The accuracy, stability, and filtering properties of a linear pulsed phase-locked loop system for tracking the rate of Doppler shift changes

An expression for the optimal filter of a pulsed phased-locked loop for tracking a target having an acceleration is presented. The coefficients in the expression, which derives from Wiener's theory, are functions of the signal/noise ratio, the rate of the Doppler shift change, and the loop parameters. A pulsed phase-locked loop system with this type of filter can be described by a nonlinear third-order difference equation. Reference is made to Lindsay's study (1978), in which the qualitative indicators of second- and third-order continuous phase-locked loop systems are compared. At present, however, there is no such comparison for pulsed systems. The optimal pulsed phase-locked loop system in a synchronization mode is investigated and compared with an ideal second-order system.