Efficient recursive estimation of the parameters of a radar or radio astronomy target

In radar or radio astronomy we observe a signal whose covariance function depends on some target parameters of interest. We consider here the problem of estimating the values of these parameters from our observation of the signal. One possible procedure is to use the method of maximum likelihood estimation. This method has the advantage that, as the duration of the observation interval becomes long, the mean square error in the maximum likelihood estimate approaches the minimum given by the Cramér-Rao bound. However, the maximum likelihood estimate is usually difficult to compute. We present here a recursive estimation procedure which divides the observation interval up into subintervals of short length; on each subinterval the signal is processed quadratically and the resulting calculation used to improve our estimate. This method has many computational advantages and, under certain conditions, we can show that the error in the resulting sequence of estimates approaches the Cramér-Rao bound. We begin by giving brief consideration to the problem of determining the functional dependence of the covariance function of the received signal on the target parameters. We then present expressions for the terms that appear in the Cramér-Rao inequality. Lastly, we describe the recursive estimation method and state conditions under which it is applicable.