Technical Literature. Leica System 1200 High Performance GNSS Technology for RTK Applications

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1 Leica System 00 High Performance GNSS Technology for RTK Applications September 006 Takac, F. and Walford, J. Technical Literature Takac, F. and Walford, J., (006), Leica System 00 High Performance GNSS Technology for RTK Applications, Proceedings of ION GNSS 006, September 6-9, Fort Worth, Texas.

2 Leica System 00 - High Performance GNSS Technology for RTK Applications Frank Takac and Justin Walford Leica Geosystems AG Heerbrugg, Switzerland ABSTRACT Leica s newly developed SmartTrack+ technology is designed to track all of the available GNSS positioning signals. SmartTrack+ is now available in the System 00 range of high performance GNSS sensors. Integrating GNSS technologies effectively increases satellite availability, redundancy and geometry. This paper discusses how these three elements can influence the productivity, reliability, precision and accuracy of RTK positioning. An analysis of real-time data collected using System 00 sensors illustrates the advantages of a combined GPS and GLONASS constellation in terms of positioning continuity, the time-to-fix ambiguities, the reliability of the ambiguity solution and the precision of the fixed position. INTRODUCTION Global Navigation Satellite System (GNSS) is the general term that describes satellite-based positioning technologies such as GPS, GLONASS and Galileo. GPS has been the system of choice for high-precision real-time kinematic (RTK) positioning applications for over a decade. In that time, the GPS system itself has changed very little apart from the discontinuation of selective availability in 000. However, GPS is currently undergoing modernization, which promises to further increase the effectiveness of the system for RTK applications. A major goal of the GPS modernization program is the addition of two new signals for civil use. The first is the LC code modulated on the existing L carrier frequency. The benefits of LC include higher signal power, faster signal acquisition and robustness compared to the L C/A signal (Leveson, 006). However, there is currently only one satellite on orbit broadcasting the new civil code. Furthermore, the U.S will not guarantee the availability or quality of this signal until initial operational capability (IOC). Nevertheless, the deployment schedule of LC is not expected to impact heavily on RTK positioning since state-of-the-art sensors already recover the code and phase measurements from the encrypted L signal using innovative signal processing techniques. The second addition to the signal structure is a third carrier frequency known as L5. For RTK applications, the availability of three carrier signals will have important advantages for ambiguity resolution and bias estimation such as multipath (Simsky, 006). The deployment of L5 is scheduled to begin in 008 with the launch of the first GPS Block IIF satellite (Leveson, 006). GPS is not the only GNSS currently broadcasting positioning signals to civilian users. GLONASS, developed by the Russian Federation, shares many similarities with its U.S counterpart. In 995, the system comprised 4 satellites; however, the constellation was not maintained due to a lack of funding. The turning point came in 00 via a government approved modernization program designed to restore the service (Polischuk et al., 00). Figure shows the constellation status and satellite deployment schedule. Figure. The GLONASS constellation deployment schedule (adapted from Dvorkin and Karutin, 006). A minimum constellation of 8 GLONASS is scheduled for deployment by 007. The full constellation of 4 satellites is planned for 009. At the time of writing (September 006), 6 GLONASS satellites were in orbit of which 5 were set healthy. Other milestones of the modernization program include an upgrade of the GLONASS ground segment and time keeping system to improve navigation accuracy and interoperability with GPS. In addition, a third carrier frequency will be introduced with the GLONASS-K satellite. The first GLONASS-K flight test is scheduled for 008 (Dvorkin and Karutin, 006).

