Guobin Chang

China University of Mining and Technology · School of Environment Science and Spatial Informatics

We derived an error analysis of the Davenport’s q method solving a general Wahba’s problem from first principle. The error analysis is direct because it does not use the null attitude simplification, and is general because it is applicable no matter whether the vector measurements are unit. It is shown that the conventional results presented in the...

Precise Point Positioning Library (PPPLib) is a multi-GNSS data processing software designed to process multi-frequency data from GPS, BeiDou, Galileo, GLONASS, and QZSS. PPPLib is written in the C/C++ programming language. It can compile and run on both Linux and Windows operating systems. PPPLib mainly performs precise point positioning from sing...

A new method is proposed to determine instantaneous velocities and accelerations with a stand-alone GNSS receiver. It is based on sparse kernel learning theory. Kernel trick is employed to represent the kinematics, and L1 norm regularization is used to get sparse solution. Analytical models rather than data series are provided, with which velocity...

In order to incorporate the time smoothness of ionospheric delay to aid the cycle slip detection, an adaptive Kalman filter is developed based on variance component estimation. The correlations between measurements at neighboring epochs are fully considered in developing a filtering algorithm for colored measurement noise. Within this filtering fra...

The functional analysis of the least-squares collocation (LSC) for gravity potential modeling using m measurements is revisited starting from an explicit spherical harmonic expansion. A spherical harmonic representer theorem (SHRT) is given: the model of the potential is a linear combination of m kernels or covariances. This theorem is independent...

Point-mass inversion is widely employed in GRACE level-2 data processing. Conventionally, the spherical harmonic (SH) coefficients are used indirectly: a set of pseudo measurements is generated first using the SH coefficients through SH synthesis; then the point-mass inversion is done with these pseudo measurements. To be statistically optimal, the...

Considering that a unit dual quaternion can describe elegantly the rigid transformation including rotation and translation, the point-wise weighted 3D coordinate transformation using a unit dual quaternion is formulated. The constructed transformation model by a unit dual quaternion does not need differential process to eliminate the three translat...

Filtering for GRACE temporal gravity fields is a necessary step before calculating surface mass anomalies. In this study, we propose a new denoising and decorrelation kernel (DDK) filtering scheme called adaptive DDK filter. The involved error covariance matrix (ECM) adopts nothing but the monthly time-variable released by several data centers. The...

High-frequency and correlated noise filtering is one of the important preprocessing steps for GRACE level-2 products before calculating mass anomaly. Decorrelation and denoising kernel (DDK) filters are usually considered as such optimal filters to solve this problem. In this work, a sparse DDK filter is proposed. This is achieved by replacing Tikh...

Accurate three-dimensional (3D) atmospheric water vapor distribution, which plays a crucial role in understanding the meteorological phenomena and hazards, has been successfully retrieved using Global Navigation Satellite System (GNSS) tomography technique. Presently, the problem of the ill-posed tomography system, that results from poor GNSS acqui...

The attitude algorithm is the most important part of the whole strapdown inertial navigation (SINS) processing. It calculates the attitude of certain parameterization by integrating the gyro outputs or measurements in a specifically tailored way according to the attitude kinematic differential equation. The measurements or some angular velocity mod...

Considering coordinate errors of both control points and non-control points, and different weights between control points and non-control points, this contribution proposes an extended weighted total least squares (WTLS) iterative algorithm of 3D similarity transformation based on Gibbs vector. It treats the transformation parameters and the target...

Suffering from hardware phase biases originating from satellites and the receiver, precise point positioning (PPP) requires a long convergence time to reach centimeter coordinate accuracy, which is a major drawback of this technique and limits its application in time-critical applications. Ambiguity resolution (AR) is the key to a fast convergence...

With the development of GNSS, many open-source software packages have become available for GNSS data processing. However, there are only a handful of open-source software that can handle GNSS/INS integrated data, even though GNSS/INS integration schemes have been widely used in vehicle navigation systems due to their high accuracy, stability, and c...

Global Navigation Satellite System (GNSS) coordinate time series inevitably suffer from random and even continuous missing data. However, many processing methods of GNSS time series analysis require continuous data, namely without any gaps. Therefore, interpolating data or filling the gaps is an important preprocessing step. Conventional methods in...

The downward continuation (DWC) of airborne gravity data usually adopts the Poisson integral equation, which is the first kind Fredholm integral equation. To improve the stability and accuracy of the DWC, based on the traditional regularization methods and Landweber iteration method, we introduce two other iterative algorithms, namely Cimmino and c...

This paper proposes a one-step forecasting method based on the LS+AR prediction model that calculates LS and AR model parameters simultaneously. The EOPs products released by the IERS were used as primary data to predict changes in LOD parameters over spans of 1–500 days for 1230 experiments. The experimental results showed that the proposed method...

