Carrier Phase Biases Research Articles

A STAP anti-interference technology with zero phase bias in wireless IoT systems based on high-precision positioning

Fog computing has been applied to the data processing for the Internet of Things (IoT) based on distributed high-precision Global Navigation Satellite Systems (GNSS). However, the space-time adaptive processing (STAP) interference suppression technology in the system will cause fog computing data deviation that includes carrier phase bias and pseudocode offset. An unbiased STAP technique is proposed to eliminate these deviations. First, it is analyzed that the carrier phase bias and pseudocode offset are caused by the non-linear phase response of the STAP equivalent filter. Then, a coefficient-constrained method based on practical engineering processing is proposed, which can eliminate these deviations by restricting the tap coefficients to be symmetrically equal around the center-tap. Moreover, by analyzing the coherent integral function of the pseudocode after filtering, the tap structure of STAP is modified to eliminate the group offset of the pseudocode without increasing the computational complexity and hardware resources. Finally, the unbiased performance and anti-interference performance of the system are verified by numerical and real data simulations.

Carrier Characteristic Bias Estimation between GNSS Signals and Its Calibration in High-Precision Joint Positioning

A distinctive feature of modern Global Navigation Satellite System (GNSS) signals is that they transmit multiple signal components at the same carrier frequencies. The idea of joints across the signal channels from the same carrier frequency and even across different frequencies has been presented in many studies for tracking purposes. Carrier joint tracking is required on the premise that the frequency and phase relationship between signals are nominal values, and the bias of carrier characteristics between signals is drowned in noise as the signal reaches the ground, which requires high-gain receiving equipment to restore the original signal. The space signal-quality monitoring and evaluation system built by the National Timing Center of the Chinese Academy of Sciences is based on a 40 m dish antenna, which can automatically track a single satellite and achieve a high-fidelity reception of navigation signals to a certain extent, realizing fine signal quality monitoring (SQM) of GNSS satellites. Based on this platform, we discuss four types of time distributions of the combined signals among different signal components and provide a method to estimate the carrier characteristic bias between GNSS signals. We derived the correction method of carrier characteristic bias in the joint reception by the joint tracking mathematical model. Under the conditions of narrow correlation and unobstructed case, the carrier characteristic deviation does not vary significantly with the correlator interval and the satellite elevation angle. Based on the results of stability analysis, it is recommended that the receivers should update the carrier frequency bias correction number of the intra-frequency signal and carrier phase bias correction number of the intra-frequency signal monthly. The carrier phase deviation correction number of the inter-frequency signal is performed daily. The measured data from satellites show that the phase accumulation error of the joint tracking carrier loop can be eliminated to achieve long-term stable tracking after frequency bias correction. After the carrier phase bias correction, the joint positioning accuracy of the B2a and B2b signals was improved by 0.81%, and those of the B1C, L1C, E1C, and B2a signals were improved by 0.35%, 0.04%, 0.20%, and 0.11%, respectively. The positioning accuracy improvement effect of inter-frequency signals was greater than that of intra-frequency signals after carrier phase correction.

Time-differenced double difference method for measurement of Navigation with Indian Constellation (NavIC) receiver differential phase bias

The pseudo-range (PR) and carrier phase (CP) observations of Global Navigation Satellite System (GNSS)/Navigation with Indian Constellation (NavIC) receivers are influenced due to various errors like ionosphere delay, troposphere delay, receiver and satellite clock error, multipath, integer ambiguity, receiver hardware noise etc. However, the real-time positioning and navigation applications are in quest of high-quality carrier phase measurements with zero bias. The GNSS/NavIC receiver hardware noise is one of the critical error sources that degrade the quality of carrier phase measurements. And it can be measured by computing the differential phase bias or carrier phase bias employing the double-difference method. This research article proposes a novel approach called Time Differenced Double Difference Carrier Phase (TDDDCP) for estimating differential phase bias or carrier phase bias of NavIC receiver. Moreover, the proposed TDDDCP technique has the advantage over the Double Difference Carrier Phase (DDCP) because it requires data from only one satellite with two zero base length receivers for which the differential phase bias is to be measured. The experimental results show that the differential phase bias value differs for different satellites, ranging from −0.3904 m to 0.3168 m. The bias-free carrier phase observations based on position coordinates (X, Y, Z) found improved precision of standard deviation of 0.4176 m, 0.645 m, and 0.328 m, respectively.

