Nonlinear Analysis of GPS Aided by INS

Bjørnar Vik, Thor I. Fossen

Abstract:	The advantages of integrating GPS and INS are well known. One of the bene¿ts is that in the event of jamming or high dynamics, the GPS correlator loops can be aided by corrected INS measurements. The external INS mea-surement allows the bandwidth of the tracking loops to be lowered, thus making it possible for the receiver to track weak satellite signals. The aiding creates an addi-tional feedback loop that is potentially destabilizing, and careful tuning of both the loop ¿lters and the GPS/INS integration ¿lter is necessary. When analyzing tracking loops and GPS/INS integration ¿lters, it is usually as-sumed that the tracking/estimation errors are small so that linear models and linear analysis can be applied. In this paper we present a nonlinear observer for tight integra-tion of GPS and INS that has been designed using non-linear system design methodologies. This observer esti-mates IMU and GPS errors directly within the nonlinear strapdown equations. The corrected INS measurements are used to aid the GPS carrier loops which also are rep-resented with nonlinear models. The amount of feedback coming from the correlator loop output, via the integra-tion ¿lter, and back into the loop, is dependent from the tuning of the integration ¿lter. It is therefore evident that the integration ¿lter and the correlator loops should be tuned to eachother. In this paper we use the concept of In-tegral Quadratic Constraints (IQCs) to derive conditions for stability. First the stability of a nonlinear third order carrier loop is analyzed using IQCs, and conditions for stability of the system are given. Furthermore, we look at the interconnected GPS/INS system using IQCs. Finally, simulations that show the difference between the linear and nonlinear stability conditions in the ¿rst case, will be given.
Published in:	Proceedings of the 55th Annual Meeting of The Institute of Navigation (1999) June 27 - 30, 1999 Royal Sonesta Hotel Cambridge, MA
Pages:	683 - 688
Cite this article:	Vik, Bjørnar, Fossen, Thor I., "Nonlinear Analysis of GPS Aided by INS," Proceedings of the 55th Annual Meeting of The Institute of Navigation (1999), Cambridge, MA, June 1999, pp. 683-688.
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