Single Point Positioning Research Articles

Initial assessment of BDS-3 preliminary system signal-in-space range error

The basic constellation of the BeiDou global satellite navigation system (BDS-3) had been successfully completed by the end of 2018. It included 18 medium earth orbit satellites and 1 geostationary orbit satellite. An initial assessment of BDS-3 broadcast orbit and clock accuracy based on 55 days of broadcast message data is presented in this contribution. Satellite positions and clock offsets derived from broadcast ephemeris are compared with precise orbit determination orbits and clock offsets. Furthermore, the corresponding signal-in-space range error (SISRE), which is of most interest to navigation users, is computed. Thanks to the new inter-satellite link payloads on BDS-3 satellites, the statistics of age-of-data-ephemeris and age-of-data-clock demonstrate that more than 98% of ephemerides and 93% of clock parameters are updated within only one hour. Experimental results show that the 3D root mean square (RMS) of broadcast orbit errors is less than 0.6 m for the overall constellation. The broadcast orbit is also assessed by satellite laser ranging measurements, giving an RMS of 7.3 cm. The orbit-only SISRE is about 0.1 m. With respect to clock errors, the timescale differences between two clock products are eliminated to assess the accuracy of broadcast clock offsets. The standard deviation value of 0.25 m shows a good performance, but the RMS value is regrettably nearly 0.5 m due to a nonzero mean bias. RMS of BDS-3 SISRE amounts to approximately 0.5 m, which is largely attributed to clock errors. Finally, a positioning experiment is conducted to analyze the accuracy of single point positioning (SPP). With 95% confidence level, the horizontal accuracy is less than 5 m, and the vertical accuracy is close to 6 m. Considering that the nonzero mean bias in clock errors may affect the performance of SPP, we correct the nonzero mean value by a satellite-specific constant to analyze the influence of clock bias on the SPP performance. The results show that improvement in the 3D position accuracy can be up to 11%, especially in the up direction.

Real-time single-frequency pseudorange positioning in China based on regional satellite clock and ionospheric models

Improving performance of single-point positioning (SPP) with single-frequency pseudorange measurement is important for users equipped with mass-market or low-cost receivers. Considering a regional single-frequency SPP service is available, it is not necessary to realize precise orbit determination for single-frequency SPP. Instead, the ionospheric modeling is of utmost importance. Based on BDS/GPS broadcast ephemeris, we establish a regional satellite clock model (CLK) and two regional ionospheric models in China using 155 reference stations and investigate their efficiency in improving the performance of BDS/GPS SPP with additional 499 reference stations. Two ionospheric models are established based on different total electron content (TEC) observables; one is the low-order spherical harmonic function model (SHF) with vertical TEC observables and the other is the satellite-based ionospheric model (SIM) with slant TEC observables. It is demonstrated that the SIM model performs better than SHF model as it avoids the error due to the ionospheric mapping function. Overall, the positioning results with CLK + SIM perform the best for BDS-only, GPS-only, and BDS/GPS SPP. Compared to the positioning results with the broadcast ephemeris and the Klobuchar model, the SPP positioning accuracy with the CLK + SIM model improves by about 50% on average. By using the improved model CLK + SIM, the BDS/GPS SPP positioning accuracy is better than 1.5 m and 2.0 m at the 95% confidence level in the horizontal and vertical directions, respectively. Also, by comparing the SPP performance with IGS final products, including the GeoForschungsZentrum precise orbits and clock products and Center for Orbit Determination in Europe final GIMs, the proposed model in this study performs better than that with the IGS final products in terms of positioning accuracy and model complexity.