A new blind anti‐jamming algorithm based on a novel antenna array design

The next-generation navigation tools are developed to enable precision and reliability. Military users are more likely to encounter jamming, so it is necessary to seek the technologies which can steadily provide high-precision positioning services in all-weather and harsh conditions. However, when users use an array antenna for interference suppression, it usually introduces pseudorange and carrier phase biases, which deteriorates the accuracy and integrity of positioning. To address this issue, the authors propose a blind anti-interference algorithm with biases suppression. Compared to the commonly used blind space–time adaptive anti-jamming algorithms, this algorithm can not only retain the advantages of the simple structure of the blind anti-jamming algorithm but also suppress pseudorange biases and carrier phase biases, both of which are crucial for users to obtain the availability of positioning. Moreover, the algorithm proposed can be applied easily and quickly to the actual high-precision positioning system with minor hardware changes in some cases. The relevant theoretical analysis and experiments have proved the effectiveness of the proposed algorithm: (1) code phase biases and carrier phase biases can almost be ignored and (2) it also can significantly improve the accuracy and integrity of positioning; the average positioning error is 1.6 mm, and it can keep the positioning accuracy better than 0.1 m for 97.5% of the time.

An optimal indoor trust-region PPP algorithm with constrain of homologous array pseudolite

Homologous array pseudolite with simple time synchronization technique can provide high-precision larger-area indoor location service with outdoor GNSS receiver, but this architecture is born with several drawbacks, such as poor geometry, larger linearization error and multi-path error caused by signal reflection, and indoor positioning with this homologous array pseudolite can easily lead to potential divergence. Besides, fluctuation of time-delay, error of phase center and potential multipath error break integer propriety of carrier phase ambiguity and can’t be ignored for indoor PPP (Precise Point Positioning). Under these constrictions, optimal ambiguity-float indoor PPP algorithm with trust region is proposed, and performance of this optimal algorithm with the modified Levenberg-Marquardt technique, which is designed to avoid potential divergence particularly for poor geometry, is assessed with simulation and observation filed experiment. Meanwhile, the domain factor affecting performance of PPP and mechanism of accumulative error when moving are analyzed. The experimental result reveals that: unavoidable inaccuracy of position of pseudolite transmitting antenna can cause larger error of carrier phase bias that can be larger than 0.105 cycles, and it along with fluctuation of hardware group delay and multi-path error will cause position error that can be larger than 0.12 for most cases, the indoor static and kinematic PPP can obtain a few centimeter and smooth trace respectively, and the accuracy of indoor positioning based on this optimal algorithm can be better than 0.1668 m even at the corner of experiment area with poor geometry. Still there is particular circumstance that accuracy of this algorithm can be larger than 0.5741 m due to serious accumulative error with less satellite available when moving, the mechanism for it is analyzed with relationship between error of position and measurement error and depicted as follows: when some satellites with cycle slip occurs, the accuracy of position determined will reduce greatly due to less satellite available particularly with indoor homologous array pseudolite. Afterwards, the error of the position determined will lead to error of carrier phase ambiguity biases, which will cause large biases of subsequent position determined.

Carrier phase correction for GNSS space‐time array processing based on frequency jerk detection

The signals of Global Navigation Satellite System (GNSS) are so vulnerable that can be easily jammed by intentional or unintentional interferences. One of the effective ways to protect GNSS signals from jamming is to use the Space-Time Array Processing (STAP) technology. However, undesired carrier phase bias would be induced to the signals because of the STAP, which significantly influences the precision of positioning. Many algorithms have been proposed to deal with this carrier phase bias, but most of them need the directional information of signals or the pre-test of antennas. In this paper, a carrier phase correction algorithm without the need of prior information is proposed. Alarmed by the jerk of carrier frequency, the algorithm can detect the change of jamming and calculate the induced carrier phase bias. Then it can correct this bias from the signal and alleviate its influence. The simulation results show that the algorithm can limit the bias from more than 60° to less than 10°, which verifies that the proposed algorithm is effective in the low dynamic receiver.