3 The European Union (EU) is also developing an independent GNSS known as Galileo. The EU launched the first experimental satellite GIOVE A on 8th December 005. The launch is part of the development and validation phase of the Galileo program, which does not provide service functionality. According to the Commission of the European Communities (006), the full constellation of 30 satellites is scheduled for deployment between 008 and 00. Commercial operation will follow the deployment phase at the beginning of 0. Galileo will also broadcast on three carrier frequencies and be interoperable with GPS. This paper discusses the advantages of combining these GNSS technologies for RTK applications. It shows that a combined constellation can improve satellite availability, redundancy and geometry compared to the GPS constellation alone. In turn, these improvements can lead to gains in productivity, reliability, precision and accuracy. The paper tests this hypothesis using the new Leica System 00 sensors incorporating SmartTrack+ technology. This new technology is designed to track all the available GNSS positioning signals for high precision RTK positioning. WHY COMBINE GNSS TECHNOLOGIES? Essentially, combining GNSS technologies will effectively increase the number of available satellites for RTK positioning. For example, a nominal modernized GPS + modernized GLONASS + Galileo constellation will comprise 78 satellites. These extra satellites provide a level of redundancy not offered by the nominal constellation of 4 GPS satellites alone. This redundancy has some practical advantages for positioning that are well known from conventional adjustment theory. Redundant observations, especially from an independent source, are useful for detecting and rejecting poor quality measurements, which might otherwise lead to inaccurate position estimates. Furthermore, redundant measurements can also help to increase the precision of the solution. In order to understand how redundancy improves the performance of RTK positioning it is useful to reflect on the position estimation process itself. In real-time processing schemes, the precise coordinates of points of interest are usually obtained in three steps. The process starts with a linear functional model that relates the unknown parameters with the code and carrier phase observations in the form of: y = Aa+ Bb+ v () The vector a contains the integer ambiguities inherent in the carrier phase observations, b is a vector containing all other unknown parameters including the sought after coordinates, v is a vector of measurement residuals, A and B are the appropriate design matrices and y is a vector of observed minus computed measurement terms. The functional model is normally solved using the technique of least squares such that: φ= v T Q v min y where Q y is a covariance matrix describing the relative precisions and correlations of the observations. This initial step is commonly known as the float solution and it yields the real-valued estimates â and bˆ of the unknown parameters. In the second step, the float estimate â is used to solve the so-called integer least squares solution of the ambiguities such that: φ a = ( aˆ a) T a n () Q ˆ ( aˆ a) min, a Z (3) where Qa ˆ is the covariance matrix of the float ambiguity n estimate and Z is the global space of integers. The reader is referred to Teunissen (994) for a detailed description of the integer least squares process. Once the integer estimate of the ambiguities a ( has been found and verified, it remains valid provided that signal tracking is not interrupted. In the final step, the phase measurements are adjusted by the fixed ambiguities to yield precise unbiased ranges, which are subsequently applied to solve the fixed position solution denoted as b (. In this case, the functional model described in () reduces to: y Aa ( = Bb+ v (4) The sole purpose of ambiguity resolution is to increase, via the integer constraints, the precision of the position estimate. Although the ambiguity parameters are not interesting in their own right, their correct identification and verification is the key to precise RTK positioning. It should be evident from (3) that the precision of the float ambiguities described by Qa ˆ plays an important role in the integer least squares solution. In fact, a successful validation of the ambiguities cannot be expected when the precision is poor. Teunissen (997a) uses the ambiguity dilution of precision (ADOP) as a means of linking precision with the reliability of the integer solution. Q n a ˆ ADOP= (cycle) (5) The ADOP captures the precision the ambiguity cofactor matrix of order n through the determinant operator. A decrease in the ADOP implies a more precise estimate of the float ambiguities and a better chance of successfully validating the ambiguities. For short observation time spans the ADOP can be approximated by:

