Efficient multisensor fusion using multidimensional dataassociation

We present the development of a multisensor fusion algorithm using multidimensional data association for multitarget tracking. The work is motivated by a large scale surveillance problem, where observations from multiple asynchronous sensors with time-varying sampling intervals (electronically scanned array (ESA) radars) are used for centralized fusion. The combination of multisensor fusion with multidimensional assignment is done so as to maximize the “time-depth” in addition to “sensor-width” for the number S of lists handled by the assignment algorithm. The standard procedure, which associates measurements from the most recently arrived S-1 frames to established tracks, can have, in the case of S sensors, a time-depth of zero. A new technique, which guarantees maximum effectiveness for an S-dimensional data association (S⩾3), i.e., maximum time-depth (S-1) for each sensor without sacrificing the fusion across sensors, is presented. Using a sliding window technique (of length S), the estimates are updated after each frame of measurements. The algorithm provides a systematic approach to automatic track formation, maintenance, and termination for multitarget tracking using multisensor fusion with multidimensional assignment for data association. Estimation results are presented for simulated data for a large scale air-to-ground target tracking problem     

An interacting multiple model approach for target tracking withglint noise

The application of the interacting multiple model (IMM) estimation approach to the problem of target tracking when the measurements are perturbed by glint noise is considered. The IMM is a very effective approach when the system has discrete uncertainties in the dynamic or measurement model as well as continuous uncertainties. It is shown that this method performs better than the “score function” method. It is also shown that the IMM method performs robustly when the exact prior information of the glint noise is not available     

Interacting multiple model fixed-lag smoothing algorithm forMarkovian switching systems

We investigate a suboptimal approach to the fixed-lag smoothing problem for Markovian switching systems. A fixed-lag smoothing algorithm is developed by applying the basic Interacting Multiple Model (IMM) approach to a state-augmented system. The computational load is roughly d (the fixed lag) times beyond that of filtering for the original system. In addition, an algorithm that approximates the “fixed-lag” mode probabilities given measurements up to current time is proposed. The algorithm is illustrated via a target tracking simulation example where a significant improvement over the filtering algorithm is achieved at the cost of a time delay (i.e., data up to time k are used to produce the smoothed state estimate at time k-d where the fixed large d>0). the IMM fixed-lag smoothing performance for the given example is comparable to that of an existing IMM fixed-interval smoother. Compared with fixed-interval smoothers, the fixed-lag smoothers can be implemented in real-time with a small delay     

Rate-aided multisignal time delay detection and tracking

Time delay detection and tracking problems have been investigated in previous papers. The approach used is applicable to many problems. In those papers, a first-order Markov process was assumed for the signal parameter (time delay) dynamic model and a constant signal parameter value was assumed within a “block”, or processing unit of time. A performance degradation is incurred when the signal parameter value is “nearly constant-rate”. Also, “crossing” signal parameter values from different signals cannot be tracked. The detector-trackers will “switch” signals. To combat these difficulties, the signal parameter dynamic model is assumed to be a second-order Markov process, and signal parameter rate of change information is computed within a block. A rate-aided multisignal detection and tracking system is developed with these assumptions     

Multiassignment for tracking a large number of overlapping objects[and application to fibroblast cells]

In this paper we present a new technique for data association using multiassignment for tracking a large number of closely spaced (and overlapping) objects. The algorithm is illustrated on a biomedical problem, namely the tracking of a group of fibroblast (tissue) cells from an image sequence, which motivated this work. Because of their proximity to one another and due to the difficulties in segmenting the images accurately from a poor-quality image sequence, the cells are effectively closely spaced objects (CSOs). The algorithm presents a novel dichotomous, iterated approach to multiassignment using successive one-to-one assignments of decreasing size with modified costs. The cost functions, which are adjusted depending on the “depth” of the current assignment level and on the tracking results, are derived. The resulting assignments are used to form, maintain and terminate tracks with a modified version of the probabilistic data association (PDA) filter, which can handle the contention for a single measurement among multiple tracks in addition to the association of multiple measurements to a single track. Estimation results are given and compared with those of the standard 2D one-to-one assignment algorithm. It is shown that iterated multiassignment results in superior measurement-to-track association. The algorithms presented can be used for other general tracking problems, including dense air traffic surveillance and control     

