Optimal Use of Both GPS Carrier and Code Tracking Observations

John Lukesh

Abstract:	Add a state variable to the Kalman filter to represent carrier cycle count error. Some applications, such as using GPS together with air data measurements to obtain estimates of prevailing and turbulent winds local to a low flying aircraft, need better velocity accuracy than can be obtained from code tracking alone. For the wind estimation problem I have developed a non-stationary 2 nd order GPS error model that conservatively represents GPS instability from the various error sources, particularly ionosphere effects. This assumes use of an (L1 only) C/A code receiver with a 50% reduction in ionospheric lag error obtained through the use of model based compensation with coefficients from the nav message. One way of using carrier tracking information is to create a range-rate observation; this to get around the problem of not knowing the carrier cycle count. Instead of this, I added a new state variable to the Kalman filter to represent the carrier phase error due to cycle count ambiguity. With this the accumulated delta range can be used directly (no need to create a range-rate observation) and concurrently with the normal pseudorange observation (the carrier track observation includes the error; the code pseudorange observation does not). The white noise standard deviation appropriate for the carrier phase observation is orders of magnitude less than that for the code phase observation (0.008 meter versus 1.4 meters), thus the additional carrier phase observation is very beneficial. By the way, representing the occurrence of carrier tracking cycle slips when they occur (due to antenna shadowing for example) is simply a matter of “Q-bumping” the carrier cycle count state. Results. The following are from a single axis GPS-INS simulation run for 1000 cycles with a Kalman period of 1.0 second: Without the accumulated delta range observation: • position error standard deviation = 6.048 meters • velocity error standard deviation = 0.08619 m/s • carrier cycle count error std dev = 10.000 meters With the accumulated delta range observation: • position error standard deviation = 6.013 meters • velocity error standard deviation = 0.00689 m/s • carrier cycle count error std dev = 0.047 meters This paper gives the derivation of the 2 nd order GPS error model and the carrier phase cycle count state addition to the filter. Three axis inertial velocity results from my GPS-INS Matlab simulation are given.
Published in:	Proceedings of the 1999 National Technical Meeting of The Institute of Navigation January 25 - 27, 1999 Catamaran Resort Hotel San Diego, CA
Pages:	447 - 454
Cite this article:	Lukesh, John, "Optimal Use of Both GPS Carrier and Code Tracking Observations," Proceedings of the 1999 National Technical Meeting of The Institute of Navigation, San Diego, CA, January 1999, pp. 447-454.
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