Multiple-target tracking (MTT) poses difficult computational challenges related to the measurementto-track data association problem, especially in the presence of spurious and missing measurements.Different approaches have been proposed to tackle this problem, including various approximations and heuristic optimization tools. The Cross Entropy (CE) method and the related Parametric MinxEnt (PME) method are recent optimization heuristics that have proved useful in many combinatorial optimization problems. They are akin to evolutionary algorithms in that a population of solutions is evolved, however generation of new solutions is based on statistical methods of sampling and parameter estimation. In this work we apply the Cross-Entropy method and its recent MinxEnt variant to the multi-scan version of the data association problem in the presence of misdetections, false alarms, and unknown number of targets. We formulate the algorithms, explore via simulation their efficiency and performance compared to other recently proposed techniques, and show that they obtain state-of-the-art performance in challenging scenarios.

The problem of fault tolerant state estimation is considered. We propose a unified, general formulation of the problem in which two different types of faults affect the system's output simultaneously. This problem statement generalizes previously reported formulations that may be obtained as special cases. Three families of state estimation methods for fault-prone systems are presented, generalizing several classical estimation algorithms. These families include: one-step nearoptimal filters, which are closely related to the GPB filter family, IMMbased filters, and linear optimal estimators.

We address the problem of estimating a random vector from two sets of measurements and , such that the estimator is linear in . We show that the partially linear minimum mean-square error (PLMMSE) estimator does not require knowing the joint distribution of and in full, but rather only its second-order moments. This renders it of potential interest in various applications. We further show that the PLMMSE method is minimax-optimal among all estimators that solely depend on the second-order statistics of and . We demonstrate our approach in the context of recovering a signal, which is sparse in a unitary dictionary, from noisy observations of it and of a filtered version. We show that in this setting PLMMSE estimation has a clear computational advantage, while its performance is comparable to state-of-the-art algorithms. We apply our approach both in static and in dynamic estimation applications. In the former category, we treat the problem of image enhancement from blurred/noisy image pairs. We show that PLMMSE estimation performs only slightly worse than state-of-the art algorithms, while running an order of magnitude faster. In the dynamic setting, we provide a recursive implementation of the estimator and demonstrate its utility in tracking maneuvering targets from position and acceleration measurements.Index Terms-Bayesian estimation, deblurring, denoising, minimum mean-square error, target tracking.

-We consider the problem of tracking the state of a hybrid system capable of performing a bounded number of mode switches. The system is assumed to follow either a nominal or an anomalous model, where the nominal model may stand for, e.g., the nonmaneuvering motion regime of a target or the fault-free operation mode of a sensor, and the anomalous model may stand for, e.g., the abrupt evasive maneuvers of a target or the faulty operation of a sensor. As is well known, the optimal algorithm requires implementation of an exponentially growing number of primitive Kalman filters. On the other hand, the system's switching dynamics is not Markov because of the a priori bounded number of model switches, thus ruling out the use of popular estimation schemes such as the interacting multiple model (IMM) and generalized pseudoBayesian (GPB) filters. We derive an efficient scheme that uses a number of primitive Kalman filters that is linear in the number of possible maneuvers. The scheme resembles the IMM algorithm in that it uses interaction between some of the primitive filters before every estimation cycle, thus reducing the number of such filters. The algorithm's performance is evaluated via a simulation study, and shown to outperform the state-of-the-art IMM filter in a typical example.

We present a simple approach for sensor registration in target tracking applications. The proposed method uses targets of opportunity and, without making assumptions on their dynamical models, allows simultaneous calibration of multiple three-and two-dimensional sensors. Whereas for two-sensor scenarios only relative registration is possible, in practical cases with three or more sensors unambiguous absolute calibration may be achieved. The derived algorithms are straightforward to implement and do not require tuning of parameters. The performance of the algorithms is tested in a numerical study.