Yaakov Bar-Shalom

The interacting multiple model algorithm for systems with Markovian switching coefficients

An important problem in filtering for linear systems with Markovian switching coefficients (dynamic multiple model systems) is the management of hypotheses, which is necessary to limit the computational requirements. A novel approach to hypotheses merging is presented for this problem. The novelty lies in the timing of hypotheses merging. When applied to the problem of filtering for a linear system with Markovian coefficients, the method is an elegant way to derive the interacting-multiple-model (IMM) algorithm. Evaluation of the IMM algorithm shows that it performs well at a relatively low computational load. These results imply a significant change in the state of the art of approximate Bayesian filtering for systems with Markovian coefficients. >

Multiple-model estimation with variable structure

Existing multiple-model (MM) estimation algorithms have a fixed structure, i.e. they use a fixed set of models. An important fact that has been overlooked for a long time is how the performance of these algorithms depends on the set of models used. Limitations of the fixed structure algorithms are addressed first. In particular, it is shown theoretically that the use of too many models is performance-wise as bad as that of too few models, apart from the increase in computation. This paper then presents theoretical results pertaining to the two ways of overcoming these limitations: select/construct a better set of models and/or use a variable set of models. This is in contrast to the existing efforts of developing better implementable fixed structure estimators. Both the optimal MM estimator and practical suboptimal algorithms with variable structure are presented. A graph-theoretic formulation of multiple-model estimation is also given which leads to a systematic treatment of model-set adaptation and opens up new avenues for the study and design of the MM estimation algorithms. The new approach is illustrated in an example of a nonstationary noise identification problem.

The Effect of the Common Process Noise on the Two-Sensor Fused-Track Covariance

This note deals with the effect of the common process noise on the fusion (combination) of the state estimates of a target based on measurements obtained by two different sensors. This problem arises in a multisensor environment where each sensor has its information processing (tracking) subsystem. In the case of an ¿-ß tracking filter the effect of the process noise is that, over a wide range of its variance, the uncertainty area corresponding to the fused estimates is about 70 percent of the single-sensor uncertainty area as opposed to 50 percent obtained if the dependence is ignored.

On the track-to-track correlation problem

The testing of the hypothesis whether two tracks represent the same target is considered. Previous works in the literature assumed that the estimates of the same targets state from two track files are uncorrelated. A test that includes their correlation is presented.

Tracking with debiased consistent converted measurements versus EKF

In tracking applications target motion is usually best modeled in a simple fashion using Cartesian coordinates. Unfortunately, in most systems the target position measurements are provided in terms of range and azimuth (bearing) with respect to the sensor location. This situation requires either converting the measurements to a Cartesian frame of reference and working directly on converted measurements or using an extended Kalman filter (EKF) in mixed coordinates. An accurate means of tracking with debiased consistent converted measurements which accounts for the sensor inaccuracies over all practical geometries and accuracies is presented. This method is compared with the mixed coordinates EKF approach as well as a previous converted measurement approach which is an acceptable approximation only for moderate cross-range errors. The new approach is shown to be more accurate in terms of position and velocity errors and provides consistent estimates (i.e., compatible with the filter calculated covariances) for all practical situations. The combination of parameters (range, range accuracy, and azimuth accuracy) for which debiasing is needed is presented in explicit form. >

Tracking methods in a multitarget environment

The objective of this paper is to survey and put in perspective the existing methods of tracking in multitarget environment. In such an environment the origin of the measurements can be uncertain: they could have come from the target(s) of interest or clutter or false alarms or be due to the background. This compact and unified presentation of the state-of-art in multitarget tracking was motivated by the recent surge of interest in this problem. It is also hoped to be useful in view of the need to adapt and modify existing techniques before using them for specific problems. Particular attention is paid to the assumptions underlying each algorithm and its applicability to various situations.

Tracking a maneuvering target using input estimation versus the interacting multiple model algorithm

Two maneuvering-target tracking techniques are compared. The first, called input estimation, models the maneuver as constant unknown input, estimates its magnitude and onset time, and then corrects the state estimate accordingly. The second models the maneuver as a switching of the target state model, where the various state models can be of different dimension and driven by process noises of different intensities, and estimates the state according to the interacting multiple model (IMM) algorithm. While the first requires around twenty parallel filters, it is shown that the latter, implemented in the form of the IMM, performs equally well or better with two or three filters. >

A generalized S-D assignment algorithm for multisensor-multitarget state estimation

We develop a new algorithm to associate measurements from multiple sensors to identify the real targets in a surveillance region, and to estimate their states at any given time. The central problem in a multisensor-multitarget state estimation problem is that of data association-the problem of determining from which target, if any, a particular measurement originated. The data association problem is formulated as a generalized S-dimensional (S-D) assignment problem, which is NP-hard for S/spl ges/3 sensor scans (i.e., measurement lists). We present an efficient and recursive generalized S-D assignment algorithm (S/spl ges/3) employing a successive Lagrangian relaxation technique, with application to the localization of an unknown number of emitters using multiple high frequency direction finder sensors (S=3, 5, and 7).

A new relaxation algorithm and passive sensor data association

The static problem of associating measurements at a given time from three angle-only sensors in the presence of clutter, missed detections, and an unknown number of targets is addressed. The measurement-target association problem is formulated as one of maximizing the joint likelihood function of the measurement partition. Mathematically, this formulation leads to a generalization of the 3-D assignment (matching) problem, which is known to be NP hard. The solution to the optimization problem developed is a Lagrangian relaxation technique that successively solves a series of generalized two-dimensional (2-D) assignment problems. The algorithm is illustrated by several application examples. >

Unbiased converted measurements for tracking

The exact compensation for the bias in the classical polar-to-Cartesian conversion is shown to be multiplicative and to depend on the statistics of the cosine of the angle measurement errors. An unbiased conversion is presented. A comparison between this unbiased conversion and the previously presented debiased conversion is made. The unbiased spherical-to-Cartesian conversion is also presented and evaluated.