GPS receiver tracking loop optimization based on a behavioral approach

• Authors: He-Sheng Wang
• Venue: ACACOS'10 Proceedings of the 9th WSEAS international conference on Applied computer and applied computational science
• Year: 2010

In this paper, the GPS tracking loop design problem is investigated by using a behavioral approach. The concept of behavioral framework was first proposed by Jan C. Willems in a series of papers (J.C. Willems, "From time series to linear system - part I, II, and III," Automatica Vol. 22, 1986.) as a generic tool for mathematical modeling of dynamical systems. In the last decade, the behavioral point of view has received an increasingly broader acceptance as an approach for modeling dynamic systems, and now it is generally viewed as a cogent framework for system analysis. One of the reasons for its success has to be looked for in the fact that it does not start with the input/output point of view for describing how a system interacts with its environment, but focuses on the set of system trajectories, the behavior, and hence on the mathematical model describing the relations among all system variables. In the proposed approach, the dynamical model of the GPS receiver tracking loop (carrier loop and code loop) is firstly described by a kernel representation. We will then show that the loop filter design can be cast in a global total lease-squares problem, which can be solved by a structured total least-squares (STLS) algorithm. STLS algorithm is a modified version of the traditional total least-squares (TLS) method. It can be shown that the STLS algorithm is able to provide better performance than the TLS algorithm for the problems that possess a particular structure. In the case of the present paper, it is shown that the tracking loop filter design problem has a Hankel structure, therefore the problem can be solved by an STLS algorithm subject to a Hankel structure.