De-noising of GPS Receivers Positioning Data Using Wavelet Transform and Bilateral Filtering

The need for precise position and navigation aids in many areas of industry is becoming increasingly apparent. There are many errors associated with the navigation solution of the global positioning system (GPS), including satellite ephemeris error, satellite clock error, ionospheric delay, tropospheric delay, multipath, receiver measurement error and selective availability (SA). Noise can create an error between centimeters to several meters. In this paper, the proposed technique applied to smooth noise for GPS receiver positioning data is based upon the analysis of wavelet transform (WT), bilateral filter (BF) and diffusivity function. The WT is a powerful tool of signal processing for its multiresolutional possibilities. BF is a local, non-linear and non-iterative technique. It is applied to approximation subband. We decompose a GPS positioning data into low-frequency and high-frequency components and apply BF on the approximation coefficients and diffusivity function on the detail coefficients at each decomposition level for data smoothing. A single-frequency and low-cost commercial GPS receiver manufactured by Rockwell Company is used to test our method. The experimental results on measurement data demonstrate the effectiveness of the proposed method; so that the total root mean square (RMS) error reduces to less than 0.29 m with SA on and 0.15 m with SA off using Daubechie wavelet.