4 ADOP m ( m ) σ σ φ p m 4 4( m ) σφσ p kλλ (cycle) (6) The precision of the ambiguity estimate depends on the precision of the phase and codes observations denoted as σ φ and σ p respectively, the wavelengths of the L and L carriers λ and λ, and the number of epochs k. The ADOP also clearly shows the influence of the number of satellites m on the strength of float ambiguity estimate. As the number of satellites increase, the ADOP decreases. Figure. The precision of the float ambiguities (ADOP) increases as the number of redundant satellites increase ( σ = 3 mm, σ = 60 cm and k = ). φ p Note that the ADOP is only defined when m 4. In this case, the magnitude of the ADOP equals approximately a third of a cycle. However, Teunissen and Odijk (997) adopt 0. cycles as the threshold for an expected successful validation of the ambiguities. For short observation time spans, which is typically the case in real-time applications, the ADOP only falls below this threshold when m 5. In fact, the chance of success increases as the number of redundant satellites increase. The discussion on ADOP illustrates why satellite availability and redundancy are so important in RTK processing. Ambiguity resolution is not possible when the number of available satellites falls below the critical threshold, which implies that a precise fixed position will also not be available. In case there are a sufficient number of satellites, then any redundancy can increase the performance and reliability of the ambiguity resolution process. The instantaneous precision of the position estimate after ambiguity fixing is given by: T [ B Q ] y + σ Q( = B b (7) σ Proof: Following Teunissen (997b) pg. 35 and letting the number of epochs k =. position solution. An increase in the strength of the geometry is reflected as an increase in the precision of the position estimate. Unlike ADOP, increasing in the number of redundant satellites does not guarantee better geometry. However, in practice the improved satellite availability of a combined constellation coupled with different orbit configurations will often result in stronger receiversatellite geometry, especially in poor observing environments. This topic is examined further in the next section. It is important to mention that observations from independent systems such as GPS and GLONASS are heterogeneous. Combined observations are affected by differences in coordinate reference frames, time scales and signal frequencies as well as system dependent hardware biases (Takac et al, 005). The observation and stochastic models of a combined processing scheme must account for these dependencies to avoid introducing systematic biases into the position solution. As a result, the combined functional model will not always have the same degrees of freedom as the GPS only solution. That is, 8 combined satellites does not provide the same redundancy as 8 GPS satellites. This section has shown that the performance of RTK positioning is dependent on satellite availability, redundancy and geometry. The motive for combining GNSS technologies is to improve these dependent variables by increasing the number of satellites. Any such improvements will translate into improved position availability or productivity, reliability, precision and accuracy. The next sections examine the practical advantages of a combined GNSS constellation for RTK applications using the new Leica System 00 GNSS sensors. SATELLITE AVAILABILITY AND GEOMETRY In the future, Galileo and modernized GPS promise to improve the performance of RTK systems. However, these technologies will not be available before the end of the decade. Nevertheless, RTK users can already benefit from a combined GNSS satellite constellation comprising of 9 GPS and 6 GLONASS satellites. To illustrate the impact of combining these two technologies on satellite availability and geometry, 4 hours of real-time data was collected with a GX30 GG sensor in Heerbrugg, Switzerland. The sensor was connected to an AX0 GG geodetic antenna established with a relatively clear view of the sky. Figure 3 compares the cumulative satellite availability for the GPS, GLONASS and combined constellations. The precision depends not only on the standard deviation of the phase observations described by σ i but also on the receiver-satellite geometry captured in the design matrix B. Note that B is also an ( m ) 3 matrix, which implies that a minimum of four satellites is required to solve the

