The Study of Position Accuracy Using Precise Point Positioning (PPP) In Perspective of Indonesian National Standard of Horizontal Reference Network

. Precise point positioning is a GNSS based positioning method that is known to regaining more precise information about major systematical errors in its functional model. This method is seen as an advanced version of the conventional absolute positioning method that is able to offer higher accuracy of the estimate parameter. Contrarily, the relative positioning method is able to achieve high precise of the estimated parameters by using two or more receiver. Consequently, it utilizes more resources in performing observation. Hence, this contribution attempts to explore some considerable aspects that can make the PPP method has a comparable precision of the National Standard of Horizontal Reference Network (SNI JKH). Based on the experiments, with data rate of 0.03 Hz for GPS and GLONASS observation shown that result of the PPP method is comparable to the relative method, whenever the observation is performed in minimum duration of six hours. Moreover, the 3th order of accuracy can be achieved after a demanding observation period, depends on processing strategy.


Introduction
Precise point positioning (PPP) is an advanced version of the conventional GNSS-based absolute positioning. The method regains more precise information about systematical errors in its functional model, so that it can offer higher accuracy of the estimate parameter more than the absolute positioning. The quality of PPP method depends on its ability to eliminate the observation related errors. This contribution focuses on the minimum observational duration that is required to fulfill a certain level of accuracy standard. Consequently, the accuracy standard demands particular information about specific orbit products.
Relative positioning method requires more effort by using two or more receivers with one of receiver acting as a reference station. This method eliminates the observation errors with double difference technique. Relative positioning method quality depends on the distance between receivers. In case of PPP, direct usage of reference station is no longer needed, so that the spatial operating range limit is no longer exist, hence the coverage is global [6].
The experiments expect to fulfill the 3th order of the Indonesia National Standard of horizontal reference network (SNI JKH). Furthermore, this contribution attempts to investigate some considerable aspects that can make accuracy of the PPP method is comparable to the accuracy of relative positioning method.

Precise Point Positioning versus relative positioning
PPP method uses only one receiver without respecting to reference station. It makes common mode errors do not cancel in PPP [3], such as orbital error, tropospheric delay, ionospheric delay, multipath, satellite clock error and receiver clock error. The absolute observation model using pseudorange and phase range data, expressed by the following equations: Where * is the superscript identifying satellite s, * is the subscript identifying receiver r, * , is the subscript identifying the L1 or L2 frequency, , ( ) is the orbital error (m), ( ) is the tropospheric delay (m), , ( ) is the ionospheric delay (m), , ( ) is the multipath (m), ɸ , ( 0 ) is the receiver initial phase at t0 (cycle), ɸ , ( 0 ) is the satellite initial phase at t0 (cycle), , ( ) is the Pseudorange noise (cycle), and ԑ , ( ) is the Phase noise (cycle) In PPP method, utilizing precise product from IGS can eliminate the observational error. Moreover, the duration of observation can affect the result. In this contribution we assume that the observations are multipath free. Ionospheric delay can be eliminated by utilizing the ionospheric-free linear, while tropospheric delay can be eliminated by using troposphere model like saastamoinen. Utilizing precise clock product from IGS can eliminate of satellite and receiver clock errors, and using precise orbit from IGS can reduce the orbital error.
On the other side, the relative positioning method uses two or more receivers. This method requires simultaneous observations at both receivers to determine the coordinates of an unknown point with respect to a known point [2]. Assuming such simultaneous observation at the two points A and B to satellites j and k, linear combination can be formed leading to single difference, double difference, and triple difference. For example, the double difference model can be expressed with [2]: , ( ) = , ( ) + , ( ) + , + ԑ , ( ) (4) By using the double difference technique, common errors can be eliminated. However, quality of the result of relative method depends on the distance between receivers. Based on SNI JKH, relative method can be performed with a maximum distance of 20 km length (short baseline) between receivers, with the absence of the tropospheric and ionospheric influences.

The experiment of PPP
The observation was using two points with the approximately distance of 8.5 kilometers length; which is short baseline. The reason to use short baseline is for good quality result of the relative method. Therefore, this study attempts to investigate some aspects that can make accuracy of the PPP method is comparable to the relative method.
One station is acting as reference station, CLBG, which is located at Lembang. Another station is acting as rover, ITN1, which is located at Itenas. The CLBG station is a CORS maintained by Badan Informasi Geospasial. Observation was held for 48 hours duration. Station position was obtained using goGPS and RTKLIB. Accuracy of position of each method is based on the standard deviation and the error ellipse parameters. The order of position is defined by horizontal error ellipse parameters. To define the PPP method order, it has to do some procedure.
The order of relative method must be defined by defining the 3rd order position based on SNI JKH from the relative error ellipse perspective, and its corresponding absolute error ellipse. The PPP method order can be achieved by comparing the absolute error ellipse of PPP method and relative method. This procedure purposes to define the quality of position accuracy from PPP process by referring to the absolute error ellipse, which corresponds to the SNI standard.

Fig 1. Location of two CORS used in the experiment
The observation was held in two days with phase and pseudorange data. Technical specification of each station is shown in Table 1. From the observation with 10 degree of mask angle and 0.03Hz of data rate, obtained the number of satellite, PDOP, and GDOP that is shown in Fig. 2. From Nsat graphic in Fig. 2 shown that station of ITN1 receive more satellite signal than CLBG station. It makes each of stations have different value of PDOP and GDOP, where the lowest value of GDOP is 1.1 and the highest value is 2.2 at ITN1, while the CLBG has the lowest value of GDOP is 1.2 and the highest value is 4.0. Each stations are on acceptable condition as the average of GDOP value is smaller than 5 [5].   Fig. 3 shown that the observation at ITN1 station is normally distributed. The observation with carrier phase is more accurate than pseudorange, it can be seen from the class interval of carrier phase is every 5 cm and pseudorange is 2 m.
The observation at CLBG station is also normally distributed. It is similar with ITN1 station that carrier phase observation is more accurate than pseudorange. The class interval of carrier phase observation is 5 cm while at pseudorange observation is 5 m. This also shows that the observation on ITN1 is better than CLBG.   The coordinates differences between the product from PPP processing method and the known point can be seen at CLBG station. The known point of CLBG station refers to report from BIG. In this case, PPP method has three different results by utilizing three precise orbit products (IGS final, IGS rapid, and IGS ultra-rapid). Fig.7 shows the coordinates difference between PPP product and known point that using RTKLIB software. It shows that the using of IGS final and IGS rapid product gives more convergence than the IGS ultra products by 6 hours duration of observation.  The coordinates difference figure shows that the vertical position difference is less convergent than horizontal [2]. Coordinates difference between PPP and relative positioning method can be seen at ITN1 station. The result of relative positioning on ITN1 station is referring to CLBG station. Relative Method Fig.9 shows that coordinate difference between the PPP against the relative method is going to be convergent after 2 hours duration of observation for North component. Coordinates difference for East and Up components is not good as North component.

Standard deviations
Standard deviations of precise products are also can be seen in this station. Standard deviation comparisons between IGS Final, IGS Rapid, and IGS Ultra-rapid products are shown in Fig.10.   Fig.11 Standard deviation of precise product on CLBG station Fig.10 shows that the using of goGPS is more accurate than RTKLIB. Standard deviation from goGPS software is in millimeter level after 3 hours duration of observation, yet the standard deviation from RTKLIB is still in centimeter level. The Standard deviation of RTKLIB is in millimeter level after 36 hours duration of observation. The difference between goGPS and RTKLIB standard deviation after convergence is 7 mm for East and North components, and 10 mm for Up component. The using of precise product IGS final and IGS rapid gives a very small difference of standard deviation for both softwares.
Comparison of standard deviation between PPP and relative positioning method can be seen on ITN1 station. The relative positioning method is computed for ITN1 by taking CLBG as the master station.

Classification of horizontal reference point network
The classification depends on the relative error ellipse. Relative error ellipse can be obtained only in relative positioning method. Hence, the horizontal position order of PPP method is assumed by regarding absolute error ellipse from relative positioning that has been accepted in 3 rd order of horizontal position.
Based on SNI JKH, the 3 rd order of horizontal position can be achieve by regarding on empiric value of 30 ppm. By the distance between CLBG and ITN1 station of 8.41 km length and 30 ppm of empiric value, the maximum semi-major axis (r) can be achieved by r = c (d +0.2) r = 30 (8.41 + 0.2) (5) r = 258.291 mm = 25.83 cm Calculating of equation 5, maximum value of semimajor axis is 25.83 cm, then the 3 rd order of horizontal position can be achieved after value of semi major-axis of relative error ellipse is less than 25.83 cm. The semimajor axis value of relative error ellipse is shown at Table.2 By referring to SNI JKH and technical specification, the 3 rd order can be reached after 1 hours duration of observation. The absolute error ellipse parameters of relative positioning method after 1 hours duration of observation are a = 0.0116 m, b = 0.0043 m, and θ = 17˚ 40' 55.55". If the absolute error ellipse of PPP method is lower than the value above, it means that the PPP method reaches the 3 rd order of horizontal position.
The semi major axis value of absolute error ellipse for PPP method with 1 hour observation of relative positioning method is shown by Fig.13.   Fig.13 Semi major axis of absolute error ellipse Fig.13 implies that longer observation period causes the absolute error ellipse is getting smaller. By assuming the position of absolute error ellipses is at the same position, the comparison of both methods can be seen (Fig.14). Based on the experiments, the 3 rd order of horizontal position accuracy for PPP method can be achieved by using goGPS within 1.5 hours duration of observation, or by using RTKLIB within 22 hours duration of observation. In the case of time efficiency, the usage of goGPS gives more effective time than RTKLIB. It is possible to have different result for using other softwares. The value of absolute error ellipse parameters by using goGPS is 0.0102 m for semi-major axis, 0.0026 m for semi-minor axis, and 13˚54'58.86" for azimuth angle. The value of absolute error ellipse parameters by using RTKLIB is 0.0102 m for semi-major axis, 0.0026 m for semi-minor axis, and 13˚54'58.86" for azimuth angle.