GNSS has become a widely accessible technique for vehicle instantaneous velocimetry. GNSS time difference carrier phase (TDCP) velocimetry can provide high-accuracy displacement increments, through which the between-epoch average velocity can be derived. However, there are always so-called modelling errors in such velocity, i.e., the deviation betw...

Adaptive Kalman filtering with unknown constant or varying process noise covariance matrix is studied. A resolution is proposed to directly estimate or tune the process noise covariance matrix in Kalman filtering using variational Bayesian technique. By state augmentation, conjugacy of the process noise covariance matrix's inverse-Wishart distribut...

Conventional polar motion (PM) parameter modelling and forecasting research is directly based on observation data for PM parameters. For any given PM, its periodic characteristics are basically the same since it is affected by the same excitation source. However, the time-varying patterns of PM in different coordinates or with different parameteriz...

Filtering for state space model with time-integral measurement is studied. In this model, the measurement is an integral function, rather than an algebraic function, of the state vector. To be more specific, in the problem studied, the measurement is the between-epoch integral of a linear combination of the state vector. This is a new measurement t...

An improved global navigation satellite system (GNSS)/inertial navigation system (INS) tightly coupled scheme based on a time-differenced carrier phase (TDCP) was proposed for a low-cost vehicle navigation system. The proposed scheme aims to improve the navigation performance and computational efficiency of the system for low-cost GNSS receivers an...

As a crucial parameter in the process of converting the zenith wet delay into precipitable water vapor at Global Navigation Satellite System (GNSS) stations, the weighted mean temperature (Tm) influences the accuracy of GNSS-based water vapor retrievals. We propose an improved atmospheric Tm modeling method by introducing sparse kernel learning to...

The 3D similarity coordinate transformation is fundamental and frequently encountered in many areas of work such as geodesy, engineering surveying, LIDAR, terrestrial laser scanning, photogrammetry, machine vision, etc. The algorithms of 3D similarity transformation are divided into two categories. One is a closed-form algorithm that is straightfor...

Instantaneous velocity is an important variable for navigation and measurement tasks, and its estimation using a stand-alone global navigation satellite system (GNSS) receiver has important theoretical and practical significance for many applications. Adopting a stand-alone receiver to determine the instantaneous velocity in real-time has the advan...

In order to use a stand‐alone global navigation satellite system (GNSS) receiver to determine the stable instantaneous velocity, a new hybrid GNSS velocimetry approach combining carrier phase and Doppler measurements is proposed. This is a data fusion problem. The problem is expressed as a state‐space model, in which the deviation between the avera...

Integer ambiguity resolution is critical for achieving positions of high precision and reliability of precise point positioning (PPP). However, as an important error source in global navigation satellite system (GNSS), multipath interference limits the ability of PPP in high-accuracy GNSS positioning applications. Thus, to guarantee the performance...

The instantaneous kinematic velocity obtained by using a stand-alone global navigation satellite system (GNSS) receiver has attracted increasing attention, and has significant for numerous applications. Using the time difference carrier phase (TDCP) measurements, or the displacements they produced, we propose two real-time instantaneous velocity de...

A new smoother for a continuous dynamical state space model with sampled system coefficients is proposed. This is completely different from conventional approaches, such as Rauch–Tung–Striebel smoother. In the proposed method, the state vector as a continuous function of time is represented by kernel models. The state process model, namely the diff...

GNSS (global navigation satellite system) compass is a low-cost, high-precision, and temporally stable north-finding technique. While the nonlinear baseline length constraint is widely known to be important in ambiguity resolution of GNSS compass, its direct effect on yaw angle estimation is theoretically analyzed in this work. Four different metho...

Regularization is often necessary in parameter estimation of spherical radial basis function (SRBF) based regional gravity modelling. In this work, a new regularization method, namely the L1-norm regularization, also called the least absolute shrinkage selection operator (Lasso), is employed. This is different from the commonly used L2-norm regular...

Airborne vector gravimetric data have become increasingly available. A general band-limited horizontal boundary value problem using horizontal components of these vector gravimetric data is formulated and solved to compute regional geoid. The disturbing potential on the geoid is determined directly using the data in the air. This one-step approach...

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 para...

Carrier‐phase multipath effect is one of the major error sources in static global navigation satellite systems positioning applications. Sidereal filtering is an effective approach for mitigating multipath error, utilising the multipath error of the previous day to improve the positioning result of the next day. In this study two interpolation meth...

High-precision attitude estimation in real time plays a vital role in spacecraft flight. In this work, the attitude filtering using gyros and vector measurements is studied in the framework of the traditional multiplicative extended Kalman filtering (MEKF). An adaptive online kinematic modeling is proposed to aid the filtering, resulting in the so...

