Triple-frequency Global Navigation Satellite Systems Research Articles

Ionospheric delay prediction based on online polynomial modeling for real-time cycle slip repair of undifferenced triple-frequency GNSS signals

In real-time cycle slip repair of undifferenced triple frequency Global Navigation Satellite Systems (GNSS) phase signals, ionospheric delay prediction is crucial in estimating the narrow lane part of the cycle slips. A quadratic model is recursively constructed using estimated ionospheric delays and used to perform one-step prediction. The model errors are distinguished from the data introduced errors and the model error variance is adaptively tuned online. In estimating the float narrow-lane cycle slips, a statistically rigorous error model is followed where the correlations between the predicted ionospheric delays and the epoch-differenced phases are given full considerations. An efficient algorithm for implementing the proposed method is developed where matrix inversion is avoided. A real Beidou System (BDS) data set is employed to check the performance of the proposed method. The manually introduced cycle slips have been all correctly repaired.

A method for precise point positioning with integer ambiguity resolution using triple-frequency GNSS data

This paper proposes a method for precise point positioning with integer ambiguity resolution (PPP-AR) using triple-frequency global navigation satellite systems (GNSS) data. Firstly, an enhanced linear combination is developed for rapid fixing of the extra wide-lane (EWL) and wide lane (WL) ambiguities. This combination has improved performance compared to the Melbourne–Wübbena linear combination, and has 6.7% lower measurement error for the GPS L1/L2 signals, 12.7% lower error for L1/L5, and 0.7% lower error for L2/L5. Comparable improvements were also determined for the Beidou and Galileo constellations.After fixing the EWL/WL ambiguities, a full-rank, triple-frequency carrier-phase-only PPP model is proposed with ionosphere constraints. The probability of AR success rate (Ps) is analysed with the LAMBDA method, using a range of carrier phase and regional ionospheric model (RIM) precisions. Results show that a Ps of 99% is achieved within four epochs of data with carrier phase std = 0.002 m and RIM std = 0.1 total electron content unit (TECU); and within six epochs when RIM std = 0.5 TECU. When the carrier phase std was increased to 0.02 m (depicting high multipath conditions), and with use of a low-precision RIM (std = 0.5 TECU), the proposed method gave significantly improved performance over the method proposed by Li et al (2014 GPS Solut. 18 429–42).The direct estimation of the more challenging narrow-lane (NL) integer ambiguity is analysed by multi-epoch averaging of a proposed geometry-free and ionosphere-free triple-frequency linear combination. Tests with GPS data showed that 65.4% of the NL ambiguities were fixed within 10 min, 90.2% within 20 min, and 95.6% within 30 min.

Cycle Slip Detection during High Ionospheric Activities Based on Combined Triple-Frequency GNSS Signals

The current cycle slip detection methods of Global Navigation Satellite System (GNSS) were mostly proposed on the basis of assuming the ionospheric delay varying smoothly over time. However, these methods can be invalid during active ionospheric periods, e.g., high Kp index value and scintillations, due to the significant increase of the ionospheric delay. In order to detect cycle slips during high ionospheric activities successfully, this paper proposes a method based on two modified Hatch–Melbourne–Wübbena combinations. The measurement noise in the Hatch–Melbourne–Wübbena combination is minimized by employing the optimally selected combined signals, while the ionospheric delay is detrended using a smoothing technique. The difference between the time-differenced ambiguity of the combined signal and this estimated ionospheric trend is adopted as the detection value, which can be free from ionospheric effect and hold the high precision of the combined signal. Five threshold determination methods are proposed and compared to decide the cycle slip from the magnitude aspect. This proposed method is tested with triple-frequency Global Navigation Satellite System observations collected under high ionospheric activities. Results show that the proposed method can correctly detect and fix cycle slips under disturbed ionosphere.