An unbiased carrier-phase anti-interference filter based on mirror frequency amplitude compensation

Anti-interference and high-precision measurement are two important indicators of the performance of a satellite navigation receiver. However, current receiver designs do not simultaneously satisfy these two criteria. While the carrier-phase ranging technique is necessary for high-precision receivers, frequency domain interference suppression (FDIS) results in tracking error biases for nonideal analog receiver channels. Importantly, as the FDIS filter is adaptive, the bias will vary with the jamming pattern, particularly when the frequency of interference varies. For precision navigation applications, this bias must be mitigated. Therefore, a new FDIS filter based on the mirror frequency amplitude compensation (MFAC) method is proposed in this paper. The amplitude at the symmetry position of the notch frequency is doubled in the MFAC method to mitigate this carrier-phase bias. The simulation results showed that the MFAC method can reduce the range of the carrier-phase bias by more than 60% for different interference bandwidths, which substantially exceeds that achieved using the conventional FDIS and calibration filter methods of 20 orders.

Determination and analysis of front-end and correlator-spacing-induced biases for code and carrier phase observations

Global navigation satellite system (GNSS) biases preclude integer ambiguity resolution and degrade positioning accuracy if they are not corrected in GNSS precise applications. Biases in GNSS positioning applications occur because of imperfections and physical limitations in satellite and receiver hardware. Consequently, these biases will affect the accuracy of positioning solutions, particularly for precise applications due to the existence of biases in the code and carrier phase observations. Various types of biases between systems, frequencies, and satellites have been defined and analyzed. In addition, receiver biases are often assumed to be eliminated by differencing observations between satellites, although this is not always true. This paper investigates the determination of the receiver front-end and correlator-spacing-induced biases in code and carrier phase observations with a focus on how receiver front-end and correlator spacing affect the code and carrier phase measurements, and how such biases vary with respect to the use of different correlator spacings and frontends. Firstly, oscillator, front-end chip, and ADC-induced biases, as well as their observability, will be discussed. Several groups of datasets with different frontends have been collected and used to determine the inter-front-end (including oscillator, chip, and ADC) pseudorange and carrier phase biases. Then, a software receiver that allows the tracking of a satellite with a series of different correlator spacings has been developed to assess measurement biases with different datasets. The results show that the inter-front-end biases and correlator-spacing-induced biases are significantly different among satellites, which can not be ignored during the GNSS positioning. This is because the single-difference of measurements between satellites can not eliminate all these biases. The results with the software receiver connected to different frontends and different correlator spacings indicate that the satellite-dependent biases depend on the configuration of the in-receiver hardware and software.

REAL TIME PPP APPLIED TO AIRPLANE FLIGTHT TESTS

The availability in real time of GNSS satellites orbits, clock corrections and code and phase biases provided the possibility of application of Real Time Precise Point Positioning (RTPPP). This paper presents the methodology concerning RTPPP and application to kinematic trajectories of airplane flight tests, but without using the carrier phase bias. So, it is PPP float solution. It requires RT positioning estimation, task that most of time presents certain difficulties due to loss of communication or of satellites during maneuvers of the airplane. However, if the corrections become unavailable for a certain period of time, the system starts using the ultra-rapid IGS orbits. The experiments were accomplished taking into account a case simulating RT and another in fact RT, but storing data and corrections for post processing. The PPP solutions obtained either simulating RT or in RT were compared against the PPP post processed solution that uses the final clock and orbit corrections. Then, statistics were generated to analyze the quality of both results. They were applied to kinematic trajectory that on average was 360 km/h, reaching about 600 km/h. The results provided accuracy better than the requisites for such cases which is of about 80 cm in height.