Aircraft positioning using GPS/GLONASS code observations

Purpose This paper aims to present the problem of the integration of the global positioning system (GPS)/global navigation satellite system (GLONASS) data for the processing of aircraft position determination. Design/methodology/approach The aircraft coordinates were obtained based on GPS and GLONASS code observations for the single point positioning (SPP) method. The numerical computations were executed in the aircraft positioning software (APS) package. The mathematical scheme of equation observation of the SPP method was solved using least square estimation in stochastic processing. In the research experiment, the raw global navigation satellite system data from the Topcon HiperPro onboard receiver were applied. Findings In the paper, the mean errors of an aircraft position from APS were under 3 m. In addition, the accuracy of aircraft positioning was better than 6 m. The integrity term for horizontal protection level and vertical protection level parameters in the flight test was below 16 m. Research limitations/implications The paper presents only the application of GPS/GLONASS observations in aviation, without satellite data from other navigation systems. Practical implications The presented research method can be used in an aircraft based augmentation system in Polish aviation. Social implications The paper is addressed to persons who work in aviation and air transport. Originality/value The paper presents the SPP method as a satellite technique for the recovery of an aircraft position in an aviation test.

Single point positioning using full and fractional pseudorange measurements from GPS and BDS

In conventional global navigation satellite system (GNSS) receivers, full pseudorange measurements are usually required to complete a single point position fix, which takes longer time than obtaining fractional pseudorange measurements. In order to shorten the time to first fix and improve the position accuracy during cold or warm start of a dual-constellation GNSS receiver, we propose a positioning algorithm using at least four full pseudorange measurements from one constellation and fractional measurements from either or both constellations. Theoretical rapid position results can be obtained with an identical accuracy to that of the conventional method using full measurements. Tests with simulated and real Global Positioning System (GPS) and BeiDou Navigation Satellite System (BDS) data validate the performance of the proposed approach.

Modeling and application of the time-varying GPS differential code bias between C1 and P1 observations

Considering the time-varying characteristic of the GPS differential code bias between C1 and P1 observations (DCB (C1-P1)), the method for estimating the time-varying DCB (C1-P1) is presented. The time-varying characteristic of the DCB (C1-P1) is analyzed using the estimated values with the twelve-month (1 Jan-31 Dec 2018) GPS data set from 120 International GNSS Service (IGS) stations. The estimated results show that the DCB (C1-P1) has the evident variation with the periods of 12, 8, 6, 4, 3.4286 h. Based on the noticed periods, the estimated single-day DCB (C1-P1) series is modeled with a harmonics-based function. The results show that the initial phase offsets (θi(i=1~5)) have the characterization of linear variation and these variations are very evident, while the amplitudes (yi(i=1~5)) of each satellite irregularly vary with time. The time-varying DCB (C1-P1) is used in single point positioning (SPP) to validate its effect on positioning. The SPP results show that the three-dimensional positioning results can be improved, when the time-varying part of the DCB (C1-P1) is corrected. The results for the 120 IGS stations indicate that the average three-dimensional positioning improvement for three days is about 3 cm. These improvements further advise that the time-varying part of DCB (C1-P1) should be corrected in GPS data processing and be serviced by IGS. The prediction performance shows that the correction rates of the predicted results for all satellites reach more than 40% accuracy and the mean prediction accuracy can reach 70%.

Multistep weighted least squares estimation method for improving single-point positioning accuracy

The integration of multiple Global Navigation Satellite Systems (GNSSs), such as the Chinese BeiDou Navigation Satellite System (BDS) and the American Global Positioning System (GPS), makes it possible to improve the accuracy of single-point positioning (SPP). However, the current accuracy of GNSS SPP with code measurement is on the order of several meters. In order to further improve SPP accuracy, we develop a multistep weighted least squares (MWLS) estimation method based on the elevation-dependent weighted least squares (EWLS) method. In this approach, the weight of each visible satellite is determined by its elevation and azimuth, and the coordinate components are semi-independently and separately calculated by MWLS. We conduct open-sky and blocked static tests as well as a vehicle-based kinematic test using single-frequency receivers to assess the effectiveness of this approach. Comparing the positioning errors of GPS and GPS/BDS SPPs between the MWLS and EWLS methods shows that the former improved the positioning accuracy more than the customary latter. Specifically, MWLS achieves a horizontal accuracy of about 1 m and a positional accuracy of 2 to 3 m in clear observational environments, about 15% better than ELWS.

