Spectral estimation applied to CFAR processing of non-stationary radar and sonar data

The purpose of this study is to investigate the application of multidimensional (m-D) power spectral density (PSD) estimation to signal processing problems caused by reverberation in sonar and clutter in radar. The study is divided into in the following manuscripts. Manuscript 1 derives the vector space solution to the Yule-Walker equations. The Yule-Walker equations are the set of equations that arise when solving for model parameters of an autoregressive (AR) model. In one dimension, AR spectral estimation is a common and important method of spectral estimation. Part of the reason for this is the equations associated with the AR approach can be put in a Toeplitz form and the Toeplitz form leads to fast and relatively simple algorithms. Unfortunately, the m-D AR spectral estimators cannot be put into Toeplitz form and the equations are more difficult to work with. The manuscript derives a vector space solution to the Yule-Walker equations. The vector space solution puts the m-D Yule-Walker equation in a simple form that is more ideally suited for developing multi-dimensional AR algorithms. Manuscript 2 derives the track initiation classifier (TIC). The TIC is an algorithm that uses a simple target model to produce a list of possible tracks from a sequence of sonar pings (range-bearing plots). Since sonar data consists of multiple pings, the data can be thought of as three dimensional (3-D). The main step in the TIC is a target classifier derived using the generalized ratio test (GLRT). In the derivation of the classifier, a normalization step is necessary. The goal of normalization is to equalize the noise power of the data. We propose a novel approach to the normalization of three dimensional (3-D) data using PSD estimation techniques. Manuscript 3 explores the normalizer introduced in the second manuscript, and compares it to a standard split window normalizer (SWN). The SWN is a common method of normalization. In radar the SWN is known as a cell averaging constant false alarm rate (CA-CFAR) processor. The SWN normalizes each cell of the data by finding a local noise power estimate, and dividing the cell by that local estimate. The local power estimate is found by averaging the data in a window around the cell to be normalized. By averaging the data over a window, the SWN implicitly assumes the noise is stationary in that window. So, when the data is stationary (or nearly stationary) the SWN performs well. The normalizer in this work is based on the minimum variance spectral estimator (MVSE). The MVSE is a PSD estimator that easily extends to multiple dimensions, in this case, the dimensions of range, bearing, and ping. PSD estimators estimate power as it changes over frequency. This is mathematically similar to estimating power as it changes over range or other independent variables. A normalizer based on a PSD estimator dose not assume the background power is stationary. Removing the stationarity assumption allows the use of larger data windows to estimate the power of each cell. Since the MVSE normalizer uses more data, it should produce a better estimate of the background power. Manuscript 4 presents and compares algorithms that reduce the amount of data needed when processing radar data with angle dependent clutter. A moving radar causes angle dependent clutter, and optimal processing of two dimensional clutter requires estimating a large covariance matrix. Estimating a large covariance matrix using the sample covariance matrix (SCM) requires the data to be stationary over a large range extent. The methods presented here don\u27t average over large numbers of range bins, and therefore avoid the implicit assumption that the data are stationary over large range extents. The procedures fall into two categories. The first category uses PSD techniques to normalize the detected data. The second category uses PSD estimation techniques to estimate the covariance matrix. The new methods are compared to the SCM, and are shown to greatly reduce the stationary requirements on the data