Removal of Out-of-Sequence Measurements from Tracks

In multisensor tracking systems that operate in a centralized or distributed information processing architecture, measurements from the same target obtained by different sensors can arrive at the processing center out of sequence due to system latencies. In order to avoid either a delay in the output or the need for reordering and reprocessing entire sequences of measurements, such latent measurements have to be processed by the tracking filter as out-of-sequence measurements (OOSM). Recent work developed a "one-step" procedure for incorporating OOSM with multiple-time-step latency into the tracking filter, which, while suboptimal, was shown to yield results very close to those obtained by reordering and reprocessing an entire sequence of measurements. The counterpart of this problem is the need to remove (revocate) measurements that have already been used to update a track state. This can happen in real-world systems when such measurements are reassigned to another track. Similarly to the problem of update with an OOSM, it is desired to carry out the removal of an earlier measurement without recomputing the track estimate (and the data association) using possibly a long sequence of subsequent measurements one at a time. A one-step algorithm is presented for this problem of removing a multistep OOSM.     

Precision large scale air traffic surveillance using IMM/assignmentestimators

We present the development and implementation of a multisensor-multitarget tracking algorithm for large scale air traffic surveillance based on interacting multiple model (IMM) state estimation combined with a 2-dimensional assignment for data association. The algorithm can be used to track a large number of targets from measurements obtained with a large number of radars. The use of the algorithm is illustrated on measurements obtained from 5 FAA radars, which are asynchronous, heterogeneous, and geographically distributed over a large area. Both secondary radar data (beacon returns from cooperative targets) as well as primary radar data (skin returns from noncooperative targets) are used. The target IDs from the beacon returns are not used in the data association. The surveillance region includes about 800 targets that exhibit different types of motion. The performance of an IMM estimator with linear motion models is compared with that of the Kalman filter (KF). A number of performance measures that can be used on real data without knowledge of the ground truth are presented for this purpose. It is shown that the IMM estimator performs better than the KF. The advantage of fusing multisensor data is quantified. It is also shown that the computational requirements in the multisensor case are lower than in single sensor case, Finally, an IMM estimator with a nonlinear motion model (coordinated turn) is shown to further improve the performance during the maneuvering periods over the IMM with linear models     

Particle filters for tracking with out-of-sequence measurements

An extension is presented to the particle filtering toolbox that enables nonlinear/non-Gaussian filtering to be performed in the presence of out-of-sequence measurements (OOSMs) with arbitrary lag, without the need to adopt linearising approximations in the filter and without the degradation of performance that would occur if the OOSMs were simply discarded. An estimate of the performance of the OOSM particle filter (OOSM-PF) is obtained for bearings-only tracking scenarios with a single target and a small number of sensors. These performance estimates are then compared with the posterior Cramer-Rao lower bound (CRLB) for the state estimate rms error and similar performance estimates obtained from the oosm extended Kalman filter (OOSM-EKF) algorithms recently introduced in the literature. For a mildly nonlinear bearings-only tracking problem the OOSM-PF and OOSM-EKF are shown to achieve broadly similar performance.     

Interacting multiple model methods in target tracking: a survey

The Interacting Multiple Model (IMM) estimator is a suboptimal hybrid filter that has been shown to be one of the most cost-effective hybrid state estimation schemes. The main feature of this algorithm is its ability to estimate the state of a dynamic system with several behavior modes which can “switch” from one to another. In particular, the IMM estimator can be a self-adjusting variable-bandwidth filter, which makes it natural for tracking maneuvering targets. The importance of this approach is that it is the best compromise available currently-between complexity and performance: its computational requirements are nearly linear in the size of the problem (number of models) while its performance is almost the same as that of an algorithm with quadratic complexity. The objective of this work is to survey and put in perspective the existing IMM methods for target tracking problems. Special attention is given to the assumptions underlying each algorithm and its applicability to various situations     

One-step solution for the multistep out-of-sequence-measurement problem in tracking

