Positioning simulation using a 3D map and verification of positional estimation accuracy in urban areas using actual measurement.
Positional accuracy of GPS measurement has been based on simulation and actual measurement due to the difficulty of conducting 24-hour actual running tests. However, the conventional measurement is only based on brief evaluation; hence variability of positional accuracy which varies depending on measurement time and location had been an issue. Thus, it is significant to show the validity by the estimation of positional accuracy, and actual measurement using of lengthy simulation.
In this study, actual measurement data in an urban area was obtained for long hours, and a simulation using 3D maps was implemented. A high precision positional measurement system was equipped on a vehicle in order to collect actual measurements and positional data at each measurement time. The data obtained by the measurement system was used as the reference coordinate for both the simulation and the actual measurements. Consequently, comparison between the simulation and actual measurement data on positional accuracy was able to be implemented for the first time. A dominant deterioration factor of positional accuracy is multipath error caused by reflection from the likes of buildings. Thus, reception status of incoming waves from GPS at each measurement time and reception point by simulation. Specifically, if a satellite which receives direct waves was exclusively used in simulation, measurement accuracy shall be improved. Thus, improvement of the accuracy was verified by choosing the same satellite used in simulation. Consequently, significant improvement in the measurement accuracy was affirmed, and the validity of satellite measurement simulation using 3D maps was partially verified.
CITATION: Komatsu, S., Nagao, A., Suzuki, T., and Kubo, N., "Positioning Simulation Using a 3D Map and Verification of Positional Estimation Accuracy in Urban Areas Using Actual Measurement," SAE Int. J. Passeng. Cars--Electron. Electr. Syst. 9(1):2016.
When the Global Positioning System (GPS) operated by the United States is integrated with the positioning satellite systems of other countries, the number of satellites that can be referenced increases greatly, and the positioning accuracy of navigation services is therefore increased. On the other hand, positional accuracy is degraded by waves reflected from buildings and other such multipath waves when driving in urban areas. GPS has multiple satellites in circular orbits with a period of approximately 24 hours, so that the configuration of the satellite cluster that can be referenced from a given location differs with the time of positioning. Consequently, the positioning accuracy varies with the time of positioning even at the same location.
In order to bypass the variation in positioning accuracy resulting from multipath error and the time of positioning, it is necessary to carry out simulation over an extended period and indicate that its positioning accuracy is valid according to actual measurement. In urban areas, however, actual measurement cannot readily be carried out by extended driving over a 24-hour period, and the only reports to date have concerned research on positional accuracy using short periods of simulated driving and actual measurement [1, 2]. Since the signal strength of simulations and actual measurements were compared in these reports, there was an issue with variation of simulation positioning accuracy according to the time of positioning and the measurement location.
In previous work on GPS positioning in urban areas, the authors of the present study reported on simulation using 3D maps with the ray tracing method and work on positional accuracy and the positional ratio using actual measurement .
For the present research, actual measurement data for urban areas made over periods of time as long as possible was acquired and applied in simulations using 3D maps, orbital information on GPS satellites and the ray tracing method. For the actual measurement, a high-accuracy position measurement system was mounted in a test vehicle, and the position data that could be acquired at each point in time employing this system was used as reference coordinates for the simulation and for the actual measurement. This made it possible for the first time to compare the estimated results from simulation with the actual measurement results for positional accuracy.
The main causal factor in the reduction of positional accuracy in urban areas is multipath error due to reflection from buildings and other such structures. If the satellites that give rise to multipath signals are detected and eliminated, then positional accuracy can be improved.
First, therefore, simulation was used to analyze the reception state (direct wave, reflected wave, diffracted wave and waves that are combinations of these) of incoming waves from GPS at each point in time and each reception point. Next, the information on incoming wave reception state obtained by simulation was used to select the satellite to be received for actual measurement.
When the satellite received in the simulation was designated to be the satellite received to perform actual measurement, the positional accuracy of the actual measurement matched with the positional accuracy of the simulation. The result was greatly improved positional accuracy, and this verified the validity of satellite positioning simulation using 3D maps.