5 Figure 3. A comparison of the cumulative satellite availability for the GPS, GLONASS and combined constellations. Five GPS satellites were visible for approximately 98% of the test period. This period represents the time when RTK positioning is theoretically possible. As shown in the previous section, the performance of the RTK system can benefit if redundant satellites are available. However, Figure 3 also shows that availability decreases as the number of satellites increase. For example, the availability of 7 GPS satellites decreases to less than 50%. In the case of GLONASS, the availability of 5 satellites was also less than 50%. This example illustrates that the current state of the GLONASS constellation limits its potential as an effective standalone positioning tool. However, notice that at least satellites were visible almost 94% of the time. When combined with GPS, the GLONASS constellation changes the satellite availability profile considerably. Table. The satellite availability of the GPS and the combined GPS and GLONASS constellations. Satellite Availability (%) Constellation GPS Combined During the test period, the number of combined satellites did not fall below 6; in fact, the availability of 8 or more combined satellites was 96%. In terms of redundancy, this compares favorably with the GPS constellation in which case 8 satellites were only visible 6% of the time. In addition to improved satellite availability and redundancy, combining GNSS technologies can also strengthen receiver-satellite geometry. Figure 4 shows the GPS satellite skyplot generated by the GNSS QC data analysis software package (Leica Geosystems, 006a). Figure 4. The lack of GPS satellites north of the local zenith is due to the inclination angle of the satellite orbit. The absence of GPS satellites to the north of the local zenith results in a relatively weak geometry along the north-south axis. This gap is due to the 55º inclination angle of the satellite orbit. The inclination of the GLONASS orbit is approximately 9.8º larger than GPS (ICD, 00). The effect of the different orbit configurations is illustrated in Figure 5. Figure 5. The combined GPS and GLONASS satellite skyplot. The higher inclination angle means that the GLONASS satellites track a wider portion of the satellite visibility profile. The impact is greatest in high or low latitude regions. The influence of the prevailing satellite geometry on positioning is often measured using various dilution of precision (DOP) factors such as dilution of position in the horizontal domain (HDOP), the vertical domain (VDOP), the position domain (PDOP) and the geometric domain (GDOP). In general, σ x = xdop σ 0 (8) where σ x is the precision of position component x and σ 0 is the standard deviation of a measurement of unit weight (Leick, 990). The xdop is computed from the

6 trace of the position cofactor matrix Q b, which captures the receiver-satellite geometry. According to (8), a decrease in the xdop will increase the precision of the corresponding position component. Various DOP values for the GPS and combined satellite constellations are compared in Table. Table. A comparison of commonly used DOP factors for the GPS and combined satellite constellations. The average and maximum DOPs are listed on the left and right side of each column respectively. DOP Factors Statistic GPS Combined Difference HDOP VDOP PDOP GDOP The geometrical strength of the combined satellite constellation is greater when compared to GPS for all the DOP values listed in Table. The improved receiver-satellite geometry has the potential to increase the precision of the fixed position solution. This section has shown that augmenting the GPS constellation with GLONASS satellites can improve the measures of satellite availability, redundancy and geometry measures. The next section tests the hypothesis that improvements in these measures benefit the performance of the ambiguity resolution process. The GX30 typically fixed ambiguities in under 0 seconds, which illustrates the effectiveness of GPS for productive real-time positioning. In comparison, the mean time-to-fix for the GX30 GG approached only 8 seconds, which represents a performance improvement of almost 0%. In addition, the maximum time-to-fix was reduced by approximately 66% to only 40 seconds. The two sensors showed equal levels of performance in terms of reliability since no incorrect ambiguity solutions were detected in the test data. A solution was considered incorrect if the height component of the fixed position deviated by more than half a cycle from the known reference position. The excellent reliability results can be attributed to SmartCheck technology, which uses a repeated search strategy to reduce the probability of selecting an incorrect set of integer ambiguities (Euler and Ziegler, 000). The new GX30 GG features SmartCheck+, which is an enhanced ambiguity resolution algorithm designed to process combined GNSS observables. The