In multisensor target tracking systems measurements from the same target can arrive out of sequence. Such "out-of-sequence" measurement (OOSM) arrivals can occur even in the absence of scan/frame communication time delays. The resulting problem - how to update the current state estimate with an "older" measurement - is a nonstandard estimation problem. It was solved first (suboptimally, then optimally) for the case where the OOSM lies between the two last measurements, i.e, its lag is less than a sampling interval - the 1-step-lag case. The real world has, however, OOSMs with arbitrary lag. Subsequently, the suboptimal algorithm was extended to the case of an arbitrary (multistep) lag, but the resulting algorithm required a significant amount of storage. The present work shows how the 1-step-lag algorithms can be generalized to handle an arbitrary (multistep) lag while preserving their main feature of solving the update problem without iterating. This leads only to a very small (a few percent) degradation of MSE performance. The incorporation of an OOSM into the data association process is also discussed. A realistic example with two GMTI radars is presented. The consistency of the proposed algorithm is also evaluated and it is found that its calculated covariances are reliable.     

Reduced state estimators for consistent tracking of maneuvering targets

Linear Kalman filters, using fewer states than required to completely specify target maneuvers, are commonly used to track maneuvering targets. Such reduced state Kalman filters have also been used as component filters of interacting multiple model (IMM) estimators. These reduced state Kalman filters rely on white plant noise to compensate for not knowing the maneuver - they are not necessarily optimal reduced state estimators nor are they necessarily consistent. To be consistent, the state estimation and innovation covariances must include the actual errors during a maneuver. Blair and Bar-Shalom have shown an example where a linear Kalman filter used as an inconsistent reduced state estimator paradoxically yields worse errors with multisensor tracking than with single sensor tracking. We provide examples showing multiple facets of Kalman filter and IMM inconsistency when tracking maneuvering targets with single and multiple sensors. An optimal reduced state estimator derived in previous work resolves the consistency issues of linear Kalman filters and IMM estimators.     

Multisensor tracking of a maneuvering target in clutter

An algorithm is presented for tracking a highly maneuvering target using two different sensors, a radar and an infrared sensor, assumed to operate in a cluttered environment. The nonparametric probabilist data association filter (PDAF) has been adapted for the multisensor (MS) case, yielding the MSPDAF. To accommodate the fact that the target can be highly maneuvering, the interacting multiple model (IMM) approach is used. The results of single-model-based filters and of the IMM/MSPDAF algorithm with two and three models are presented and compared. The IMM has been shown to be able to adapt itself to the type of motion exhibited by the target in the presence of heavy clutter. It yielded high accuracy in the absence of acceleration and kept the target in track during the high acceleration periods     

Track segment association, fine-step IMM and initialization with Doppler for improved track performance

In this work we present a new track segment association technique to improve track continuity in large-scale target tracking problems where track breakages are common. A representative airborne early warning (AEW) system scenario, which is a challenging environment due to highly maneuvering targets, close target formations, large measurement errors, long sampling intervals, and low detection probabilities, provides the motivation for the new technique. Previously, a tracker using the interacting multiple model (IMM) estimator combined with an assignment algorithm was shown to be more reliable than a conventional Kalman filter based approach in tracking similar targets but it still yielded track breakages due to the difficult environment. In order to combine the broken track segments and improve track continuity, a new track segment association algorithm using a discrete optimization approach is presented. Simulation results show that track segment association yields significant improvements in mean track life as well as in position, speed, and course rms errors. Also presented is a modified one-point initialization technique with range rate measurements, which are typically ignored by other initialization techniques, and a fine-step IMM estimator, which improves performance in the presence of long revisit intervals. Another aspect that is investigated is the benefit of "deep" (multiframe or N-dimensional, with N > 2) association, which is shown to yield significant benefit in reducing the number of false tracks.     

Radar Measurement Noise Variance Estimation with Several Targets of Opportunity

A number of methods exist to track a target's uncertain motion through space using inherently inaccurate sensor measurements. A powerful method of adaptive estimation is the interacting multiple model (IMM) estimator. In order to carry out state estimation from the noisy measurements of a sensor, however, the filter should have knowledge of the statistical characteristics of the noise associated with that sensor. The statistical characteristics (accuracies) of real sensors, however, are not always available, in particular for legacy sensors. A method is presented of determining the measurement noise variances of a sensor, assumed to be constant, by using multiple IMM estimators while tracking targets whose motion is not known---targets of opportunity. Combining techniques outlined in [2] and [6], the likelihood functions are obtained for a number of IMM estimators, each with different assumptions on the measurement noise variances. Then a search is carried out over a varying grid of IMMs to bracket the variances of the sensor measurement noises. The end result consists of estimates of the measurement noise variances of the sensor in question.     

