<title>2M-PDAF: an integrated two-model probabilistic data association filter</title>

Object-Oriented Environment for Assessing Tracking Algorithms

Square-root formulations have not been developed for state-of-the-art tracking algorithms. The only exception is the square-root implementation of the PDAF by R. Kenefic (1990). It is shown that there is a substantially better implementation of the square-root probabilistic data association filter (PDAF) than Kenefic's algorithm in terms of both numerical robustness and computational efficiency. On the average, the proposed algorithm requires half the number of computations required by Kenefic's algorithm for square-root PDAF. The same approach is extended to develop computationally efficient square-root algorithms for the interesting multiple model (IMM) and IMM probabilistic data association (IMMPDA) filters. >

Vision sensors are widely used not only for detection and recognition, but also measurement of the pose of the moving objects. But in the crowded environment, occlusion often disrupts the measurement, and wrong data association due to misrecognition deteriorates the tracking performance. Probabilistic data association filter (PDAF) is known as useful to address such issues, in which observed features are weighted by probability to deal with multiple observations as well as to cope with occlusion and false recognition. This paper presents a novel object tracking method in which PDAF is incorporated into moving horizon estimation (MHE) framework to deal with multiple frame tracking and physical constraints. The performance of the proposed method is evaluated by comparing with the PDAF.

A single-sensor, single-target mixture reduction (MR) data association algorithm is extended for use in multisensor, multitarget tracking situations. MR is extended for tracking an arbitrary number of targets using an arbitrary number of sensors under the assumption that the sensor measurement errors are independent across sensors. Like the single-sensor, single-target MR algorithm, which gives better performance than the probabilistic data association (PDA) filter, the multisensor, multitarget MR extensions give similar improvements in performance compared to the joint PDA (JPDA) and multisensor JPDA (MSJPDA) algorithms. Further, in the formulations for the multisensor and multitarget MR algorithms, the equations for the calculation of the data association probabilities have been put in the same form as for the JPDA, thus allowing previously developed fast JPDA computational techniques to be applicable. N the problem of tracking targets in random clutter, the optimal Bayesian solution leads to Gaussian mixture distributions that consist of an exponentially increasing number of components.1 In practice, the number of components in each mixture is kept in check by approximating it with fewer components. The nearest neighbor (NN) approximation reduces each target's mixture to its largest component.13 The joint probabilistic data association (JPDA) approximation merges the components of each target's mixture into a single Gaussian component.1'4 However, when there are several significant, well-spaced components in the original mixture, important information may be lost by using the NN or JPDA methods. A more flexible approximation method for single-sensor, single-target tracking, known as mixture reduction (MR), has been proposed by Salmond.5 This MR algorithm preserves the mean and covariance of the original mixture of components, successively merging components until the number of components is reduced to some userspecified limit. In this paper, we first review Salmond's MR algorithm for single-sensor tracking of a single target in clutter. We then derive extensions to Salmond's MR algorithm for use in tracking multiple targets and when there are measurements available from multiple sensors. Just as the single-sensor, single-target MR algorithm gives better performance5 than the probabilistic data association (PDA) filter, the multisensor, multitarget MR extensions are shown to give similar improvements in performance as compared to the JPDA and multisensor JPDA (MSJPDA)6 algorithms. Extension of the MR algorithm for tracking of multiple targets is necessary for use in realistic tracking scenarios where there are usually many targets that need to be tracked. Moreover, many current tracking systems have been designed with multiple sensors, thus requiring the further extension to a multisensor algorithm. The paper is organized as follows. In Sec. II, the target dynamics and measurement equations are defined. We review the singlesensor, single-target MR algorithm5 in Sec. Ill, and we extend the algorithm to the multitarget and multisensor cases in Sec. IV and V, respectively. In Sec. VI, simulation results evaluating the performances of the MR extensions are presented. Finally, concluding remarks are given in Sec. VII.

A methodology for the use of the multirate sampling technique in the measurement acquisition process of a probabilistic data association (PDA) filter is presented. The proposed filter, called the multirate sample probabilistic data association (MSPDA) filter, increases the computational efficiency of the tracking system without compromising the accuracy of the tracking algorithm. The use of multirate sampling enhances the utilization of the central processor, since the time spent in acquiring and processing certain measurements relevant to the components of a state vector is considerably saved. The performance of the MSPDA filter is compared with that of the traditional PDA tracker and other presently used filters. It is shown that the computational saving is about 25% while the degradation in accuracy is only to the extent of 5% of the MSE of the corresponding state vector component. >

Object tracking is widely utilized and becomes indispensable in automation technology. In environments containing many objects, however, occlusion and false recognition frequently occur. To alleviate these issues, in this paper, we propose a novel object tracking method based on moving horizon estimation incorporating probabilistic data association (MHE-PDA) through a probabilistic data association filter (PDAF). Since moving horizon estimation (MHE) is accomplished through numerical optimization, we can ensure that the estimation is consistent with physical constraints and robust to outliers. The robustness of the proposed method against occlusion and false recognition is verified by comparison with PDAF through simulations of a cluttered environment.

