The well-known Space-Alternating Generalized Expectation Maximisation (SAGE) algorithm has been recently considered for multipath mitigation in Global Navigation Satellite System (GNSS) receivers. However, the implementation of SAGE in a GNSS receiver is a challenging issue due to the numerous number or parameters to be estimated and the important size of the data to be processed. A new implementation of the SAGE algorithm is proposed in this paper in order to reach the same efficiency with a reduced complexity. This paper focuses on the trade-off between complexity and performance thanks to the Cramer Rao bound derivation. Moreover, this paper shows how the proposed algorithm can be integrated with a classical GNSS tracking loop. This solution is thus a very promising approach for multipath mitigation. 1. Introduction In Global Navigation Satellite System (GNSS) applications, multipath (MP) errors are still one of the major error sources for conventional receivers. The additional signal replicas due to reflections on the local environment introduce a bias in the delay lock loops (DLLs), which finally leads to a positioning error [1, 2]. Several techniques have been developed for multipath mitigation. One of the most popular approaches is the Narrow Correlator Spacing , which reduces the chip spacing between the early and late correlators in order to mitigate the impact of multipath. However, this technique suffers from high sensitivity to noise and cannot perform with short delay multipath (<0.1？chip). Based on the Maximum Likelihood (ML) estimation, the Multipath Estimating Delay-Lock-Loop (MEDLL)  algorithm has also been proposed to estimate the delay and the power of all the paths by studying the shape of the cross-correlation function. This approach shows better performances than the Narrow Correlator Spacing technique, but short delay multipath mitigation is still an issue . More recently, Bayesian approaches have been proposed [5–7]. Indeed, most of the time, prior information could be used in order to improve the delays estimations. However in practice, it is difficult to get correct prior information. Measurement campaigns can be used to build a first-order Markov process for a sequential estimation, but the performance will consequently be strongly dependent on the measured environment (design of the city…). Last, the use of array antenna algorithms has been proposed for multipath mitigation [8, 9]. Array antennae enable a spatial sampling that makes it possible to distinguish different sources in the spatial domain. Therefore,
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