Calibration of BeiDou Triple-Frequency Receiver-Related Pseudorange Biases and Their Application in BDS Precise Positioning and Ambiguity Resolution.

Global Navigation Satellite System pseudorange biases are of great importance for precise positioning, timing and ionospheric modeling. The existence of BeiDou Navigation Satellite System (BDS) receiver-related pseudorange biases will lead to the loss of precision in the BDS satellite clock, differential code bias estimation, and other precise applications, especially when inhomogeneous receivers are used. In order to improve the performance of BDS precise applications, two ionosphere-free and geometry-free combinations and ionosphere-free pseudorange residuals are proposed to calibrate the raw receiver-related pseudorange biases of BDS on each frequency. Then, the BDS triple-frequency receiver-related pseudorange biases of seven different manufacturers and twelve receiver models are calibrated. Finally, the effects of receiver-related pseudorange bias are analyzed by BDS single-frequency single point positioning (SPP), single- and dual-frequency precise point positioning (PPP), wide-lane uncalibrated phase delay (UPD) estimation, and ambiguity resolution, respectively. The results show that the BDS SPP performance can be significantly improved by correcting the receiver-related pseudorange biases and the accuracy improvement is about 20% on average. Moreover, the accuracy of single- and dual-frequency PPP is improved mainly due to a faster convergence when the receiver-related pseudorange biases are corrected. On the other hand, the consistency of wide-lane UPD among different stations is improved significantly and the standard deviation of wide-lane UPD residuals is decreased from 0.195 to 0.061 cycles. The average success rate of wide-lane ambiguity resolution is improved about 42.10%.

Reducing the Effect of Positioning Errors on Kinematic Raw Doppler (RD) Velocity Estimation Using BDS-2 Precise Point Positioning.

In the traditional raw Doppler (RD) velocity estimation method, the positioning error of the pseudorange-based global navigation satellite system (GNSS) single point positioning (SPP) solution affects the accuracy of the velocity estimation through the station-satellite unit cosine vector. To eliminate the effect of positioning errors, this paper proposes a carrier-phase-based second generation of the BeiDou navigation satellite system (BDS-2) precise point positioning (PPP) RD velocity estimation method. Compared with the SPP positioning accuracy of tens of meters, the BDS-2 kinematic PPP positioning accuracy is significantly improved to the dm level. In order to verify the reliability and applicability of the developed method, three dedicated tests, the vehicle-borne, ship-borne and air-borne platforms, were conducted. In the vehicle-borne experiment, the GNSS and inertial navigation system (INS)-integrated velocity solution was chosen as the reference. The velocity accuracy of the BDS-2 PPP RD method was better than that of SPP RD by 28.4%, 27.1% and 26.1% in the east, north and up directions, respectively. In the ship-borne and air-borne experiments, the BDS-2 PPP RD velocity accuracy was improved by 17.4%, 21.4%, 17.8%, and 38.1%, 17.6%, 17.5% in the same three directions, respectively, compared with the BDS-2 SPP RD solutions. The reference in these two tests is the real-time kinematic (RTK) Position Derivation (PD)-based velocity.

