Accurate Time-to-Go Estimation for Proportional Navigation Guidance

Proportional navigation (PN) is a popular guidance law because of its robustness, simplicity, and ease of implementation. PN guidance law is capable of intercepting both non-maneuvering and maneuvering targets. PN is also an optimal control effort guidance law in the linearized setting. An interesting application requiring the estimation of time-to-go is in salvo attack problems, in which several missiles, launched at different times, need to achieve interception of the target simultaneously. Using PN guidance law to achieve this task requires an accurate estimation of time-to-go. Impact time, impact angle, and other optimal guidance laws also need information of the time-to-go to compute the guidance command. The method is accurate for large heading errors and is easily obtained by numerical interpolation. The base solution and the polynomial coefficients can be computed offline. By storing the base solution and the coefficients, the interception time for any initial condition and any navigation gain can be obtained very accurately with minimal computational effort.