The Target Guarding Problem (TGP) consists of a pursuer P, an evader E and a stationary target T. The goal of P is to prevent E from capturing T, by intercepting E as far away from T as possible. An optimal solution to this problem, referred to as Command to Optimal Interception Point (COIP), was proposed recently. This guidance law requires the positions of the agents involved. The computational complexity of the expressions in the COIP law also make it difficult for a real time implementation. Here the TGP is revisited and the optimal solution is reformulated to expressions that are suitable for autonomous systems with ranging sensors mounted on them. The case of T lying in E's dominance region is then analysed and an optimal strategy for P is derived in this case.

The pursuer may lose the game from a position of advantage due to lack of perfect data. To overcome this, a strategy is derived for the pursuer when the evader's position and speed measurements are corrupted by noise. The evader data is estimated using an Extended Kalman Filter. The probability of the target falling within the dominance regions of the pursuer is then calculated. Based on this, a real time strategy is designed for the pursuer.

The TGP is then analyzed in a game-theoretic framework and a Nash Equilibrium is derived. The Bayesian counterpart of the game, where the attacker's information is ambiguous to the defender, is studied by extending the same framework and a Bayesian Nash Equilibrium is derived for this case.

Thereafter, the TGP is studied in a single pursuer-multi evader setting. The optimal strategy of the pursuer is derived using Pareto Optimality and Convex optimization techniques. A real time strategy is also derived for this case. Sufficient and necessary conditions for the pursuer to win the game are derived.