Radar Micro-Doppler Signal Encoding in Siegel Unit Poly-Disk for Machine Learning in Fisher Metric Space

For classification of Radar micro-Doppler signature by Machine Learning techniques, first step consists in coding the data in well adapted metric space. We propose a new approach to code the time series of I&Q raw data by a Matrix Autoregressive model from a sequence of covariance Toeplitz Hermitian Positive matrices, estimated on a sliding window. We use matrix extension of Trench-Verblunsky theorem proving that a Toeplitz-Block-Toeplitz matrix is parameterized by Matrix Verblunsky coefficients lying in Siegel Unit Poly-Disk, to introduce a Fisher metric space from Information Geometry for this canonical parameterization. We present the coding procedure of micro-Doppler signal in Siegel space and conclude with examples of Machine Learning based on Mean-Shift algorithm in this metric space.