By the estimation of positional accuracy by means of simulation over an extended period in urban areas together with actual measurement, the validity of such simulation was shown for the first time.
The estimation of position using simulation and the field operational trial were carried out in the Nishi-Shinjuku district, which is a virtual forest of tall buildings.
ESTIMATION AND CALCULATION OF GPS POSITIONAL ACCURACY
Principles of Estimating Positional Accuracy Using GPS
GPS positioning is performed by measuring the distance between the satellite and the receiver. When the distances to three satellites at known positions in outer space are known, the location of the receiver can be identified. The distances are derived from the time taken for the signal from the satellite to arrive at the receiver. The atomic clocks on the satellites provide accurate timing for transmission of the positioning codes. Therefore, if the clock in the receiver and the clocks on all the satellites are on exactly the same time, then the time taken for the positioning code to arrive (the propagation delay) can be determined by measuring the time of arrival. It is, however, impossible to perfectly synchronize these various clocks, so another satellite becomes necessary. In other words, GPS positioning captures four or more satellite signals simultaneously, then use them to solve for four unknown quantities, namely the three 3D coordinates ([X.sub.0], [Y.sub.0], [Z.sub.0]) of the receiver and one clock error. In actuality, the clock in the receiver is used to measure the arrival time of the positioning code and calculate the propagation delay time, which is then used to derive the distance.
Figure 1 shows the principle of GPS positioning for derivation of the user's position coordinates.
The satellite's coordinates ([X.sub.i], [Y.sub.i], [Z.sub.i]), the geometrical distance [[rho].sub.i], the propagation time [tau]+[DELTA][tau] measured by the receiver, the delay error [DELTA][tau] in the receiver clock and other elements, and the speed of light [C.sub.0] are related by the Pythagorean theorem as shown in Equation (1). The right side of Equation (1) shows the algebraic sum that includes the geometrical distance and the delay error of the clock in the receiver ([[rho].sub.i]+[C.sub.0][DELTA][tau]), which is known as the pseudorange.
In order to use GPS to derive the positional accuracy, therefore, it is important to make an accurate measurement of the pseudorange.
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
Derivation of Positional Accuracy Using a GPS Receiver
The correlator shown in Fig. 2 is used in deriving the actual positional accuracy. This correlator uses a replica (early) signal with a slightly advanced phase and a replica (late) signal with its phase slightly delayed to measure the correlation with the received GPS signal. If the reception signal is acquired, the early correlator captures where the correlation function goes high and the late correlator captures where the correlation function goes low. Figure 3 shows the correlation waveform when a direct wave is received.
Figure 4 shows the correlation waveform when a direct wave and a reflected wave are received. The delay error when a Multipath wave is received corresponds to the difference (the pseudorange error) between the correlation peak (vertical axis) generated by the direct wave alone and the center point of the correlator spacing (the spacing between the late correlation waveform and the early correlation waveform). The correlator spacing can be assigned as an arbitrary parameter.
The correlation waveform (red line) of the multipath wave is distorted by comparison with the waveform of the direct wave (blue triangle).
GPS Positioning Error
The error factors  that determine GPS positioning accuracy are enumerated below.
1. Satellite clock modeling error
2. Error in ephemeris prediction value
3. Error related to ionospheric delay
4. Error related to tropo spheric delay
5. General multipath error
6. Error related to receiver noise
The aggregation of these error factors is referred to as user equivalent range error (UERE), which is defined as the square root of the sum of the squares of each error component.
Positioning accuracy is improved using correction information and reliability information from the satellite-based augmentation system (SBAS). Table 1 shows the magnitude of the error factors in the case when SBAS is not used (point positioning) and in the case when it is
used, together with the UERE. The magnitude of error is la (a is the standard deviation of the positional accuracy). When simulation is used to perform the positioning calculation, the UERE shown in Table 1 is added to the pseudorange obtained by that calculation.
