T. Kirubarajan

Multisensor resource deployment using posterior Cramer-Rao bounds

The development of a general framework for the systematic management of multiple sensors in target tracking in the presence of clutter is described. The basis of the technique is to quantify, and subsequently control, the accuracy of target state estimation. The posterior Cramer-Rao lower bound (PCRLB) provides the means of achieving this aim by enabling us to determine a bound on the performance of all unbiased estimators of the unknown target state. The general approach is then to use optimization techniques to control the measurement process in order to achieve accurate target state estimation. We are concerned primarily with the deployment and utilization of limited sensor resources. We also allow for measurement origin uncertainty, with sensor measurements either target-generated or false alarms. An example in which the aim is to track a submarine by deploying a series of constant false-alarm rate passive sonobuoys is presented. We show that by making some standard assumptions, the effect of the measurement origin uncertainty can be expressed as a state-dependent information reduction factor which can be calculated off-line. This enables the Fisher information matrix (FIM) to be calculated quickly, allowing Cramer-Rao bounds to be utilized for real-time, dynamic sensor management. The sensor management framework is shown to determine deployment strategies that enable the target to be accurately localized, and at the same time efficiently utilize the limited sensor resources.

IMMPDAF for radar management and tracking benchmark with ECM

A framework is presented for controlling a phased array radar for tracking highly maneuvering targets in the presence of false alarms (FAs) and electronic countermeasures (ECMs). Algorithms are presented for track formation and maintenance; adaptive selection of target revisit interval, waveform and detection threshold; and neutralizing techniques for ECM, namely, against a standoff jammer (SOJ) and range gate pull off (RGPO). The interacting multiple model (IMM) estimator in combination with the probabilistic data association (PDA) technique is used for tracking. A constant false alarm rate (CFAR) approach is used to adaptively select the detection threshold and radar waveform, countering the effect of jammer-induced false measurements. The revisit interval is selected adaptively, based on the predicted angular innovation standard deviations. This tracker/radar-resource-allocator provides a complete solution to the benchmark problem for target tracking and radar control. Simulation results show an average sampling interval of about 2.5 s while maintaining a track loss less than the maximum allowed 4%.

Multiple-model probability hypothesis density filter for tracking maneuvering targets

Tracking multiple targets with uncertain target dynamics is a difficult problem, especially with nonlinear state and/or measurement equations. With multiple targets, representing the full posterior distribution over target states is not practical. The problem becomes even more complicated when the number of targets varies, in which case the dimensionality of the state space itself becomes a discrete random variable. The probability hypothesis density (PHD) filter, which propagates only the first-order statistical moment (the PHD) of the full target posterior, has been shown to be a computationally efficient solution to multitarget tracking problems with a varying number of targets. The integral of PHD in any region of the state space gives the expected number of targets in that region. With maneuvering targets, detecting and tracking the changes in the target motion model also become important. The target dynamic model uncertainty can be resolved by assuming multiple models for possible motion modes and then combining the mode-dependent estimates in a manner similar to the one used in the interacting multiple model (IMM) estimator. This paper propose a multiple-model implementation of the PHD filter, which approximates the PHD by a set of weighted random samples propagated over time using sequential Monte Carlo (SMC) methods. The resulting filter can handle nonlinear, non-Gaussian dynamics with uncertain model parameters in multisensor-multitarget tracking scenarios. Simulation results are presented to show the effectiveness of the proposed filter over single-model PHD filters.

Precision large scale air traffic surveillance using IMM/assignment estimators

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.

Multisensor multitarget bias estimation for general asynchronous sensors

A novel solution is provided for the bias estimation problem in multiple asynchronous sensors using common targets of opportunity. The decoupling between the target state estimation and the sensor bias estimation is achieved without ignoring or approximating the crosscovariance between the state estimate and the bias estimate. The target data reported by the sensors are usually not time-coincident or synchronous due to the different data rates. Since the bias estimation requires time-coincident target data from different sensors, a novel scheme is used to transform the measurements from the different times of the sensors into pseudomeasurements of the sensor biases with additive noises that are zero-mean, white, and with easily calculated covariances. These results allow bias estimation as well as the evaluation of the Cramer-Rao lower bound (CRLB) on the covariance of the bias estimate, i.e., the quantification of the available information about the biases in any scenario. Monte Carlo simulation results show that the new method is statistically efficient, i.e., it meets the CRLB. The use of this technique for scale and sensor location biases in addition to the usual additive biases is also presented.

