Third-Order Loop Filter Design for Acceleration-Rate Tracking

A perfect third-order loop filter design that can be implemented as a digital filter is obtained which minimizes the noiseless steady-state acceleration rate (jerk) error for a fixed loop noise bandwidth. Simulations were performed to obtain transient responses of the third-order loop plus a sample fourth-order loop under a jerk input. The results enable one to obtain a loop design that minimizes the loop noise bandwidth required for a given steady-state jerk error and thus obtain better noise jitter performance.