Detection and Correction of Cycle Slip in Triple-Frequency GNSS Positioning

High precision positioning requires correct carrier phase observation. However, signal block will cause the discontinuity of the carrier phase named as cycle slip, which will severely depress the positioning efficiency and accuracy. Triple-frequency global navigation satellite system measurements bring benefit to the detection and repair of cycle slip. We propose a modified method to detect cycle slip based on combinations of triple-frequency signals. Cycle slips on the three combinations with longer wavelengths and lower noises are determined by the geometry-free model. Then, original cycle slips on three carriers are determined uniquely by the linear equations. To deal with the insensitive cycle slips, an alternative combination is presented as a supplementary. However, the residual of the first-order time-differenced ionospheric error cannot be ignored in this step or will be mistaken as cycle slip if not eliminated. To remove this interference, the residual is compensated by pre-estimations calculated by previous wide-lane combination with no cycle slips have been detected. In the end, real triple-frequency GPS data provided by IGS is processed by this method. The results show that the proposed method can detect all cycle slips in real time even under high ionospheric activity.

An analytical study on the carrier-phase linear combinations for triple-frequency GNSS

The linear combinations of multi-frequency carrier-phase measurements for Global Navigation Satellite System (GNSS) are greatly beneficial to improving the performance of ambiguity resolution (AR), cycle slip correction as well as precise positioning. In this contribution, the existing definitions of the carrier-phase linear combination are reviewed and the integer property of the resulting ambiguity of the phase linear combinations is examined. The general analytical method for solving the optimal integer linear combinations for all triple-frequency GNSS is presented. Three refined triple-frequency integer combinations solely determined by the frequency values are introduced, which are the ionosphere-free (IF) combination that the Sum of its integer coefficients equal to 0 (IFS0), the geometry-free (GF) combination that the Sum of its integer coefficients equal to 0 (GFS0) and the geometry-free and ionosphere-free (GFIF) combination. Besides, the optimal GF, IF, extra-wide lane and ionosphere-reduced integer combinations for GPS and BDS are solved exhaustively by the presented method. Their potential applications in cycle slip detection, AR as well as precise positioning are discussed. At last, a more straightforward GF and IF AR scheme than the existing method is presented based on the GFIF integer combination.

A new triple-frequency cycle slip detecting algorithm validated with BDS data

Triple-frequency global navigation satellite systems allow the introduction of additional linear observation combinations. We define two geometry-free phase combinations and one geometry-free pseud...

Real-time detection and repair of cycle slips in triple-frequency GNSS measurements

Cycle slip detection and repair are prerequisites to the use of the global navigation satellite system (GNSS) carrier phases for precise positioning. Modern GNSS techniques introduce triple- or multi-frequency signals that are beneficial for cycle slip detection and repair. We present a new real-time cycle slip detection and repair method based on the independent linear combinations of undifferenced triple-frequency GNSS observations. The proposed method forms three types of linear combinations based on the original observations. These combinations are called extra-wide lane (EWL), wide lane (WL), and narrow lane (NL). Cycle slips on the combinations are determined sequentially in three cascaded steps. The first step employs the geometry-free and ionosphere-free Hatch–Melbourne–Wübbena combination to determine and repair the EWL cycle slips. The second step subtracts the cycle-slip-repaired EWL combination from the WL combination to eliminate the geometry part of the WL combination. This subtraction results in a new function that contains the WL ambiguity and residual ionospheric delay. This function is differenced at two consecutive epochs to determine the WL cycle slips. The residual ionospheric delay difference is ignored because of its small magnitude relative to WL wavelength. The third step determines the NL cycle slips in the same manner as in the second step. The difference is that the cycle-slip-repaired EWL combination is replaced with the more accurate cycle-slip-repaired WL combination. Moreover, the residual ionospheric delay difference is compensated by the ionospheric delay rate derived from the original carrier phase observations. When the EWL, WL, and NL cycle slips are determined, cycle slips on the original carrier phase observations can be uniquely identified. The proposed approach has been tested on 30-s triple-frequency BeiDou navigation satellite system data under different levels of ionospheric variations, and on 30-s triple-frequency global positioning system and quasi-zenith satellite system data. Results indicate that the approach can effectively detect and correct cycle slips even for one cycle under low sampling rate or active ionospheric conditions on each frequency in real time.

