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ML Estimation of Position in a GNSS Receiver using the SAGE Algorithm

In this paper, the maximum likelihood estimator (MLE) of the position in satellite based navigation systems is studied. Recent results have shown that this novel approach provides an interesting way of introducing prior information in the position estimation and that the estimator is consistent for large sample sizes. However, one of the main drawbacks of this approach is the lack of a computationally efficient optimization algorithm due to the high dimensionality and nonlinearity of the resulting cost function, since there is not a closed form solution for this estimator. The aim of this paper is to investigate the application of the space-alternating generalized expectation maximization (SAGE) algorithm to the estimation of position. The SAGE algorithm is a low-complexity generalization of the EM (expectation-maximization) algorithm, which iteratively approximates the MLE. Computer simulation results are provided, comparing the performance obtained by the algorithm with the Cramer-Rao bound.