In allocating radar beam for tracking a target, it is attempted to maintain the signal-to-noise ratio (SNR) of signal returning from the illuminated target close to an optimum value for efficient track updates. An estimate of the average radar cross section (RCS) of the target is required in order to adjust transmitted power based on the estimate such that a desired SNR can be realized. In this paper, a maximum-likelihood (ML) approach is presented for estimating the average RCS, and a numerical solution to the approach is proposed based on a generalized expectation maximization (GEM) algorithm. Estimation accuracy of the approach is compared to that of a previously reported procedure.