Least-squares array processing for signals of unknown form

Statistical methods are applied to the estimation of the velocity, arrival-angle and waveform of a signal appearing in an array of sensors in the presence of random noise. The signal is assumed to be a plane wave propagating through a linear, homogeneous, non-dispersive medium so that it is the same in each sensor except for a time delay due to its finite velocity. A novel formulation is introduced which requires no assumptions concerning the signal waveform but permits its estimation along with the vector of time delays per unit distance. The method is appropriate for applications such as seismology and passive sonar in which the signal waveform is unknown, yet cannot be realistically represented as a stationary random process (as is required, for example, by Wiener filtering theory). A least-squares procedure is described which does not depend on any assumptions regarding the noise. This simple criterion is found to imply time-shift and sum processing which is related to other techniques previously employed. For known noise statistics the mean-square response of the processor to the noise is calculated and the covariance matrix of the estimates is approximated for the high signal-to-noise ratio case. The resulting array pattern is evaluated in terms of the signal spectrum and the array geometry. The results are compared with a more elaborate maximumlikelihood approach based on stationary Gaussian noise with a known spectral density matrix.