Time-to-go Estimation for Guidance Law with Impact Angle Constraint

In this paper, we focus on the time-to-go estimation problem for the impact-angle-constrained guidance law. To facilitate the time-to-go estimation, the whole guidance process is divided into two stages. The sliding mode guidance law based on the constant reaching law is designed for the first stage and the proportional guidance law is utilized in the second stage. By choosing the sliding mode variable appropriately, not only an attack with a small miss distance but also a prescribed impact angle can be achieved. According to the feature of the constant reaching law, the time-to-go estimation for the first stage can be established easily. To obtain the time-to-go of the second stage, the estimated look-ahead angle and range at the switching point between the first stage and second stage are calculated. Further, the time-to-go estimation of the second stage is obtained according to the trajectory shape of the missile steered by the proportional guidance law. In the second stage, rather than the estimated look-ahead angle and range but the current look-ahead angle and range are used to calculate the time-to-go. In this way, an actual time-to-go estimation of the second stage can be obtained. Last, various numerical simulations are provided to show the effectiveness and superiority of the proposed estimation scheme.