Hatch Filter Research Articles

An Improved Doppler-Aided Smoothing Code Algorithm for BeiDou-2/BeiDou-3 un-Geostationary Earth Orbit Satellites in Consideration of Satellite Code Bias

The extensive use of carrier-aided smoothing code (CSC) filters has led to a reduction in the noise level of raw code measurements in GNSS positioning and navigation applications. However, the existing CSC technique is sensitive to the changes in the integer ambiguity, and then the smoothing procedure needs to be restarted in the presence of cycle slips. As the Doppler shift is instantaneously observed and immune to cycle slips, the Doppler-aided smoothing code (DSC) algorithm would be more promising in a challenged environment. Based on the Hatch filter, an optimal DSC approach is proposed with the principle of minimum variance. Meanwhile, to inhibit the effect of the integral cumulative error of the Doppler, a balance factor is adopted to adjust the contributions of raw code and DSC. The noise level of code observable is not only affected by thermal noise, but also limited by systematic bias. Satellite code bias (SCB) was identified in the raw code observable on each frequency for each BDS-2 satellite. By minimizing the sum of the absolute value of residuals, the polynomial segment fitting algorithm as a function of elevation angles is applied to establish the SCB correction model based on epoch-differenced multipath (MP) deviations. Finally, different types of experiments demonstrate the validity and efficiency of the refined DSC filter with SCB corrections on each available frequency for BDS un-GEO satellites.

An improved phase-smoothed-code algorithm using GNSS dual-frequency carrier epoch-difference geometry-free combination observations

The Hatch filter has been widely used in global navigation satellite system (GNSS) single point positioning (SPP). However, the classic phase-smoothed-code (PSC) method is vulnerable to ionospheric cumulative errors, resulting in filter divergence and accuracy degradation in the positioning solution. In this paper, an improved method, i.e, phase epoch-difference geometry-free (GF) combination smoothed code (PESC), is proposed for SPP with raw GNSS measurements. In other words, the dual-frequency carrier-phase observations are used to form epoch-difference GF combinations to obtain the precise between-epoch variations of ionospheric delays. Then, the ionospheric delays of code observations during a continuous satellite arc are converted to the initial epoch’s value. Subsequently, the initial epoch’s ionospheric delay of each arc, setting as a constant value, is estimated along with other parameters through the Kalman filter. GNSS measurements from 20 globally distributed stations from multi-GNSS experiment (MGEX) network on July 7 2021 are selected to validate the feasibility of the new algorithm. Results indicate that the average root mean square (RMS) of PESC-SPP errors is 0.404 m, 0.340 m, and 1.491 m in east (E), north (N), and Up (U) components, respectively, with the improvement of 30.5%, 50.5%, 52.1% and 36.5%, 55.1%, 54.3% in comparison with that of PSC-SPP and SPP, respectively. Data collected in the kinematic experiment on 28th November 2021 is used to evaluate the PESC positioning performance. Results demonstrate that the deviations of epoch-difference slant total electron content (STEC) derived from the PESC-SPP are much smoother and more stable than those of PSC-SPP during continuous satellite arcs, with the average RMS improvements of 33.5%, 66.9%, and 32.9% for GPS, Galileo, and BDS satellites, respectively. The PESC positioning solutions can converge after a few minutes, and the RMS of PESC-SPP errors is 0.779 m, 0.609 m, and 2.060 m in E/N/U components, which is 32.2%, 24.1%, 32.0%, and 27.8%, 18.2%, 16.5% lower than that of SPP and PSC-SPP results, respectively.

Kalman–Hatch dual‐filter integrating global navigation satellite system/inertial navigation system/on‐board diagnostics/altimeter for precise positioning in urban canyons