statistics for the GX30 presented in Table 3 do not include the times when less than 5 GPS satellites were observed. These periods, which amounted to approximately 30 minutes or % of the test data, represent outages when no GPS fix was possible. Although these outages represent only a small percentage of the total period, 30 minutes of downtime could still prove significant on the job site. In contrast, the number of combined satellites did not fall below 6 and the GX30 GG continued to fix throughout these outage periods. An example period of 4 minutes is shown below. AMBIGUITY RESOLUTION AND RELIABILITY The timely and correct identification of the integer ambiguities is the key to productive RTK positioning. Therefore, the time-to-fix and reliability of the solution are important metrics for assessing the performance of an RTK system. Table 3 compares these statistics for the GX30 GG and GX30 GPS-only sensors connected to the same AX0 GG antenna used in the previous test. A GRX00 GG Pro reference station sensor located 5km from the two test units supplied the real-time corrections. This medium length baseline represents a typical operating range for a real-time rover. Data was collected for 4 hours during which time both sensors were configured to reinitialize following a successful fix. Table 3. A comparison of the time-to-fix and reliability statistics for the GX30 and GX30 GG sensors. Time-To-Fix [sec] Statistic GX30 GX30 GG % Difference Mean Maximum Reliability 00% 00% 0 Figure 6. The GX30 GG provided precise fixed positions during periods when there were an insufficient number of available satellites for a GPS-only solution. The GX30 GG recorded 98 independent fixes with an average time-to-fix of 4 seconds and a maximum of 4 seconds. The plot of the horizontal and height position errors reveal no significant outliers that might indicate an incorrect solution. The GX30 typically fix ambiguities when 5 GPS satellites are available; however, successful ambiguity resolution is still not guaranteed. In such cases,

7 redundant observations can play a vital role in the ambiguity resolution process. The addition of GLONASS satellites can help to maintain position continuity when the prevailing GPS constellation alone is insufficient to provide an RTK solution. Even when a sufficient number of GPS satellites are available, redundancy provided by a combined constellation can reduce the time-to-fix ambiguities. Position availability and the timely identification of the integers are the key requirements for productive RTK positioning. The final section of this paper examines the precision of the fixed position estimate. POSITION PRECISION Figure 7. Redundant satellites provided by a combined satellite constellation can improve ambiguity resolution, especially in poor observing environments such as under trees. To further illustrate the relationship between redundancy and ambiguity resolution performance, real-time data was collected in the relatively poor observing environment depicted in Figure 7. As in the previous tests, the baseline length was approximately 5km. The main objective of RTK positioning is the precise determination of the coordinates of points of interest in a timely manner. This final section examines the effect of a combined GPS and GLONASS constellation on the precision of the fixed position. The receiver and baseline configuration used in the previous test was adopted for this analysis. However, the GX30 GG and GX30 sensors were configured in full kinematic mode; that is, independent positions were computed at each measurement epoch. Position statistics were recorded for 4 hours at a second update rate. The first graph in Figure 9 compares the horizontal position errors of the two test sensors. Figure 9. A comparison of the horizontal position errors for GPS and combined solutions. The horizontal position derived from the GX30 GG sensor is visually more precise. Figure 8. Despite the availability of 5 GPS satellites, no GPS-only fixed solutions were recorded. In contrast, the GX30 GG maintained a fixed position. Although 5 GPS satellites were observed throughout the survey, no GPS-only fixed positions were available. In comparison, the GX30 GG was able to confirm 49 independent fixes with an average time-to-fix of 3 seconds. Once again, the plot of the continuous position errors does not reveal any significant outliers that would indicate a wrong ambiguity solution. In Figure 9, the spread of the GX30 GG position errors visually less than the spread of the GPS-only positions, especially along the north-south axis. This result is consistent with the satellite skyplots presented earlier that show a general lack of satellites north of the local zenith. The standard deviation of the horizontal position was measured using an unbiased estimate of the sample variance given by: s x = n n i= ( x x) i (9)

