Maximum Likelihood GNSS Parameter Estimation: Part 2, Bessel Distribution-Theory and Simulation

Ilir F. Progri

Peer Reviewed

Abstract:	This paper is an extension of maximum likelihood (ML) GNSS parameter estimation based on the assumption that complex interference is Bessel distributed. When we proposed to perform the ML GNSS parameter estimation the main assumption was that the receiver noise is Gaussian distributed. The main issue with this assumption is that it limits the capability of the ML GNSS parameter estimation in non-Gaussian environments. Therefore, the main objective of this paper is to demonstrate the enhanced capability of ML GNSS parameter estimation in nonGaussian environments namely in Bessel Distributed ones in three steps. First, we utilize the results from a separate reference that we have computed the complex signal distribution and complex matrix variate signal distribution. Second, we utilize the results from a separate reference that provides complete derivations of the complex Bessel interference distribution models and Complex Matrix Variate Bessel Interference Distribution that require the computation of functions such as Kampé de Fériet function and Jack functions of matrix arguments, to derive the maximum likelihood objective function. This is an original new and very powerful result never published before. Third, we perform the ML GNSS parameter estimation, in both the scalar case and complex matrix variate cases we observe that maximum likelihood objective function. This is an original new and very powerful result never published before. Simulation results illustrate that a ML GNSS indoor adaptive DDS stable detection structure reduces by half the average acquisition time and significantly outperform its predecessor against interference and jamming. Simulation results show further advancements of the Giftet Inc. MATLAB library capability to perform advanced numerical computations based on closed form expressions of the generalized Bessel function distributions via Kampé de Fériet function and Jack functions.
Published in:	Proceedings of the 2018 International Technical Meeting of The Institute of Navigation January 29 - 1, 2018 Hyatt Regency Reston Reston, Virginia
Pages:	589 - 610
Cite this article:	Progri, Ilir F., "Maximum Likelihood GNSS Parameter Estimation: Part 2, Bessel Distribution-Theory and Simulation," Proceedings of the 2018 International Technical Meeting of The Institute of Navigation, Reston, Virginia, January 2018, pp. 589-610. https://doi.org/10.33012/2018.15540
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