Lower bounds on the localization errors of a moving source observed by a passive array

The Cramér-Rao inequality is used to set absolute bounds on the accuracy of location and velocity estimates obtainable by observing the signal radiated from a moving acoustic source at an array of stationary sensors. The source radiates a zero mean Gaussian random process and the observations are made in a background of spatially incoherent Gaussian noise. Results are first obtained for the error covariance matrix of a set of parameters characterizing the time variable differential delays observed at various sensor pairs. These are then translated into bounds on the error covariance matrix of a set of parameters describing source location and track. Numerical results are presented for the specific case of a source moving in a straight line course at constant velocity.