Highest density gates for target tracking

The problem of forming validation regions or gates for new sensor measurements obtained when tracking targets in clutter is considered. Target dynamics and measurement characteristics are modeled with, possible non-Gaussianities or nonlinearities, so that some degree of approximation is usually required in the computation of the filtering densities for the target position and predictive densities for future measurements. Highest density gates (HDGs) are proposed as summaries of the predictive densities. These gates are constructed numerically, via simulation from the filtering density approximation. The algorithm results in gates that are “exact” (up to numerical accuracy) regardless of the approximation used for the filtering density. That is, given an approximation to the filtering density, the gating procedure accounts for all further nonlinearities and non-Gaussianities. Numerical example show that when the predictive density is markedly non-Gaussian, HDGs offer advantages over the more common rectangular and ellipsoidal gates     

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     

Tracking in clutter with nearest neighbor filters: analysis andperformance

The measurement that is “closest” to the predicted target measurement is known as the “nearest neighbor” (NN) measurement in tracking. A common method currently in wide use for tracking in clutter is the so-called NN filter, which uses only the NN measurement as if it were the true one. The purpose of this work is two fold. First, the following theoretical results are derived: the a priori probabilities of all three data association events (updates with correct measurement, with incorrect measurement, and no update), the probability density functions (pdfs) of the NN measurement conditioned on the association events, and the one-step-ahead prediction of the matrix mean square error (MSE) conditioned on the association events. Secondly, a technique for prediction without recourse to expensive Monte Carlo simulations of the performance of tracking in clutter with the NN filter is presented. It can quantify the dynamic process of tracking divergence as well as the steady-state performance. The technique is a new development along the line of the recently developed general approach to the performance prediction of algorithm with both continuous and discrete uncertainties     

Active sonar application of a U-D square root PDAF

The probabilistic data association filter (PDAF) is a suboptimal approach to tracking a target in the presence of clutter. In the PDAF implementation, the Kalman measurement update is performed over the set of validated measurements and the Kalman time update is used to propagate the PDAF measurement update. A popular approach to obtaining a numerically stable set of Kalman update equations is to propagate the U-D factors of the covariance in the measurement and time updates. The PDAF measurement update equation is obtained in U-D factored form by applying the modified weighted Gram-Schmidt (MWG-S) algorithm to the three factored terms. The factors of the first two terms are determined from the U-D factors of the a priori and conditional a posteriori covariances. The third term is factored analytically using the Agee-Turner factorization. The resulting U-D square-root PDAF is then applied to the problem of active tracking of a submarine in reverberation using polar coordinates     

Data fusion and tracking using HMMs in a distributed sensor network

This work deals with the problem of multiple target tracking, from the measurements made on a field of passive sonars activated by an active sonar (multistatic network). The difficulties encountered then are of two kinds: each sensor alone does not provide full observability of a target, and multiple, possibly maneuvering targets moving in a cluttered environment must be dealt with. The algorithm presented here is based on a discrete Markovian modelization of the targets evolution in time. It starts with a fusion of the detections obtained at each measurement time. Tracking and target motion analysis (TMA) are next achieved thanks to dynamic programming (DP). This approach leads to multiple and maneuvering target tracking, with few assumptions; for instance, the use of deterministic target state models are avoided. Simulation results are presented and discussed.     

Predetection fusion: resolution cell grid effects

If members of a suite of sensors from which fusion is to be carried out are not colocated, it is unreasonable to assume that they share a common resolution cell grid; this is generally ignored in the data fusion community. We explore the effects of such “noncoincidence”, and we find that what at first seems to be a problem can in fact be exploited. The idea is that a target is known to be confined to an intersection of overlapping resolution cells, and this overlap is generally small. We examine noncoincidence from two viewpoints: tracking and detection. With respect to tracking our analysis is first static, by which is meant that we establish the decrease in measurement error; and then dynamic, meaning that the overall effect in the tracking problem is quantified. The detection viewpoint considers noncoincidence as it has impact on a predetection fusion system. Specifically, the role of the fusion rule is examined, and the use of noncoincidence to improve detection performance (rather than that of tracking) is explored     

