Cramer-Rao lower bound for motion parameter estimation of an approaching missile with constant acceleration

Motion parameter estimation plays a crucial role in evaluating missile performance. At present, a basic assumption of the analyzing this problem is that the approaching missile moves with a constant velocity (CV) along a straight line. However, in realistic measurement scenarios, the approaching missile usually has a negative acceleration due to the depletion of missile propellant or the resistance to air. Therefore, the missile is not usually moving with CV in space, but rather moving with a constant negative acceleration. The research on the Cramer-Rao lower bounds (CRLB) of motion parameter of an approaching missile moves in the CV model is extensive. However, the CRLB of motion parameter of an approaching missile moves in the constant acceleration (CA) model has not been discussed until now. This paper aims to derive the CRLB of motion parameter of an approaching missile when the missile is assumed to move according to the CA model. The simulation verifies the correctness of our derivation by comparing with the variance of the maximum likelihood estimation. Our work provides a strong theoretical basis for modern high-precision missile motion parameter measurement error analysis and a guide for future missile motion parameter measurement system design.