Unified Time-to-Go Algorithms for Proportional Navigation Class of Guidance

This paper presents unified time-to-go algorithms that achieve generalizations in several aspects. In particular, they are applicable to the general class of proportional navigation guidance laws in which the navigation gain ranges from negative to positive values. They are also applicable to a general class of targets: stationary targets, targets with speeds lower than the interceptor, and targets with speeds that are several times higher than the interceptor. Finally, they are applicable to general three-dimensional engagements that subsume the traditional planar engagements addressed in the literature. First, a time-to-go algorithm is derived as a closed-form approximation function of range, navigation gain, and heading error. This is followed by an algorithm that is based on simple recursive numerical computations. In terms of accuracy over the engagement period, the first is found to be comparable, and sometimes better, with respect to existing algorithms, while the latter is found to perform the best in almost all cases.