Global Navigation Satellite System Positioning Research Articles

Rotating GNSS Antennas: Simultaneous LOS and NLOS Multipath Mitigation

Urban environments present significant challenges to global navigation satellite system (GNSS) positioning. GNSS signals are often obstructed by buildings and other obstacles, leading to reflection and diffraction, which cause major line-of-sight (LOS) and non-line-of-sight (NLOS) multipath positioning errors. We propose a new, precise GNSS positioning technique that can simultaneously mitigate LOS and NLOS multipath errors by rotating the GNSS antenna arm horizontally at a certain angular velocity. The key idea behind this technique is to use the antenna motion to mitigate the LOS multipath effect and detect the NLOS multipath signals. The relative carrier phase between the direct signal and the multipath signal frequently changes when a GNSS antenna is moving. As a result, the effect that the strong reflected signal affects the direct signal can be reduced. We use this characteristic to mitigate LOS multipath errors by generating antenna motion. By rotating a GNSS antenna, the Doppler frequency is produced by the antenna motion. If the received GNSS signal is the NLOS signal, the direction of incoming signals is different from that of direct signals. In this situation, the phase of the generated Doppler frequency will be different, and NLOS signals can be detected by comparison with the ideal Doppler frequency. We conducted an experiment to evaluate the proposed method. The positioning error of the proposed method using LOS multipath mitigation and NLOS exclusion by the rotating antenna was decreased from 18.96 to 2.83 m. In addition, the availability of GNSS positioning increased from 44.29 to 100%.

Assessment of Empirical Troposphere Model GPT3 Based on NGL's Global Troposphere Products.

Tropospheric delay is one of the major error sources in GNSS (Global Navigation Satellite Systems) positioning. Over the years, many approaches have been devised which aim at accurately modeling tropospheric delays, so-called troposphere models. Using the troposphere data of over 16,000 global stations in the last 10 years, as calculated by the Nevada Geodetic Laboratory (NGL), this paper evaluates the performance of the empirical troposphere model GPT3, which is the latest version of the GPT (Global Pressure and Temperature) series model. Owing to the large station number, long time-span and diverse station distribution, the spatiotemporal properties of the empirical model were analyzed using the average deviation (BIAS) and root mean square (RMS) error as indicators. The experimental results demonstrate that: (1) the troposphere products of NGL have the same accuracy as the IGS (International GNSS Service) products and can be used as a reference for evaluating general troposphere models. (2) The global average BIAS of the ZTD (zenith total delay) estimated by GPT3 is −0.99 cm and the global average RMS is 4.41 cm. The accuracy of the model is strongly correlated with latitude and ellipsoidal height, showing obviously seasonal variations. (3) The global average RMS of the north gradient and east gradient estimated by GPT3 is 0.77 mm and 0.73 mm, respectively, which are strongly correlated with each other, with values increasing from the equator to lower latitudes and decreasing from lower to higher latitudes.

Experimental Evaluation of the Impact of Different Types of Jamming Signals on Commercial GNSS Receivers

The received global navigation satellite system (GNSS) signal has a very low power due to traveling a very long distance and to the nature of the signal’s propagation medium. Thus, GNSS signals are easily susceptible to signal interference. Signal interference can cause severe degradation or interruption in GNSS position, navigation, and timing (PNT) services which could be very critical, especially in safety-critical applications. The objective of this paper is to evaluate the impact of the presence of jamming signals on a high-end GNSS receiver and investigate the benefits of using a multi-constellation system under such circumstances. Several jamming signals are considered in this research, including narrowband and wideband signals that are located on GPS L1 or GLONASS L1 frequency bands. Quasi-real dynamic trajectories are generated using the Spirent™ GSS6700 GNSS signal simulator combined with an interference signal generator through a Spirent™ GSS8366 unit. The performance evaluation was carried out using several evaluation metrics, including signal power degradation, navigation solution availability, dilution of precision (DOP), and positioning accuracy. The multi-constellation system presented better performance over the global positioning system (GPS)-only constellation in most cases. Moreover, jamming the GPS band caused more critical effects than jamming the GLONASS band.