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.     

Update with out-of-sequence measurements in tracking: exact solution

In target tracking systems measurements are typically collected in "scans" or "frames" and then they are transmitted to a processing center. In multisensor tracking systems that operate in a centralized manner, there are usually different time delays in transmitting the scans or frames from the various sensors to the center. This can lead to situations where measurements from the same target arrive out of sequence. Such "out-of-sequence" measurement (OOSM) arrivals can occur even in the absence of scan/frame communication time delays. The resulting "negative-time measurement update" problem, which is quite common in real multisensor systems, was solved previously only approximately in the literature. The exact state update equation for such a problem is presented. The optimal and two suboptimal algorithms are compared on a number of realistic examples, including a GMTI (ground moving target indicator) radar case.     

Ground target tracking with variable structure IMM estimator

In this paper we present the design of a Variable Structure Interacting Multiple Model (VS-IMM) estimator for tracking groups of ground targets on constrained paths using Moving Target Indicator (MTI) reports obtained from an airborne sensor. The targets are moving along a highway, with varying obscuration due to changing terrain conditions. In addition, the roads can branch, merge or cross-the scenario represents target convoys along a realistic road network with junctions, changing terrains, etc. Some of the targets may also move in an open field. This constrained motion estimation problem is handled using an IMM estimator with varying mode sets depending on the topography, The number of models in the IMM estimator, their types and their parameters are modified adaptively, in real-time, based on the estimated position of the target and the corresponding road/visibility conditions. This topography-based variable structure mechanism eliminates the need for carrying all the possible models throughout the entire tracking period as in the standard IMM estimator, significantly improving performance and reducing computational load. Data association is handled using an assignment algorithm. The estimator is designed to handle a very large number of ground targets simultaneously. A simulated scenario consisting of over one hundred targets is used to illustrate the selection of design parameters and the operation of the tracker. Performance measures are presented to contrast the benefits of the VS-IMM estimator over the Kalman filter and the standard IMM estimator, The VS-IMM estimator is then combined with multidimensional assignment to gain “time-depth.” The additional benefit of using higher dimensional assignment algorithms for data association is also evaluated     

Interacting multiple model filter for tactical ballistic missile tracking

An interacting multiple model (IMM) filter is presented for the real-time tracking of tactical ballistic missiles (TBMs). The novel aspects of the proposed IMM filter include the development of a constant axial force (CAF) Kalman filter, asymmetric IMM state interaction, and an entropy-based variation of the IMM mode probability update equation. Using data from a recent TBM defense (TBMD) test event, the proposed IMM filter is shown to yield consistent state estimates throughout the entire TBM trajectory, which includes a dual-stage boost during launch.     

Interacting acceleration compensation algorithm for trackingmaneuvering targets

The two-stage Kalman estimator has been studied for state estimation in the presence of random bias and applied to the tracking of maneuvering targets by treating the target acceleration as a bias vector. Since the target acceleration is considered a bias, the first stage contains a constant velocity motion model and estimates the target position and velocity, while the second stage estimates the target acceleration when a maneuver is detected, the acceleration estimate is used to correct the estimates of the first stage. The interacting acceleration compensation (IAC) algorithm is proposed to overcome the requirement of explicit maneuver detection of the two-stage estimator. The IAC algorithm is viewed as a two-stage estimator having two acceleration models: the zero acceleration of the constant velocity model and a constant acceleration model. The interacting multiple model (IMM) algorithm is used to compute the acceleration estimates that compensate the estimate of the constant velocity filter. Simulation results indicate the tracking performance of the IAC algorithm approaches that of a comparative IMM algorithm while requiring approximately 50% of the computations     