METHOD USED IN THE PRESENT STUDY
The previously reported comparative data for positional accuracy using simulation and actual measurement had issues like the following:
1. Since a high-accuracy positioning system that acquires a reference position for the test vehicle is not used, the reference positions for the vehicle while in movement are not accurate. For this reason, the reference coordinates for the simulation and the actual measurement do not agree.
2. The only condition that can realize agreement between the simulation and the actual measurement is the use of Coordinated Universal Time (UTC). The positioning satellite used in the simulation and the positioning satellite used in the actual measurement will not necessarily agree. In other words, the various positioning differ in their dilution of precision (DOP).
Consequently, the positioning conditions for the simulation and actual measurement do not agree, and the validity of the positional accuracy in simulation could not be verified by actual measurement.
For the present study, the issues were resolved by the method described in the following section.
Method Used in the Present Study
Figure 5 shows the component elements of the present study.
a. Test vehicle component equipped with high-accuracy position measurement system
b. Simulation component using ray tracing method
c. Actual measurement component using high-sensitivity GPS receiver
The respective items of UTC navigation data transmitted by all the satellites and the reference position of the test vehicle while driving are registered in the test vehicle recorder.
In the simulation, the test vehicle reference position, the satellite orbital information, and the 3D map are used with the ray tracing method to estimate the position of the driving vehicle at each UTC time. At the same time, a list of satellite catalog numbers is created for each UTC time used to estimate position, and a list of incoming wave states (presence or absence of direct wave, reflected wave and diffracted wave) at the reception points is created.
The receiver used for actual measurement cross-references the navigation data sent from (a) with the list of satellite catalog numbers at each UTC time sent from (b). Only the satellite numbers that are the same as those in the simulation are then extracted and the test vehicle reference position at each UTC time is used to perform the positioning calculation.
Configuration of Test Vehicle Using a High-Accuracy Position measurement System
A test vehicle was equipped with a POS LV 520 (hereafter, POSLV) high-accuracy position measurement system, which performed high-accuracy detection of the test vehicle position while driving. The unit was set up so that the center of the vehicle roof would always be the origin for the reference coordinates.
Figure 6 shows the test vehicle equipped with a high-accuracy position measurement system.
This system is made up of a high-accuracy three-axis gyroscope sensor and a Real Time Kinematic (RTK) system. The POSLV positioning accuracy is X=[+ or -]12 cm, Y[+ or -]12 cm.
The test vehicle position obtained as a reference with the POSLV is registered by the recorder with the UTC time. At the same time, navigation data acquired with a commercially available GPS receiver is also registered by the recorder. All the data registered in the recorder is used to make an off-line calculation of the positional accuracy of the commercially available GPS receiver with respect to the reference position of the test vehicle.
The POSLV uses the RTK system, which is capable of high-accuracy positioning in real time. Specifically, it uses the carrier wave phase together with the two frequencies sent from the GPS ([L.sub.1] 1575.42 MHz and [L.sub.2]: 1227.60 MHz) and received simultaneously in order to reduce the ionospheric delay error. Consequently, the following conditions are required of the antenna when the POSLV is installed on a vehicle.
1. Use an antenna configured for both the [L.sub.1] and [L.sub.2] frequencies.
2. Two sets of the above two-frequency antenna are used to accurately detect the phase difference in the radio waves. Therefore it is necessary to place the antennas as far apart as possible.
According to the above antenna conditions, the two-frequency ([L.sub.1] and [L.sub.2]) antenna sets were placed at the left and right edges of the vehicle roof, as shown in Figure 7.
The commercially available GPS unit is a system that uses only the Lj frequency, so a commercially available patch antenna was used. Also, since the center of the vehicle roof was defined as the reference for the test vehicle position, the commercially available GPS antenna that is the object of positioning was placed at the center of the roof and positioning error relative to the reference point was measured by simulation and actual measurement.
There are various systems of notation for positioning accuracy . The median (50% value) of horizontal error is called the circular error probable (CEP). This is defined as the radius of a circle, of which the center is the true position, and for which there is a probability of 0.5 that the estimated position value is included within that circle. As shown in Fig. 8, the reference coordinates ([X.sub.0], [Y.sub.0]) that can be acquired by the POSLV were placed at the center of the test vehicle roof.
