Proportional Navigation Against Multiple Targets

The basic block diagrams of proportional navigation are revisited. The effect of initial conditions on the miss distance is studied. Using the important case of multiple targets, two proportional navigation block diagrams are compared. The first, the ideal proportional navigation, applies the true line-of-sight rate, which is calculated by an analytic derivative of the line-of-sight angle. The block diagram resulting from this guidance loop is minimal. The second applies an approximate derivative of the line-of-sight angle. Because of zero-pole cancellation at the origin, the block diagram resulting from this guidance loop is unobservable with respect to target displacement. The consequence is that for the target-displacement initial condition the two diagrams do not result in the same miss distance. Moreover, several solutions that can resolve the above difficulty are suggested. One of the solutions is to reset the derivative filter with the correct initial conditions. Another solution is to skip the first few samples of the derivative filter right after target separation. [PUBLISHER ABSTRACT]