Bearings-only tracking of maneuvering targets using abatch-recursive estimator

We present a new batch-recursive estimator for tracking maneuvering targets from bearings-only measurements in clutter (i.e., for low signal-to-noise ratio (SNR) targets), Standard recursive estimators like the extended Kalman Iter (EKF) suffer from poor convergence and erratic behavior due to the lack of initial target range information, On the other hand, batch estimators cannot handle target maneuvers. In order to rectify these shortcomings, we combine the batch maximum likelihood-probabilistic data association (ML-PDA) estimator with the recursive interacting multiple model (IMM) estimator with probabilistic data association (PDA) to result in better track initialization as well as track maintenance results in the presence of clutter. It is also demonstrated how the batch-recursive estimator can be used for adaptive decisions for ownship maneuvers based on the target state estimation to enhance the target observability. The tracking algorithm is shown to be effective for targets with 8 dB SNR     

MAP estimation of target manoeuvre sequence with theexpectation-maximization algorithm

Two algorithms are derived for the problem of tracking a manoeuvring target based on a sequence of noisy measurements of the state. Manoeuvres are modeled as unknown input (acceleration) terms entering linearly into the state equation and chosen from a discrete set. The expectation maximization (EM) algorithm is first applied, resulting in a multi-pass estimator of the MAP sequence of inputs. The expectation step for each pass involves computation of state estimates in a bank of Kalman smoothers tuned to the possible manoeuvre sequences. The maximization computation is efficiently implemented using the Viterbi algorithm. A second, recursive estimator is then derived using a modified EM-type cost function. To obtain a dynamic programming recursion, the target state is assumed to satisfy a Markov property with respect to the manoeuvre sequence. This results in a recursive but suboptimal estimator implementable on a Viterbi trellis. The transition costs of the latter algorithm, which depend on filtered estimates of the state, are compared with the costs arising in a Viterbi-based manoeuvre estimator due to Averbuch, et al. (1991). It is shown that the two criteria differ only in the weighting matrix of the quadratic part of the cost function. Simulations are provided to demonstrate the performance of both the batch and recursive estimators compared with Averbuch's method and the interacting multiple model filter     

ALGORITHMS FOR TRACKING MANEUVERING TARGET WITH PHASED ARRAY RADAR

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An efficient algorithm for multisensor track fusion

An efficient algorithm for track-to-track fusion by incorporating cross-covariance between tracks created by dissimilar sensors is described. An analytical solution of this problem is complicated if cross-correlation between sensors tracking the same target is taken into account. An explicit solution of the cross-covariance matrix at steady state is derived in terms of an integral. It is shown that solution of this integral involves inversion of a matrix whose elements are functions of parameters of individual trackers. Structure of this matrix is analyzed. An efficient analytical solution for inversion of this matrix is obtained. For fusion of similar sensors, it is shown that this matrix is reduced to the Routh-Hurwitz matrix which arises in the study of steady state stability of linear systems. Numerical results showing the amount of reduction of fused track covariance by taking into account the effects of cross-correlation between candidate tracks for fusion is also presented     

Application of Road Information in Ground Moving Target Tracking

A new algorithm is developed to achieve accurate state estimation in ground moving target tracking by means of using road information. It is an adaptive variable structure interacting multiple model estimator with dynamic models modification （DMM VS-IMM for short）. Firstly, road information is employed to modify the target dynamic models used by filter, including modification of state transition matrix and process noise. Secondly, road information is applied to update the model set of a VS-IMM estimator. Predicted state estimation and road information are used to locate the target in the road network on which the model set is updated and finally IMM filtering is implemented. As compared with traditional methods, the accuracy of state estimation is improved for target moving not only on a single road, but also through an intersection. Monte Carlo simulation demonstrates the efficiency and robustness of the proposed algorithm with moderate computational loads.     

Novel Nonlinear Filtering & Prediction Method for Maneuvering Target Tracking

A new nonlinear filtering and prediction (NFP) algorithm with input es?imation is proposed for maneuvering target tracking. In the proposed method, the acceleration level is determined by a decision process, where a least squares (LS) estimator plays a major role in detecting target maneuvering within a sliding window. We first illustrate that the optimal solution to minimize the mean squared error (MSE) must consider a trade-off between the bias and error variance. For the application of target tracking, we then derive the MSE of target positions in a closed form by using orthogonal space decompositions. Then we discuss the NFP estimator, and evaluate how well the approach potentially works in the case of a set of given system parameters. Comparing with the traditional unbiased minimum variance filter (UMVF), Kalman filter, and interactive multiple model (IMM) algorithms, numerical results show that the newly proposed NFP method performs comparable or better in all scenarios with significantly less computational requirements.