The difference between the position that can be acquired with the GPS antenna (X, Y) and the reference coordinates ([X.sub.0], [Y.sub.0]) shows the discrepancy between positions.
Estimation of Positional Accuracy Using the Ray Tracing Method
Estimating the position of the test vehicle at an arbitrary time using simulation requires satellite position coordinates derived from a satellite orbit model, a 3D map model for the area around the test vehicle position, a signal propagation model from the satellite to the reception point and other such information. The simulation model employed in this method can be described as follows.
1. Satellite orbit model: Keplerian orbital elements (YUMA, NORAD two-line element set) distributed on the Internet are used to calculate the orbit according to Kepler's model and estimate the satellite's position coordinates.
2. 3D map model: 3D building data from the Tokyo Reduced Scale 1/25,000 Topographic Map, which was created in 2004, was used. Flat surface positional accuracy is [+ or -]1.75 m. Vertical accuracy is 0.66 m.
3. Signal propagation model: The above 3D map model and the ray tracing method were applied to calculate the propagation route of the GPS signal from the satellite position to the reception point.
Reports on analysis of propagation routes using GPS signals have been published [5, 6, 7, 8]. These were used for reference.
Figure 9 is a figure illustrating the principle of a propagation route model for GPS signals from satellites received in an urban area. It is conceivable from this figure that the environment around the test vehicle may result in the incoming wave from a satellite being received directly, for example, or being reflected from a building or other structure, or being diffracted by the edge of a building or other structure, or being a combination of various of these incoming waves.
When using simulation, therefore, it becomes important to determine the reception state of the incoming wave at the reception point.
When determining whether a wave is reflected, the propagation distance of a direct wave from a visible satellite to the reception point is taken as the reference, and the propagation distance of an arbitrary incoming wave that arrives at the reception point together with its signal strength are used to decide whether or not it includes a reflected wave. Actual signals are multiple reflections. After a second reflection, however, the attenuation of the signal is so great that it has little influence on positional accuracy. It was therefore assumed that only one reflection occurs and that the signal attenuation is 30% .
Determination as to whether a wave is diffracted uses the knife-edge effect, whereby a portion of the incident wave strikes the edge of a building or other such structure and is diffracted . There are visible satellites for which just a slight change in the angle of elevation of the line of sight (LoS) can make the satellite invisible, and conversely, there are invisible satellites that are made visible, and an incoming wave of either type is defined as a diffracted wave. In order to investigate the reception state (direct wave, reflected wave, diffracted wave, etc.) of the wave from a satellite, the buildings within a 300 m radius from the receiving vehicle were made objects of analysis.
Environment of Route Driven for Positioning and UTC Time Table
Nishi-Shinjuku was chosen for the route because of the high probability that satellite signals would become multipath waves or would be shielded because of high buildings in the surroundings. Positional accuracy was estimated using simulation and was actually measured on repeated test drives.
Figure 10 shows the test drive route (the red line) and UTC time table that was used to synchronize the simulation and actual measurement times.
Figure 11 shows the appearance of the buildings in the area according to the 3D map together with the route driven (the yellow line).
The route driven was a total of approximately 3 km in length and has many tall buildings along the way. Driving one circuit takes an average of approximately 10 minutes, and from beginning to end, the test drive took 5 hours and 22 minutes. The driving test using a test vehicle was arranged so that the vehicle speed would be generally constant.
POSITIONAL ACCURACY ESTIMATION RESULTS BY THE CONVENTIONAL METHOD AND THE PRESENT METHOD
The conventional method described in section 4 and the method of the present study was used to estimate the positional ratio and positional accuracy in the Nishi-Shinjuku test environment by simulation and by actual measurement. The results were as follows.
In order to make a quantitative comparison of the conventional method and current method of obtaining the positional ratio and positional accuracy, the following conditions (1) and (2) were set up.
1. Correction relating to positional accuracy is not applied using vehicle speed and other such information.
2. Incoming waves with an angle of elevation of 10 degrees or less are deleted by processing with an elevation mask angle.
