Optimal Recursive Bayesian Phase Estimation with Dynamic Compensation in Nonlinear Code Tracking Loops

Gary Fay and Jason Speyer

Abstract:	An optimal recursive Bayesian phase estimation algorithm for code tracking is presented in this paper. Maximum power is recovered from the correlators in a low signal-to-noise environment by optimal alignment of the signal replica with the true incoming signal. This is accomplished by using the conditional mean or maximum a posteriori estimate of the code phase as feedback to the replica generators. A novel approach for integrating dynamic models within the Chapman- Kolmogorov equation is shown which uses IMU outputs or feedback from the navigation filter. By using feedback from the navigation filter, a vectorized approach could be implemented allowing aiding between tracking loops. The Chapman-Kolmogorov equation is used to compute the a priori probability density function (pdf), and the a posteriori pdf is computed using the correlator outputs as measurements. In a low signal-to-noise environment, the code phase error probability densities are neither Gaussian nor symmetric, and can often become multi-modal. An analytic closed form solution to compute the pdf of a general code tracking loop does not exist requiring one to employ computationally intensive numerical methods. A description of a potential method for computing the pdf in real-time using particle filters will be described.
Published in:	Proceedings of the 2008 National Technical Meeting of The Institute of Navigation January 28 - 30, 2008 The Catamaran Resort Hotel San Diego, CA
Pages:	317 - 328
Cite this article:	Fay, Gary, Speyer, Jason, "Optimal Recursive Bayesian Phase Estimation with Dynamic Compensation in Nonlinear Code Tracking Loops," Proceedings of the 2008 National Technical Meeting of The Institute of Navigation, San Diego, CA, January 2008, pp. 317-328.
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