XR. Target perceivability and its applications. IEEE Trans Signal Process. 2001;49(11):2588–2604.

69. Li XR, Jilkov V. Survey of maneuvering target tracking Part III Measurement models. In: July 2001; Proceedings of SPIE Conference on Signal and Data Processing of Small Targets, San Diego, CA. vol. 4473.

70. Li XR, Jilkov V. Survey of maneuvering target tracking Part IV Decision-based methods. In: April 2002; Proceedings of SPIE Conference on Signal and Data Processing of Small Targets, Orlando, FL. vol. 4728.

71. Li XR, Jilkov V. Survey of maneuvering target tracking Part I Dynamic models. IEEE Trans Aerosp Electron Syst. 2003;39(4):1333–1364.

72. Li XR, Jilkov V. Survey of maneuvering target tracking Part V Multiple-model methods. IEEE Trans Aerosp Electron Syst. 2005;41(4):1255–1321.

73. Li XR, Jilkov V. Survey of maneuvering target tracking Part II Motion models of ballistic and space targets. IEEE Trans Aerosp Electron Syst. 2010;46(1):96–119.

74. Lin X, Bar-Shalom Y, Kirubarajan T. Multisensor multitarget bias estimation for general asynchronous sensors. IEEE Trans Aerosp Electron Syst. 2005;41(3):899–921.

75. R. Mahler, An Introduction to Multisensor-Multitarget Statistics and its Application, Lockheed Martin Technical Monograph, 2000.

76. Mahler R. Multi-target moments and their application to multi-target tracking. In: Proceedings of the Workshop on Estimation, Tracking and Fusion: A Tribute to Yaakov Bar-Shalom, Monterey, CA. 2001;134–166.

77. Mahler R. Random set theory for target tracking and identification. In: Hall DL, Lindas J, eds. Handbook of Multisensor Data Fusion. Boca Raton, FL: CRC Press; 2002; (Chapter 14).

78. Mahler R. Multitarget bayes filtering via first-order multitarget moments. IEEE Trans Aerosp Electron Syst. 2003;39(4):1152–1178.

79. Mahler R. PHD filter of higher order in target number. IEEE Trans Aerosp Electron Syst. 2007;43(4):1523–1541.

80. Mahler R. The multisensor PHD filter: I General solution via multitarget calculus. In: April 2009; Proceedings of SPIE Conference on Signal Processing, Sensor Fusion and Target Recognition XVIII, Orlando, FL. vol. 7336.

81. Mahler R. CPHD and PHD filters for unknown backgrounds I: Dynamic data clustering. In: 2009; Proceedings of SPIE Conference on Sensors and Systems for Space Applications III, Orlando, FL, USA. vol. 7330.

82. Mahler R. CPHD and PHD filters for unknown backgrounds II: Multitarget filtering in dynamic clutter. In: 2009; Proceedings of SPIE Conference on Sensors and Systems for Space Applications III, Orlando, FL, USA. vol. 7330.

83. Mahler R. Approximate multisensor CPHD and PHD filters. In: Proceedings of 10th International Conference on Information Fusion, Edinburgh, UK. July 2010.

84. Mallick M, Scala BL. Comparison of single-point and two-point difference track initiation algorithms using position measurements. Acta Automat Sinica. 2008;34(3):258–265.

85. Mušicki D, Evans R, Stankovic S. Integrated probabilistic data association. IEEE Trans Automat Control. 1994;39(6):1237–1241.

86. Mušicki D, Evans R. Joint integrated probabilistic data association: JIPDA. IEEE Trans Aerosp Electron Syst. 2004;40(3):1093–1099.

87. Mušicki D, Suvorova S, Morelande M, Mora B. Clutter map and target tracking. In: Proceedings of Eighth International Conference on Information Fusion, Wyndham Philadelphia, PA, USA. July 2005;69–76.

88. Mušicki D, Evans R. Multiscan multitarget tracking in clutter with integrated track splitting filter. IEEE Trans Aerosp Electron Syst. 2009;45(4):1432–1447.

