Proportional Navigation Guidance with Variable Navigation Ratio in terms of the angle of relative velocity with respect to Line-of-Sight and its Rate

In the present work, the performance of True Proportional Navigation (TPN) with different profiles for effective navigation ratio in terms of the relative velocity angle with respect to line-of-sight is investigated due to initial heading errors and target maneuvers. Since an appropriate profile of effective navigation ratio for heading error is almost in contrary with the appropriate profile for maneuvering targets, a variable effective navigation ratio in terms of the relative velocity angle and its rate is introduced. In this way, the miss distance (MD) for the first two peaks of the normalized MD graph versus normalized final time, for example under an effective navigation ratio of 4, is reduced together. The analysis is carried out using normalized equations in polar coordinates for perfect and binomial fifth-order control systems without acceleration limit. Due to practical consideration, the effective navigation ratio is tuned and limited between 3 and 5.