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While it is generally recognized that conditional expectation parameter estimates are statistically optimum for quadratic loss functions, the difficulties inherent in multidimensional numerical integration have largely prevented their use except in linear problems. In this paper it is shown that Monte Carlo methods can sometimes be used to obtain conditional expectation estimates for non-linear dynamic systems with an acceptable expenditure of computing time. The efficiency of the methods proposed results from the application of variance reduction techniques developed in this paper. The resulting algorithm is tested by an application to the optimal radar tracking and impact point prediction problem for a ballistic vehicle atmospheric reentry. Experimental results obtained with a hybrid analog-digital computer are included.