Using Sky‐pointing fish‐eye camera and LiDAR to aid GNSS single‐point positioning in urban canyons

Robust and globally-referenced positioning is indispensable for autonomous driving vehicles. Global navigation satellite system (GNSS) is still an irreplaceable sensor. Satisfactory accuracy (about 1 m) can be obtained in sparse areas. However, the GNSS positioning error can be up to 100 m in dense urban areas due to the multipath effects and non-line-of-sight (NLOS) receptions caused by reflection and blockage from buildings. NLOS is currently the dominant factor degrading the performance of GNSS positioning. Recently, the camera has been employed to detect the NLOS and then to exclude the NLOS measurements from GNSS calculation. The exclusion of NLOS measurements can cause severe distortion of satellite distribution, due to the excessive NLOS receptions in deep urban canyons. Correcting the NLOS receptions with the aid of 3D light detection and ranging after detection of NLOS receptions using a fish-eye camera was proposed in this study. Finally, the GNSS positioning was improved by using the healthy and corrected NLOS pseudo-range measurements. The proposed method is evaluated through real road tests in typical highly urbanised canyons of Hong Kong. The evaluation results show that the proposed method can effectively improve the positioning performance.

Indirect-Inversion Algorithm via Precise Integration for Ill-Conditioned Matrix in Ambiguity Resolution

Global navigation satellite system (GNSS) positioning depends on the correct integer ambiguity resolution (AR). If the double difference equation for solving the float solution remains ill-conditioned, often happening due to the environment complexity and the equipment mobility, the correct AR is difficult to achieve. Concerning the ill-conditioned problem, methods of modifying the equation coefficient matrix are widely applied, whose effects are heavily dependent on modifying parameters. Besides, the direct-inversion of the ill-conditioned coefficient matrix can lead to a reduction in the accuracy and stability of the float solution. To solve the problem of ill-conditioned matrix inversion and further improve the accuracy, the present study for the first time proves the positive definite symmetry of the coefficient matrix in AR model and employs precise integration method to the indirect inverse of coefficient matrix. AR model for the GNSS positioning and the general resolving strategies introduction are briefly introduced. An indirect-inversion algorithm via precise integration for ill-conditioned coefficient matrix is proposed. According to the simulations and comparisons, the proposed strategy has higher precision and stability on float solution, and less dependence on modifying parameters.

A Refined Regional Model for Estimating Pressure, Temperature, and Water Vapor Pressure for Geodetic Applications in China

Pressure, temperature, and water vapor pressure are basic meteorological parameters that are frequently required in Global Navigation Satellite System (GNSS) positioning/navigation and GNSS meteorology. Although models like Global Pressure and Temperature (GPT) and Global Pressure and Temperature 2 wet (GPT2w) were developed for these demands, their spatial resolutions are lower than 0.75° and temporal resolutions are below 6 h, which limits their achievement. The publication of European Centre for Medium-Range Weather Forecasts (ECMWF) ERA5 hourly 0.25° × 0.25° data offers the opportunity to lift this limitation. In this work, the ERA5 surface data are used to evaluate the temporal variabilities of pressure, temperature, and water vapor pressure in the area of China. We characterize their diurnal variations using hourly data and take into account their geographical variations by 0.25° × 0.25° grids. In addition, we improve the height corrections for the three parameters employing the ERA5 pressure level data. Through these efforts, we build a new regional model named Chinese pressure, temperature, and water vapor pressure (CPTw), which has the advanced resolution of 0.25° × 0.25° and temporal resolution of 1 h. We evaluate the performance using ERA5 data and radiosonde data compared with the approved GPT2w model. Results demonstrate that the accuracies of the new model are superior to the GPT2w model in all meteorological parameters. The validation with the radiosonde data shows RMS for pressure, temperature, and water vapor pressure of the CPTw model is reduced by 14.1%, 25.8%, and 4.8%, compared with that of the GPT2w model. The new model catches especially well the diurnal changes in pressure, temperature, and water vapor pressure, which have never been realized before. Since the CPTw model can provide accurate empirical pressure, temperature, and water vapor pressure for any time and location in China and its surrounding areas, it can not only meet the need of empirical meteorological parameters in real-time geodetic applications like GNSS positioning and navigation, but it is also useful for GNSS meteorology.

