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.     

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     

Adaptive detection threshold optimization for tracking in clutter

The adaptive optimization of detection thresholds for tracking in clutter is investigated for the probabilistic data association (PDA) filter. Earlier work on this problem by T.E. Fortmann et al. (1985) involved an approximate steady-state analysis of the state error covariance and is only suitable for time-invariant systems. Furthermore, the method requires numerous assumptions and approximations about the error covariance update equation, and uses a cumbersome graphical optimization algorithm. In this work we propose two adaptive schemes for threshold optimization, namely prior and posterior optimization algorithms which minimize the mean-square state estimation error over detection thresholds which depend on data up to the previous and current time-step, respectively. These algorithm are suitable for real-time implementation in time-varying systems. Some simulation results are presented     

Censoring sensors: a low-communication-rate scheme for distributeddetection

We consider a new scheme for distributed detection based on a “censoring” or “send/no-send” idea. The sensors are assumed to “censor” their observations so that each sensor sends to the fusion center only “informative” observations, and leaves those deemed “uninformative” untransmitted. The main result of this work is that with conditionally independent sensor data and under a communication rate constraint, in order to minimize the probability of error, transmission should occur if and only if the local likelihood ratio value observed by the sensor does not fall in a certain single interval. Similar results are derived from Neymarr-Pearson and distance-measure viewpoints. We also discuss simplifications for the most interesting case that the fusion center threshold is high and the communication constraint is severe. We compare censoring with the more common binary-transmission framework and observe its considerable decrease in communication needs. Finally, we explore the use of feedback to achieve optimal performance with very little communication     

Effectiveness of the likelihood function in logic-based trackformation

A logic-based track formation procedure was presented by C.B. Chang et al. (1984). In addition to the conventional gating logic, it utilized the negative log-likelihood function (goodness of fit or sum of residuals) to further reduce the false track acceptance probability. An analytical technique for the evaluation of the effectiveness of this reduction is presented. The exact solution in closed form and a Gaussian approximation are given and compared. It is shown that the goodness of fit provides an additional reduction of the false track acceptance probability by a factor of two to three     

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.     

IMM estimator with out-of-sequence measurements

In multisensor tracking systems that operate in a centralized information processing architecture, measurements from the same target obtained by different sensors can arrive at the processing center out of sequence. In order to avoid either a delay in the output or the need for reordering and reprocessing an entire sequence of measurements, such measurements have to be processed as out-of-sequence measurements (OOSMs). Recent work developed procedures for incorporating OOSMs into a Kalman filter (KF). Since the state of the art tracker for real (maneuvering) targets is the interacting multiple model (IMM) estimator, the algorithm for incorporating OOSMs into an IMM estimator is presented here. Both data association and estimation are considered. Simulation results are presented for two realistic problems using measurements from two airborne GMTI sensors. It is shown that the proposed algorithm for incorporating OOSMs into an IMM estimator yields practically the same performance as the reordering and in-sequence reprocessing of the measurements. Also, it is shown how the range rate from a GMTI sensor can be used as a linear velocity measurement in the tracking filter.     

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