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Using GPS Velocity Information in Enhancement of GPS Position Accuracy
Dr. K. Mohammadi, Mohammad Reza Zamani
College of Electrical Engineering
Iran University of Science and Technology
Tehran, Iran
mohammadi@iust.ac.ir , 79708704@iust.ac.ir
Abstract
Position information obtained from standard GPS receivers is known to be corrupted with coloured (time-correlated) noise. To make effective use of GPS information in a navigation system it is essential to model this coloured noise and to incorporate additional information to de-correlate and eliminate its effect. In this paper frequency domain, techniques are employed to generate a model for GPS noise sources. This model shows clearly, what type additional information such as velocity information is necessary to separate GPS errors and for improving the GPS position accuracy in navigation tasks.
Introduction.
GPS provides worldwide positioning with acceptable accuracy, if four or more satellites are in view. Various dynamic models for GPS positioning have been proposed over the years, differing in their complexity . However, there are problems inherent in the system such as correlated errors on the satellite signal, which mean that GPS alone does not meet the requirements for such a system . State estimators, such as the Kalman filter, which are often used as the main navigation algorithm, implicitly reflect these models and act as low-pass filters for the observation information. Therefore, true high frequency information, associated with vehicle maneuvers such as turning, is lost. To overcome this, inertial information is often fed-forwarded through the state estimator as a prediction to be corrected by absolute information. The net effect of this is that while absolute information is subjected to a low-pass filter, prediction information is subjected to a complimentary high-pass filter. Together these two sources of information span the complete frequency spectrum in a complimentary manner . The approach adopted in this paper is to develop and exploit frequency domain error and system models to specify and compare different GPS velocity information. Section 2 in this paper introduces an experimentally derived frequency domain error model for standard GPS position estimates. This model is obtained directly from , data provided by a commercial GPS receiver. Section 3 describes how this model is exploited in a state estimator (Kalman filter), extended with an appropriate shaping filter to take into account the coloured noise and incorporating an additional information to de-correlate the position state from the shaping state. Section 4 shows how the filter is tuned and how the quality of aiding information is studied in the frequency domain.
GPS Error model
State estimation methods such as the Kalman filter assume that measurement noise is white or non-correlated. If this is not the case then a shaping filter must be constructed whose input is white noise and whose output is the observed coloured noise . This filter can be obtained by obtaining a power spectral density for the measurement errors on the assumption that the true states are known. In the work described in this paper, we exploit this knowledge and construct only shaping models for and errors by using real GPS position information.
Figure 1 shows the and errors in meters obtained with a GPS unit working without differential correction. It is clear from the figure that the error is time correlated, showing a characteristic oscillatory behavior with amplitude between 10m and 20m.
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