The design of optimal controllers for air-to-air missiles has been of much recent interest. Many control laws require a good estimate of the time-to-go (tgo) before intercept. This paper presents an algorithm for estimating time-to-go using the current relative position and velocity characteristics of the missile and target. By constructing an objective function representing teminal miss distance, one is able to obtain an iterative scheme for estimating tgo. Simulation studies using a smart target algorithm and this methodology have yielded good results that show improvement over conventional algorithms for estimating tgo. A comparative investigation of the methodology developed in this paper with other algorithms is presented.
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Gordon K. F. Lee (1985) studied this question.