A suboptimal algorithm is proposed for target tracking in clutter. The exact posterior density of a target state conditioned on the past observation history is a Gaussian mixture with the number of terms equal to the number of possible ways to associate observations and targets. In order to avoid an exponentially growing complexity, the algorithm performs an approximation by naturally partitioning and grouping the target state estimates into a set of approximate sufficient statistics. A new criterion function is introduced in this approximation process. The well-known probabilistic data association (PDA) filter is a special case of the algorithm.

This letter proposes a new frequency domain turbo equalization algorithm based on nonlinear minimum-mean- squared-error (MMSE) estimation. The conceptual basis of the proposed equalizer is the probabilistic data association (PDA) filtering. It is shown that by performing internal equalizer iterations, of which structure is resulted from the algorithm derivation according to the PDA concept, the convergence properties, analytical and verified by simulations, can be significantly improved over conventional MMSE turbo equalization techniques. Results of the simulations conducted to demonstrate the superiority of the proposed algorithm and to verify the accuracy of the analysis are presented in this letter.

The interacting multiple model (IMM) and probabilistic data association (PDA) filter (IMMPDAF), is developed to support the air surveillance of the Track While Scan (TWS) radar systems. Take advantage of both, IMM and PDA algorithms to increase the tracking efficiency of fast maneuvers targets. The known algorithm was implemented in a radar tracking application for the purpose of modernizing the ‘L’ band radar, as a replacement for the conventional NN (Nearest Neighbor) algorithm which proved to be ineffective in situations with airborne targets in the air. In extensive experiments with complex, target maneuver and non-maneuver scenarios has been shown that proposed algorithm to have robust tracking characteristics with small position and velocity error.

Hybrid fuzzy probabilistic data association filter and joint probabilistic data association filter

In this paper, we consider the problem of radar detector threshold optimization for maneuvering targets in clutter. In the earlier works, the problem was studied in the context of the probabilistic data association filter (PDAF) for non-maneuvering targets. In this study, we have extended the ideas, which were applied to the PDAF, to the interacting multiple model PDAF (IMM-PDAF) for maneuvering targets. The proposed optimization problem and its solution show better results over the traditional approaches in terms of track loss percentage and RMS position error criteria.

Distributed Adaptive Estimation with Probabilistic Data Association

In tracking a single target in clutter, many algorithms have been developed ranging in complexity from nearest neighbor (NN) and probabilistic data association (PDA) to the optimal Bayesian filter. In multiple-target tracking, a number of the techniques have been exercised such as the JPDA and the multiple hypothesis (MHT) schemes. Sub-optimal algorithms, such as the PDA filter, have been used widely since the optimal algorithms have an exponentially increasing computational complexity since all the possible sequences of target-to-measurement associations must be considered. In this paper, the Viterbi algorithm (VA) is used to develop a parallel search data association algorithm, called the Viterbi Data Association (VDA) technique. This algorithm includes the gating, automatic track initiation and termination modules. Simulations have been carried out to verify the performance and the robustness of the proposed algorithms Moreover, the VDA algorithm is compared with the fuzzy data association (FDA) algorithm when tracking a target in a cluttered, low signal-to-noise ratio (SNR) environment.

The authors present a new tracking algorithm for targets in a cluttered environment. The basic idea is to use all the data that fall into a validation gate. A weighted sum of these data is processed by means of a modified Kalman filter. A weighting coefficient is the distance between a given radar return and the predicted target position. The derived filter has a better performance than the nearest neighbor filter. It is also computationally more attractive than the probabilistic data association (PDA) filter. >

Practical detection systems generally are operated using a fixed threshold, optimized to the Neyman-Pearson criterion. An alternative is Bayes detection, in which the threshold varies according to the ratio of prior probabilities. This prior information is available in a tracking situation, but appears little used. The effect here is of a depressed detection threshold near the predicted measurement. We explain the appropriate modification to the commonly used probabilistic data association and tracking filter (PDAF). The implementation is simple, and the performance is remarkably good, and a considerable advantage with respect to the fixed-threshold PDAF is observed.