Initial Positioning Assessment of BDS New Satellites and New Signals

With the official announcement of open service since the end of 2018, the BeiDou navigation satellite system (BDS) has started to provide global positioning, navigation and timing (PNT) services. Thus, it is worth assessing the positioning service of new BDS satellites and signals. In this paper, we comprehensively assess the system status and the global positioning performance of BDS regarding single point positioning (SPP) and real-time kinematic (RTK) performance. Results show that the signal in space range error (SISRE) of BDS-3 satellites is superior to that of BDS-2 satellites, showing an overall accuracy of 0.71 m versus 0.97 m, which is competitive with GPS and Galileo. With the contribution of BDS-3, the number of global average visible satellites has increased from 5.1 to 10.7, which provides a mean global position dilution of precision (PDOP) value better than 6 at 99.88% and the mean availability of basic PNT performance is also improved from 35.25% to 98.84%. One week of statistical results from 54 globally distributed international GNSS service (IGS) stations show that the root mean square (RMS) of SPP accuracy is 1.1 m in horizontal and 2.2 m in vertical, which is at the same level of GPS. The new B1c and B2a signals show a smaller observation noise than B1I, and SPP performance of B1c is similar to that of B1I. However, the positioning precision is slightly worse at the B2a frequency, which may be due to the inaccurate BDS ionosphere correction. As for short baseline RTK, baseline accuracy is also improved due to the increased number of new BDS satellites.

Performance Evaluation of the CNAV Broadcast Ephemeris

The new Global Positioning System (GPS) Civil Navigation Message (CNAV) has been transmitted by Block IIR-M and Block IIF satellites since April 2014, both on the L2C and L5 signals. Compared to the Legacy Navigation Message (LNAV), the CNAV message provides six additional parameters (two orbit parameters and four Inter-Signal Correction (ISC) parameters) for prospective civil users. Using the precise products of the International Global Navigation Satellite System Service (IGS), we evaluate the precision of satellite orbit, clock and ISCs of the CNAV. Additionally, the contribution of the six new parameters to GPS Single Point Positioning (SPP) is analysed using data from 22 selected Multi-Global Navigation Satellite System Experiment (MGEX) stations from a 30-day period. The results indicate that the CNAV/LNAV Signal-In-Space Range Error (SISRE) and orbit-only SISRE from January 2016 to March 2018 is of 0·5 m and 0·3 m respectively, which is improved in comparison with the results from an earlier period. The ISC precision of L1 Coarse/Acquisition (C/A) is better than 0·1 ns, and those of L2C and L5Q5 are about 0·4 ns. Remarkably, ISC correction has little effect on the single-frequency SPP for GPS users using civil signals (for example, L1C, L2C), whereas dual-frequency SPP with the consideration of ISCs results have an accuracy improvement of 18·6%, which is comparable with positioning accuracy based on an ionosphere-free combination of the L1P (Y) and L2P (Y) signals.

Low-cost versus high-grade global navigation satellite system receivers: kinematic global positioning system–BeiDou navigation satellite system single-point positioning performance evaluation for vehicular urban navigation

Low-cost receivers have already entered the mass market over the past few years. The high-precision real-time kinematic and precise-point positioning evaluation based on low-cost receivers has been analyzed and verified by many other studies in the past. With the integration of the multiglobal navigation satellite system (GNSS) and advances in technology, low-cost GNSS receivers are expected to be widely used in vehicle navigation. To investigate the kinematic single-point positioning (SPP) performance of low-cost receivers, we first assembled a low-cost receiver that can receive both American global positioning system (GPS) L1 and Chinese BeiDou Navigation Satellite System (BDS) B1 signals simultaneously. Then, a vehicle-positioning experiment is conducted in Fuzhou, China. For comparison purposes, the assembled low-cost receiver and a higher-grade receiver are connected to a survey-grade antenna via a power divider. The positioning accuracy and position dilution of the precision of GPS, BDS, and GPD/BDS SPP with both receivers are compared and analyzed. The results indicate that the low-cost receiver can achieve horizontal precision better than 1 m in the combined GPS/BDS case, when the car is positioned in the urban main road and expressway. This result is competitive and similar to that of the higher-grade receiver. Moreover, although the positioning precision of the low-cost receiver is worse than that of the higher-grade receiver in the GPS-only and BDS-only SPP case, it outperforms the higher-grade receiver in terms of satellite tracking, especially for tracking GPS satellite.

