A new tracking approach for multipath mitigation based on antenna array

Abstract

In Global Navigation Satellites Systems (GNSS), multipaths (MP) are still one of the major error sources. The additional signal replica due to reflection will introduce a bias in conventional Delay Lock Loops (DLL) which will finally cause a strong positioning error. Several techniques, based on Maximum Likelihood estimation (ML), have been developed for multipaths mitigation/estimation such as the Narrow correlator spacing [1] or the Multipath Estimating Delay-Lock-Loop (MEDLL) [2] algorithm. These techniques try to discriminate the MP from the Line Of Sight Signal (LOSS) on the time and frequency domains and thus, short delay multipaths (<0.1Chips) can not be completely mitigated. Antenna array perform a spatial sampling of the wave front what makes possible the discrimination of the sources on the space domain (azimuth and elevation). As the time-delay domain and space domain can be assumed independent, we can expect to mitigate/estimate very short delay MP by using an antenna array. However, we don't want to increase too much the size, the complexity and the cost of the receivers and thus, we focus our study on small arrays with a small number of antennas: typically a square 2x2 array. Consequently, conventional beamforming (space Fast Fourier Transform) is not directive enough to assure the mitigation of the multipaths, and then this first class of solutions was rejected. In order to improve the resolution, adaptive beamformers have also been tested. However, the LOSS and the MP signal are strongly correlated and thus, classical adaptive algorithms [3] are not able to discriminate the sources. These preliminary studies have shown that the mitigation/estimation of multipaths based on the space domain will exhibit limited performances in presence of close sources. Then, in order to propose robust algorithms, we decided to investigate a space-time-frequency estimation of the sources. Space Alternating Generalized Expectation maximisation (SAGE) algorithm [4], which is a low-complexity generalization of the Expectation Maximisation (EM) algorithm, has been considered. The basic concept of the SAGE algorithm is the hidden data space [4]. Instead of estimating the parameters of all impinging waves in parallel in one iteration step as done by the EM algorithm, the SAGE algorithm estimates the parameters of each signal sequentially. Moreover, SAGE algorithm breaks down the multi-dimensional optimization problem into several smaller problems. In [5], it can be seen that SAGE algorithm is efficient for any multipaths configurations (small relative delays, close DOAs) and space-time-frequency approach is clearly outperforming classical time-frequency approaches. Notwithstanding, SAGE algorithm is a post processing algorithm. Thus, it's necessary to memorise in the receiver the incoming signal in order to apply SAGE estimation. For example, if we want to process 10ms of signal with a 10MHz sampling rate, we need to store a matrix of m*105 with m the number of antennas. In such condition, we can understand than SAGE algorithm is hardly implemented in real time. The challenge is then to find a new type of algorithms that reach the efficiency of the SAGE algorithms, but with a reduced complexity in order to enable real time processing. Furthermore, the implementation should be compatible with conventional GNSS tracking loops (DLL and PLL). To cope with these two constraints, we propose to apply the SAGE algorithm on the post-correlated signal. Indeed, the correlation step can be seen as a compression step and thus, the size of the studied signal is strongly reduced. In such a way, SAGE algorithm is able to provide estimates of the relative delay and Doppler of the received signals with respect to the local replicas. Thus, a post correlation implementation of SAGE can be seen as a discriminator for both the DLL and the PLL.