Abhijit Sinha

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 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.

Decentralized Sensor Selection for Large-Scale Multisensor-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.

Estimation and decision fusion: A survey

Data fusion has been applied to a large number of fields and the corresponding applications utilize numerous mathematical tools. This survey limits the scope to some aspects of estimation and decision fusion. In estimation fusion our main focus is on the cross-correlation between local estimates from different sources. On the other hand, the problem of decision fusion is discussed with emphasis on the classifier combining techniques

Autonomous Ground Target Tracking by Multiple Cooperative UAVs

With the recent advent of moderate-cost unmanned (or uninhabited) aerial vehicles (UAV) and their success in surveillance, it is natural to consider the cooperative management of groups of UAVs. The problem considered in this paper is the optimization of the information obtained by a group of UAVs carrying out surveillance of several ground targets distributed over a large area. The UAVs are assumed to be equipped with ground moving target indicator (GMTI) radars, which measure the locations of moving ground targets as well as their radial velocities (Doppler). In this paper, a cooperative control algorithm is proposed, according to which each UAV decides its path independently based on an information theoretic criterion function. The criterion function also incorporates target detection probability and survival probability for sensors corresponding to hostile fire by targets as well as collision with other UAVs. The control algorithm requires limited communication and modest computation

A sequential Monte Carlo probability hypothesis density algorithm for multitarget track-before-detect

In this paper, we present a recursive track-before-detect (TBD) algorithm based on the Probability Hypothesis Density (PHD) filter for multitarget tracking. TBD algorithms are better suited over standard target tracking methods for tracking dim targets in heavy clutter and noise. Classical target tracking, where the measurements are pre-processed at each time step before passing them to the tracking filter results in information loss, which is very damaging if the target signal-to-noise ratio is low. However, in TBD the tracking filter operates directly on the raw measurements at the expense of added computational burden. The development of a recursive TBD algorithm reduces the computational burden over conventional TBD methods, namely, Hough transform, dynamic programming, etc. The TBD is a hard nonlinear non-Gaussian problem even for single target scenarios. Recent advances in Sequential Monte Carlo (SMC) based nonlinear filtering make multitarget TBD feasible. However, the current implementations use a modeling setup to accommodate the varying number of targets where a multiple model SMC based TBD approach is used to solve the problem conditioned on the model, i.e., number of targets. The 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. We propose a PHD filter based TBD so that there is no assumption to be made on the number of targets. Simulation results are presented to show the effectiveness of the proposed filter in tracking multiple weak targets.

Application of the Kalman-Levy Filter for Tracking Maneuvering Targets

Among target tracking algorithms using Kalman filtering-like approaches, the standard assumptions are Gaussian process and measurement noise models. Based on these assumptions, the Kalman filter is widely used in single or multiple filter versions (e.g., in an interacting multiple model (IMM) estimator). The oversimplification resulting from the above assumptions can cause degradation in tracking performance. In this paper we explore the application of Kalman-Levy filter to handle maneuvering targets. This filter assumes a heavy-tailed noise distribution known as the Levy distribution. Due to the heavy-tailed nature of the assumed distribution, the Kalman-Levy filter is more effective in the presence of large errors that can occur, for example, due to the onset of acceleration or deceleration. However, for the same reason, the performance of the Kalman-Levy filter in the nonmaneuvering portion of track is worse than that of a Kalman filter. For this reason, an IMM with one Kalman and one Kalman-Levy module is developed here. Also, the superiority of the IMM with Kalman-Levy module over only Kalman-filter-based IMM for realistic maneuvers is shown by simulation results.

Joint detection and tracking of unresolved targets with monopulse radar

Detection and estimation of multiple unresolved targets with a monopulse radar is a challenging problem. For ideal single bin processing, it was shown in the literature that at most two unresolved targets can be extracted from the complex matched filter output signal. A new algorithm is developed to jointly detect and track more than two unresolved targets from a single detection with the help of tracking information. That is, the method involves the use of tracking information in the detection process. For this purpose, target states are transformed into detection parameter space, which involves high nonlinearities. In order to handle the nonlinearities, the particle filter, which has proven to be effective in nonlinear non-Gaussian estimation problems, is used as the basis of the closed loop system for tracking multiple unresolved targets. In addition to the standard particle filtering steps, the detection parameters corresponding to the predicted particles are evaluated using the nonlinear monopulse radar beam model. This in turn enables the evaluation of the likelihood of the monopulse signal given tracking data. Bayesian model selection is then used to find the correct detection event. The corresponding particle set is taken as the correct representation of the target posterior. A simulated amplitude comparison monopulse radar is used to generate the data and validate the joint detection and tracking of more than two unresolved targets.

PHD filtering for tracking an unknown number of sources using an array of sensors

In this paper, direction of arrival (DOA) tracking of an unknown number of sources in a highly non-stationary environment is considered. Conventional DOA estimation techniques, such as MUSIC, fail when the stationary assumption is violated. Furthermore, the time-varying number of sources makes the problem even more challenging. Recently, a particle filtering approach, which propagates the approximate posterior of the target states and then adopts a reversible jump Markov chain Monte Carlo (RJMCMC) diversity step to resolve the number of targets, was proposed. However, this algorithm is sensitive to incorrect model order initialization. In this paper, we propose a new algorithm for tracking an unknown number of sources based on the probability hypothesis density (PHD) filter, which propagates only the first moment of the joint posterior distribution of targets in terms of particles, as a computationally efficient alternative to the RJMCMC method. The PHD algorithm provides an automatic way to estimate the number of sources, eliminating the need for a separate model order initialization or update step, which is typically the source of problem in particle-filtering based methods. In addition to the fact that the PHD implementation is simple, simulation results show that, the PHD implementation yields superior performance over the other method

Track quality based multitarget tracking algorithm

In multitarget tracking alongside the problem of measurement to track association, there are decision problems related to track confirmation and termination. In general, such decisions are taken based on the total number of measurement associations, length of no association sequence, total lifetime of the track in question. For a better utilization of available information, confidence of the tracker on a particular track can be used. This quantity can be computed from the measurement-to-track association likelihoods corresponding to the particular track, target detection probability for the sensor-target geometry and false alarm density. In this work we propose a multitarget tracker based on a track quality measure which uses assignment based data association algorithm. The derivation of the track quality is provided. It can be noted that in this case one needs to consider different detection events than that of the track quality measures available in the literature for probabilistic data association (PDA) based trackers. Based on their quality and length of no association sequence tracks are divided into three sets, which are updated separately. The results show that discriminating tracks on the basis of their track quality can lead to longer track life while decreasing the average false track length.

Joint Classification and Pairing of Human Chromosomes

We reexamine the problems of computer-aided classification and pairing of human chromosomes, and propose to jointly optimize the solutions of these two related problems. The combined problem is formulated into one of optimal three-dimensional assignment with an objective function of maximum likelihood. This formulation poses two technical challenges: 1) estimation of the posterior probability that two chromosomes form a pair and the pair belongs to a class and 2) good heuristic algorithms to solve the three-dimensional assignment problem which is NP-hard. We present various techniques to solve these problems. We also generalize our algorithms to cases where the cell data are incomplete as often encountered in practice.