The evaluation of IRNSS/NavIC system’s performance in its primary and secondary service areas–data quality, usability and single point positioning

The Navigation with Indian Constellation (NavIC), also known as Indian regional navigation satellite system, is a regional navigation satellite system recently developed by India. Its service area covers from 30°E to 130°E and from 30°S to 50°N. In this contribution, an assessment of NavIC from aspects of data quality, usability and single point positioning (SPP) performance is carried out using real measured data collected from four sites both within NavIC’s primary and secondary service areas. Data quality of NavIC’s signal is assessed measuring its carrier-to-noise-density ratio and each satellite’s orbital period is calculated using its broadcast ephemeris. Visible satellite number and DOPs values of each site in modes of NavIC-only, GPS-only and GPS/NavIC are counted and calculated respectively. SPP solutions in modes of NavIC-only, GPS-only and GPS/NavIC are also carried out for these four sites. The results show that: the signal strength of NavIC’s L5 frequency generally equals that of GPS in site IISC (Fig. 1); mean orbital periods of IGSO and GEO satellites are 86160.70 s and 86152.03 s respectively; in site IISC (within the primary service area), currently NavIC system can provide an independent positioning service with an accuracy of less than 1 m in the east direction and less than 2 m in north and up directions respectively; the usability and SPP performance can be improved significantly in the mode of GPS/NavIC compared with those in either single mode.

Assessment of Dual Frequency GNSS Observations from a Xiaomi Mi 8 Android Smartphone and Positioning Performance Analysis

On May 2018 the world’s first dual-frequency Global Navigation Satellite System (GNSS) smartphone produced by Xiaomi equipped with a Broadcom BCM47755 chip was launched. It is able to receive L1/E1/ and L5/E5 signals from GPS, Galileo, Beidou, and GLONASS (GLObal NAvigation Satellite System) satellites. The main aim of this work is to achieve the phone’s position by using multi-constellation, dual frequency pseudorange and carrier phase raw data collected from the smartphone. Furthermore, the availability of dual frequency raw data allows to assess the multipath performance of the device. The smartphone’s performance is compared with that of a geodetic receiver. The experiments were conducted in two different scenarios to test the smartphone under different multipath conditions. Smartphone measurements showed a lower C/N0 and higher multipath compared with those of the geodetic receiver. This produced negative effects on single-point positioning as showed by high root mean square error (RMS). The best positioning accuracy for single point was obtained with the E5 measurements with a DRMS (horizontal root mean square error) of 4.57 m. For E1/L1 frequency, the 2DRMS was 5.36 m. However, the Xiaomi Mi 8, thanks to the absence of the duty cycle, provided carrier phase measurements used for a static single frequency relative positioning with an achieved 2DRMS of 1.02 and 1.95 m in low and high multipath sites, respectively.

Walker: Continuous and Precise Navigation by Fusing GNSS and MEMS in Smartphone Chipsets for Pedestrians

The continual miniaturization of mass-market sensors built in mobile intelligent terminals has inspired the development of accurate and continuous navigation solution for portable devices. With the release of Global Navigation Satellite System (GNSS) observations from the Android Nougat system, smartphones can provide pseudorange, Doppler, and carrier phase observations of GNSS. However, it is still a challenge to achieve the seamless positioning of consumer applications, especially in environments where GNSS signals suffer from a low signal-to-noise ratio and severe multipath. This paper introduces a dedicated android smartphone application called Walker that integrates the GNSS navigation solution and MEMS (micro-electromechanical systems) sensors to enable continuous and precise pedestrian navigation. Firstly, we introduce the generation of GNSS and MEMS observations, in addition to the architecture of Walker application. Then the core algorithm in Walker is given, including the time-differenced carrier phase improved GNSS single-point positioning and the integration of GNSS and Pedestrian Dead Reckoning (PDR). Finally, the Walker application is tested and the observations of GNSS and MEMS are assessed. The static experiment shows that, with GNSS observations, the RMS (root mean square) values of east, north, and up positioning error are 0.49 m, 0.37 m, and 1.01 m, respectively. Furthermore, the kinematic experiment verifies that the proposed method is capable of obtaining accuracy within 1–3 m for smooth and continuous navigation.

