Efficient Multipath Mitigation in Navigation Systems

The main objective of the thesis is the development of efficient multipath mitigation techniques for navigation systems. By efficient mitigation we refer to the use of asymptotic efficient estimators, and also to the minimisation of their computational burden. In this thesis, the efficient estimators are derived from the Maximum Likelihood Principle in several important scenarios. The computational burden is reduced in two ways. One is through data compression techniques that yield receiver implementations of small complexity and small data sizes. The other consists of the efficient implementation of Newton-type methods for the computation of the Maximum Likelihood estimators. The first part of the thesis is dedicated to present the fundamentals of synchronisation in a navigation receiver, and to the state of the art in multipath mitigation. Afterwards, several results concerning the interpolation of a band limited signal in a finite interval are introduced, that will later make possible to design efficient estimators. After this introductory part, several data compression methods are presented, wellsuited for a DS-CDMA navigation signal that has been corrupted by multipath. The Principal Components and Canonical Components methods are the theoretical tools employed in their derivation. Once the data compression methods have been researched, the thesis deals with the design of efficient computation methods for the Maximum Likelihood estimators. For this, the Newton-type methods are proposed. Though these methods are the most efficient in unconstrained optimisation problems, they are not usually employed because they require the computation of the gradient and the Hessian of the cost function, or an approximation to the latter. However, in this part of the thesis a new symbolic methods is presented that makes possible to derive compact expressions of these differentials. In this way, it is possible to compute the Maximum Likelihood estimators through the Newton-type methods in a small number of operations. In the last part of the thesis, the former results are applied to the multipath mitigation in a receiver equipped with a single antenna and an antenna array, respectively. For a single antenna receiver, two channels are discussed, the static and the slowly fading. In the case of the static channel, a complete numerical example is presented, in which the best achievable performance only through signal processing is evaluated. The main performance measure is the Root-Mean-Square error. In the case of a fading channel, it is shown that the best achievable performance only through signal processing is better than in the static case, with a small complexity increase. For an antenna array receiver, several Maximum Likelihood estimators are presented, and the subspace methods based on a polynomial structure are applied, respectively. For the Maximum Likelihood estimators, the main question is how the antenna array should be modelled, so that the estimator is able to distinguish short-delayed navigation signal replicas, being at the same time robust against calibration errors. Three antenna array models are presented: the deterministic, the one parameterised in angles of arrival, and the one parameterised in angles of arrival and calibration errors. For the subspace methods, an interpolation technique is designed that builds on the antenna array technique and on the Principal Components method. Using this interpolation technique, a new TLS-ESPRIT algorithm is derived in which a continuous range of frequencies is interpolated.