Asian GPS ---> Proceeding ---> 2002---> GPS: Emerging Trends

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

M. R. Mosavi
Department of Computer Engineering
Shahid Rajaee Teachers Training University
Lavizan, Tehran, Iran

K. Mohammadi
Department of Electrical Engineering
Iran University of Science and Technology
Narmak, Tehran, Iran

M. H. Refan
Department of Electrical Engineering
Shahid Rajaee Teachers Training University
Lavizan, Tehran, Iran

This paper presents a method to determine an accurate position by using a low cost GPS receiver and proposes a fuzzy system for better accuracy in GPS positioning. At first the fixed position parameters, such as Geometric Dilution of Precision (GDOP) and Signal to Noise Ratio (SNR), are measured. Then those are applied to fuzzy system. Fuzzy system output defines as Reliable Factor (R.F.). Based on the R.F. values, the more accurate positions are selected. The steps design and implementation of the fuzzy system are presented and the experimental result of the tests are stated with real data, before and after Selective Availability (S/A) is turned off. Those show the errors of position components decrease due to using of the fuzzy system.

Global Positioning System (GPS) has replaced prior positioning systems. It can cover all the earth by satellites to measure accurate time, altitude, longitude and latitude in every desirable point [1,2]. Positioning began from 1950s and improved in 1970s. In 1980s, GPS became an operational positioning system. At first it was designed and used for military purposes. But later its commercial applications have been increased. Nowadays commercial receivers take a great part in its market [1,2]. During past several years, the main problem to improve the positioning accuracy was S/A error, which was produced and fed into GPS system by U.S. Department of Defense (DoD) in order to degrade the achievable navigation accuracy when nonmilitary GPS receivers are used [3,4]. In addition to S/A, there is some other error sources that cause the position and time measuring from GPS receivers to be inaccurate. Other significant error sources are signal delays from ionospheric and tropospheric effects, satellite clock drift, satellite orbital position errors, signal multi path and noise generated within the receiver itself. Table1 shows the average errors introduced of GPS system in meter.

Table 1. The average errors introduced of GPS system in meter [5,6]
Error Source Average (meters) Time Constant
Receiver Noise 0.4 -
Troposphere 0.5 More Than 1 Hour
Signal Multi Path 0.6 0.5 to 10 Minute
Satellite Clocks 1.5 -
Orbit Errors 2.5 More Than 1 Hour
Ionosphere 5 More Than 1 Hour
Selective Availability 30 2 Minute

Because of above mentioned error sources, all GPS receivers have a certain number of errors. This means that received data from GPS receiver will not reflect the real location. Therefore, users who wish to increase the accuracy of their GPS receiver must take steps to minimize the errors. In this paper an intelligent method to decrease the positioning measurement errors in a low cost GPS receiver is described. The theoretical background for better accuracy is based on the principle of fuzzy logic.

GPS Receiver
To achieve information of position and implementing an operational system, MicroTracker Low Power (MLP) as a low cost GPS engine manufactured by Rockwell Company was used. This miniature receiver with a small volume is appropriate for a vast range of Original Equipment Manufacturer (OEM) products. OEM receiver provides the possibility of improving software by presenting raw data [7,8]. This receiver has 5 parallel channels. It can track up to 9 satellites simultaneously. This receiver supports approved and improved NMEA-0183 protocol. It can receive differential RTCM messages to improve the accuracy of positioning in differential mode. Its serial port can receive and transmit NMEA or Binary data with the rate of 4800 or 9600 bit per second. The Binary protocol provides more detailed information compare with NMEA protocol [7,8].

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 Xi,Yi,Zi 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].

The GDOP and the sum of Signal to Noise Ratio (SNR) are used as input fuzzy variables to the fuzzy processing unit. Fuzzy system output is defined as Reliable Factor. The main block diagram of fuzzy processing is shown in Fig.3 [12].

Fig.3. The main block diagram of fuzzy processing [12]

SNR and GDOP are divided into three and four segments for partition the rule space, respectively. R.F. is fuzzified with a singleton membership function. The membership functions are shown in Fig.4.

Fig.4. Membership functions: (a) GDOP, (b) SNR and (c) R.F. [12]

The approximate reasoning method is used for the inference process and the center of area method is employed for the defuzzification [13]. There are twelve rules in the rule base, which are shown in Table2.

Table2. Twelve rules in the rule base of proposed fuzzy system of Fig. 3 [12]

Experimental Results
At first, 3926 original data for a fix position were collected on the building of Computer Control and Fuzzy Logic Research Lab in the Iran University of Science and Technology. Then, the reliable factor of the fix position is obtained after the fuzzy processing.

As shown in Table3 and Table4, the reliable factor is compared with a desired value. If it exceeds the desired value, these fix positions are selected. By this principle, the appropriate fix positions can be selected from the original ones. Fuzzy selected positions have low value deviations.

Table3. Deviation x, Deviation y and Deviation z with desired Reliable Factor value (S/A on)
R.F. value The number of fuzzy selected position D.x [m] D.y [m] D.z [m]
0.0000 3926 196 219 190
0.1250 2271 160 219 89
0.2000 2185 160 219 83
0.2500 2182 160 135 83
0.3000 1694 160 125 83
0.4000 1689 160 125 83
0.4500 1524 160 125 73
0.4600 1257 146 121 73
0.4650 1052 135 105 72
0.4700 804 135 69 60
0.4750 198 77 49 42
0.4755 143 68 49 41
0.4756 129 67 49 41
0.4757 124 47 41 41
0.4758 118 47 41 41
0.4759 110 47 37 38

Table4. Deviation x, Deviation y and Deviation z with desired Reliable Factor value (S/A off)
R.F. value The number of fuzzy selected position D.x [m] D.y [m] D.z [m]
0.0000 3926 24 46 56
0.1250 2498 24 36 48
0.2000 1858 22 27 41
0.2500 1724 22 24 37
0.3000 684 21 21 35
0.3100 443 19 16 35
0.3125 342 14 16 15
0.3150 251 14 15 13
0.3200 222 14 13 11
0.3400 103 6 9 8
0.3550 15 4 7 8

According to Table3 and Table4, deviations of position components decrease due to increasing of Reliable Factor.

This paper has described how the positioning accuracy of a low cost GPS receiver can be greatly improved with a fuzzy system. Fuzzy logic was used to selection of appropriate data according to the measurement or available information. The result is a highly effective technique for accurate positioning. The validity of the proposed fuzzy system was confirmed by experimental results on implemented unit in this paper (Fig.5). So that position components deviation before turning off the S/A, were decreased from more than 215 to less than 50 meters after fuzzy processing. Similarly, the position components deviation were reduced to less than 10 meters after turning off the S/A, while it was about 55 meters before fuzzy processing.

Fig.5. Implemented unit in this paper

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