A new recursive algorithm is proposed for jointly estimating the time-varying number of targets and their states from a sequence of observation sets in the presence of data association uncertainty, detection uncertainty, noise, and false alarms. The approach involves modelling the respective collections of targets and measurements as random finite sets and applying the probability hypothesis density (PHD) recursion to propagate the posterior intensity, which is a first-order statistic of the random finite set of targets, in time. At present, there is no closed-form solution to the PHD recursion. This paper shows that under linear, Gaussian assumptions on the target dynamics and birth process, the posterior intensity at any time step is a Gaussian mixture. More importantly, closed-form recursions for propagating the means, covariances, and weights of the constituent Gaussian components of the posterior intensity are derived. The proposed algorithm combines these recursions with a strategy for managing the number of Gaussian components to increase efficiency. This algorithm is extended to accommodate mildly nonlinear target dynamics using approximation strategies from the extended and unscented Kalman filters

The Gaussian Mixture Probability Hypothesis Density Filter

Multiple hypothesis tracking (MHT) is generally accepted as the preferred method for solving the data association problem in modern multiple target tracking (MTT) systems. This paper summarizes the motivations for MHT, the basic principles behind MHT and the alternative implementations in common use. It discusses the manner in which the multiple data association hypotheses formed by MHT can be combined with multiple filter models, such as used by the interacting multiple model (IMM) method. An overview of the studies that show the advantages of MHT over the conventional single hypothesis approach is given. Important current applications and areas of future research and development for MHT are discussed.

/pdf/multiple-hypothesis-tracking-for-multiple-target-tracking-3fzibddaoe.pdf

Multiple hypothesis tracking for multiple target tracking

The multitarget recursive Bayes nonlinear filter is the theoretically optimal approach to multisensor-multitarget detection, tracking, and identification. For applications in which this filter is appropriate, it is likely to be tractable for only a small number of targets. In earlier papers we derived closed-form equations for an approximation of this filter based on propagation of a first-order multitarget moment called the probability hypothesis density (PHD). In a recent paper, Erdinc, Willett, and Bar-Shalom argued for the need for a PHD-type filter which remains first-order in the states of individual targets, but which is higher-order in target number. In this paper we show that this is indeed possible. We derive a closed-form cardinalized PHD (CPHD) filter, which propagates not only the PHD but also the entire probability distribution on target number.

PHD filters of higher order in target number

The multitarget recursive Bayes nonlinear filter is the theoretically optimal approach to multisensor-multitarget 
detection, tracking, and identification. For applications in which this filter is appropriate, it is likely to be tractable 
for only a small number of targets. In earlier papers we derived closed-form equations for an approximation of 
this filter based on propagation of a first-order multitarget moment called the probability hypothesis density 
(PHD). In a recent paper, Erdinc, Willett, and Bar-Shalom argued for the need for a PHD-type filter which 
remains first-order in the states of individual targets, but which is higher-order in target number. In this paper 
we show that this and much more is possible. We derive a closed-form cardinalized PHD (CPHD), filter, which 
propagates not only the PHD but also the entire probability distribution on target number.

A theory of PHD filters of higher order in target number

This paper presents a dynamic relief-demand management model for emergency logistics operations under imperfect information conditions in large-scale natural disasters. The proposed methodology consists of three steps: (1) data fusion to forecast relief demand in multiple areas, (2) fuzzy clustering to classify affected area into groups, and (3) multi-criteria decision making to rank the order of priority of groups. The results of tests accounting for different experimental scenarios indicate that the overall forecast errors are lower than 10% inferring the proposed method's capability of dynamic relief-demand forecasting and allocation with imperfect information to facilitate emergency logistics operations.

https://ir.nctu.edu.tw:443/bitstream/11536/6074/1/000271409100001.pdf

Dynamic Relief-Demand Management for Emergency Logistics Operations Under Large-Scale Disasters

Tracking multiple targets with uncertain target dynamics is a difficult problem, especially with nonlinear state and/or measurement equations. With multiple targets, representing the full posterior distribution over target states is not practical. The problem becomes even more complicated when the number of targets varies, in which case the dimensionality of the state space itself becomes a discrete random variable. The probability hypothesis density (PHD) filter, which propagates only the first-order statistical moment (the PHD) of the full target posterior, has been shown to be a computationally efficient solution to multitarget tracking problems with a varying number of targets. The integral of PHD in any region of the state space gives the expected number of targets in that region. With maneuvering targets, detecting and tracking the changes in the target motion model also become important. The target dynamic model uncertainty can be resolved by assuming multiple models for possible motion modes and then combining the mode-dependent estimates in a manner similar to the one used in the interacting multiple model (IMM) estimator. This paper propose a multiple-model implementation of the PHD filter, which approximates the PHD by a set of weighted random samples propagated over time using sequential Monte Carlo (SMC) methods. The resulting filter can handle nonlinear, non-Gaussian dynamics with uncertain model parameters in multisensor-multitarget tracking scenarios. Simulation results are presented to show the effectiveness of the proposed filter over single-model PHD filters.

