Tracking wide-band targets having significant Doppler shift

A method is derived for passively locating wide-band targets (typically acoustic targets) which may be moving at speeds sufficient to produce significant Doppler shift. The method involves a relatively straightforward adaptation of standard beam forming techniques. It is shown that conventional beam forming techniques have less discrimination in the direction of motion of the sources, whereas the proposed technique exhibits no such degradation. The derivative and Hessian of the likelihood function are derived. These may be used for locating the maximum likelihood solution or for deriving a Gaussian approximation to the likelihood function for particle filtering applications. The expressions are applicable for subsonic and supersonic sources. The computation required for implementing a system based on the model is at present prohibitive.