RTK model and positioning performance analysis using Galileo four-frequency observations

This paper proposes a real-time kinematic (RTK) model that uses one common reference satellite for the Galileo system with four frequency observations. In the proposed model, the double-differenced (DD) pseudorange and carrier phase biases among the different frequencies are estimated as unknown parameters to recover the integer features of the DD ambiguities among the different frequencies for ambiguity resolution and precise positioning. Analysis results show that the E5a, E5b, and E5 frequencies have virtually the same performance in terms of the positioning accuracy, observation residuals, and ratio values of ambiguity resolution. However, the E1 frequency performs worse than the E5a, E5b, and E5 frequencies. The RTK results for the combination of multiple frequencies are much better than those for a single-frequency observation, the coordinates’ standard deviation is improved about 20–30%, and the ambiguity fix time is improved about 10%.

Adaptive blind anti-jamming algorithm using acquisition information to reduce the carrier phase bias

Jamming destroys the integrity and functionality of the Global Satellite Navigation System (GNSS) in various applications. Hence, anti-jamming techniques are critical. The most significant problem with the existing array-based anti-jamming technique in GNSS is the errors introduced in the carrier phase, which affects the GNSS solution, especially for high-precision measurement applications. We present an adaptive array-based blind anti-jamming algorithm for GNSS high-precision applications. The main advantages of the proposed algorithm include (1) the received data containing multiple satellite signals are processed in parallel channels simultaneously thanks to the acquisition information. (2) The adaptive weight is constructed in each individual channel, directly from an eigenvector of the despread data covariance matrix, resulting in low implementation complexity. (3) The carrier phase of the weighted data at the initial moment is used to normalize the subsequent ones, so as to completely remove the introduced carrier phase bias by adaptive weighting. (4) Since the array manifold is not used, the proposed algorithm is robust to array errors. Theoretical and numerical simulations verify the superiority of the proposed algorithm.

Effects of power inversion spatial only adaptive array on GNSS receiver measurements

The Spatial Only Processing Power Inversion (SOP-PI) algorithm is frequently used in Global Navigation Satellite System (GNSS) adaptive array receivers for interference mitigation because of its simplicity of implementation. This study investigates the effects of SOP-PI on receiver measurements for high-precision applications. Mathematical deductions show that if an array with a centro-symmetrical geometry is used, ideally, SOP-PI is naturally bias-free; however, this no longer stands when non-ideal factors, including array perturbations and finite-sample effect, are added. Simulations are performed herein to investigate how exactly the array perturbations affect the carrier phase biases, while diagonal loading and forward-backward averaging are proposed to counter the finite-sample effect. In conclusion, whether SOP-PI with a centro-symmetrical array geometry will satisfy the high precision demands mainly depends on the array perturbation degree of the element amplitude and the phase center.

Carrier phase bias estimation of geometry-free linear combination of GNSS signals for ionospheric TEC modeling

The ionosphere can be modeled and studied using multi-frequency GNSS signals and their geometry-free linear combination. Therefore, a number of GNSS-derived ionospheric models have been developed and applied in a broad range of applications. However, due to the complexity of estimating the carrier phase ambiguities, most of these models are based on low-accuracy carrier phase smoothed pseudorange data. This, in turn, critically limits their accuracy and applicability. Therefore, we present a new methodology of estimating the phase bias of the scaled L1 and L2 carrier phase difference which is a function of the ambiguities, the ionospheric delay, and hardware delays. This methodology is suitable for ionospheric modeling at regional and continental scales. In addition, we present its evaluation under varying ionospheric conditions. The test results show that the carrier phase bias of geometry-free linear combination can be estimated with a very high accuracy, which consequently allows for calculating ionospheric TEC with the uncertainty lower than 1.0 TECU. This high accuracy makes the resulting ionosphere model suitable for improving GNSS positioning for high-precision applications in geosciences.

