Matrix filters for passive sonar

This paper introduces matrix filters as a tool for localization and detection problems in passive sonar. The outputs of an array of sensors, at some given frequency, can be represented by a vector of complex numbers. A linear filtering operation on the sensor outputs can be expressed as the multiplication of a matrix (called a matrix filter) times this vector. The purpose of a matrix filter is to attenuate unwanted components in the measured sensor data while passing desired components with minimal distortion. Matrix filters are designed by defining an appropriate pass band and stop band and solving a convex optimization problem. This paper formulates the design of matrix filters for passive sonar and gives two examples.