Estimating the terminal state of a maneuvering target

Consider a maneuvering target whose state x/sub t/ is governed by the linear stochastic system dx/sub t/=(Ax/sub t/+Bu/sub t/)dt+/spl sigma/dW/sub t/ in which u/sub t/ is the target´s control law and W/sub t/ is a Wiener process of disturbances. Let linear observations y/sub t/ satisfying dy/sub t/=Hx/sub t/dt+dV/sub t/ be made, where V/sub t/ is a Wiener process of measurement errors. V/sub t/ and W/sub t/ are assumed to be statistically independent random processes. It is desired to estimate where the target will be, at a fixed final time T, from the measurements y/sub s/ made on the interval 0/spl les/s/spl les/t. However, the target´s maneuverings, that is the function it selects for its control law, are unobservable. Since this is the case, treat the target´s control law as a random process, and assume that it is possible to give a prior probability distribution for this random process. Let us also assume that there is a prior probability distribution for the target´s initial state so which is Gaussian with mean C1 and covariance matrix C. The objective of this paper is to give computationally implementable formulas for computing the conditional expectation of the target´s terminal state given the past measurements.