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Using GPS Velocity Information in Enhancement of GPS Position Accuracy
A transfer function may be fitted to these PSD estimates in the form
Where parameters are as shown in following table.
This model may be described by a shaping filter with process model as:
Where the driving noise w (t) is now white noise with unit variance.
Filter Implementation
It is well known that if the process can be approximated with a linear model plus white noise with known statistics, then an optimal (minimum mean squared error) Kalman Gain can be evaluated. In this application, the observation is composed of the GPS position measurement that is corrupted with coloured and white noise. In order to de-correlate the GPS position information from the coloured noise, it is necessary to obtain other information free of coloured noise in the frequency range of interest. The additional information used in this example is the GPS velocity information corrupted by white noise only. We will show that the quality of the additional information is of fundamental importance to de-correlate the position information from the non-white noise.
In this application, we consider a constant velocity model. A full implementation for , and estimation will require 12 states to account for the coloured noise. The results presented in this work correspond to the estimation of information.
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