Mr. K. Mike Tao Profile

K. Mike Tao

Engineer at SRI International

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Proceedings Article | 24 December 2003 Paper

Optimal inversions of uncertain matrices - an estimation and control perspective

K. Mike Tao

Proceedings Volume 5205, (2003) https://doi.org/10.1117/12.504611

KEYWORDS: Error analysis, Matrices, Filtering (signal processing), Signal processing, Monte Carlo methods, Process modeling, Interference (communication), Control systems, Electronic filtering, Statistical analysis

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Many system and signal related problems involve matrix inversion of some kind. For example, in estimation and signal recovery applications, inversion of the channel response matrix is often required in order to estimate the source signals. In the control of multivariable systems, inverting a process gain matrix may be called for in order to deliver appropriate control actions. There are situations where these matrices should be considered as uncertain (or random): for example, when the process/channel environments vary randomly, or when significant uncertainties are involved in estimating these matrices. Based on a unified approach, this paper considers both the right inversion (for control) and the left inversion (for estimation) of random matrices. In both cases, minimizing a statistical error function leads to the determination of optimal or linear optimal inversion. Connections with related techniques, such as the total least squares (TLS), the ridge regression, the Levenberg-Marquardt algorithm and the regularization theory are discussed. A variant Kalman filtering problem with randomly varying measurement gain matrix is among the applications addressed. Monte Carlo simulation results show substantial benefits by taking process/model uncertainty into consideration.

Proceedings Article | 13 July 2000 Paper

Multiple-target tracking in dense noisy environments: a probabilistic mapping perspective

K. Mike Tao, Ronald Abileah, John Lowrance

Proceedings Volume 4048, (2000) https://doi.org/10.1117/12.392000

KEYWORDS: Detection and tracking algorithms, Palladium, Motion models, Target detection, Target acquisition, Sensors, Binary data, Lawrencium, Image resolution, Computer simulations

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A new approach is taken to address the various aspects of the multiple- target tracking (MTT) problem in dense and noisy environments. Instead of fixing the trackers on the potential targets as the convention tracking algorithms do, this new approach is fundamentally different in that an array of parallel-distributed trackers is laid in the search space. The difficult data-track association problem that has challenged the conventional trackers becomes a nonissue with this new approach. By partitioning the search space into cells, this new approach, called PMAP (probabilistic mapping), dynamically calculates the spatial probability distribution of targets in the search space via Bayesian updates. The distribution is spread at each time step, following a fairly general Markov-chain target motion model, to become the prior probabilities of the next scan. This framework can effectively handle data from multiple sensors and incorporate contextual information, such as terrain and weather, by performing a form of evidential reasoning. Used as a pre- filtering device, the PMAP is shown to remove noiselike false alarms effectively, while keeping the target dropout rate very low. This gives the downstream track linker a much easier job to perform. A related benefit is that with PMAP it is now possible to lower the detection threshold and to enjoy high probability of detection and low probability of false alarm at the same time, thereby improving overall tracking performance. The feasibility of using PMAP to track specific targets in an end-game scenario is also discussed. Both real and simulated data are used to illustrate the PMAP performance. Some related applications based on the PMAP approach, including a spatial-temporal sensor data fusion application, are mentioned.

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