3D Mapping Database Aided GNSS Based Collaborative Positioning Using Factor Graph Optimization

The recent development in vehicle-to-everything (V2X) communication opens a new opportunity to improve the positioning performance of the road users. We explore the benefit of connecting the raw data of the global navigation satellite system (GNSS) from the agents. In urban areas, GNSS positioning is highly degraded due to signal blockage and reflection. 3D building model can play a major role in mitigating the GNSS multipath and non-line-of-sight (NLOS) effects. To combine the benefits of 3D models and V2X, we propose a novel 3D mapping aided (3DMA) GNSS-based collaborative positioning method that makes use of the available surrounding GNSS receivers’ measurements. By complementarily integrating the ray-tracing based 3DMA GNSS and the double difference technique, the random errors (such as multipath and NLOS) are mitigated while eliminating the systematic errors (such as atmospheric delay and satellite clock/orbit biases) between road user. To improve the accuracy and robustness of the collaborative algorithm, factor graph optimization (FGO) is employed to optimize the positioning solutions among agents. Multiple low-cost GNSS receivers are used to collect both static and dynamic data in Hong Kong and to evaluate the proposed algorithm by post-processing. We reduce the GNSS positioning error from over 30 meters to less than 10 meters for road users in a deep urban canyon.

GNSS attitude estimation based on adaptive Kalman filtering using phase measurement

Attitude estimation using multi-antenna Global Navigation Satellite System (GNSS) has caught broad attention in recent years. The methods of indirectly calculating attitude parameters based on baseline vectors have been widely used. However, the accuracy of such methods needs to be further improved. An algorithm of directly estimating attitude parameters based on adaptive Kalman filtering (AKF) is proposed. The high-precision phase measurements are used and the system noise covariance matrix corresponding to Euler angles and angle rates is adaptively adjusted according to the maximum a posteriori estimation principle. To decrease the linearisation errors and speed the filtering convergence, a switching strategy is implemented. Namely, when the number of fixed ambiguities is equal to or more than three, the authors deem that the attitude estimate is sufficiently accurate, hence the initial state vector is constructed to start filtering. Otherwise, the attitude parameters are indirectly obtained. The static and simulation experiments are carried out. A comparative study is implemented with the two methods of indirectly calculating attitude parameters. The static and simulation results demonstrate that the proposed method has a competent performance in both accuracy and fixing success rate. The simulation results also show that the adaptability of the AKF method is nice.

Design of a Compact, Multifrequency, Multiconstellation GNSS Precise Point Positioning Correction Format

High-accuracy, high-precision global navigation satellite systems (GNSSs) have been utilized by specialized user markets for over two decades. Traditional high-accuracy GNSS systems are not scalable as they require local infrastructure. Precise point positioning (PPP) is a GNSS position estimation technique that allows positioning and navigation with centimetre-level accuracy without local infrastructure. The caveat of PPP is the timely transmission of corrections to errors in the GNSS signals. Next-generation GNSS satellites such as Galileo, BeiDou, QZSS, and other local systems have plans to broadcast corrections for PPP services broadcast corrections for PPP services. However, since these services are expected to have limited channel capacity, the development of efficient formats for PPP corrections is needed. In this article, a messaging strategy for PPP corrections and testing its performance, in terms of data rate and obtained positioning accuracy, is proposed. Message formats in the literature require 522 bps or more to transmit corrections for 70 satellites. By contrast, the message format proposed in this article can transmit information corrections for more than 70 satellites using 52% of the standard satellite-based augmentation system channel's 212 bps capacity, while incurring less than 1 cm of positioning accuracy degradation.

Deeply Integrated GNSS/Gyro Attitude Determination System.

Attitude determination systems based on Global Navigation Satellite Systems (GNSS) work on principle of phase interferometer, using multiple receiving antennas. They rely on a good quality of carrier phase tracking, that is not the case in real dynamic environment with low signal-to-noise ratio (SNR), for example, in a ground vehicle moving through an urban area or forest. There is still a problem in providing a GNSS attitude in such common conditions. This research is focused on improving sensitivity (i.e., the capability of providing attitude at a low SNR) and the reliability of the GNSS attitude determination system. It is contrasted with the majority of publications, where precision or computational efficiency is the main goal, but sensitivity and reliability are out of their scope. In the proposed system, sensitivity improved by using two measures: (a) tracking only phase differences instead of tracking full carrier phases—this is more sensitive due to the lower dynamics of the underlying process, and (b) using deep integration with gyroscope, where all phase differences are tracked in a vector gyro-aided loop closed on user’s attitude in state vector. The algorithm synthesis is given, and simulation results are presented in this article. This shows that the minimal working SNR is lowered from 27–36 dBHz (typical) down to 20 dBHz, even with a low-cost MEMS gyroscope.