A hidden Markov model-based algorithm for fault diagnosis with partial and imperfect tests

We present a hidden Markov model (HMM) based algorithm for fault diagnosis in systems with partial and imperfect tests. The HMM-based algorithm finds the most likely state evolution, given a sequence of uncertain test outcomes over time. We also present a method to estimate online the HMM parameters, namely, the state transition probabilities, the instantaneous probabilities of test outcomes given the system state and the initial state distribution, that are fundamental to HMM-based adaptive fault diagnosis. The efficacy of the parameter estimation method is demonstrated by comparing the diagnostic accuracies of an algorithm with complete knowledge of HMM parameters with those of an adaptive one. In addition, the advantages of using the HMM approach over a Hamming-distance based fault diagnosis technique are quantified. Tradeoffs in computational complexity versus performance of the diagnostic algorithm are also discussed.

Kalman filter versus IMM estimator: when do we need the latter?

In this paper, a performance comparison between a Kalman filter and the interacting multiple model (IMM) estimator is carried out for single-target tracking. In a number of target tracking problems of various sizes, ranging from single-target tracking to tracking of about a thousand aircraft for air traffic control, it has been shown that the IMM estimator performs significantly better than a Kalman filter. In spite of these studies and many others, the condition under which an IMM estimator is desirable over a single model Kalman filter versus an IMM estimator are quantified here in terms of the target maneuvering index, which is a function of target motion uncertainty, measurement uncertainty, and sensor revisit interval. Using simulation studies, it is shown that above a certain maneuvering index an IMM estimator is preferred over a Kalman filter to track the target motion. These limits should serve as a guideline in choosing the more versatile, but somewhat costlier, IMM estimator over a simpler Kalman filter.

PCRLB-based multisensor array management for multitarget tracking

In this paper we consider the general problem of managing an array of sensors in order to track multiple targets in the presence of clutter. There are three complicating factors. The first is that because of physical limitations (e.g., communication bandwidth) only a small subset of the available sensors can be utilized at any one time. The second complication is that the associations of measurements to targets/clutter are unknown. The third complication is that the total number of targets in the surveillance region is unknown and possibly time varying. It are these second and third factors that extend previous work [ Tharmarasa, R., Kirubarajan, T., and Hernandez, M. L. Large-scale optimal sensor array management for multitarget tracking. IEEE Transactions on Systems, Man, and Cybernetics, to be published.]. Hence sensors must be utilized in an efficient manner to alleviate association ambiguities and to allow accurate estimation of the states of a varying number of targets. We pose the problem as a bi-criterion optimization with the two objectives of (1) controlling the posterior Cramer-Rao lower bound ((PCRLB) which provides a measure of the optimal achievable accuracy of target state estimation), and (2) maximizing the probability of detecting new targets. Only recently have expressions for multitarget PCRLBs been determined [Hue, C, Le Cadre, J.-P., and Perez, P]. Performance analysis of two sequential Monte Carlo methods and posterior Cramer-Rao bounds for multitarget tracking. In Proceedings of the 5th International Conference on Information Fusion, vol. 1, Annapolis, MD, July 2002, 464-473.], and the necessary simulation techniques are computationally expensive. However, in this paper we show the existence of a multitarget information reduction matrix (IRM) which can be calculated off-line in most cases. Additionally, we propose some approximations that further reduce the computational load. We present solution methodologies that, in simulations, are shown to determine efficient utilization strategies for the available sensor resources, with some sensors selected to track existing targets and others given the primary task of surveillance in order to identify new threats.

Exact multisensor dynamic bias estimation with local tracks

An exact solution is provided for the multiple sensor bias estimation problem based on local tracks. It is shown that the sensor bias estimates can be obtained dynamically using the outputs of the local (biased) state estimators. This is accomplished by manipulating the local state estimates such that they yield pseudomeasurements of the sensor biases with additive noises that are zero-mean, white, and with easily calculated covariances. These results allow evaluation of the Cramer-Rao lower bound (CRLB) on the covariance of the sensor bias estimates, i.e., a quantification of the available information about the sensor biases in any scenario. Monte Carlo simulations show that this method has significant improvement in performance with reduced rms errors of 70% compared with commonly used decoupled Kalman filter. Furthermore, the new method is shown to be statistically efficient, i.e., it meets the CRLB. The extension of the new technique for dynamically varying sensor biases is also presented.

Bearings-only tracking of maneuvering targets using a batch-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.