Real-time cycle slip detection in triple-frequency GNSS

The modernization of the global positioning system and the advent of the European project Galileo will lead to a multifrequency global navigation satellite system (GNSS). The presence of new frequencies introduces more degrees of freedom in the GNSS data combination. We define linear combinations of GNSS observations with the aim to detect and correct cycle slips in real time. In particular, the detection is based on five geometry-free linear combinations used in three cascading steps. Most of the jumps are detected in the first step using three minimum-noise combinations of phase and code observations. The remaining jumps with very small amplitude are detected in the other two steps by means of two-tailored linear combinations of phase observations. Once the epoch of the slip has been detected, its amplitude is estimated using other linear combinations of phase observations. These combinations are defined with the aim of discriminating between the possible combinations of jump amplitudes in the three carriers. The method has been tested on simulated data and 1-second triple-frequency undifferenced GPS data coming from a friendly multipath environment. Results show that the proposed method is able to detect and repair all combinations of cycle slips in the three carriers.

Potentialities of multifrequency ionospheric correction in Global Navigation Satellite Systems

The first-order ionospheric error is reduced in the dual-frequency Global Navigation Satellite Systems (GNSS). In this paper, the possibility of eliminating ionospheric higher-order errors in the multifrequency GNSS is explored. Since the second-order error associated with the geomagnetic field effect on the refractive index can be eliminated in dual-frequency measurements, we explore the possibility of eliminating third-order errors in triple-frequency GNSS in view of phase scintillations. A connection between the possibility of improving the multifrequency GNSS accuracy and diffraction effects in radio signal propagation through the randomly inhomogeneous ionosphere is shown. The numerical simulation has revealed that the systematic, residual ionospheric error is considerably reduced when we pass on from dual-frequency to triple-frequency measurements. The change in the residual error variance during such a transition depends however on the relationship between the inner scale of the turbulent spectrum of ionospheric irregularities and the Fresnel radius. Given the inner scale larger than the Fresnel radius, not only the systematic error, but also the standard deviation reduces when we pass on from dual-frequency to triple-frequency measurements. Otherwise, when the Fresnel radius exceeds the inner scale, the variance increases with increasing number of frequencies in use.

Modelling of ionospheric high-order errors for new generation GNSS

In dual frequency Global Positioning System receivers, the ionospheric propagation delays are commonly estimated and corrected using the “ionosphere free” combinations of pseudo-range observables. With this method, the ionospheric delay is estimated at the first-order proportional to the inverse of the frequency square. However, higher-order terms exist that may be taken into account when precise corrections are required. The second-order term results from the influence of the geomagnetic field on the ionospheric propagation of the signals. The third-order term includes the refractive effects due to the bending of the ray. Contributions of the second- and third-order terms typically amount to values in the centimetre and millimetre ranges, respectively. In a near future, triple-frequency Global Navigation Satellite Systems transmitting high-resolution codes will become available. These systems are expected to provide a noticeable improvement in accuracy. This paper focuses on the Galileo signals as Galileo In-Orbit Validation Element (GIOVE) signals are now available for acquisition. A solution relying on the triple-frequency characteristics of a signal-in-space is investigated with results based on first measurements of GIOVE-A signals. Eventually, a method is described that relies on precise dual-frequency phase measurements to evaluate the second-order ionospheric contribution for Galileo data.

Total electron content monitoring using triple frequency GNSS data: A three-step approach

Global Navigation Satellite Systems (GNSS) are very useful tools to study the ionosphere. Nevertheless, the precision of the usual dual frequency total electron content (TEC) monitoring technique is affected by code delays (hardware and multipath), and is therefore limited. This paper introduces a TEC monitoring technique based on triple frequency GPS and Galileo measurements. The three steps of this technique are validated on triple frequency simulated data. In fact, as it is not affected by code delays, the precision of the reconstructed TEC is improved in regards with the dual frequency technique.