Advanced Anti-Jam Indoor Adaptive GNSS Signal Acquisition: Part 2, Bessel Distribution - Theory

Ilir F. Progri

Peer Reviewed

Abstract:	This paper is an extension of advanced anti-jam indoor adaptive GNSS signal acquisition: Part 1, normal distribution-Theory based on the assumption that complex interference is Bessel distributed. In order to determine a suitable advanced anti-jam indoor adaptive GNSS signal acquisition and tracking algorithm for DDS we first perform the Bayesian parameter estimation; i.e., we analytically compute the posterior Bayes probability density function (pdf) and cumulative distribution function (cdf) by applying the Bayes theorem 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 Bayes posterior density. This is an original new and very powerful result never published before. Third, we perform the Bayes theorem, in both the scalar case and complex matrix variate cases we observe that the complex matrix variate Bayesian posterior pdf or cdf is invariant of the observation data or is identical to the prior complex matrix variate signal distribution model. This is an original new and very powerful result never published before. Why this result is so powerful is because up until now we never had a complete theoretical validation of our GNSS receiver design based on either autocorrelation or cross-correlation properties since, the complex matrix variate Bayesian posterior pdf or cdf is invariant of the observation data or is identical to the prior complex matrix variate signal distribution model. Future simulation results will illustrate that an anti-jam indoor adaptive DDS stable detection structure reduces by half the average acquisition time and significantly outperform its predecessor against interference and jamming. Future simulation results will 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:	440 - 466
Cite this article:	Progri, Ilir F., "Advanced Anti-Jam Indoor Adaptive GNSS Signal Acquisition: Part 2, Bessel Distribution - Theory," Proceedings of the 2018 International Technical Meeting of The Institute of Navigation, Reston, Virginia, January 2018, pp. 440-466. https://doi.org/10.33012/2018.15541
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