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

• DOI: 10.1049/iet-rsn.2020.0168
• Publication Date: 2020-06-09T02:40:05Z
• Authors: Daniel Medina; Lorenzo Ortega; Jordi Vilà‐Valls; Pau Closas; Francois Vincent; Eric Chaumette
• Keywords: GNSS; RTK; Satellite navigation; Phase estimation; 621; 02 engineering and technology; Carrier Phase; Maximum likelihood estimation; CRB; Nautische Systeme; Global Positioning System; 0202 electrical engineering, electronic engineering, information engineering; Traitement du signal et de l'image; Signal sampling; [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing

The derivation of tight estimation lower bounds is a key tool to design and assess the performance of new estimators. In this contribution, first, the authors derive a new compact Cramér–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 particularised 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. They exploit this CRB to properly characterise the achievable performance of satellite‐based navigation systems and the so‐called real‐time kinematics (RTK) solution. To the best of the authors’ knowledge, this is the first time these techniques are theoretically characterised from the baseband delay/phase estimation processing to position computation, in terms of the CRB and maximum‐likelihood estimation.