Testing the Accuracy of Autonomous GPS in Ground Speed Measurement

MATERIALS AND METHODS

A passenger vehicle was instrumented with a hand-held GPS receiver to provide GPS-derived ground speed data and a pulse transmitter to obtain vehicle's wheel speed. GPS-derived speed data was compared with the ground speed measurements based on wheel speed data (reference ground speed) and errors in GPS speed measurements were determined. The vehicle's speedometer was utilized as an initial indicator of the ground speeds targeted for this study which were 5, 10, 15, 20, 25, 30, 40 and 50 km h^-1. These ground speed values were chosen to cover the ground speed range required for most, if not all, agricultural operations.

GPS speed data acquisition: A hand-held Garmin eTrex Venture GPS receiver^[9] operated in autonomous mode was used to provide GPS ground speed data. A study by Al-Gaadi^[10] showed that this receiver maintained, on the average, a position determination accuracy of less than 2.10 m when the Selective Availability (S/A) was off. The same study revealed that the S/A, which is the biggest source of error in GPS data^[3], was not in effect since at least October, 2003. Therefore, the GPS data for this test which was acquired on October, 2004 was assumed to be S/A error free. GPS speed data was acquired by internally programming the GPS receiver to output data in National Marine Electronic Association (NMEA) string format. Due to design and hardware limitations, it was found through preliminary testing that the receiver used in this study repeated a group of NMEA strings every 2 sec, therefore, it could output ground speed data, which was included in one of the strings, every two seconds as its only sampling rate. Since a sampling rate of ten seconds was decided to be used for this study, the sampling rate of the receiver was found to be sufficient. The GPS receiver was placed in the vehicle with a clear vision to the sky and connected to a lap top computer where collected raw data (NMEA strings) for the eight different test ground speeds could be monitored in real time and directly stored in a computer text file. A custom-written program was employed to filter the GPS raw data and pull the desired string (the RMC string) to another file that was imported into a work sheet for data analysis. The RMC data string was selected because it contained the ground speed data required for the purpose of this study. The RMC string containing file was further filtered to have the string repeated every ten seconds, instead of two seconds, where the records in between were removed. A total of 593 data points were contained in the last filtered work sheet GPS data file.

Reference ground speed data acquisition: The reference ground speed measurements were obtained by measuring the rotational velocity of the vehicle's wheel for the eight test ground speeds. Wheel velocity was measured by utilizing a pulse transmitter that sent a pulse every time a magnet fixed on one of the vehicle's wheels passed by it indicating one full rotation of the wheel. The pulse transmitter was fixed close to the tire where the horizontal distance between the transmitter and the magnet, when it passed by the transmitter, was about 1 cm. When passed by the transmitter, the magnet caused it to close the circuit providing a pulse. Pulses for ten seconds, which represented the number of wheel rotations occurred in ten seconds, were recorded for the eight test speeds by connecting the transmitter to an on-board CR23X micrologger, which was programmed to measure and record pulse data from the pulse transmitter at the specified sampling rate of ten seconds^[11]. Data from the micrologger was downloaded to a computer text file which was imported into a work sheet for analysis. For each of the resulting 593 pulse data points, vehicle ground speed per ten seconds was calculated by multiplying the number of pulses by the known wheel circumference (2.07 m) divided by ten seconds. The ground speed in km h^-1 was then calculated for each data point to match the unit of ground speed measurements produced by the GPS. Since the test was conducted on an asphalt surface, wheel slippage was negligible and pulses indicating numbers of wheel rotations were directly proportional to the forward vehicle ground speed.

At the beginning of the field data acquisition, the micrologger time was synchronized with the time on the GPS receiver. Synchronization was conducted so that the data records from the GPS and the micrologger could be tagged using matching times, therefore, a time-specific data comparison could be achieved.

RESULTS AND DISCUSSION

GPS-derived ground speeds were tagged to reference ground speeds using record matching times. For each data point, the difference between GPS-derived speed and reference ground speed (error in GPS-derived speed) was calculated. For the whole test data set, the average error was found to be equal to 1.27 km h^-1 (6.9%). An error of 0.51 km h^-1 or less and an error of 5.54 km h^-1 or less were associated with 50 and 95% of the data, respectively. High fluctuations of vehicle's speed greatly increased the error of GPS-derived speed. An error of -80.16% was produced due to a drop of vehicle's ground speed, based on reference ground speed measurements, from 18.65 to 11.19 km h^-1 and an error of 47% was produced due to an increase of ground speed from 13.43 to 30.59 km h^-1. This leads to the conclusion that the GPS was not proportionally responsive to sudden big changes in ground speed.