For improved positioning in urban canyons, this study proposes an efficient dual-filter method integrating multi-constellation global navigation satellite system (GNSS), an inertial navigation system (INS), a barometric altimeter and an on-board diagnostics (OBD) module. The proposed method consists of a position-domain (PD) Hatch filter and velocity Kalman filter. The Hatch filter is operated as the main positioning filter and the Kalman filter is operated as a sub-filter to aid the main filter for the occasional GNSS outages. The Hatch filter combines barometric altimeter measurements with GNSS pseudorange and carrier phase measurements. The Kalman filter integrates the inertial measurement unit (IMU) measurements with GNSS Doppler shift and OBD speed measurements. A semi-simulation method is applied for the accurate performance evaluation of the proposed method compared with the several conventional methods under deficient satellite visibility, multipath errors and cycle slips caused by urban canyons. By the test results, it is demonstrated that the proposed method can bound the positioning errors effectively by utilising low-cost all-weather sensors. The RMSEs of the proposed Kalman–Hatch dual-filter algorithm were shown as 0.05, 0.19 and 0.11 m, respectively, and the maximum errors were shown as 0.16, 0.26 and 0.40 m, respectively, in the east, north and upward directions.

A Method for Real-Time Decimeter Solutions Over Long Baseline With BDS Triple-Frequency Signals

Relative positioning with global navigation satellite system (GNSS) is one of the main techniques to achieve high precision positioning, however, due to the influence of spatial errors such as atmospheric errors, there are still some problems with a single reference station over long baseline. In this paper, based on the BDS triple-frequency carrier, a real-time decimeter-level positioning method for long-distance under a single reference station is proposed to meet the requirements in daily life. Firstly, the ambiguity of extra-wide-lane (EWL) observation is fixed by a single epoch, which is characterized by long wavelength and small error. Then, the initial value of the ionospheric delay is solved on this basis, and the idea of smoothing is introduced to further optimize the ionospheric delay by Hatch filter. Finally, the optimal combined observation with a minimum standard deviation (STD) of positioning is constructed. Both static and kinematic tests are conducted to verify the effectiveness and performance of the proposed method. The results show that under different lengths of baseline, the positioning accuracy of each epoch can be controlled within 0.5m in the north (N), east (E), and up (U) three directions and is uniform among all epoch. In the long baseline, the positioning result based on the optimal combined observations is much better than the pseudo-range and other combined observations in terms of accuracy and stability. Moreover, the method can realize real-time and decimeter-level positioning in static and low kinematic environments, especially in the time when the ionosphere is more active.

BDS triple-frequency carrier phase combination smoothing pseudo-range algorithm

The carrier phase smoothing pseudo-range algorithm can effectively reduce the influence of multi-path effect and observation noise on pseudo-range positioning and improve the accuracy of pseudo-range positioning. Aiming at the problem that the existing classic Hatch filter smoother is susceptible to the cumulative interference of ionospheric delay in the pseudo-range smoothing process, the ionospheric delay and observed noise of the original double-difference observation are further weakened by constructing the optimal Beidou triple-frequency linear combination. The triple-frequency double-difference carrier phase combination are used to smooth the pseudo-range combination to replace the original observations. Finally, four groups of Beidou triple-frequency measured data with different baseline lengths, including 4m, 14.4km, 61.7km and 131.6km, are used to verify the algorithm. The theoretical derivation and effectiveness of the algorithm are verified by comparing and analyzing the smoothing effect of the algorithm in the following four groups of baseline conditions.

An Improved Divergence-Free Hatch Filter Algorithm Toward Sub-Meter Train Positioning With GNSS Single- Frequency Observations Only

Train positioning is the core function in the application of Global Navigation Satellite Systems (GNSS) in Railway Transportation. However, the use of the differential GPS (DGPS) along the Qinghai-Tibet Railway is expensive and difficult to maintain. Thus, a novel single-frequency algorithm based on the divergence-free Hatch filter is proposed, and no real-time augmentation correction input is required. The classical Hatch filter is severely affected by the divergence problem due to the ionospheric variation. In our algorithm, a novel decomposition-ensemble model is proposed for denoising and modeling the ionospheric variation, where the Variational Mode Decomposition (VMD) method is applied. With the aid of a sliding ionospheric variation fitting window, the divergence-free Hatch filter is constructed. The entire method is a so-called self-modeling method, but more efficient than recent studies. Besides, the Kalman filter is used for keeping continuous positioning accuracy. Finally, a static experiment in Tibet and a kinematic field test on the Qinghai-Tibet Railway is performed. In the ionospheric variation calculation-experiment, the experimental results show that the sliding window of our method can be shortened to 5 minutes with the data of 1s sampling rate, which basically meets the requirements of train positioning. In terms of train positioning accuracy, only the horizontal accuracy is concerned. In the static experiment, our method satisfies the accuracy requirements of the sub-meter level with a Root Mean Square Error (RMSE) value of better than 0.5m. In the kinematic test, the accuracy of our method is basically at the sub-meter level, with an RMSE value of approximately 0.6m.

