Cramér-Rao bound analysis of positioning approaches in GNSS receivers

Recently, Direct Position Estimation (DPE) has arisen as a potential approach to deal with the positioning problem in Global Navigation Satellite System receivers. The conventional navigation solution is obtained in two steps: synchronization parameters are estimated and then a trilateration procedure is in charge of computing user’s position, based on those parameters. In contrast, DPE estimates receiver’s position directly from digitized signal. DPE was seen to provide GNSS receivers with appealing capabilities, such as multipath mitigation. However, a theoretical bound for those estimates is still missing and the answer to “how better can DPE perform compared to the conventional approach?” has not been addressed in the literature. Aiming at clarifying those issues, this paper presents the derivation of the Cramér-Rao Bound of position for both conventional and DPE approaches. We present the derivation for a multi-antenna receiver as a general case. In addition, a number of realistic scenarios are tested in order to compare the theoretical performance bounds of both alternatives and the actual Root Mean Squared Error performance of the corresponding Maximum Likelihood Estimator.