Maximum likelihood track-before-detect with fluctuating targetamplitude

An important problem in target tracking is the detection and tracking of targets in very low signal-to-noise ratio (SNR) environments. In the past, several approaches have been used, including maximum likelihood. The major novelty of this work is the incorporation of a model for fluctuating target amplitude into the maximum likelihood approach for tracking of constant velocity targets. Coupled with a realistic sensor model, this allows the exploitation of signal correlation between resolution cells in the same frame, and also from one frame to the next. The fluctuating amplitude model is a first order model to reflect the inter-frame correlation. The amplitude estimates are obtained using a Kalman filter, from which the likelihood function is derived. A numerical maximization technique avoids problems previously encountered in “velocity filtering” approaches due to mismatch between assumed and actual target velocity, at the cost of additional computation. The Cramer-Rao lower bound (CRLB) is derived for a constant, known amplitude case. Estimation errors are close to this CRLB even when the amplitude is unknown. Results show track detection performance for unknown signal amplitude is nearly the same as that obtained when the correct signal model is used     

Fast data association using multidimensional assignment withclustering

We present a fast data association technique based on clustering and multidimensional assignment algorithms for multisensor-multitarget tracking Assignment-based methods have been shown to be very effective for data association. Multidimensional assignment for data association is an NP-hard problem and various near-optimal modifications with (pseudo-)polynomial complexity have been proposed. In multidimensional assignment, candidate assignment tree building consumes about 95% of the time. We present the development of a fast data association algorithm, which partitions the problem into smaller sub-problems. A clustering approach, which attempts to group measurements before forming the candidate tree, is developed for various target-sensor configurations. Simulation results show significant computational savings over the standard multidimensional assignment approach without clustering     

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.     

Modeling and Estimation for Tracking Maneuvering Targets

A new approach to the three-dimensional airborne maneuvering target tracking problem is presented. The method, which combines the correlated acceleration target model of Singer [3] with the adaptive semi-Markov maneuver model of Gholson and Moose [8], leads to a practical real-time tracking algorithm that can be easily implemented on a modern fire-control computer. Preliminary testing with actual radar measurements indicates both improved tracking accuracy and increased filter stability in response to rapid target accelerations in elevation, bearing, and range.     

Periodic acoustic source tracking using propagation delayed measurements

There exist a large class of acoustic sources which have an underlying periodic phenomenon. Unlike the well-studied Bearings-Only Tracking(BOT) of an aperiodic acoustic source,this paper considers the problem of tracking a periodic acoustic source. For periodic acoustic tracking, the signal emission time is known. However, the true measurement reception time is unknown because it is corrupted by noise due to propagation delay. We augment the sensor’s signal reception time onto bearing measuremen...     

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.     

Tracking of Spawning Targets with Multiple Finite Resolution Sensors

In this paper the problem of tracking multiple spawning targets with multiple finite-resolution sensors is considered and a new algorithm for measurement-to-track association with possibly unresolved measurements is presented. The goal is to initialize new tracks of spawned targets before they are resolved from the mother platform so that one has the ability to carry out early discrimination when they become resolved. The multiple scan data association problem is first formulated as a multidimensional assignment problem with explicit new constraints for the unresolved measurements. Then the top M hypotheses tracking (TMHT) is presented where the state estimates and their covariances are modified based on the M best hypotheses through the assignment solutions. A modification to the assignment problem is developed that leads to a linear programming (LP) where the optimal solution can be a noninteger in [0,1]. The fractional optimal solution is interpreted as (pseudo) probabilities over the N - 1 frame sliding window. The best hard (binary) decision assignment solution and the M best via TMHT are compared with the soft decision solution for 2-D tracking scenarios with various sensor configurations. Based on the simulation results, the soft assignment approach has better track maintenance capability than the single best hard assignment and a performance nearly as good as the TMHT. Its computational load is slightly higher than the single best hard assignment but much lighter than TMHT.     

Nonparametric methods for clutter removal

Methods of clutter rejection are discussed which furnish an inherent counterpart of target tracking and detection algorithms. We describe how nonparametric curve estimation methods reduce the original sensor data to a “signal-plus-noise” model which is well suited for various hypotheses testing and dynamical filtering algorithms. We also verify a “white noise” assumption for the model of residuals