8 Where x represents a position component, x is the arithmetic mean and n is the number of samples. The values of the standard deviations ( s ) for the east and north components together with the minimum and maximum errors are tabled below. Table 4. A comparison of the position statistics for the east component. East Error [mm] Statistic GX30 GX30 GG Difference Min Max 7 5 s 7 6 rms Table 5. A comparison of the position statistics for the north error component. North Error [mm] Statistic GX30 GX30 GG Difference Min Max s 9 7 rms The standard deviations of the horizontal position errors are smaller for the GX30 GG sensor, which indicates that the combined solution is more precise. This hypothesis was tested formally using the F-test statistic (Devore, 99). The F-test for both position components was significant at the α = 0. 0 level of significance. That is, the data supports the inference that the combined solution is more precise. However, the magnitude of the improvement is only modest. The standard deviations of the east and north errors decreased by only mm and mm respectively. In fact, the horizontal precisions for the GPS solution are already better than ±0 mm, which emphasizes the effectiveness of GPS as a standalone positioning tool for high-precision RTK applications. The results demonstrate that the GX30 and GX30 GG systems do indeed produce high precision solutions. However, high precision does necessarily imply high accuracy. Differences between GPS and GLONASS, such as the coordinate reference frames and time scales, can introduce systematic biases into the combined position solution if they are handled incorrectly. Consider the mean square error given by: m n = ( x x) n i= + ( x a) 3 b (0) where a represents an accepted constant (Deakin and Kildea, 999). Recognizing that the first term on the right hand side of the equation is the variance given in (9), this statistic measures precision and any uncorrected systematic errors via the bias term b. Therefore, just as an increase in s reflects a decrease in precision, an increase in m, more commonly referred to as rms, indicates a decrease in accuracy (Mikhail and Gracie, 98). The rms values given in Table 4 and Table 5 were calculated using the expected value of the GPS solution as the accepted value a. That is, a = E{ x } = x () g g g The variable x g represents one of the GPS position components. In both tables, the rms equals the standard deviation, which implies that the bias term b in (0) equals 0. This result is significant because it shows that the augmentation of GLONASS observations has not introduced any systematic errors into the position solution. Figure 0 illustrates the height position errors for the two sensors. Figure 0. A comparison of the height position errors for the GPS and combined solutions. Heights derived from GPS are typically less precise than horizontal positions due to a lack of satellites below the observer s horizon. The geometry of the combined constellation also suffers from a lack of satellites below the horizon. Nevertheless, the GX30 GG combined solution is visually more precise than the GX30 solution. The statistical measures of dispersion are given in Table 6. Table 6. A comparison of the height error statistics for the GPS and combined solutions. Height Error [mm] Statistic GX30 GX30GG Difference Min Max s 5 3 rms A comparison of the rms and standard deviation (s) demonstrates that no systematic biases were introduced into the combined position solution. Again, the improvement in the precision of the combined solution, while statistically significant, is only mm. The results presented in this section illustrate that the System 00 GPS and combined solutions both provide centimeter level precision for RTK applications. In general, the combined solution is more precise than GPS

9 alone. However, the gains in precisions are modest compared to the gains achieved by constraining the integer ambiguities in the position solution. The benefit of the combined GNSS constellation for ambiguity resolution was already proven in the previous sections. CONCLUSION Combining GNSS technologies effectively increases satellite availability, redundancy and geometry. The increased satellite availability provided by a combined constellation mitigates the risk of position outages. Redundant satellites are useful for detecting and rejecting poor quality measurements that might otherwise lead to inaccurate solutions. Furthermore, redundancy improves the speed and reliability of the ambiguity resolution process, which is the key to precise RTK positioning. Finally, an improvement in the receiver-satellite geometry will increase the