Model-based array processing in a fading channel

Model-based processing is a method of including physical models in the processing scheme in order to enhance the performance (smaller error variance) of the processor. The method is based on a state-space approach which leads to Kalman type estimators. A major advantage of this approach is that the stochastic aspects of the problem (system and measurement noise) can be included in a natural way, thereby allowing modeling errors to be accommodated by the processor. In the case of array processing, one can consider several types of signal models. Indeed, in the case of a standard beamformer, the linear phase or time delay progression associated with a particular signal direction or “beam” implicitly assumes a plane wave model for the signal. However, the fact that the array is moving is not considered. It has been shown that the inclusion of the array motion in the proper way results in a significantly smaller variance on the bearing error, thereby providing a passive synthetic aperture effect. In this work the model-based method is applied to simulated towed array data in a fading channel. The amplitude of the signal, along with its source frequency and bearing are considered as the elements of a state vector to be estimated in a Kalman type estimation scheme. In this manner, the Kalman filter provides a recursive type of estimator, i.e. an adaptive processor which provides estimates of the relevant parameters, even when they are varying slowly in time. Results are shown where the data were generated with a random (Rayleigh) amplitude. The results show that the processor can track the amplitude variations and render high quality estimates of the bearing angle and source frequency, even at very low signal to noise ratios