A New Cycle Slip Detection and Repair Method for Galileo Four-Frequency Observations

Galileo four-frequency cycle slip detection and repair (CDR) is susceptible to the noise of pseudo-range observations. In this study, the Galileo four-frequency carrier phase smoothed pseudo-range (CPSP) assisted CDR method was proposed. Such method was conducted in three steps in sequence. First, the four linear independent combinations of the Galileo four-frequency observation were taken for CDR. Second, the non-divergent Hatch filter was employed to carry out the pseudo-range observation smoothly. Third, the true cycle slip was determined by rounding the float value using the least square method. To take the optimal combination of the CDR and verify the feasibility of the proposed method, the Galileo observations with satellites in different types were performed. According to the experimental results, (1) the four linear independent combinations of the geometry-free carrier phase combination (0, 1, 0, −1), (1, 1, −1, −1), (1, 2, −2, −1) and geometry-free and ionosphere-free combination (0, 0, 1, −1) were adopted for the cycle slip detection; (2) The success rate of cycle slip repair reached over 99.99% after four-frequency CPSP processing. With the CPSP assisted CDR method, the differences of the root mean square (RMS) between float and true values were down-regulated by 79.61%, 70.03%, 66.25% and 72.75%, respectively. (3) The differences of the root mean square (RMS) between float and true values were down-regulated by 13.62%, 10.67%, 10.67% and 10.67% after smoothing, respectively. In summary, the Galileo four-frequency CDR was effectively performed by the proposed method in active ionospheric area.

GNSS pseudorange and time‐differenced carrier phase measurements least‐squares fusion algorithm and steady performance theoretical analysis

In Global Navigation Satellite System (GNSS) community, pseudorange observables, without integer ambiguity, have large measurement noise, while carrier phase observables, with high measurement accuracy, have integer ambiguity, which restricts the direct use either of them for high-accuracy navigation and positioning. In this regard, fusing pseudorange and ambiguity-free time-differenced carrier phase (TDCP) is a popular data processing technique. In this Letter, the least-squares fusion is studied. A theoretical analysis of the steady performance of this fusion is conducted. A set of formulas of the steady performance is derived, based on which simulations are carried out for different pseudorange-carrier-phase precision ratios. Results showed that the steady accuracy of fusion pseudorange is about two orders of magnitude higher than that of the original pseudorange, and is close to that of carrier phase observables. Besides, the convergence speed and the comparison to the Hatch filter are also checked in the simulations.

An Improved Hatch Filter Algorithm towards Sub-Meter Positioning Using only Android Raw GNSS Measurements without External Augmentation Corrections

In May 2016, the availability of GNSS raw measurements on smart devices was announced by Google with the release of Android 7. It means that developers can access carrier-phase and pseudorange measurements and decode navigation messages for the first time from mass-market Android-devices. In this paper, an improved Hatch filter algorithm, i.e., Three-Thresholds and Single-Difference Hatch filter (TT-SD Hatch filter), is proposed for sub-meter single point positioning with raw GNSS measurements on Android devices without any augmentation correction input, where the carrier-phase smoothed pseudorange window width adaptively varies according to the three-threshold detection for ionospheric cumulative errors, cycle slips and outliers. In the mean time, it can also eliminate the inconsistency of receiver clock bias between pseudorange and carrier-phase by inter-satellite difference. To eliminate the effects of frequent smoothing window resets, we combine TT-SD Hatch filter and Kalman filter for both time update and measurement update. The feasibility of the improved TT-SD Hatch filter method is then verified using static and kinematic experiments with a Nexus 9 Android tablet. The result of the static experiment demonstrates that the position RMS of TT-SD Hatch filter is about 0.6 and 0.8 m in the horizontal and vertical components, respectively. It is about 2 and 1.6 m less than the GNSS chipset solutions, and about 10 and 10 m less than the classical Hatch filter solution, respectively. Moreover, the TT-SD Hatch filter can accurately detect the cycle slips and outliers, and reset the smoothed window in time. It thus avoids the smoothing failure of Hatch filter when a large cycle-slip or an outlier occurs in the observations. Meanwhile, with the aid of the Kalman filter, TT-SD Hatch filter can keep continuously positioning at the sub-meter level. The result of the kinematic experiment demonstrates that the TT-SD Hatch filter solution can converge after a few minutes, and the 2D error is about 0.9 m, which is about 64%, 89%, and 92% smaller than that of the chipset solution, the traditional Hatch filter solution and standard single point solution, respectively. Finally, the TT-SD Hatch filter solution can recover a continuous driving track in this kinematic test.