A Time‐Varying 3‐D Displacement Model of the ~5.9‐Year Westward Motion and its Applications for the Global Navigation Satellite System Positions and Velocities

AbstractTo advance geodynamics and geophysical research, high precision Global Navigation Satellite System (GNSS) observations of velocity and position are needed. In this study, we construct a 3‐D model of a ~5.9‐year periodic signal for the Earth surface displacements. This model is mainly based on the determined time sequences and the Y22 spatial pattern of this ~5.9‐year periodic signal from the global Global Positioning System (GPS) observations. Based on the constructed model, we calculate synthetic temporal 3‐D displacements on the Earth surface and the velocity changes, and we compare them to observed GPS displacements. Our results reveal that the ~5.9‐year signal contributes to surface displacements and velocity fields. Maximum displacements for the N, E, and U components can reach up to 0.28, 0.55, and 1.69 mm, respectively; maximum velocity effects can up to 1.69 mm/year for the U component (depending on record length). For those studies which need millimeter or even submillimeter accuracy (e.g., tectonic deformations, glacial isostatic adjustment, and deformations caused by core motions), these effects cannot be simply ignored. Our results also confirm that the model we present here can heavily reduce the ~5.9‐year signal in the original GPS time series. We suggest that our model should be used to pretreatment the GPS data at the observation level, which could improve signals used for geophysical or geodynamic interpretations.

A Novel UAV-Assisted Positioning System for GNSS-Denied Environments

Global Navigation Satellite Systems (GNSS) are extensively used for location-based services, civil and military applications, precise time reference, atmosphere sensing, and other applications. In surveying and mapping applications, GNSS provides precise three-dimensional positioning all over the globe, day and night, under almost any weather conditions. The visibility of the ground receiver to GNSS satellites constitutes the main driver of accuracy for GNSS positioning. When this visibility is obstructed by buildings, high vegetation, or steep slopes, the accuracy is degraded and alternative techniques have to be assumed. In this study, a novel concept of using an unmanned aerial system (UAS) as an intermediate means for improving the accuracy of ground positioning in GNSS-denied environments is presented. The higher elevation of the UAS provides a clear-sky visibility line towards the GNSS satellites, thus its accuracy is significantly enhanced with respect to the ground GNSS receiver. Thus, the main endeavor is to transfer the order of accuracy of the GNSS on-board the UAS to the ground. The general architecture of the proposed system includes hardware and software components (i.e., camera, gimbal, range finder) for the automation of the procedure. The integration of the coordinate systems for each payload setting is described, while an error budget analysis is carried out to evaluate and identify the system’s critical elements along with the potential of the proposed method.

Signal Extraction from GNSS Position Time Series Using Weighted Wavelet Analysis

The daily position time series derived by Global Navigation Satellite System (GNSS) contain nonlinear signals which are suitably extracted by using wavelet analysis. Considering formal errors are also provided in daily GNSS solutions, a weighted wavelet analysis is proposed in this contribution where the weight factors are constructed via the formal errors. The proposed approach is applied to process the position time series of 27 permanent stations from the Crustal Movement Observation Network of China (CMONOC), compared to traditional wavelet analysis. The results show that the proposed approach can extract more exact signals than traditional wavelet analysis, with the average error reductions are 13.24%, 13.53% and 9.35% in north, east and up coordinate components, respectively. The results from 500 simulations indicate that the signals extracted by proposed approach are closer to true signals than the traditional wavelet analysis.

Multipath Mitigation in GNSS Positioning by the Dual-Path Compression Estimation

The combinations of triple-frequency carrier phase have been widely used for precise positioning in the global navigation satellite system (GNSS). However, the position accuracy of this system is negatively affected by multipath (MP) interference and highly kinematic problems. To bridge this gap, in this paper, a dual-path compression estimation algorithm based on generalized least absolute shrinkage and selection operator (LASSO) method with penalty terms is proposed to mitigate MP. We establish a linear observation model, taking into account triple-frequency carrier phase and Doppler shift. In order to improve the accuracy of the compression estimation, a small penalty term is added after the re-weighted L1 regularization. Accordingly, the linear observation model is transformed into the MP estimation model, with the weight matrix consisting of the carrier-to-noise ratio function and satellite elevation. We use the dual-path algorithm to solve the LASSO problem in the MP estimation model. QR decomposition and the specialized implementation strategy are applied to improve the dual-path LASSO with penalty (DPLP) algorithm. The results on real-world dataset show that the sparse estimation method proposed in this study can effectively reduce the carrier phase MP errors at triple-frequency so long as the number of MP-affected satellites is less than five (the visible satellites is eight-ten).