The positional ratio (1) and positional accuracy (2) were compared by simulation and actual measurement.
1. Positional ratio: The rate at which the number of satellites
needed for positioning can be captured within the time interval (called the epoch) when GPS data is recorded.
Ordinarily, the epoch is about 15 to 60 seconds.
2. Positional accuracy: The relative frequency distribution was derived from all of the positional accuracy data from six circuits based on the driven route shown in Fig. 10 together with the UTC.
The standard deviation a of this relative frequency distribution was designated the positional accuracy.
Estimating Positional Ratio and Positional Accuracy Using the Conventional Method
The simulation and actual measurement of the positional ratio and positional accuracy were compared using the conventional method under conditions (1) and (2) above together with the UTC in Fig. 10. Table 2 shows a comparison of the simulation and actual measurement of the positional ratio and positional accuracy. The simulation was assumed to receive incoming waves from all the positioning satellites. For the actual measurement, the figures that have conventionally been used for carrier power-to-noise density (C/[N.sub.0]) per 1 Hz were used and the threshold value for reception sensitivity was divided into 20, 25, 30 and 35 dB-Hz.
The positional ratio in Table 2 was 99.3% in the simulation and 92% or more in actual measurement (except where C/[N.sub.0]>35 dB-Hz). Therefore the simulation and actual measurement generally coincide. The reason that the positional ratio is smaller in the actual measurement where C/[N.sub.0]>35 dB-Hz is that although the simulation included incoming waves from all the satellites, the actual measurement excludes satellites with signals received at low sensitivity, and the number of satellites is smaller as a result. The other C/[N.sub.0] instances are for reception at high sensitivity to ensure a sufficient number of satellites for measurement.
The positional accuracy in Table 2 shows that simulation and actual measurement do not coincide for all C/[N.sub.0]. However, where C/[N.sub.0]>35 dB-Hz, the positional accuracy is better than at the other C/[N.sub.0] figures. The reason for this is that at C/[N.sub.0]>35 dB-Hz, the multipath satellites that are a factor degrading positional accuracy have been excluded.
With the conventional method, which delimits the C/[N.sub.0] figures and changes the reception sensitivity threshold figures, the validity of the simulation cannot be verified through actual measurement.
In addition, 16 circuits were made of the Nishi-Shinjuku test course, at an average time of approximately 30 minutes per circuit, for a total of approximately eight hours of actual measurement data on positional ratio and positional accuracy over extended periods of time. Analysis using the conventional method produced the same tendency shown in Table 2.
With the conventional method, the positional ratio and positional accuracy estimated using simulation cannot have their validity verified by actual measurement.
Estimating Positional Ratio and Positional Accuracy Using the Present Method
In the method of the present study, the simulations and actual measurements for the propagation paths from the satellites to the receiver are caused to match. The simulation makes a determination as to whether the incoming waves include multipath waves or not.
Table 3 shows the results for the reception state of incoming waves from each satellite derived by simulation based on the test course and UTC in Fig. 10. The reception state for incoming waves from each satellite changes by the second.
Next, simulation was used to extract the numbers of the positioning satellite for which the incoming waves at the UTC times in Fig. 10 had a reception state of (1) direct wave or (2) direct wave combined with reflected wave. These were then used to derive the positional accuracy.
The same conditions described above were also applied to actual measurement, and only the numbers of the same positioning satellites as in the simulation were extracted. The receiver was then used to derive the positional accuracy.
Table 4 shows a comparison of the simulation and actual measurement at the same UTC times for the positional ratio when the incoming waves are limited to (1) direct waves or (2) direct waves combined with reflected waves, and for the positional accuracy of the X axis (the lateral direction of the vehicle) and the Y axis (the direction of the vehicle's movement).
For the positional ratio, the simulation and actual measurement values coincide. The reason for this is that making the positioning satellite numbers agree causes the number of positioning satellites to generally agree. However, the positional ratios are both low, ranging from 60% to 69%. The reason for this is that limiting the incoming waves from all the satellites to (1) direct waves and (2) direct waves combined with reflected waves reduced the number of positioning satellites.
