The three-body engagement where a target aircraft protects itself by using a cooperative defender missile to intercept an attacking missile is investigated. It is formulated as a constrained linear quadratic optimal problem. Two different optimal cooperative guidance laws for the target and defender are proposed in two cooperation schemes. Since any control effort to reduce the miss distance to smaller than missile's lethal radius is wasted, the guidance laws are derived to achieve an upper bound on the missile-defender miss distance. In the two-way cooperation scheme, the target and the defender act as a team. How the target makes a trade-off between aiding the defender and evading the missile is investigated by considering both the missile-target zero-effort miss distance and the control effort into the cost function. Without the penalty weight on the missile-target zero-effort miss distance, the two-way minimum control effort guidance laws are available. In the one-way cooperation scheme, the target uses a known evasion strategy independently. The optimal cooperative guidance law is derived for minimizing the control effort of the defender. Simulation results show that these proposed guidance laws can provide a specified missile-defender miss distance and save the control effort compared with the zero-miss-distance guidance law. Two-way cooperation scheme outperforms one-way cooperation scheme.

The active aircraft defense problem is investigated for the stochastic scenario wherein a defending missile (or a defender) is employed to protect a target aircraft from an attacking missile whose pursuit guidance strategy is unknown. For the purpose of identifying the guidance strategy, the static multiple model estimator (sMME) based on the square-root cubature Kalman filter is proposed, and each model represents a potential attacking missile guidance strategy. Furthermore, an estimation enhancement approach is provided by using pseudo-measurement. For each model in the sMME, the model-matched cooperative guidance laws for the target and defender are derived by formulating the active defense problem as a constrained linear quadratic problem, where an accurate defensive interception and the minimum evasion miss distance are both considered. The proposed adaptive cooperative guidance laws are the result of mixing the model-matched optimal cooperative guidance laws in the criterion of maximum a posteriori probability in the framework of the sMME. By adopting the adaptive cooperative guidance laws, the target can facilitate the defender’s interception with the attacking missile with less control effort. Also, simulation results show that the proposed guidance laws increase the probability of successful target protection in the stochastic scenario compared with other defensive guidance laws.

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