Improved Mathematical Modeling for GPS Based Navigation
Abstract
This thesis is concerned with the development of new closed form GPS position determination algorithms that work in the presence of pseudorange measurement noise. The mathematical derivation of two closed form algorithms, based on stochastic modeling and estimation techniques, is presented. The algorithms provide an estimate of the GPS solution parameters (viz., the user position and the user clock bias) as well as the estimation error covariance. The experimental results are analyzed by comparison to the baseline results from the conventional Iterative Least Squares (ILS) algorithm. In typical GPS scenarios, the closed form algorithms are extremely sensitive to noise, making them unsuitable for stand-alone use; however, they perform very well at estimating horizontal position parameters in ground-based pseudolite planar array scenarios where the ILS algorithm breaks down due to poor geometry. For typical scenarios, the use of a supplementary algorithm is required to refine the solution. Thus, the derivation of two supplementary algorithms is presented; the first based on a maximum likelihood approach and the second uses a Kalman like update approach. Both supplementary algorithms produce results comparable to the ILS results, but the Kalman update approach is preferred. The advantages introduced by the closed form, supplemented by the Kalman update, algorithm are: (1) The capability to estimate its estimation error covariance, and (2) The potential for computational efficiency due to the closed form nature of the solution.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1998
- Accession Number
- ADA342014
Entities
People
- Salvatore Nardi
Organizations
- Air Force Institute of Technology