<title>Maneuvering target tracking in clutter using VSIMM-PDA</title>

For the problem of maneuvering target tracking in clutter, an adaptive probabilistic data association algorithm is proposed based on modified input estimation (MIE). An adaptive weighted factor is introduced in MIE in order to adjust the prediction covariance and the corresponding filter gain in real time, which enables the adaptive MIE (AMIE) method track a maneuvering target well. Then, the AMIE method is combined with the probabilistic data association (PDA) technique so that the proposed method can track a maneuvering target in clutter. Simulation results show the effectiveness of the proposed algorithm. Compared with the traditional algorithm, the proposed algorithm has better tracking performance.

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.

Tracking targets in clutter, with the inherent data association problem, naturally leads to a Gaussian mixture representation of the probability density function (pdf) of the target state vector, conditioned on the measurements observed. Online trackers require reduction of the number of components in the mixture on each processing cycle, and the integral square error (ISE) based mixture reduction algorithm (MRA) significantly outperforms known alternative algorithms. Moreover, to handle target maneuver onset and changing trajectory characteristics, one can use multiple model adaptive estimation in the form of either multiple model adaptive estimation (MMAE) or interacting multiple model (IMM) algorithms. For maneuvering targets in clutter, one can replace each Kalman filter within a conventional MMAE or IMM with an ISE-based MRA, or better yet, replace each Kalman filter within an ISE-based algorithm with an MMAE or IMM, to yield superior tracking of aggressive maneuvers in deep clutter. Such an ISE-based algorithm of MMAEs is seen to have performance attributes significantly superior to that of a current state-of-the-art tracker.

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.

Gating techniques for maneuvering target tracking using an IMM-PDA filter are considered in this paper. Existing gating techniques, namely, centralized gating and model based gating are reviewed and new gating techniques, called model probability weighted gating and two-stage model probability weighted gating, are proposed. A benchmark trajectory and a random scenario are considered for performance evaluation of the gating techniques in terms of RMS errors, percentage of track loss and computational load.

Fault detection and diagnosis based on particle filters combined with interactive multiple-model estimation in dynamic process systems

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.

Target tracking based on frequency spectrum amplitude

This paper presents a simple yet efficient adaptive Kalman filter for tracking targets expected to perform varying turn maneuvers. The process noise covariance level of a second order Kalman filter is adjusted at each time step according to the calculated turn rate. The turning rate is estimated from the magnitude of the calculated acceleration divided by the estimated speed of the target. At each scan the previous and current velocity estimates are used to calculate the acceleration. The comparison of the performance of the proposed algorithm is made with that of an interacting multiple model (IMM) algorithm, employing three models with different levels of process noise covariance and also to that of a second order Kalman filter. Two different assumptions have been made for selecting the process noise values for the the IMM and Kalman filter algorithms, in the first case it was assumed that there was no prior information about the target motion whereas in the second case it was assumed that the largest turn rate that the target of interest could perform was known. The IMM algorithm utilizing three models gives slightly better estimates during the nonmaneuvering periods, but the proposed algorithm is superior to the IMM algorithm during maneuvering periods in terms of estimation errors. Also the proposed algorithm requires 78% less computation, almost the same number of calculations required by a single fixed process noise Kalman filter, than the IMM algorithm.

Control of the time between sawtooth crashes, necessary for ITER and DEMO, requires real-time detection of the moment of the sawtooth crash. In this paper, estimation of sawtooth crash times is demonstrated using the model-based interacting multiple model (IMM) estimator, based on simplified models for the sawtooth crash. In contrast to previous detectors, this detector uses the spatial extent of the sawtooth crash as detection characteristic. The IMM estimator is tuned and applied to multiple ECE channels at once. A model for the sawtooth crash is introduced, which is used in the IMM algorithm. The IMM algorithm is applied to seven datasets from the ASDEX Upgrade tokamak. Five crash models with different mixing radii are used. All sawtooth crashes that have been identified beforehand by visual inspection of the data, are detected by the algorithm. A few additional detections are made, which upon closer inspection are seen to be sawtooth crashes, which show a partial reconnection. A closer inspection of the detected normal crashes shows that about 42% are not well fitted by any of the full reconnection models and show some characteristics of a partial reconnection. In some case, the measurement time is during the sawtooth crashes, which also results in an incorrect estimate of the mixing radius. For data provided at a sampling rate of 1 kHz, the run time of the IMM estimator is below 1 ms, thereby fulfilling real-time requirements.

