Identification of multichannel linear non-Gaussian processes using higher-order statistics

This paper is concerned with the problem of estimating the matrix impulse response function of a multiple-input multiple-output system given only the measurements of the vector output of the system. The system is assumed to be driven by a temporally i.d.d. and spatially independent non-Gaussian vector sequence (which is not observed). An iterative, inverse filter criteria based approach is developed using the third-order or the fourth-order normalized cumulants of the inverse filtered data at zero-lag. Stationary points of the proposed cost functions are investigated. The approach is input-iterative, i.e., the inputs are extracted and removed one-by-one. The matrix impulse response is then obtained by cross-correlating the extracted inputs with the observed outputs. Identifiability conditions are analyzed. Computer simulation examples are presented to illustrate the proposed approaches.