Vector Tracking Loop Jitter

Note: This manuscript has been submitted to NAVIGATION, Journal of the Institute of Navigation. Abstract: The vector architecture is an advanced signal tracking algorithm of global navigation satellite system (GNSS)receivers. It has long been the subject of much research for its ability to deal with GNSS vulnerability.This paper presents a methodology to find the total jitter of the non-coherent vector tracking architectureusing its state space (SS) formulation, referred to as SS jitter, and relates it to that determined with transferfunction (TF) models. Thus, a theoretical framework for evaluating the performance of non-coherentvector loops is developed. In this regard, vector TFs are derived in the z-domain without decoupling thedelay and frequency locked loops, unlike previous work. Two different noise equivalent bandwidths fromthe z-domain TF are also calculated. A close agreement between the SS and TF jitters is demonstrated,proving their equivalence. A metric to represent the collective performance of vector loops for loss of lockdetection is identified using dynamically allocated bounds on the jitter. Steady state jitter performanceat different noise levels in the absence of dynamic stress error is analyzed in detail. Finally, using highdynamic simulations of the global positioning system and navigation with Indian constellation signals, it isillustrated that the proposed metric holds promise for detecting loss of lock in the presence of jerk. Keywords: Vector Tracking Loops, State Space Jitter, Transfer Function Jitter, Noise Equivalent Bandwidth, Loss ofLock