Determination of the Number of Stages of the Multistage Wiener Filter

Reduced rank adaptive detection techniques are employed in airborne radar when the clutter returns have insufficient sample support due to the non-stationarity and non-homogeneity of the data. A number of approaches to combat this problem exist, including the single data set algorithms which eliminate the need for training data, and reduced rank detectors such as those employing the principal components, cross-spectral metric and the multistage Wiener filter (MWF). This latter approach is superior to other rank reduction techniques in terms of computational efficiency and sample support requirements. The benefit of the MWF is maximised when the number of stages is kept at a minimum. In this paper, we propose an algorithm to determine the number of stages that is formulated as a model order estimation problem and utilises the minimum description length (MDL). This overcomes the main drawback of the Ritz-value estimation which requires a threshold to be set. We give a computationally efficient implementation of the MDL and demonstrate its effectiveness using simulations.