A Stochastic Approach to Optimal Guidance with Uncertain Time-to-go

The paper presents a stochastic approach to optimal guidance with significant uncertainty in time until intercept. The uncertain intercept time is modeled as a random variable, with discrete probability density. An optimal guidance law is derived by solving the appropriate Hamilton-Jacobi recursion, under the assumptions: (1) the target maneuver is modeled as a first order Gauss-Markov process; (2) the missile´s guidance commands are based on observing the line of sight angle to the target in additive observation noise; (3) the missile acceleration response to the acceleration commands is well described by a linear first order transfer function. Although the present problem is formulated in the LQG frame work, the certainty equivalence principle does not apply since the optimal guidance law depends on the discrete probability density of the time until intercept. A simple simulation example shows that when the interceptor has a large acceleration advantage over the target, the miss distances resulting from the use of the proposed law are essentially equivalent to those obtained when using the optimal guidance law, which requires full knowledge of the time until intercept