For each of the eight ground speed data sets, a steady state analysis of GPS-derived ground speed measurement accuracy was conducted (Fig. 1). In this text, a steady state ground speed was defined as being the state where ground speed variation was limited to ±15% between two consequent data points. Therefore, the records which contained data points that caused variations exceeding the limit were removed from the reference ground speed data along with the corresponding GPS data records. This was accomplished to eliminate the effect of sudden high fluctuations of vehicle's ground speed on GPS-derived ground speed measurement accuracy. These fluctuations could not be avoided during the field test as they occurred when, for example, turning or passing another vehicle given the fact that the field test was conducted on public roads.

Fig. 1:	GPS-derived and reference ground speed measurements

Fig. 2:	Error in ground speed measurement for the 5 km h-1 data set

Fig. 3:	Error in ground speed measurement for the 10 km h-1 data set

Fig. 4:	Error in ground speed measurement for the 15 km h-1 data set

Fig. 5:	Error in ground speed measurement for the 20 km h-1 data set

For all test speeds, the steady state analysis revealed that the GPS maintained, on the average, an error of less than 1 km h^-1 except for the 15 km h^-1 data set where the average error reached 1.72 km h^-1. Figure 2 to 9 show the errors in ground speed measurements produced by the GPS for the 5, 10, 15, 20, 25, 30, 40 and 50 km h^-1 data sets, respectively, when compared with the reference ground speed measurements.

The maximum error in GPS-derived speed measurement was found in the 20 km h^-1 data set, where this error reached 13.11 km h^-1 (Fig. 5 and Table 1). This individual extreme error was attributed to noise in the GPS hardware. For the 5 km h^-1 data set, steady state analysis showed that the maximum error was 0.79 km h^-1 (Fig. 2), however, 50 and 95% of the data points had an error of less than or equal to 0.22 and 0.51 km h^-1, respectively. The maximum error for the 10 km h^-1 data set was 2.11 km h^-1, however, 50 and 95% of the data points had an error of less than or equal to 0.29 and 1.39 km h^-1, respectively (Fig. 3). A maximum error of 6.66 km h^-1 was associated with the 15 km h^-1 data set (Fig. 4), however, 50 and 95% of the data points had an error of less than or equal to 1.42 and 4.99 km h^-1, respectively. An extreme individual error of 13.11 km h^-1 was found in the 20 km h^-1 data set, however, 50 and 95% of the data had an error of less than or equal to 0.55 and 2.21 km h^-1, respectively. For the 25 km h^-1 data set, a maximum error of 3.74 was produced (Fig. 6) and an error of less than or equal to 0.39 and 1.68 km h^-1 was associated with 50 and 95% of the data points, respectively. The maximum errors for the 30, 40 and 50 km h^-1 data sets were 5.20 km h^-1 (Fig. 7), 3.11 km h^-1 (Fig. 8) and 6.33 km h^-1 (Fig. 9), respectively. For these data sets, 50% of the data points had an error of less than or equal to 0.43 km h^-1 and 95% of these points had a maximum error of 1.85 km h^-1.

Table 1:	Errors of GPS-derived ground speed in steady state

Fig. 6:	Error in ground speed measurement for the 25 km h-1 data set

Fig. 7:	Error in ground speed measurement for the 30 km h-1 data set

Fig. 8:	Error in ground speed measurement for the 40 km h-1 data set

Fig. 9:	Error in ground speed measurement for the 50 km h-1 data set

Table 1 summarizes the findings of the steady state analysis for the eight data sets.

For all test speeds, the GPS produced, in steady state, a ground speed measurement with an average error of no more than 5.23%, except for the 15 km h^-1 data set where this error reached 9.92% (Table 1). It can also be seen that the magnitude of error was not related to the amount of ground speed. However, it was thought that the reference speed, based on which GPS-derived speed was evaluated, reflected the true ground speed of the vehicle as it was almost impossible to maintain constant vehicle ground speed under test field conditions.

CONCLUSIONS

The time-specific accuracy of an autonomous GPS receiver in measuring vehicle's ground speed was tested for eight different ground speeds. A pulse transmitter and a magnet were utilized to measure vehicle's wheel speed and a reference ground speed measurement was obtained. GPS-derived speeds were compared to the reference speed measurements and the following conclusions are drawn from the study: