Long-range Single Baseline RTK GNSS Positioning for Land Cadastral Survey Mapping

. In Indonesia, Global Navigation Satellite System (GNSS) has become one of the important tool in survey mapping, especially for cadastral purposes like land registration by using Real Time Kinematic (RTK) GNSS positioning method. The conventional RTK GNSS positioning method ensure high accuracy GNSS position solution (within several centimeters) for baseline less than 20 kilometers. The problems of resolving high accuracy position for a greater distance (more than 50 kilometers) becomes greater challenge. In longer baseline, atmospheric delays is a critical factor that influenced the positioning accuracy. In order to reduce the error, a modified LAMBDA ambiguity resolution, atmospheric correction and modified kalman filter were used in this research. Thus, this research aims to investigate the accuracy of estimated position and area in respect with short baseline RTK and differential GNSS position solution by using NAVCOM SF-3040. The results indicate that the long-range single baseline RTK accuracy vary from several centimeters to decimeters due to unresolved biases.

In Indonesia, GNSS is mostly used in surveying and mapping purposes, especially for cadastral purposes like land registration by using Real Time Kinematic (RTK) GNSS positioning method [13][14][15]. RTK GNSS ensure the high accuracy in point determination, however, in conventional RTK GNSS the high accuracy can only be obtained for baseline less than 20 kilometers [16]. For medium to long baseline RTK GNSS, the atmospheric bias is considered as the dominant factor which lead into unresolved ambiguity resolution. Consider GNSS signal travelling from a satellite to two receivers that are in a distant, the signal would be subjected to a different atmospheric effects. Several approaches have been proposed to mitigate the atmospheric bias [17][18]. Network RTK is also considered to mitigate the atmospheric bias [19].
It has been found that atmospheric bias affect more error in vertical component rather than in horizontal component which up to several decimeters in RTK GNSS positioning [20,21]. Fig. 1 shows the comparison of code absolute method positioning error using corrected pseudorange and uncorrected pseudorange. It could be seen that the deviation could vary up to 20 meters in vertical component. The corrected terms indicate the used of troposphere and ionosphere model. Red dots indicate when no atmospheric correction was applied on the data, while blue dots indicate when atmospheric correction was applied on the data Thus, several researches has stated that orbital error [22] and satellite clock error [23] also indicate as the problems in GNSS-based positioning system. The orbital trajectory of GNSS satellites disturbed by surrounding environments e.g. the Earth's gravity, the attraction of the sun and the moon and as well as solar radiation, while the satellite clocks are subject to relativistic effects. The GNSS satellite clock tends to run faster than the clocks in the receivers. In a relatively short baseline, the double difference (DD) observations could reduce and eliminate both of orbital and clock satellite error, however, for a far baseline orbital and clock satellite error still contained on the data observation. The connection between baseline length, observing time and rms accuracy were summarize in Fig.  3. Fig. 3. Accuracy of GNSS static in cm and its correlation with the baseline length and observing time when using broadcast orbit and precise orbit [22] In this research, a relatively new algorithm [23] was used to enhance the RTK GNSS accuracy in a long baseline for land cadastral survey mapping. This method used a modified LAMBDA method which can be separated into several aspects e.g. modified functional model to estimate the atmospheric bias, the usage of precise orbit correction from WADGPS, a modified Kalman filter and a partial search and ambiguity fixing strategies.

Data
Base station was established at the rooftop building. Bandung, Indonesia, while the land cadastral survey mapping were simulated on three land parcels in Pamengpeuk, Indonesia which located for about 85 kilometers away from the base station and has significant height differences for about 800 meters. Eight benchmarks were also used to assess the performance of the algorithm. In general, to assess the performance of the algorithm, the long-range RTK coordinate results were then compared with a priori coordinates. The term a priori coordinate refers to reference coordinate based on static differential observation method or shorter baseline RTK GNSS method.

Basic Concept
This section describe the general concept in RTK GNSS method and the Kalman filter design to enhance the accuracy of RTK GNSS in long-range baseline.

Observation Models in RTK
The observation model for code and carrier phase measurement are described as follows: where: ( ) is the measured pseudorange on Li frequency (i = 1, 2) ( ) is the measured carrier phase on Li frequency is the true geometric range is the satellite orbital error is the tropospheric error is the ionospheric error is the speed of light is the satellite clock error is the receiver clock error is the multipath effect on measured code is the multipath effect on measured phase is the noise DD then performed to eliminate the orbital error, clock error and atmospheric error in short baseline. The DD (∆∇) observation model for code and carrier phase measurement can be described as follows: Linearization of the DD observation then can be represented as follows: where V is the residual matrix, A is the design matrix. L is the observation data and X is the estimated parameters containing three baseline components and ambiguities. In a longer baseline the estimated parameters including residual ionospheric bias and residual tropospheric bias.

General Kalman Filter System Design
Kalman filter predicts the a priori parameters using the recent estimate of the observation data. The prediction is based on some assumed model for how the parameters changes in time [24,25]. The dynamic model on Kalman filter can be represented as follows: which then continued along with measurement model, where: Φ is the transition matrix (k = epoch) is the noise from the dynamic model is the noise from the observation data Kalman filter also applied recursive least square which then can be defined into two main parts as follows [26]: where: is the gain matrix is the covariance matrix observation model I is the identity matrix is the prediction from previous epoch is the covariance matrix for dynamic model is the weighting matrix The estimated parameter is summarized in Table 1.

Precise Satellite Ephemeris
As stated on the introduction, precise satellite ephemeris is needed in GNSS-based point positioning for a longer baseline. In static differential method, the precise satellite ephemeris can be easily obtained two weeks after the observation is done. However, in conventional RTK such a precise ephemeris cannot be obtained. Several researches indicate that the satellite's position error might vary up to 5 meters [22,27]. The satellite's position error is generally the biggest error source after atmospheric bias is estimated in Kalman filter for long-range RTK.
Thus several GNSS industries have developed their own system to accommodate the use of precise satellite ephemeris. John Deere, as one of the GNSS industry has developed the StarFire TM system which transmits the needed data correction in near real-time using satellites communication.

Ambiguity Resolution
The ambiguities are considered as constant. However, due to remaining tropospheric and ionospheric biases, the ambiguities can be modeled as a random walk with very small dynamic noise, such as 0.001 cycle. Thus, the ambiguities are modeled as constants once the ambiguities are fixed. The use of these small dynamic noise is useful in resolving the ambiguities in several condition, such as bad site condition, excessive multipath, or the movement of receiver from a severe shading surrounding to the open sky surrounding.
In a longer baseline, the ambiguities are resolved improperly due to significant bias. [7] implemented the modified partial search technique to fixing the ambiguities. The ambiguity for the L1/L2 signal and its variance were first converted into L1/Wide Lane (WL) as described in following vector equation: The used of WL is important due to its wavelength characteristic. With 0.86 cm wavelength, WL's ambiguities are easy to resolve. If the ambiguities are resolved, the original L1 and L2 ambiguities and the variance-covariance in the Kalman filter can be recovered as follows:

Result and Discussion
Over 1840 epoch were collected within 23 point observations. Only resolved ambiguities data showed and considered in further analysis. Coordinates derived from differential static method were considered as reference coordinates in bench mark point, while coordinates derived from short baseline GNSS RTK method were used as reference coordinates in land parcel point. Short baseline GNSS RTK (under 3 km) was considered because in shorter baseline and in the open-sky condition (Fig. 6) the biases were assumed reduced or eliminated [28].  Accuracy   Fig 7. shows the overall accuracy for benchmark point, while Fig 8. shows the overall accuracy for land parcel point. The accuracy of long-baseline GNSS RTK in benchmark points were within 3 cm and only 1 point was slightly worse than the other, however still within RTK accuracy. The accuracy of long-baseline GNSS RTK in land parcel points were within 12 cm. It could be seen that there was a systematic compared with those for benchmark point. As mentioned before, coordinate estimated from short baseline RTK GNSS used to assess the accuracy of long baseline RTK GNSS in land parcel points. To evaluate the consistency of the used reference coordinate on all off the observation method, benchmark points were also observed using short baseline RTK GNSS.  Fig. 9. shows the overall accuracy for both short and long baseline GNSS RTK. It could be seen that there was a shift tendencies to South-East. It indicates that the system coordinate might be different.  Accuracy   Fig 10. shows the overall vertical accuracy for benchmark point, while Fig 11. shows the overall vertical accuracy for land parcel point. The accuracy of long-baseline GNSS RTK in benchmark points were within 15 cm and the accuracy of long-baseline GNSS RTK in land parcel points were vary from -20 cm to 15 cm. There is one point that indicates the unresolved bias. A linear trend of the up component is found on that point, there is also deviation in horizontal component as shown on Fig. 7. Further analysis is needed to explain this phenomenon.    Table 1. shows the overall precision for long baseline GNSS RTK. Precision indicated the repeatability of the estimated coordinate. Over 90% of estimated coordinate met the 95% of confidence interval as shown on Fig.13. This indicate that this algorithm is reliable to used.

Area Estimation
Government policy about land and building tax in Indonesia indicates that the errors tolerances is about 10%. Table.2. shows the differences in calculated area with the reference area, there is no significant differences between reference and calculated area. The deviation in under 0.05% for each area. This result indicates that the long baseline GNSS RTK algorithm can be used for land parcel mapping.

Conclusion
The algorithm gives significant improved in long-range single baseline GNSS RTK for up to 90 km. The accuracy vary from several centimeters to decimeters due to unresolved biases. For land cadastral purposes, the algorithm can be used as one of the method, the observed area shows no significant difference compared with the reference area.