Abstract: A multi-stage maximum likelihood target estimator for use with radar and sonar systems is provided. The estimator is a software implemented algorithm having four computational stages. The first stage provides angle smoothing for data endpoints thereby reducing angle errors associated with tie-down times. The second stage performs a coarse grid search to obtain the initial approximate target state to be used as a starting point for stages 3 and 4. The third stage is an endpoint Gauss-Newton type maximum likelihood target estimate which determines target range along two time lines. The final refinement of the target state is obtained by the fourth stage which is a Cartesian coordinate maximum likelihood target estimate. The four-stage processing allows the use of target historic data while reducing processing time and computation power requirement.