ADS-B and radar will coexist for a long time in the future. For the ADS-B and multi-radar asynchronous track fusion problem in the air traffic control system, an ADS-B and radar fusion architecture and an asynchronous multi-sensor track fusion algorithm based on augmented state interacting multiple model(IMM) filter with probability data association(PDA) are proposed in this paper. The fusion algorithm is developed by applying the standard IMM approach, the PDA technique, and asynchronous measurement updating to a state-augmented system for the target motion. The state vector is augmented to include the past states which correspond to those asynchronous measurements. A PDA filter for parallel sensor processing is developed for target tracking under clutter. Real data from the ADS-B equipped aircraft and radar are used to test the performance of the algorithm. The simulation result shows that the track accuracy can be improved by this algorithm and the performance is comparable with the distributed multi-rate track fusion algorithm.

In most of the existing state estimation algorithms for maneuvering target tracking, the formulation of the mode switching process fails to accurately capture the deterministic law that the target mode will persist for a period of time once it turns to be in effect. In this paper, two strategies are presented to describe this characteristic. First, a constraint that model switching occurs no more than once over three consecutive time steps is proposed to provide a deterministic description that mode does not switch continuously. Second, considering target mode always lasts for some time while mode switching is completed instantly, the transition probabilities from one model to itself are fixed at extremely large values to enhance the certainty in mode sojourn segments. Based on these strategies, two recursive multiple model (MM) filters are derived in the framework of generalized pseudo-Bayesian (GPB) estimation and interacting multiple model (IMM) estimation, respectively. In both algorithms, although the large probability of model staying unchanged causes high peak errors at mode switching instants, the introduction of the switching constraint prevents the input to the mode-matched filter from being affected by the model transition probability, thereby obtaining a near-optimal performance in mode sojourn segments. Additionally, in order to reduce the peak estimation errors, a mode switching detector based on likelihood function is presented to work in parallel with the recursive MM filters. Once the detector declares that a mode switch occurs, the final estimate is adjusted from the output of the recursive MM filters to the estimate of the corresponding elemental filter, performance of which is guaranteed by the switching constraint. Simulation results demonstrate the capability of the proposed recursive MM filters to obtain performance close to that of a filter without model uncertainty in mode sojourn segments and the effectiveness of the mode switching detector to reduce peak errors at the same time.

A simplified dynamic Cramer-Rao lower bound (CRLB) is derived for the general case of target tracking in clutter with non-IID measurement noise components, discussed recently in.

This paper proposes a new multiple model estimation method which employs the square root version of unscented information filter (SRUIF) in the framework of interacting multiple model (IMM). Comparing with the general UIF, the square root version has better numerical characteristics, such as improved numerical accuracy, double order precision and preservation of the symmetry for the covariance matrix. However, the SRUIF has to been further improved in order to achieve better performance in case the system has multiple models, e.g., maneuvering object tracking. Therefore, we here propose to use the IMM with the SRUIF (IMM-SRUIF) for solving multiple model estimation problem. A classical simulation of the maneuvering object tracking problem is demonstrated, which shows the advantages of the proposed IMM-SRUIF method.

This paper presents two methods for maneuvering radar target tracking, one is called variable structure multiple model particle filter (VSMMPF), which combines the variable structure multiple model (VSMM) filter with a Sampling-Importance Resampling (SIR) particle filter (PF); The other one is called modified adaptive gird multiple model (AGMM), which is suitable when model parameter scope is unknown beforehand. PF is used to deal with problems with arbitrary nonlinearities and non-Gaussian noise. Thus the combination of VSMM and PF is able to deal with problems of nonlinearities, non-Gaussian and maneuvering. As one of the VSMM algorithms, Grid adaptation (GA) is unique one which can produce new model-set that are not predefined and model parameter can be any value within continuous model space. However, it only used to tracking maneuvering target in 2D coordinate turn system. Our modified AGMM could track generic planar maneuvering target. Simulation results indicate that performance of the algorithm VSMMPF outperforms interacting multiple model (IMM) PF and the AGMM PF which combines AGMM with PF runs well especially when model scope is unknown in advance.