Third-order delay-locked loop: mean time to lose lock and optimal parameters

For the first time an approximation for the mean time to lose lock (MTLL) of a third-order coherent PN-code tracking loop has been derived. Such loops are essential in various spread spectrum systems (Global Positioning System, GPS, for example). The computation of the MTLL is based on the singular perturbation method. The application of this calculus to the coherent delay-locked loop (DLL) yields an algebraic expression for the dominant term of the MTLL. The influence of loop offset due to an acceleration rate (jerk) between the transmitter and receiver as well as the optimal choice of the parameters maximizing the MTLL for the loop filter is described. A case study for code tracking of objects with high jerk guided by the GPS is briefly discussed