An explicit, closed form formulae of advanced guidance laws for a linear, time-invariant, acceleration-constrained arbitrary-order missile, and a linear, time-invariant, arbitrary-order, randomly maneuvering target with noisy position measurements are derived. Two approaches are presented. The first approach derives the optimal guidance law for a quadratic objective. The solution is the guidance law for deterministic system with limiting on the commanded acceleration applied on the estimated state. The second approach is based on the idea of applying the average of the input that would have been applied to the plant if the noises were known. The formulas of the different guidance laws are given in terms of the transfer function of the missile and acceleration constraint, the shaping filter of the maneuver of the target, responses to initial conditions, error variance matrix of the estimated state and weights in the criterion. It is demonstrated by simulations that although the optimal guidance law has improved performance in terms of the miss distance, the suboptimal average input guidance law consumes less energy.
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