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The Bayesian Ziv-Zakai bound on the mean square error (MSE) in estimating a uniformly distributed continuous random variable is extended for arbitrarily distributed continuous random vectors and for distortion functions other than MSE. The extended bound is evaluated for some representative problems in time-delay and bearing estimation. The resulting bounds have simple closed-form expressions, and closely predict the simulated performance of the maximum-likelihood estimator in all regions of operation. Index Terms-Parameter estimation, performance bounds, mean square error.

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Most radar systems employ a feed-forward processing chain in which they first perform some low-level processing of received sensor data to obtain target detections and then pass the processed data on to some higher-level processor such as a tracker, which extracts information to achieve a system objective. System performance can be improved using adaptation between the information extracted from the sensor/processor and the design and transmission of subsequent illuminating waveforms. As such, cognitive radar systems offer much promise. In this paper, we develop a general cognitive radar framework for a radar system engaged in target tracking. The model includes the higher-level tracking processor and specifies the feedback mechanism and optimization criterion used to obtain the next set of sensor data. Both target detection (track initiation/termination) and tracking (state estimation) are addressed. By separating the general principles from the specific application and implementation details, our formulation provides a flexible framework applicable to the general tracking problem. We demonstrate how the general framework may be specialized for a particular problem using a distributed sensor model in which system resources (observation time on each sensor) are allocated to optimize tracking performance. The cognitive radar system is shown to offer significant performance gains over a standard feed-forward system.

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