An improved Hatch filter and its application in kinematic positioning with single-frequency GPS

The Hatch filter has been widely used in GNSS kinematic positioning and navigation. However, the classic carrier smoothing of code pseudorange observations often results in filter divergence and accuracy degradation in the positioning solution due to the influence of ionospheric delay. One solution is to reduce the impact of ionospheric delay by using the Klobuchar model, which has low correction accuracy. Another solution is to use differential ionospheric delay correction data provided by third parties, which have a high correction accuracy. However, this solution requires the support of obtaining precise ionospheric data through a customized data network. In this study, the authors model the ionospheric delay from the observations themselves and build a mathematical model of the ionospheric delay and its variations. A new and improved Hatch filtering algorithm is proposed. The carrier smoothing of code pseudorange observations in this algorithm has high accuracy and stability because it eliminates the influence of ionospheric delay and variation simultaneously. A sliding average window with an overlap segment is designed for this algorithm, which eliminates the discontinuity in the smoothed data. The analyses in this paper have been performed by means of a set of experimental tests using Trimble, some NETR9 receivers, and a GNSS data processing platform called GNSSer. The executed field tests cover two low kinematic experiments: a ship experiment and a trolley experiment. The results show that the improved Hatch filtering algorithm eliminates most of the influence of the ionosphere and obtains carrier-smoothing pseudorange observations with smoothness and high accuracy. In the kinematic experiment of the ship position, single-frequency pseudorange observations are used to establish an observation equation. The horizontal accuracy of the ship position is approximately 50 cm, and the vertical accuracy is less than 1 m, which is an order of magnitude higher than the accuracy of the classic Hatch filter. However, the kinematic positioning of the trolley is better, the accuracy is within 10 cm in the horizontal and 10–15 cm in the vertical. Both tests show consistent results that the improved Hatch filter has excellent single-frequency, single-epoch positioning performance under low kinematic conditions.

A theoretical and experimental comparison of the ionosphere‐free L1 pseudorange and the ionosphere‐free linear combination pseudorange by dual‐frequency SBAS users

This study verifies the performance of the ionosphere-free L1 pseudorange for dual-frequency space-based augmentation systems (SBAS) users by both of theoretical analysis and experiments with actual GPS data. Although the dual-frequency pseudorange from ionosphere-free linear combinations is commonly used as a standard method, the ionosphere-free L1 range based on the weighted Hatch filter has advantages in terms of the amplification factor caused by a dual-frequency combination and filter weights optimised by the least-squares method. For the experimental analysis, RINEX data were collected from five National Geographic Information Institute reference stations on the Korean peninsula and used to generate an SBAS correction message following international SBAS specifications. The experimental results show that using the proposed method results in a 29% improvement in the range domain compared with the use of a traditional ionosphere-free linear combination filter. In the position domain, the proposed method shows a horizontal accuracy improvement of 16% after the application of post-processed SBAS orbit/clock corrections w.r.t. the traditional filter. Finally, this study also demonstrates that the accuracy of dual-frequency users can surpass than that of single-frequency SBAS users only if corrections are estimated with ionospheric delay-free measurements in the master station as well.

