A Nonparametric Procedure for Designing Adaptive Gain (αβ) Trackers for Passive Sonar Systems

The process of extracting parameters from acoustic signals is called "estimation" when the parameters are presumed constant over the observation interval, and is called "tracking" when the parameters are dynamic functions of time and must be estimated in real time by a causal processor. The αβ tracker configuration has become increasingly popular for tracking dynamic signal parameters in submarine sonar applications. This selection is natural for a number of reasons. The design procedure is simple and easy to implement in a digital processor. The configuration estimates rate explicitly and corrects for the lag normally encountered in a smoothing process. Finally, for a number of classes of signal models, the configuration results from a Kalman Filter development with "optimum" gains de- fined from the model. However, for some applications important to modern passive sonar systems, the tracking scenario cannot be modeled as a stationary, statistical model encompassing both signal- and geometry-related parameters. The design of any tracker involves a trade-off between dynamic following error and (signal processing related) random error. An αβ configuration has only two design parameters which can be optimized at a single design point. This point can be chosen to provide a best compromise over some portion of the desired operating range. To extend the operating range, it is necessary to adapt the tracker constants (α and β) to changes in the tracker scenario. This must be accomplished in real time through available measurements in conjunction with an a priori model which relates those measurements to the tracking scenario. This process entails some risk because "mistuning" can result in loss of track in the original operating range. Presented herein is a design philosophy for αβ trackers and an adaptation procedure based on a combination of nonparametric estimators and heuristic logical constraints. The pr- - esentation is tutorial in nature and develops the design tools through application to both a generic tracker model and a specific (time) delay locked-loop example which is typical of many operational and developmental sonar tracking systems. Typical dynamic models are presented and the "traps" often encoun- tered in adapting tracker gains are indicated. along with solutions provided by the design procedure.