Time-Domain Evaluation Method for Clock Frequency Stability Based on Precise Point Positioning

The Global Navigation Satellite System (GNSS) and GNSS receivers can be used to measure the time-frequency errors of receiver clocks so as to evaluate their frequency stability. The calculation of receiver clock error by single point positioning (SPP) is not highly accurate, resulting in the limited evaluation of clock frequency stability. Therefore, this study proposes a precision point positioning (PPP) evaluation method. In this method, the receiver is driven by an external clock to be evaluated, and the receiver clock error calculated by PPP is used as the measured clock phase error to calculate the Allan variance. The frequency stability of three clocks with different grades (temperature compensated crystal oscillator [TCXO], oven controlled crystal oscillator [OCXO], and rubidium clock) are evaluated with the PPP evaluation method. The PPP evaluation method can evaluate the frequency stabilities of TCXO and OCXO for an average interval of more than 1 s, and the evaluation error of OCXO is less than 1.3 × 10 -11 . As for the rubidium clock, its frequency stability can be evaluated by the PPP evaluation method for an average interval of more than 66 s, and the error is less than 2 × 10 -13 . In general, the PPP evaluation method involves simple operations, achieves high accuracy, and is easily popularized.

张量衍生不变关系下的磁源单点定位

张量衍生不变关系下的磁源单点定位

Fuzzy logic applied to GNSS

Limiting the weight of bad signals can recover the accuracy of the GNSS solution in signal-degraded scenarios, where multipath reflections and obstructions can easily generate multiple blunders. The fuzzy integration of the available information related to the quality of the received signals is exploited in this paper to derive an effective weighting schema in a Weighted Least Square estimation process. To validate the proposed schema, its performance in the position domain is compared to the most common weighting strategies proposed in the literature, based on GPS data collected through two different High Sensitivity GNSS receivers placed in urban canyons and processed in Single Point Positioning using pseudorange measurements.

Enhanced Local Ionosphere Model for Multi-Constellations Single Frequency Precise Point Positioning Applications: Egyptian Case Study

Abstract The positioning accuracy of single frequency precise point positioning (SFPPP) attributes mainly to the ionosphere error, which strongly affects GNSS signals. When GNSS signals pass through the various ionosphere layers, they will be bent and their speed will be changed due to dispersive nature of ionosphere. To correct the ionosphere error, it is common to use Klobuchar ionosphere model or Global Ionosphere Maps (GIM). However, Klobuchar can deal with only about 50% of the Ionosphere effect and global Ionosphere maps are often inadequate to describe detailed features of local ionosphere because of limited precision and resolution. In this paper, an enhanced local ionosphere model was developed relying on modeling of measurements from a dense Egyptian permanent tracking GNSS network in order to achieve high precision ionosphere delay correction. The performance of the developed enhanced Egyptian ionosphere model (EIM) was verified through multi-constellations SFPPP accuracy for static and kinematic modes. For static mode, 24 hours multi-constellations datasets collected at three selected stations, Alexandria, Cairo, and Aswan, in Egypt on February 27, 2017, to investigate the performance of the developed local ionospheric model in comparison with the Klobuchar, GIM and ionosphere free models. After session time of half an hour, the results show that the performance of static SFPPP based on the developed Egyptian ionospheric map (EIM) achieved a comparable accuracy WRT using ionosphere free model. While using EIM, achieved an improvements of (38%, 28%, and 42%) and (32%, 10%, and 37%) for accuracy of latitude, longitude, and altitude in comparison with using Klobuchar and GIM models, respectively For kinematic mode, datasets of 2 hours of observations with 1 second sampling rate were logged during vehicular test; the test was carried out on the ring road of the city of Cairo, Egypt, on September 16, 2017. After half an hour of kinematic SFPPP data-processing, the performance of using Egyptian ionospheric map (EIM) for ionosphere delay correction, achieved an improvements of three dimension coordinates of (83%, 47%, and 62%) and (57%, 65%, and 21%) with respect to using Klobuchar model and GIM model, respectively.

