Range and Bearing Determination: Maximum Likelihood and Kalman—Bucy Techniques

Abstract

The paper discusses from a tutorial point of view the problem of range and bearing determination in the underwater acoustics environment. The geometric constraints are grouped in three classes: the line array shape, the array and point source relative motions, and the array and point source relative position. The representation of these constraints is considered via two alternatives: the integral and the differential descriptions. The first describes the geometry through a finite number of unknown quantities. The positioning problem is cast in the framework of Maximum Likelihood techniques. The second studies the line array and the relative motions as curves is space. The line array is appropriately parametrized by the arc length s. The trajectories are described taking the time t as parameter. The framework is that of waveform filtering, the Kalman-Bucy filter techniques being the suitable design techniques.

The paper discusses the design of the positioning receiver in both contexts, studying the tradeoffs and compromises that have to be made. The mean square error performance is quantified and simulation results presented.