precision of the final position solution. Improvements in each of these elements will benefit the productivity, reliability, precision and accuracy of RTK positioning. The Leica System 00 sensors featuring SmartTrack+ technology are designed to track all of the available GNSS positioning signals. Today, users can already benefit from a combined constellation of 9 GPS and 6 GLONASS satellites. In this paper, an analysis of real-time data collected using the new System 00 sensors illustrates the improvements in satellite availability and geometry achieved by augmenting the GPS constellation with GLONASS satellites. The combined solution was able to reduce the time-to-fix ambiguities and increase the availability of precise position when insufficient satellites were available for a GPS only solution. The tests also showed the benefits of satellite redundancy for the ambiguity resolution process even when a sufficient number of GPS satellites were available. Finally, the combined solution also improved the precision of the fixed horizontal and vertical positions; however, the magnitude of the improvement is modest compared to the gains in precision achieved by constraining the integer ambiguities. In the future, the introduction of new GNSS technologies such as Galileo and the third GPS frequency promises to yield additional performance benefits for RTK positioning. As demonstrated in this paper, the potential of these technologies will be realized by integrating all of the signals in a combined RTK system. However, the current deployment schedule of Galileo and modernized GPS means that the full benefits provided by these systems will not be available to the civilian community before the end of the decade. REFERENCES Commission of the European Communities, (006), Taking Stock of the Galileo Programme, Communication from the Commission to the European Parliament and the Council, COM(006) 7 final, Brussels, pp. Dvorkin, V. and Karutin, S., (006), GLONASS: Current Status and Perspectives, presented at: The 3rd ALLSAT Open Conference, Hannover, Germany, June. Devore, J.L., (99), Probability and Statistics for Engineering and the Sciences, 3rd edn., Brooks Cole Publishing Company, Belmont, California, 76pp. Deakin, R.E. and Kildea, D.G., (999), A Note on Standard Deviation and RMS, The Australian Surveyor, vol. 44, no., June, pp Euler, H-J. and Ziegler, C., (000), Advances in Ambiguity Resolution for Surveying Type Applications, in: Proc. of the 3th International Technical Meeting of the Satellite Division of The Institute of Navigation, Salt Lake City, Utah, September, pp ICD, (00), Global Navigation Satellite System GLONASS Interface Control Document, version 5.0, Moscow, 5 pp. Leica Geosystems, (006a), Leica GNSS QC Software For Quality Control and Analysis of GNSS Reference Stations, Leica Geosytems AG, Heerbrugg, Switzerland, pp. Leick, A., (990), GPS Satellite Surveying, Wiley- Interscience, New York, 35pp. Leveson, I., (006), Benefits of the New GPS Civil Signal The LC Study, in: Inside GNSS, vol., no. 5, July/August, pp Mikahil, E.M. and Gracie, G.G., (98), Analysis and Adjustment of Survey Measurements, Van Nostrand Reinhold, New York, New York, 340pp. Polischuk, G.M., Kozlov, V.I., Ilitchov, V.V., Kozlov, A.G., Bartenev, V.A., Kossenko, V.E., Anphimov, N.A., Revnivykh, S.G., Pisarev, A.E., Tyulyakov, A.E., Shebshaevitch, B.V., Basevitch, A.B. and Vorokhovsky, Y.L., (00), The Global Navigation Satellite System GLONASS: Development and Usage in the st Century, in: Proc. of the 34th Annual Precise Time and Time Interval (PTTI) Systems and Applications Meeting, Reston, Virginia, December, pp Simsky, A., 006, Three s the Charm Triple-Frequency Combinations in Future GNSS, in: Inside GNSS, vol., no. 5, July/August, pp

10 Takac, F., Hilker, C., Kotthoff, H. and Richter, B., (005), Combining Measurements from Multiple Global Navigation Satellite Systems for RTK Applications, in: International Symposium on GPS/GNSS, Hong Kong, December, 7pp. Teunissen, P.J.G., (994), A New Method for Fast Carrier Phase Ambiguity Estimation, in: Proc. of the Positioning, Location and Navigation Symposium, Las Vegas, Nevada, USA, April, pp Teunissen, P.J.G., (997a), A canonical theory for short GPS baselines Part I: The baseline precision, in: Journal of Geodesy, vol. 7, no. 6, pp Teunissen, P.J.G., (997b), A canonical theory for short GPS baselines Part IV: Precision versus reliability, in: Journal of Geodesy, vol. 7, no. 9, pp Teunissen, P.J.G. and Odijk, D., (997), Ambiguity Dilution of Precision: Definition, Properties and Application, in: Proc. of the 0th International Technical Meeting of the Satellite Division of The Institute of Navigation, Kansas City, Missouri, September, pp

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