An all-pass filter for compensation of ionospheric dispersion effects on wideband GNSS signals

Compared with the traditional GPS L1 C/A BPSK-R(1) signal, wideband global navigation satellite system (GNSS) signals suffer more severe distortion due to ionospheric dispersion. Ionospheric dispersion inevitably introduces additional errors in pseudorange and carrier phase observations that cannot be readily eliminated by traditional methods. Researchers have reported power losses, waveform ripples, correlation peak asymmetries, and carrier phase shifts caused by ionospheric dispersion. We analyze the code tracking bias induced by ionospheric dispersion and propose an efficient all-pass filter to compensate the corresponding nonlinear group delay over the signal bandwidth. The filter is constructed in a cascaded biquad form based on the estimated total electron content (TEC). The effects of TEC accuracy, filter order, and fraction parameter on the filter fitting error are explored. Taking the AltBOC(15,10) signal as an example, we compare the time domain signal waveforms, correlation peaks, code tracking biases, and carrier phase biases with and without this all-pass filter and demonstrate that the proposed delay-equalization all-pass filter is a potential solution to ionospheric dispersion compensation and mitigation of observation biases for wideband GNSS signals.

Challenges in Assessing PPP Performance

AbstractThe Precise Point Positioning (PPP) GPS data processing technique has developed over the past 15 years to become a standard method for growing categories of positioning and navigation applications. The technique relies on single receiver point positioning combined with precise satellite orbit and clock information, pseudorange and carrier-phase observable filtering, and additional error modelling. Uniquely addressed is the current accuracy of the technique, and explains the limits of performance, which will be used to define paths for future improvements of the technology.PPP processing of over 300 International GNSS Service (IGS) stations over one week results in few millimetre positioning rms error in the north and east components and centimetre-level in the vertical (all one sigma values). These results are categorised into quality classes in order to analyse the root causes of the resultant errors: "best", "worst", multipath, antenna displacement effects, satellite availability and geometry, etc. Also of interest in PPP performance is solution convergence period. Static, conventional solutions are slow to converge, with approximately 20 minutes required for 95% of solutions to reach a horizontal accuracy of 20 cm or better.From the above analysis, the limitations of PPP and the source of these limitations are isolated, including site displacement modelling, geometric measurement strength, pseudorange multipath and noise, etc. It is argued that new ambiguity resolution and multi-GNSS PPP processing will only partially address these limitations. Improved modelling is required for: site displacement effects, pseudorange noise and multipath, and pseudorange and carrier-phase biases. As well, more robust undifferenced carrier phase ambiguity validation and improved stochastic modelling is required for the pseudorange and carrier-phase observables to allow for more realistic position uncertainties.

Initial assessment of the COMPASS/BeiDou-2 regional navigation satellite system

An initial characterization and performance assessment of the COMPASS/BeiDou-2 regional navigation system is presented. Code and carrier phase measurements on up to three frequencies have been collected in March 2012 with a small regional network of monitoring stations. The signal and measurement quality are analyzed and compared with the Japanese Quasi Zenith Satellite System. A high level of stability is demonstrated for the inter-frequency carrier phase biases, which will facilitate the application of triple-frequency undifferenced ambiguity resolution techniques in future precise point positioning applications. The performance of the onboard Rubidium frequency standards is evaluated in comparison to ground-based hydrogen masers and shown to be well competitive with other GNSS satellite clocks. Precise orbit and clock solutions obtained in post-processing are used to study the presently achievable point positioning accuracy in COMPASS/BeiDou-2-only navigation. Finally, the benefit of triple-frequency measurements and extra-wide-lane ambiguity resolution is illustrated for relative positioning on a short baseline.

An enhanced calibration method of GLONASS inter-channel bias for GNSS RTK

A user of heterogeneous GPS and GLONASS receiver pairs in differential positioning mode will experience ambiguity fixing challenges due to the presence of inter-channel biases. These biases cannot be canceled by differencing GLONASS observations, whether pseudorange or carrier phase. Fortunately, pre-calibration of GLONASS pseudorange and carrier phase observations can make ambiguity fixing for GPS/GLONASS positioning much easier. We propose an effective algorithm that transforms an RTK (real-time kinematic) solution in a mixed receiver baseline from a float to a fixed ambiguity solution. Carrier phase and code inter-channel biases are estimated from a zero baseline. Then, GLONASS both carrier phase and code observations are corrected accordingly. The results show that a mixed baseline can be transformed from a float (~100 %) to a fixed (more than 92 %) solution.

