A Comparison of an Optimal Global and a Suboptimal Decentralized Differential GPS/INS Filter for Relative State Estimation

Walton R. Williamson, Jeehong Min and Jason L. Speyer

Abstract:	In some high accuracy GPS/INS integrated control systems, an extended Kalman filter uses GPS C/A code range, doppler, and INS measurements to determine the absolute state. When the relative state of two vehicles is desired, an extended Kalman filter uses differenced GPS carrier phase, range, and doppler measurements and the INS measurements to obtain high accuracy relative position, velocity, and attitude estimates. For real-time estimation, the designer of the control system must also consider computational and communications burdens that are placed upon the hardware. Larger Kalman filter states constructed from more measurements must be balanced to the available computational power and communication bandwidth. In the decentralized filter approach for relative state estimation, the GPS and INS measurement noise for each vehicle are modeled as independent, white noise with known covariances. One vehicle estimates its own state using its own GPS and INS measurements while the other vehicle estimates the relative state using differenced GPS and its own INS measurements. This approach decreases the computational and communication requirements and evenly distributes the computational burden to the extended Kahnan filters on each vehicle. In the global filter approach, we account for the fact that GPS measurement noise for each vehicle is not independent, white noise. GPS measurements are corrupted by various errors Selective Availability, atmospheric delays, satellite clock biases, multipath effects,and GPS receiver clock bias, to name a few. Only those errors caused by the receivers will be uncorrelated. Others due to satellites or environment will be the same or nearly so for receivers that are sufficiently near each other. These are usually called common mode errors. Two vehicles in close proximity will receive GPS signals from common satellites and the common mode errors will affect the measurements of both vehicles. The result is a large correlation between the two independent systems. The global filter correctly models this correlation. The primary drawback to this approach, however, is the heavy computational burden on one vehicle to estimate the augmented state. At the University of California at Los Angeles a GPS/INS integrated state estimation filter has been implemented to be used for formation flight of F-18 aircraft. In light of the fact that multiple aircraft will be traveling in similar trajectories and the communication and computational requirements of the formation flight hardware, a decentralized filter approach has been selected and implemented. To compare the results of the suboptimal decentralized filter, an optimal global filter has also been implemented. Results are presented which show that the suboptimal decentralized filter produces estimates that are as good as those of the optimal global filter.
Published in:	Proceedings of the 2000 National Technical Meeting of The Institute of Navigation January 26 - 28, 2000 Pacific Hotel Disneyland Anaheim, CA
Pages:	125 - 133
Cite this article:	Williamson, Walton R., Min, Jeehong, Speyer, Jason L., "A Comparison of an Optimal Global and a Suboptimal Decentralized Differential GPS/INS Filter for Relative State Estimation," Proceedings of the 2000 National Technical Meeting of The Institute of Navigation, Anaheim, CA, January 2000, pp. 125-133.
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