Time-to-go estimation for terminal sliding mode based impact angle constrained guidance

The time-to-go estimation problem is an important issue in various guidance laws' designing and implementing. In this paper, a time-to-go estimation method is proposed for missiles guided by terminal sliding mode control (TSMC) based impact angle constrained guidance (IACG). To facilitate estimating the time-to-go, a reaching law approach in the sliding mode control (SMC) is applied to design the TSMC based IACG. In this way the interception process can be clearly divided into two phases: outside of the sliding mode surface and inside of the sliding mode surface. The character of the reaching law approach is utilized to estimate the time-to-go in the first phase. And in the second phase, a geometric method is designed to estimate the rest of time-to-go. In addition, another geometric method is applied to approximately calculate an important parameter of the proposed time-to-go estimation method. This parameter measures the curve flexibility of the flight trajectory. Then, based on the conception of predicted-intercept-point (PIP), the proposed time-to-go estimation method can be extended to the scene of intercepting the constant velocity targets. In the end, numerical simulation results are presented to illustrate the effectiveness of the proposed time-to-go estimation method.