Fuzzy processing on GPS data to improve positioning accuracy, before and after S/A is turned off

Data Collection
To study the function of receiver, the GPS receiver was installed and set up in a fixed position. There are several binary messages provided by MLP. One famous and general purpose of these messages is message No.103, which is available on the first receiver output port as default, when we configure the receiver in binary mode. The message 103 is contain of very useful detail information of position and time [7,8].

In order to setup the receiver, connecting to PC and data collection, a hardware designed and implemented. Fig.1 shows the hardware structure. The output data was collected for a few months. A Pentium III computer with 450 MHZ clock speed saved it. Data collection has been in two different periods, before and after 1st of May 2000 (June to December 1999 and July to September 2001).

Fig.1. Hardware structure

Position Components Errors
Since MLP is a low cost nonmilitary receiver, its measurement errors are not neglected (188 meters RMS 3D, when S/A was on and 60 meters RMS 3D, when S/A is off) [7,8]. To study the receiver data and achieving of the errors, the data of position were studied in World Geodetic System-1984 (WGS-84). Therefore the x,y and z magnitude in the No.103 Binary message were collected and saved in separate files every 1 second period.

We focus on variation of x,y and z components in studying fuzzy system [9].A software was developed for this purpose. By calculating the average of each quantity in file length, the software provides difference of the instantaneous magnitude of each point with its corresponding quantity average according to equations (1) to (6) and saves them in other files [10].

Where X_i,Y_i,Z_i are instantaneous magnitude of x,y,z and Ax, Ay, Az are the average magnitude of x,y,z and , , are instantaneous error magnitude of x,y,z respectively. n is number of samples. We developed plotter programs (xgraph, ygraph and zgraph) to drawing the dx , dy and dz graphs. A sample from data collection for almost 7 hours is shown in Fig.2, before S/A is turned off.

Fig.2. Graphs of dx,dy and dz errors for 25000 seconds data collection (S/A on)

As they are shown in Fig.2, the average errors for x,y and z are notable.

Fuzzy System Design
During acquisition and navigation modes, the receiver maintains a constellation of four satellites (if four are available) that provides the best geometry for an accurate navigation solution [11]. The measure of the quality of a satellite constellation geometry is called the Geometric Dilution of Precision (GDOP), which reflects the influence of satellite geometry on the accuracy of the estimates of user position and user time. The best geometry is that which produces the lowest GDOP value. GDOP is a multiplier of the position error due to other sources [7,8,11]. GDOP is a composite measure. It includes Position Dilution of Precision (PDOP), which reflects the effects of geometry on three-dimensional position estimates, and Time Dilution of Precision (TDOP), which reflects geometric effects on time estimates. The relationship can be expressed as:

In turn, PDOP can be expressed in terms of Horizontal Dilution of Precision (HDOP) and Vertical Dilution of Precision (VDOP), which are the effects of geometry on two-dimensional horizontal position estimates and on vertical position (altitude) estimates, respectively. This relationship can be expressed as:

The receiver outputs each of these components, along with GDOP, in the Time Mark Solution Message [7,8,11].

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