Advanced Anti-Jam Indoor Adaptive GNSS Signal Acquisition: Part 1, Normal Distribution � Theory

Abstract

In this paper an advanced anti-jam indoor adaptive GNSS signal acquisition and tracking algorithm is considered. Initially, we were able to determine that double-dwell structure (DDS) reduces the processing time penalty caused by false alarm. Nevertheless, the double-dwell structure is still vulnerable to interference and jamming. 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 compute the complex signal distribution and complex matrix variate signal distribution. This is an original new result never published before. Second, we provide an introduction of the complex Bessel or parabolic function interference distribution due to earlier assumptions of the DDS interference distribution models. We further explain that the process that is required to produce Complex Matrix Variate Bessel Interference Distribution or Complex Matrix Variate Parabolic Function Interference Distribution is an extremely daunting task let alone the Complex Matrix Variate DDS Bayesian posterior density it would seem at the moment nearly an impossible task because it may require the computation of functions such as Kampe de Feriet function and Jack functions of matrix arguments. Third, instead of performing the second step, we relax the assumption of interference to normal distribution. 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. Moreover, 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 and generalized parabolic cylinder function distribution models via Kampe de Feriet function and Jack functions.