A single-receiver geometry-free approach to stochastic modeling of multi-frequency GNSS observables

The proper choice of stochastic model is of great importance to global navigation satellite system (GNSS) data processing. Whereas extensive investigations into stochastic modeling are mainly based on the relative (or differential) method employing zero and/or short baselines, this work proposes an absolute method that relies upon a stand-alone receiver and works by applying the least-squares variance component estimation to the geometry-free functional model, thus facilitating the characterization of stochastic properties of multi-frequency GNSS observables at the undifferenced level. In developing the absolute method, special care has been taken of the code multipath effects by introducing ambiguity-like parameters to the code observation equations. By means of both the relative and absolute methods, we characterize the precision, cross and time correlation of the code and phase observables of two newly emerging constellations, namely the Chinese BDS and the European Galileo, collected by a variety of receivers of different types at multiple frequencies. Our first finding is that so far as the precision is concerned, the absolute method yields nearly the same numerical values as those derived by the zero-baseline-based relative method. However, the two methods give contradictory results with regard to the cross correlation, which is found (not) to occur between BDS phase observables when use has been made of the relative (absolute) method. Our explanation to this discrepancy is that the cross correlation found in the relative method originates from the parts (antenna, cable, low noise amplifier) shared by two receivers creating a zero baseline. The time correlation is only of significance when the multipath effects are present, as is the case with the short-baseline-based relative method; this correlation turns out to be largely weaker (or ideally absent) in the absolute (or zero-baseline-based relative) method. Moreover, with the absolute method, the stochastic properties determined for two receivers of the same type but subject to different multipath effects are virtually the same. We take this as a convincing evidence that the absolute method is robust against multipath effects. Hence, the absolute method proposed in the present work represents a promising complement to the relative method and appears to be particularly beneficial to GNSS positioning, navigation and timing technologies based on the undifferenced observables, typically the precise point positioning.

A Novel GNSS Attitude Determination Method Based on Primary Baseline Switching for A Multi-Antenna Platform

The global navigation satellite system (GNSS)-based attitude determination system has attracted more and more attention with the advantages of having simplified algorithms, a low price and errors that do not accumulate over time. However, GNSS signals may have poor quality or lose lock in some epochs with the influence of signal fading and the multipath effect. When the direct attitude determination method is applied, the primary baseline may not be available (ambiguity is not fixed), leading to the inability of attitude determination. With the gradual popularization of low-cost receivers, making full use of spatial redundancy information of multiple antennas brings new ideas to the GNSS-based attitude determination method. In this paper, an attitude angle conversion algorithm, selecting an arbitrary baseline as the primary baseline, is derived. A multi-antenna attitude determination method based on primary baseline switching is proposed, which is performed on a self-designed embedded software and hardware platform. The proposed method can increase the valid epoch proportion and attitude information. In the land vehicle test, reference results output from a high-accuracy integrated navigation system were used to evaluate the accuracy and reliability. The results indicate that the proposed method is correct and feasible. The valid epoch proportion is increased by 16.2%, which can effectively improve the availability of attitude determination. The RMS of the heading, pitch and roll angles are 0.52°, 1.25° and 1.16°.

Robust Kalman Filtering Based on Chi-square Increment and Its Application

In Global Navigation Satellite System (GNSS) positioning, gross errors seriously limit the validity of Kalman filtering and make the final positioning solutions untrustworthy. Thus, the detection and correction of gross errors have become indispensable parts of Kalman filtering. Starting by defining an incremental Chi-square method of recursive least squares, this paper extends this definition to Kalman filtering to detect gross errors, explains its nature and its relation with the currently adopted Chi-square variables of Kalman filtering in model and data spaces, and compares them with the predictive residual statistics. Two robust Kalman filtering models based on an incremental Chi-square method (CI-RKF) were established, and the one with a better incremental Chi-square component was selected based on a static accuracy evaluation experiment. We applied the selected robust model to the GNSS positioning and the GNSS/inertial measurement unit (IMU) / visual odometry (VO) integrated navigation experiment in an occluded urban area at the East China Normal University. We compared the results for conventional Kalman filtering (CKF) with a robust Kalman filtering constructed using predictive residual statistics and an Institute of Geodesy and Geophysics (IGGШ) weight factor, abbreviated as “PRS-IGG-RKF”. The results show that the overall accuracy of CI-RKF in GNSS positioning was improved by 22.68%, 54.33%, and 72.45% in the static experiment, and 12.30%, 7.50%, and 16.15% in the kinematic experiment. The integrated navigation results indicate that the CI-RKF fusion method increased the system positioning accuracy by 66.73%, 59.59%, and 59.62% in one of the severe occlusion areas, and 42.04%, 59.04%, and 52.41% in the other.

