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

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 DDS 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 equivalence of the maximum likelihood (ML) GNSS parameter estimation based MLE with the Bayes Parameter Estimation (see Appendix A). Third, under the assumption of interference as 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 which leads to the equivalence of the MLE with the Bayes Parameter Estimation (see Appendix A). 72 Journal of Geolocation, Geo-information, and Geo-intelligence 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. Simulation results illustrate that the MLE receiver exhibits a 75 dB SINR improvement performance against a Cross-Correlator CC receiver even under extreme jamming conditions.