89. Niehsen W. Information fusion based on fast covariance intersection filtering. In: Proceedings of the Fifth International Conference on Information Fusion, Annapolis, Washington DC Area. July 2002.

90. Okello N, Ristic B. Maximum likelihood registration for multiple dissimilar sensors. IEEE Trans Aerosp Electron Syst. 2003;39(3):1074–1083.

91. Panta K, Clarak DE, Vo BN. Data association and track management for the Gaussian mixture probability hypothesis density filter. IEEE Trans Aerosp Electron Syst. 2009;45(3):1003–1016.

92. Pulford GW. Taxonomy of multiple target tracking methods. Proc IEE Radar Sonar Navig. 2005;152(5):291–304.

93. Pasha SA, Vo BN, Ma WK. A Gaussian mixture PHD filter for jump Markov system models. IEEE Trans Aerosp Electron Syst. 2009;45(3):919–936.

94. Pattipati KR, Deb S, Bar-Shalom Y, Washburn RB. A new relaxation algorithm and passive sensor data association. IEEE Trans Automat Control. 1992;37(2):198–213.

95. Pattipati KR, Kirubarajan T, Popp RL. Survey of assignment techniques for multitarget tracking. In: Proceedings of the Workshop on Estimation, Tracking, and Fusion: A Tribute to Yaakov Bar-Shalom, Monterey, CA. May 2001.

96. Popp RL, Pattipati KR, Bar-Shalom Y. Dynamically adaptable m-best 2D assignment and multi-level parallelization. IEEE Trans Aerosp Electron Syst. 1999;35(4):1145–1160.

97. Popp RL, Kirubarajan T, Pattipati KR. Survey of assignment techniques for multitarget tracking. In: Bar-Shalom Y, Blair WD, eds. Multitarget/Multisensor Tracking: Applications and Advances III. Artech House 2000; (Chapter 2).

98. Punithakumar K, Kirubarajan T, Sinha A. Multiple-model probability hypothesis density filter for tracking maneuvering targets. IEEE Trans Aerosp Electron Syst. 2008;44(1):87–98.

99. Panta K, Ba-Ngu V, Singh S. Novel data association schemes for the probability hypothesis density filter. IEEE Trans Aerosp Electron Syst. 2007;43(2):556–570.

100. Ristic B, Arulampalam S, Gordon N. Beyond the Kalman Filter: Particle Filters for Tracking Applications. Artech House Publishers 2004.

101. Ristic B, Zollo S, Arulampalam S. Performance bounds for maneuvering target tracking using asynchronous multi-platform angle-only measurements. In: Proceedings of the Fourth International Conference on Information Fusion, Montreal, Quebec. August 2001.

102. Ristic B, Vo B-N, Clark D, Vo B-T. A metric for performance evaluation of multi-target tracking algorithms. IEEE Trans Signal Process. 2011;59(7):3452–3457.

103. Rothrock R, Drummond OE. Performance metrics for multiple-sensor, multiple-target tracking. In: Proceedings of SPIE Conference on Signal and Data Processing of Small Targets, Orlando, USA. July 2000.

104. Ridley M, Nettleton E, Sukkarieh S, Durrant-Whyte H. Tracking in decentralised air-ground sensing. In: Proceedings of the Fifth International Conference on Information Fusion, Annapolis, MD. August 2002.

105. Sarkka S. On unscented Kalman filtering for state estimation of continuous-time nonlinear systems. IEEE Trans Automat Control. 2007;52(9):1631–1641.

106. Sathyan T, Sinha A, Kirubarajan T. Computationally efficient assignment-based algorithms for data association for tracking with angle-only sensors. In: August 2007; Proceedings of SPIE Conference on Signal and Data Processing of Small Targets, San Diego, CA. vol. 6699.

107. Schuhmacher D, Vo B-T, Vo B-N. A consistent metric for performance evaluation of multi-object filters. IEEE Trans Signal Process. 2008;56(8):3447–3457.