An accurate cooperative positioning system for vehicular safety applications

Typical Global Navigation Satellite System (GNSS) receivers offer precision in the order of meters. This error margin is excessive for vehicular safety applications, such as forward collision warning, autonomous intersection management, or hard braking sensing. In this work we develop a Cooperative GNSS Positioning System (CooPS) that uses Vehicle to Vehicle (V2V) and Vehicle to Infrastructure (V2I) communications to cooperatively determine absolute and relative position of the ego-vehicle with enough precision. To that end, we use differential GNSS through position vector differencing to acquire track and across-track axes projections, employing elliptical and spherical geometries. We evaluate CooPS performance by carrying out real experiments using off-the-shelf IEEE 802.11p equipment at the campus of the Federal University of Rio de Janeiro. We obtain an accuracy level under 1.0 and 1.5 m for track (where-in-lane) and across-track (which-lane) axes, respectively. These accuracy levels were achieved using a 2.5 m accuracy circular error probable (CEP) of 50% and a 5 Hz navigation update rate GNSS receiver.

The ADOP and PDOP: Two Complementary Diagnostics for GNSS Positioning

Ambiguity dilution of precision (ADOP) and position dilution of precision (PDOP) are two popular scalar-diagnostics used in Global Navigation Satellite System (GNSS) positioning. Where the ADOP is a predictor for carrier-phase ambiguity resolution performance, the PDOP is meant to predict the receiver-satellite geometry’s capability for precise positioning. We will show, however, that although the PDOP works well for code-based positioning, one has to exercise great care in using the PDOP for real-time kinematic (RTK) positioning. We show that the ADOP and PDOP have distinct behaviors, an important consequence of which is that one can have time periods with small PDOPs, and thus seemingly good geometry for precise positioning, but at the same time large ADOPs, thus showing that successful ambiguity resolution and therefore precise positioning will not be possible. Also, the reverse situation may occur, i.e., having large PDOPs with small ADOPs. In such a situation, the large PDOPs should not automatically lead to the conclusion of poor position performance, because the large gain that ambiguity resolution brings will often still make precise positioning possible. We will analyze and explain this complementary behavior of the PDOP and ADOP and demonstrate this both analytically and empirically. For this analysis we use real Global Positioning System (GPS) single- and multifrequency signals and GPS/Quasi-Zenith Satellite System (QZSS), GPS/Navigation with Indian Constellation (NAVIC) L5 signals of two baselines located in Perth, Australia.

An Improved Ambiguity-Free Method for Precise GNSS Positioning with Utilizing Single Frequency Receivers.

The solution of carrier phase ambiguity is essential for precise global navigation satellite system (GNSS) positioning. Methods of searching in the coordinate domain show their advantage over the methods based on ambiguity fixing, for example, immune to cycle slips, far fewer epochs taken for obtaining the precise solution. However, there are still some drawbacks via using the Ambiguity Function Method (AFM), such as low computation efficiency and the existence of a false global optimum. The false global optimum is a situation where the Least Square (LS) criterion achieves minimum in another place than the point of the actual position, which restricts the application of this method to single-frequency receivers. The numerical search approach derived in this paper is based on the Modified Ambiguity Function Approach (MAFA). It focuses on eliminating the false optimum solution and reducing the computation load by utilizing single-frequency receivers without solving the ambiguity fixing problem. An improved segmented simulated annealing method is used to decrease the computation load while the Kernel Density Estimator (KDE) method is used to filter out the false optimum candidates. Static experiments were carried out to evaluate the performance of the new approach. It is shown that a precise result can be obtained by handling two epochs of data with z coordinate fixed to the referenced value. Meanwhile, the new approach can achieve a millimeter level of position accuracy after dealing with nineteen epochs of observations data when searching in domain. The new approach shows its robustness even if the search region is broad, and the prior position is several meters away from the referenced value.