GNSS carrier tracking loop : Stability analysis and some improvements

Carrier tracking loops used in satellite navigation receiver are discrete-time closed loop systems that are mostly designed from their continuous time counterparts. In this paper, we analyze the stability of second order carrier tracking loop, assisted and unassisted versions, when designed from continuous time domain. It is well-known that increasing the product of loop noise bandwidth and integration time, this design approach fails and our resulting discrete time loop becomes unstable. Using Bode analysis technique, we show the effect of variation of loop filter coefficients on stability margin of the loop. Based on the discussion, some improvements have been proposed to increase the stability margin of both unassisted and assisted loops. While considering assisted loop, it is a common misconception that assisted loop is more robust to changes in loop noise bandwidth and integration time product as compared to its unassisted counterpart. We show that this is true only for small values of loop noise bandwidth and integration time product. Monte Carlo simulations verify all the presented results in the paper.