108. Schuhmacher D, Vo B-T, Vo B-N. On performance evaluation of multi-object filters. In: Proceedings of the 13th International Conference on Information Fusion, Edinburgh, Scotland. July 2010.

109. Svensson L. On Bayesian Cramér-Rao bound for Markovian switching systems. IEEE Trans Signal Process. 2010;58(9):4507–4516.

110. Svensson L, Svensson D, Guerriero M, Willett P. Set JPDA filter for multitarget tracking. IEEE Trans Signal Process. 2011;59(10):4677–4691.

111. Shea PJ, Zadra T, Klamer D, Frangione E, Brouilard R, Kastella K. Precision tracking of ground targets. In: Proceedings of IEEE Aerospace Conference, Big Sky, MT. March 2000.

112. Sidenbladh H. Multi-target particle filtering for the probability hypothesis density. In: July 2003;800–806. Proceedings of the Sixth International Conference on Information Fusion. vol. 2.

113. Smith D, Singh S. Approaches to multisensor data fusion in target tracking: a survey. IEEE Trans Knowledge Data Eng. 2006;18(12):1696–1710.

114. Tharmarasa R, Kirubarajan T, Hernandez ML. Large-scale optimal sensor array management for multitarget tracking. IEEE Trans Syst Man Cybernet. 2007;37(5):803–814.

115. Tharmarasa R, Kirubarajan T, Hernandez ML, Sinha A. PCRLB-based multisensor array management for multitarget tracking. IEEE Trans Aerosp Electron Syst. 2007;43(2):539–555.

116. Tichavsky P, Muravchik CH, Nehorai A. Posterior Cramér-Rao bounds for discrete-time nonlinear filtering. IEEE Trans Signal Process. 1998;46(5):1386–1396.

117. Van Trees H. Detection, Estimation and Modulation Theory. vol. I New York: Wiley; 1968.

118. van Doorn BA, Blom HAP. Systematic error estimation, in multisensor fusion systems. In: Proceedings of SPIE Conference on Signal and Data Processing of Small Targets, Orlando, FL. April 1993.

119. Vermaak J, Godsill SJ, Perez P. Monte Carlo filtering for multi-target tracking and data association. IEEE Trans Aerosp Electron Syst. 2005;41(1):309–322.

120. Vo B-N, Singh S, Doucet A. Sequential Monte Carlo implementation of the PHD filter for multi-target tracking. In: July 2003;792–799. Proceedings of the Sixth International Conference on Information Fusion. vol. 2.

121. Vo B-N, Ma WK. The Gaussian mixture probability hypothesis density filter. IEEE Trans Aerosp Electron Syst. 2006;54(11):4091–4104.

122. Vo B-T, Vo B-N, Cantoni A. Analytic implementations of the cardinalized probability hypothesis density filter. IEEE Trans Aerosp Electron Syst. 2007;55(7):3553–3567.

123. Wan EA, van der Merwe R. The unscented Kalman filter, for nonlinear estimation. In: Proceedings of IEEE, Adaptive Systems for Signal Processing, Communications, and Control Symposium, Alberta, Canada. October 2000.

124. Wang H, Kirubarajan T, Bar-Shalom Y. Precision large scale air traffic surveillance using an IMM estimator with assignment. IEEE Trans Aerosp Electron Syst. 1999;35(1):255–266.

125. Wang X, Musicki D. Evaluation of IPDA type filters with a low elevation sea-surface target tracking. In: Proceedings of the Sixth International Conference on Information Fusion, Queensland, Australia. May 2003.

126. Xiong N, Svensson P. Multi-sensor management for information fusion: issues and approaches. Inform Fusion. 2002;3(1):163–186.

127. You H, Jingwei Z. New track correlation algorithms in a multisensor data fusion system. IEEE Trans Aerosp Electron Syst. 2006;42(4):1359–1371.

128. Zhan R, Wan J. Iterated unscented Kalman filter for passive target tracking. IEEE Trans Aerosp Electron Syst. 2007;43(3):1155–1163.