Estimation of Synchronization Parameters using SAGE in a GNSS-Receiver

Kurzfassung

The quality of the data presented to the user in a GNSS (Global Navigation Satellite System)-receiver depends largely on the accuracy in the propagation delay estimation of the direct signal (line-of-sight signal, LOSS). Under the presence of multipath signals, a standard navigation receiver that is designed to synchronize a single signal replica through conventional circuits (Delay-Lock Loop, DLL) experiences an error in the pseudorange measurement, the so-called multipath error. For the current GPS C/A signal, this error can range from a few metres up to more than 100 metres. The synchronization of a navigation signal is usually performed by a DLL, which basically implements an approximation of the maximum likelihood estimator (MLE). The problem which arises is that the order of this estimator (the DLL) is chosen according to the assumption that only the LOSS is present. This means that this estimator tries to estimate the relative propagation delay of only one signal replica. In case the LOSS is corrupted by several superimposed delayed replicas this estimator becomes biased, because of the change of the order of the incident estimation problem. Thus, in order to perform synchronization in the presence of multipath corrupted signals we follow the approach of obtaining the MLE for estimation problems of higher order. Therefore, signal parameters of a number of superimposed delayed replicas have to be estimated jointly. As this leads to a multi-dimensional non-linear optimization problem the reduction of the complexity of this problem is the most important issue to be solved in order to perform precise positioning in a navigation receiver. Several techniques have been proposed in the literature to solve the multipath problem in navigation receivers, like the well known MEDLL [1]. Recently, interesting approaches like in [2] and in [3] have appeared. The first applies the maximum likelihood principle to the delay estimation in the presence of multipath and unintentional interference in an antenna array receiver, and the latter develops efficient multipath mitigation techniques (with low-complexity) in single antenna and array antenna navigation receivers. In both works, a connection is made between the multipath estimation problem in navigation systems and the same problem in communication systems. In this work the potential of the SAGE (Space-Alternating Generalized Expectation Maximization) algorithm for global navigation satellite systems in order to estimate synchronization parameters of the LOSS under the presence of multipath signals is to be considered. The SAGE algorithm is a low-complexity generalization of the EM (Expectation Maximization) algorithm, which iteratively approximates the MLE. It breaks down the multi-dimensional non-linear optimization problem which arises for the general maximum likelihood problem that usually is to complex to be solved with reasonable effort into problems of lower dimensions. Due to this significant reduction of complexity and its fast convergence the SAGE algorithm has been successfully applied for parameter estimation (relative delay, incident azimuth, incident elevation, Doppler frequency, and complex amplitude) in direct-sequence code-division multiple access systems (DS-CDMA) in mobile radio environments. This study discusses receivers with a single antenna, and also points out the capabilities of the proposed techniques using multiple antennas (array processing), for the application in a GNSS environment. Whereas for the single antenna case we estimate the complex amplitudes and the relative delays of the impinging waves, in the latter additionally the spatial signature (incident azimuth and incident elevation) is estimated. The performance of the algorithm is assessed by computer simulations using a simple spatial channel model and a model for the aeronautical multipath navigation channel (European Space Agency, ESA: "Navigation signal measurement campaign for critical environments"). In order to describe the behaviour of the SAGE algorithm classical concepts like the RMSE (root mean square error) and the CRLB (Cramer-Rao lower bound) are employed. On the other hand simulations with the end-to-end simulator for satellite navigation systems NAVSIM developed by the German Aerospace Center (DLR) are made in order to assess the performance of the SAGE algorithm compared to the tracking performance of a conventional navigation receiver with a single antenna (non-coherent DLL, narrow correlator, Costas-Loop used as PLL). Furthermore, we discuss critical aspects which have to be considered using SAGE, like the initialisation problem or its complexity, and we propose an approach to an easy implementation. The results of the performed computer simulations and discussion indicate that the SAGE algorithm has the potential to be a very powerful high-resolution method to successfully estimate parameters of impinging waves for navigation systems. The presented approach to synchronization in GNSS-receivers has proven to be a promising method to efficiently combat multipath for navigation applications due to its good performance, fast convergence, and low complexity. [1] R. D. J. Van Nee, J. Siereveld, P. Fenton, and B. R. Townsend, " The Multipath Estimating Delay Lock Loop: Approaching Theoretical Accuracy Limits", Proc. IEEE Position, Location Navigation Symp., pp. 246-251, Apr. 1994. [2] Gonzalo Seco, "Antenna Arrays for Multipath and Interference Mitigation in GNSS Receivers", Ph.D. thesis, Department of Signal Theory and Communications, Universitat Politecnica Catalunya, 2000. [3] Jesus Selva Vera, "Efficient Mitigation in Navigation Systems", Ph.D. thesis, Department of Signal Theory and Communications, Universitat Politecnica Catalunya, 2004.