The simulation and actual measurement values also coincide for positional accuracy. The reason for this is that making the positioning satellite numbers agree also causes the propagation characteristics from the satellites to the reception point, the DOP, and other factors to generally coincide.
Next, the difference between simulation and actual measurement with regard to positional accuracy in the X-axis and Y-axis directions was investigated.
The difference between simulation and actual measurement in the X-axis direction was +0.5 m, and similarly in the Y-axis direction it was +2.4 m. Positional accuracy in the Y-axis direction is greater than in the X-axis direction. In urban areas like the present test course, the heights of the surrounding buildings as seen from the vehicle are not uniform but asymmetrical. Consequently, the directions of the incoming waves that are reflected from buildings and other structures are not uniform but rather uneven, and they will also vary with the course chosen. Notation of positioning accuracy using the X axis and Y axis on a course in an urban area clearly shows that positional accuracy differs according to course selection, and it is therefore more effective than CEP.
The method of the present study was the first to succeed in making the simulation and actual measurements match.
Figure 12(a) shows the relative frequency distribution of positional accuracy in the X-axis direction as shown in Table 4. The class interval is 5 m.
Figure 12(b) shows the relative frequency distribution of positional accuracy in the Y-axis direction as shown in Table 4. The class interval is 5 m.
The relative frequency distributions of positional accuracy in simulation and actual measurement match.
Table 5 shows a comparison of the simulation and actual measurement figures for the positional ratio and for the positional accuracy in the X-axis and Y-axis directions at the same UTC times in the case of incoming waves that are (1) direct wave, (2) direct wave combined with reflected wave, (3) direct wave combined with diffracted wave, (4) reflected wave and (5) diffracted wave.
The positional ratio figures in Table 5 are 90% or higher for simulation and actual measurement. This is greatly improved from the positional ratio in Table 4. The reason for this is that the incoming waves of Table 4 have been augmented here by the cases of (3) direct wave combined with diffracted wave, (4) reflected wave and (5) diffracted wave, and the number of positioning satellites has increased as a result. The positional accuracy in Table 5 shows much lower figures than in Table 4. The reason for this can be explained as follows.
Figure 13(a) shows the relative frequency distribution of positional accuracy in the X-axis direction as given in Table 5. The class interval is 5 m. Figure 13(b) shows the relative frequency distribution of positional accuracy in the Y-axis direction as given in Table 5. The class interval is 5 m.
In Fig. 13, the maximum values for the relative frequency distribution in the X-axis and Y-axis directions are smaller than the figures in Fig. 12, and the positional accuracy has diminished. The reason for this is that the incoming waves of Fig. 12 have been augmented here by the cases of (3) direct wave combined with diffracted wave, (4) reflected wave and (5) diffracted wave, and the number of multipath waves has increased as a result.
The reason that the simulation and actual measurement do not match has to do with the difficulty of creating a simulation model for diffracted waves in urban areas.
The creation of a diffracted wave model that incorporates the urban environment exactly requires accurate calculation of the elevation of the edge along the upper part of buildings using 3D maps. It also requires accurate calculation of the length of the path from the edge along the upper part of buildings to the vehicle-mounted GPS receiver on the roadway.
These quantities cannot be readily calculated with accuracy, however, because they are influenced by the position of the vehicle on the roadway, the slope of the roadway, the width of the roadway, the relative positioning of the vehicle and the satellite and other such factors. Furthermore, actual urban environments have elevated tracks and other such structures, overpasses and underpasses, tunnels, roadside trees and other such environmental conditions that cannot readily be read with accuracy using current 3D maps.
Going forward, the creation of a diffracted wave simulation model that takes these considerations into account is an issue for the future. In the present study, positioning used only the pseudorange, so that the accuracy of the standard deviation and so on was poor. However, the difference between the simulation and actual measurement figures was reduced, and this makes it possible to estimate positional ratio and positional accuracy in a variety of different regions by the use of simulation alone.