Near real-time BDS GEO satellite orbit determination and maneuver analysis with reversed point positioning

The Geostationary Earth Orbit (GEO) satellite is a crucial part of the BeiDou Navigation Satellite System (BDS) constellation. However, due to various perturbation forces acting on the GEO satellite, it drifts gradually over time. Thus, frequent orbit maneuvers are required to maintain the satellite at its designed position. During the orbit maneuver and recovery periods, the orbit quality of the maneuvered satellite computed with broadcast navigation ephemeris will be significantly degraded. Furthermore, the conventional dynamic Precise Orbit Determination (POD) approach may not work well, because of a lack of publicly available satellite information for modeling the thrust forces. In this paper, a near real-time approach free of thrust forces modeling is proposed for BDS GEO satellite orbit determination and maneuver analysis based on the Reversed Point Positioning (RPP). First, the station coordinates and receiver clock offsets are estimated by GPS/BDS combined Single Point Positioning (SPP) with single-frequency phase-smoothed pseudorange observations. Then, with the fixed station coordinates and receiver clock offsets, the RPP method can be conducted to determine the GEO satellite orbits. When no orbit maneuvers occur, the proposed method can obtain orbit accuracies of 0.92, 2.74, and 8.30 m in the radial, along-track, and cross-track directions, respectively. The average orbit-only Signal-In-Space Range Error (SISRE) is 1.23 m, which is slightly poorer than that of the broadcast navigation ephemeris. Using four days of GEO maneuvered datasets, it is further demonstrated that the derived orbits can be employed to characterize the behaviors of GEO satellite maneuvers, such as the time span of the maneuver as well as the satellite thrusting accelerations. These results prove the efficiency of the proposed method for near real-time GEO satellite orbit determination during maneuvers.

Aircraft positioning using SPP method in GPS system

PurposeThe purpose of this paper is based on implementation of Global Navigation Satellite System (GNSS) technique in civil aviation for recovery of aircraft position using Single Point Positioning (SPP) method in kinematic mode.Design/methodology/approachThe aircraft coordinates in ellipsoidal frame were obtained based on Global Positioning System (GPS) code observations for SPP method. The numerical computations were executed in post-processing mode in the Aircraft Positioning Software (APS) package. The mathematical scheme of equation observation of SPP method was solved using least square estimation in stochastic processing. In the experiment, airborne test using Cessna 172 aircraft on September 07, 2011 in the civil aerodrome in Mielec was realized. The aircraft position was recovery using observations data from Topcon HiperPro dual-frequency receiver with interval of 1 second.FindingsIn this paper, the average value of standard deviation of aircraft position is about 0.8 m for Latitude, 0.7 m for Longitude and 1.5 m for ellipsoidal height, respectively. In case of the Mean Radial Spherical Error (MRSE) parameter, the average value equals to 1.8 m. The standard deviation of receiver clock bias was presented in this paper and the average value amounts to 34.4 ns. In this paper, the safety protection levels of Horizontal Protection Level (HPL) and Vertical Protection Level (VPL) were also showed and described.Research limitations/implicationsIn this paper, the analysis of aircraft positioning is focused on application the least square estimation in SPP method. The Kalman filtering operation can be also applied in SPP method for designation the position of the aircraft.Practical implicationsThe SPP method can be applied in civil aviation for designation the position of the aircraft in Non-Precision Approach (NPA) GNSS procedure at the landing phase. The typical accuracy of aircraft position is better than 220 m for lateral navigation in NPA GNSS procedure. The limit of accuracy of aircraft position in vertical plane in NPA GNSS procedure is not available.Social implicationsThis paper is destined for people who works in the area of aviation and air transport.Originality/valueThe work presents that SPP method as a universal technique for recovery of aircraft position in civil aviation, and this method can be also used in positioning of aircraft based on Global Navigation Satellite System (GLONASS) code observations.