A Novel High-precision Single-frequency BeiDou High Kinematic Positioning Algorithm with Pseudo Range and Carrier Phase

High-precision Positioning is one of the key technologies of BeiDou receiver in high dynamic situations. Its implementation requires an optimized and dedicated hardware. The real-time processing places several constraints such as area occupied, power consumption, speed, etc. Using a Hatch filter in a single frequency receiver reduces multipath and receiver noise but introduces an induced bias that depends on the rate of ionospheric delay and a carrier smoothing time. However the cycle slips may easily occur during a long carrier smoothing time. Suppose carrier phase is directly used for positioning, there will be a lot of difficulty in solving the problem of integer ambiguity. A hybrid approach for pseudo range and carrier phase is given, and adopts a current statistic jerk tracking model, which makes positioning highly accurate under the condition of single point and single frequency in high dynamic situations. Besides, the delay of electric inhibition abscission layer, the troposphere delay and the transient change of the multi-path effect have little influence on signal.

Optimal Divergence-Free Hatch Filter for GNSS Single-Frequency Measurement.

The Hatch filter is a code-smoothing technique that uses the variation of the carrier phase. It can effectively reduce the noise of a pseudo-range with a very simple filter construction, but it occasionally causes an ionosphere-induced error for low-lying satellites. Herein, we propose an optimal single-frequency (SF) divergence-free Hatch filter that uses a satellite-based augmentation system (SBAS) message to reduce the ionospheric divergence and applies the optimal smoothing constant for its smoothing window width. According to the data-processing results, the overall performance of the proposed filter is comparable to that of the dual frequency (DF) divergence-free Hatch filter. Moreover, it can reduce the horizontal error of 57 cm to 37 cm and improve the vertical accuracy of the conventional Hatch filter by 25%. Considering that SF receivers dominate the global navigation satellite system (GNSS) market and that most of these receivers include the SBAS function, the filter suggested in this paper is of great value in that it can make the differential GPS (DGPS) performance of the low-cost SF receivers comparable to that of DF receivers.

Performance Analysis for BDS Phase-smoothed Pseudorange Differential Positioning

The positioning accuracy of the BeiDou Navigation Satellite System (BDS) can reach up to 10 m (95% confidence level) in both horizontal and vertical components. In order to improve the positioning performance for metre-level navigation, BDS pseudorange differential positioning has been proposed. We introduce the basic principles of BDS pseudorange differential positioning. Then based on the traditional Hatch filter, a modified Hatch filter for dual-frequency phase-smoothed pseudorange is introduced. The phase-smoothed pseudorange differential positioning, whose observations are smoothed by the modified Hatch filter using BDS B1 and B3 and Global Positioning System (GPS) L1 and L2 carrier-phase observations, are applied to determine the roving station's position. Three strategies are used for results analysis. The results show that the longer the baseline length is, the poorer positioning accuracy gets, and the positioning accuracy decline rate of the BDS B3 signal is higher than that of the BDS B1 signal, especially for long baselines. The percentages of the position deviations less than 3 m in horizontal component and 5 m in vertical component for BDS signals can reach up to 95 %.

Comparison between CNMC and hatch filter & its precision analysis for BDS precise relative positioning

Phase smoothing Pseudorange can effectively suppress the multipath effect on pseudorange, and there is no ambiguity problem, which has been widely studied and applied in the field of GNSS data processing. This paper made a systematic analysis and comparison of mathematical models for Hatch filter and CNMC phase smoothing pseudorange method. The ionsphere free combination of single frequency pseudorange through CNMC algorithm is proved equivalence with dual frequency hatch filter. On the assumption that there exists only random errors and the various measurements are independent, the accuracy expression of the CNMC method for smoothing pseudorange is deduced. Dual band hatch filter in the initialization period observation noise is bigger than CNMC smoothed pseudorange, but after a bit more than ten minutes, observation noise gradually gets better than CNMC smoothed pseudorange. BDS navigation system is qualified with serious and low-frequency characteristic for multipath errors through the comparison of OMC of double difference observation for real BDS short baseline, the conclusion that the phase smoothing pseudorange algorithm can greatly weaken the random error of original pseudorange, however, cant improve the system error is drawn. The system error of pseudorange smoothed by CNMC is at the save level with the original pseudorange, but the system error of pseudorange smoothed by double frequency hatch filter is increased. At last, relative positioning is carried through using the different kinds of phase smoothed pseudorange of that short baseline. The positioning results show that the positioning precision is improved from 0.797 m to 0.541 m using pseudorange smoothed by CNMC and the positioning precision is decreased to 1.160 m using pseudorange smoothed by hatch filter.