/pdf/multiple-model-probability-hypothesis-density-filter-for-p2osteiibj.pdf

Multiple-model probability hypothesis density filter for tracking maneuvering targets

Tracking multiple targets with uncertain target dynamics is a difficult problem, especially with nonlinear state and/or measurement equations. With multiple targets, representing the full posterior distribution over target states is not practical. The problem becomes even more complicated when the target number varies, in which case the dimensionality of the state space itself becomes a discrete random variable. The Probability Hypothesis Density (PHD) filter, which propagates only the first-order statistical moment (or the PHD) of the full target posterior, has been shown to be a computationally efficient solution to multitarget tracking problems with varying number of targets. The integral of PHD in any region of the state space gives the expected number of targets in that region. With maneuvering targets, detecting and tracking the changes in the target motion model also become important, but current PHD implementations do not provide a mechanism for handling this. The target dynamic model uncertainty can be resolved by assuming multiple models for possible motion modes and then combining the mode-conditioned estimates in a manner similar to the one used in the Interacting Multiple Model (IMM) estimator. In this paper a multiple model implementation of the PHD filter, which approximates the PHD by a set of weighted random samples propagated over time using Sequential Monte Carlo methods, is proposed. The resulting filter can handle nonlinear, non-Gaussian dynamics with uncertain model parameters in multisensor-multitarget tracking scenarios. Simulation results are presented to show the effectiveness of the proposed filter over single-model PHD filters.© (2004) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

A Multiple Model Probability hypothesis density filter for tracking maneuvering targets

In this paper we consider the general problem of managing an array of sensors in order to track multiple targets in the presence of clutter. There are three complicating factors. The first is that because of physical limitations (e.g., communication bandwidth) only a small subset of the available sensors can be utilized at any one time. The second complication is that the associations of measurements to targets/clutter are unknown. The third complication is that the total number of targets in the surveillance region is unknown and possibly time varying. It are these second and third factors that extend previous work [ Tharmarasa, R., Kirubarajan, T., and Hernandez, M. L. Large-scale optimal sensor array management for multitarget tracking. IEEE Transactions on Systems, Man, and Cybernetics, to be published.]. Hence sensors must be utilized in an efficient manner to alleviate association ambiguities and to allow accurate estimation of the states of a varying number of targets. We pose the problem as a bi-criterion optimization with the two objectives of (1) controlling the posterior Cramer-Rao lower bound ((PCRLB) which provides a measure of the optimal achievable accuracy of target state estimation), and (2) maximizing the probability of detecting new targets. Only recently have expressions for multitarget PCRLBs been determined [Hue, C, Le Cadre, J.-P., and Perez, P]. Performance analysis of two sequential Monte Carlo methods and posterior Cramer-Rao bounds for multitarget tracking. In Proceedings of the 5th International Conference on Information Fusion, vol. 1, Annapolis, MD, July 2002, 464-473.], and the necessary simulation techniques are computationally expensive. However, in this paper we show the existence of a multitarget information reduction matrix (IRM) which can be calculated off-line in most cases. Additionally, we propose some approximations that further reduce the computational load. We present solution methodologies that, in simulations, are shown to determine efficient utilization strategies for the available sensor resources, with some sensors selected to track existing targets and others given the primary task of surveillance in order to identify new threats.

PCRLB-based multisensor array management for multitarget tracking

The problem of sensor resource management for multitarget tracking in decentralized tracking systems is considered here. Inexpensive sensors available today are used in large numbers to monitor wide surveillance regions. However, due to frequency, power, and bandwidth limitations, there is an upper limit on the number of sensors that can be used by a fusion center (FC) at any one time. The problem is then to select the sensor subsets to be used at each sampling time in order to optimize the tracking performance (i.e., maximize the tracking accuracy of existing tracks and detect new targets as quickly as possible) under the given constraints. The architecture considered in this paper is decentralized in which there is no central fusion center (CFC); each FC communicates only with the neighboring FCs, as a result communication is restricted. In such cases each FC has to decide which sensors should be used by itself at each sampling time by considering which sensors can be used by neighboring FCs. An efficient optimization-based algorithm is proposed here to address this problem in real time. Simulation results illustrating the performance of the proposed algorithms are also presented to support its efficiency. The novelty lies in the discrete optimization formulation for large-scale sensor selection in decentralized networks.

Decentralized Sensor Selection for Large-Scale Multisensor-Multitarget Tracking

Most present-day radar systems use monopulse techniques to extract angular measurements of sunbeam accuracy. The familiar "monopulse ratio" is a very effective means to derive the angle of a single target within a radar beam. For the simultaneous estimation of the angles of two closely-spaced targets, a modification on the monopulse ratio was derived in (Blair and Pearce, 2001), while (Sinha et al., 2002) presented a maximum likelihood (ML) technique via numerical search. In this paper it is shown that the ML solution can in fact be found explicitly, and the numerical search of ((Sinha et al., 2002) is unnecessary. However, the ML solution requires the signal to noise ratio (SNR) for each target to be known, and hence we generalize it so it requires only the relative SNR. Several versions of expectation maximization (EM) joint angle estimators are also derived, these differing in the degree to which prior information on SNR and on beam pattern are assumed. The performances of the different direction-of-arrival (DOA) estimators for unresolved targets are studied via Monte Carlo, and it is found that most have similar performance: this is remarkable since the use of prior information (SNR, relative SNR, beam pattern) varies widely between them. There is, however, considerable performance variability as a function of the two targets' off-boresight angles. A simple combined technique that fuses the results from different approaches is thus proposed, and it performs well uniformly.

https://www.ece.ubc.ca/~zjanew/journal/ZJW_AES_AEMonRadar_23.pdf

Abhijit Sinha

Papers

Multiple-model probability hypothesis density filter for tracking maneuvering targets

A Multiple Model Probability hypothesis density filter for tracking maneuvering targets

PCRLB-based multisensor array management for multitarget tracking

Decentralized Sensor Selection for Large-Scale Multisensor-Multitarget Tracking

Angle estimation for two unresolved targets with monopulse radar