Positional accuracy in an urban area was estimated by means of simulation over an extended period. The validity of the simulation was shown by means of actual measurement, and the effectiveness and superiority of the proposed method were clarified.
Achieving simultaneous improvement of positional ratio and positional accuracy will require more than just increasing the number of positioning satellites, which is insufficient. It will also be necessary to increase the number of positioning satellites from which direct waves can be received.
It is anticipated that future integration of the satellite systems belonging to different countries will be accompanied by widespread popularization of navigation systems in various regions. Development of the method proposed here will probably make it possible, after satellite systems have been integrated in the future, to estimate positional ratio and positional accuracy in a variety of regions using simulation alone, in place of field operational testing.
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The generous and significant assistance regarding simulation provided by Professor Ryosuke Shibasaki of the University of Tokyo and Dr. Yang-Won Lee of Pukyong National University is acknowledged with gratitude.
Satoru Komatsu and Akira Nagao
Honda R&D Co., Ltd.
Waseda Institute for Advance Study
Table 1. Measurement error factor and error magnitude Magnitude of Magnitude of error without error using using SBAS (m) SBAS (m) 1. Satellite clock 2 0 2. Ephemeris prediction value 2 0.1 3. Ionosperic delay 4 0.2 4. Tropospheric delay 0.5 0.2 5. Multipath 0.5 0.5 6. Receiver noise 0.25 0.25 UERE (rss) 5 0.64 Source:  Table 2. Comparison of simulation and measurement figures for positional ratio and positional accuracy Magnitude of Magnitude of error without error using using SBAS (m) SBAS (m) 1. Satellite clock 2 0 2. Ephemeris prediction value 2 0.1 3. Ionosperic delay 4 0.2 4. Tropospheric delay 0.5 0.2 5. Multipath 0.5 0.5 6. Receiver noise 0.25 0.25 UERE (rss) 5 0.64 Conditions of reception Positional ratio Simulation All GPS satellite reception 99.3 C/[N.sub.0]>20 (dB-Hz) 97.4 Measured C/[N.sub.0]>25 (dB-Hz) 96.6 C/[N.sub.0]>30 (dB-Hz) 92.0 C/[N.sub.0]>35 (dB-Hz) 76.6 Table 3. Change in incoming wave from each GPS satellite for UTC changing by the second in simulation UTC Satelite number 5 9 12 15 18 21 26 27 28 6:31:37 (3) (1) (2) (1) (1) (1) (3) (1) (3) 6:312:38 (3) (1) (2) (1) (1) (1) (3) (1) (5) 6:31:39 (3) (1) (3) (1) (1) (1) (3) (1) (4) Conditions of incoming wave: (1) Direct wave, (2) Direct wave + Reflected wave (3) Direct wave + Diffractive wave, (4) Reflected wave, (5) Diffractive wave Table 4. Comparison of simulation and measurement figure for positional ratio and positional accuracy for incoming wave (1) and (2) Conditions of Positional Positional accuracy incoming wave ratio (%) [+ or -] X (m) (1), (2) Simulation 68.5 14.8 Measured 61.8 15.3 Conditions of incoming wave [+ or -] Y (m) (1), (2) 11.7 14.1 Conditions of incoming wave: (1) Direct wave, (2) Direct wave + Reflected wave Table 5. Comparison of positional ratio and positioning accuracy figures from simulation and measurement Conditions of Positional incoming wave ratio (%) (1), (2), (3), (4), (5) Simulation 99.3 Measured 91.7 Conditions of Positional accuracy incoming wave [+ or -] X (m) [+ or -] Y (m) (1), (2), (3), (4), (5) 24.6 22.8 45.3 40.4 Conditions of incoming wave: (1) Direct wave, (2) Direct wave + Reflected wave (3) Direct wave + Diffractive wave (4) Reflected wave, (5) Diffractive wave
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|Author:||Komatsu, Satoru; Nagao, Akira; Suzuki, Taro; Kubo, Nobuaki|
|Publication:||SAE International Journal of Passenger Cars - Electronic and Electrical Systems|
|Date:||May 1, 2016|
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