Compact CRB for delay, Doppler, and phase estimation - application to GNSS SPP and RTK performance characterisation

Abstract

The derivation of tight estimation lower bounds is a key tool to design and assess the performance of new estimators. In this contribution, first we derive a new compact Cram\'er-Rao bound (CRB) for the conditional signal model, where the deterministic parameter's vector includes a real positive amplitude and the signal phase. Then, the resulting CRB is particularized to the delay, Doppler, phase and amplitude estimation for band-limited narrowband signals, which are found in a plethora of applications, making such CRB a key tool of broad interest. This new CRB expression is particularly easy to evaluate because it only depends on the signal samples, then being straightforward to evaluate independently of the particular baseband signal considered. We exploit this CRB to properly characterize the achievable performance of satellite-based navigation systems and the so-called Real-Time Kinematics (RTK) solution. To the best of our knowledge this is the first time these techniques are theoretically characterized from the baseband delay/phase estimation processing to position computation, in terms of the CRB and maximum likelihood estimation.