Single receiver phase ambiguity resolution with GPS data

Global positioning system (GPS) data processing algorithms typically improve positioning solution accuracy by fixing double-differenced phase bias ambiguities to integer values. These “double-difference ambiguity resolution” methods usually invoke linear combinations of GPS carrier phase bias estimates from pairs of transmitters and pairs of receivers, and traditionally require simultaneous measurements from at least two receivers. However, many GPS users point position a single local receiver, based on publicly available solutions for GPS orbits and clocks. These users cannot form double differences. We present an ambiguity resolution algorithm that improves solution accuracy for single receiver point-positioning users. The algorithm processes dual- frequency GPS data from a single receiver together with wide-lane and phase bias estimates from the global network of GPS receivers that were used to generate the orbit and clock solutions for the GPS satellites. We constrain (rather than fix) linear combinations of local phase biases to improve compatibility with global phase bias estimates. For this precise point positioning, no other receiver data are required. When tested, our algorithm significantly improved repeatability of daily estimates of ground receiver positions, most notably in the east component by approximately 30% with respect to the nominal case wherein the carrier biases are estimated as real values. In this “static” test for terrestrial receiver positions, we achieved daily repeatability of 1.9, 2.1 and 6.0 mm in the east, north and vertical (ENV) components, respectively. For kinematic solutions, ENV repeatability is 7.7, 8.4, and 11.7 mm, respectively, representing improvements of 22, 8, and 14% with respect to the nominal. Results from precise orbit determination of the twin GRACE satellites demonstrated that the inter-satellite baseline accuracy improved by a factor of three, from 6 to 2 mm up to a long-term bias. Jason-2/Ocean Surface Topography Mission precise orbit determination tests results implied radial orbit accuracy significantly below the 10 mm level. Stability of time transfer, in low-Earth orbit, improved from 40 to 7 ps. We produced these results by applying this algorithm within the Jet Propulsion Laboratory’s (JPL’s) GIPSY/OASIS software package and using JPL’s orbit and clock products for the GPS constellation. These products now include a record of the wide-lane and phase bias estimates from the underlying global network of GPS stations. This implies that all GIPSY–OASIS positioning users can now benefit from this capability to perform single-receiver ambiguity resolution.

Design and Performance Analysis of GPS Based Precise Relative Navigation for Rendezvous and Formation Flying Missions in Low Earth Orbit

Precise relative GPS navigation is essential technology for rendezvous and formation flying of spacecraft in Low Earth Orbit. Key design issues of precise relative GPS navigation software are studied and a novel formulation is proposed for the mission which requires high accuracy when the separation distance is up to several km. The navigation filter estimates float navigation solutions by extended Kalman filter with elaborate dynamics models, and resolves ambiguities of integer carrier phase biases to achieve high accuracy fix navigation solutions. A relative navigation software with the proposed formulation is implemented and evaluated in two different ways. One is a test using spacebourne GPS receivers and a GPS signal simulator to evaluate the performance and sensitivity of the software against variation of parameters. The other is a test using actual telemetry data from Gravity Recovery and Climate Experiment (GRACE) to demonstrate the software performance. The design, implementation, and results of the evaluation are presented and discussed on this paper.

Estimation of Adaptive Antenna Induced Code and Carrier Phase Bias in GNSS Receivers

An approach to estimate the adaptive antenna induced code phase and carrier phase biases in global navigation satellite systems (GNSS) receivers is described. In the approach, the in situ volumetric patterns of individual antenna elements are used. Since these patterns do not vary with the incident signal scenario, the patterns can be measured/analyzed in advance and can be stored for the estimation of antenna induced biases. We demonstrate the accuracy of the proposed approach by comparing the estimated biases with the results obtained using computer simulations. In practice, GNSS receivers use early and late time responses to find the peak of the cross-correlation function. Early minus late based discriminators assume the cross correlation function to be symmetrical. Due to the non-linear phase of GNSS antennas (fixed as well as adaptive antennas) over the satellite signal bandwidth, the cross-correlation function may not be symmetrical, leading to an additional bias. In this paper, we also present an extension to our estimation approach to include this receiver induced bias in the antenna bias.