저급 센서를 고려한 GPS/INS 결합기법 연구

This paper proposes an efficient integration method for GPS (Global Positioning System) and INS (Inertial Navigation System). To obtain accuracy and computational conveniency at the same time with low cost global positioning system receivers and micro mechanical inertial sensors, a new mechanization method and a new filter architecture are proposed. The proposed mechanization method simplifies velocity and attitude computation by eliminating the need to compute complex transport rate related to the locally-level frame which continuously changes due to unpredictable vehicle motions. The proposed filter architecture adopts two heterogeneous filters, i.e. position-domain Hatch filter and velocity-aided Kalman filter. Due to distict characteristics of the two filters and the distribution of computation into the two hetegrogeneous filters, it eliminates the cascaded filter problem of the conventional loosly-coupled integration method and mitigates the computational burden of the conventional tightly-coupled integration method. An experiment result with field-collected measurements verifies the feasibility of the proposed method.

Mitigation of Code-carrier Divergence Effect using an Optimized Filter for LAAS Applications

Local Area Augmentation System (LAAS) is an augmentation to GPS, for providing aircraft precision approach and landing. LAAS relies on Hatch Alter for code smoothing but its Altered range is affected by code-carrier divergence occurring during ionospheric storms. Substituting traditional Hatch filter by optimized filter reduces this effect to a considerable extent. The objective of this paper is to estimate code-carrier divergence and mitigate it using the optimized filter. The performance of both Hatch and optimized filters is analyzed for different ionosphere conditions such as the geomagnetic storm of October 2003 over a low latitude station. Investigations showed that the optimized filter outperforms Hatch Filter for disturbed day data, whereas for quiet day data, it does not provide any additional advantage. The results obtained are agreeing with the results published elsewhere and are encouraging.

평활화 된 의사거리 및 전리층 지연 추정을 위한 GPS 측정치 잡음 모델링

Ionospheric delay error, one of main error sources in GPS signal, varies with signal frequency. Dual-frequency user uses L1, L2 frequency pseudorange to estimate the ionospheric delay, and there are errors caused by pseudorange measurement noise. So, filter is usually used to smooth the measurement. Weighted hatch filter can estimate optimal smoothed pseudorange measurement. But measurement noise model is needed to use this filter. In this paper, measurement noise modeling is conducted for NDGPS reference station. Using noise modeling result, weighted hatch filter estimate smoothed pseudorange measurement and ionospheric delay. Standard deviation of ionospheric dealy error drops to one-twenty fifth of non-filtered result.

Nonlinear Filter for Ionosphere Divergence Error Reduction in LAAS

The Hatch filter, the industry-standard method for smoothing GPS code measurements with carrier data in the local area augmented system (LAAS), is susceptible to divergence errors during severe ionospheric storms. The work presented here develops an alternate single-frequency filter called a nonlinear divergence elimination (NLDE) filter that mitigates divergence errors without increasing measurement noise. Application of the filter to GPS data indicates that the nonlinear filter not only zeroes steady-state divergence but also reduces maximum transient errors by 0-24% relative to the Hatch filter.

Non-Gaussian Error Modeling for GBAS Integrity Assessment

Four basic error sources exist for residual pseudo-range errors in a single frequency differential GPS system for ground based augmentation (GBAS): signal multipath, increased receiver noise (carrier-to-noise density ratios ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i> / <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> )) due to interference, residual differential troposphere error, and the error induced by ionosphere gradients. Without restricting ourselves to classical Gaussian overbounding, we combine their probability density functions (pdfs) to a total pseudo-range error distribution. This distribution is propagated through the GBAS Hatch filter and then mapped into the position domain using a worst case (selected by maximum vertical dilution of precision (VDOP)) of a full 31 satellite constellation with the two most critical satellites failed observed at Braunschweig Airport, Germany. Our calculations yield a significant reduction amounting to 46% of the position domain error at the 1.5 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-7</sup> integrity risk level when compared with the classical Gaussian overbounding approach.