The Least-squares extrapolation of harmonic models and autoregressive (LS + AR) prediction is currently considered to be one of the best prediction model for polar motion parameters. In this method, LS fitting residuals are treated as data to train an AR model. But it is readily known that using too many data will result in learning a badly relevan...

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 pseudora...

Both the code–phase combination and the Geometry-Free (GF) phase combination are widely employed to detect and repair cycle slips for BeiDou Navigation Satellite System (BDS) triple-frequency observations. However, the effect of residual ionospheric delay on Narrow-Lane (NL) or GF observations must be considered to avoid incorrect cycle–slip estima...

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 e...

Attitude determination using double-differenced GNSS carrier phase measurements is studied. A realistic stochastic model is employed to take the correlations among the double-differenced measurements into full consideration. Two important issues concerning iteratively solving the nonlinear least-squares attitude determination problem are treated, n...

Carrier-smoothing-code filtering (CSCF)is widely used in GNSS signal processing to combine code pseudoranges and carrier phases. Position-domain (PD)CSCF is generally more accurate and less sensitive to visible satellite changes than range-domain (RD)CSCF. However, PD-CSCF necessitates at least four visible satellites. Intermittent satellite defici...

This work is concerned with refining the Helmert solutions in two different cases, namely combining different solutions and updating old solutions with newly available measurement data. The parameters to be estimated in the solutions here not only include the transformation parameters, namely the rotation, the translation and the scale, but also th...

In high-accuracy global navigation satellite system (GNSS) positioning applications, the multipath is one of the primary error sources because it is hard to parameterize. Being somewhat systematic rather than purely random, the multipath should be viewed more as a signal rather than a noise. On this basis, empirically modeling the multipath is real...

The Global Navigation Satellite System (GNSS) precise point positioning (PPP) technology is currently used to process GNSS water vapor observations in real time or near real time. Further developments are required to improve the accuracy and real-time performance of processing tropospheric delays from which the water vapor observations are extracte...

Rigid transformation including rotation and translation can be elegantly represented by a unit dual quaternion. Thus, a non-differential model of the Helmert transformation (3D seven-parameter similarity transformation) is established based on unit dual quaternion. This paper presents a rigid iterative algorithm of the Helmert transformation using...

In global navigation satellite system (GNSS) applications, the carrier‐smoothed code is a widely used technique to combine code pseudo‐range and carrier phase measurements. Unlike conventional methods, a method using dual‐frequency GNSS data to improve smoothing accuracy by eliminating ionosphere delay is described in this paper. In the recursive l...

The rigid motion involving both rotation and translation in the 3D space can be simultaneously described by a unit dual quaternion. Considering this excellent property, the paper constructs the Helmert transformation (seven-parameter similarity transformation) model based on a unit dual quaternion and then presents a rigid iterative algorithm of He...

In Global Navigation Satellite System (GNSS) relative positioning applications, multipath errors are non-negligible. Mitigation of the multipath error is an important task for precise positioning and it is possible due to the repeatability, even without any rigorous mathematical model. Empirical modeling is required for this mitigation. In this wor...

In GNSS applications, carrier-smoothed-code is a widely used technique to combine code pseudo-range and carrier phase measurements. A dynamical ionospheric delay modeling method is proposed based on Kalman filter and least-squares theory. The level of the process noise is adaptively tuned along with the real-time KF state estimation, based on the o...

The robust unscented Kalman filter (UKF) is revisited in this paper from a new point of view, namely the statistical linear regression (SLR) perspective of the unscented transformation (UT). When the actual distribution of the observation noise deviates from the assumed Gaussian distribution, the performance of the filter may degrade significantly...

Real-time solution of Global Navigation Satellite System (GNSS) epoch-differenced ionospheric delay (DID) is of great significance for real-time cycle slip detection and repair of multi-GNSS dual-frequency or trifrequency undifferenced measurements under high ionospheric activity. We construct a dynamic model of DID and perform a real-time estimate...

This study employs a combination of weighted least-squares extrapolation and an autoregressive model to produce medium-term predictions of polar motion (PM) parameters. The precisions of PM parameters extracted from earth orientation parameter (EOP) products are applied to determine the weight matrix. This study employs the EOP products released by...

Global navigation satellite system attitude determination based on carrier phase differencing technique is studied. A realistic stochastic model is followed to fully consider the correlations among different measurements in the least-squares problem formulation. A prior-free, computation-fixed, and averagely optimal solution is proposed suitable fo...

Helmert or similarity models are widely employed to relate different coordinate frames. It is often encountered in practice to transform coordinates from more than one old frame into a new one. One may perform separate Helmert transformations for each old frame. However, although each transformation is locally optimal, this is not globally optimal....

It is common in geodetic practice that station geodetic coordinates in an old frame are measured/estimated by adjusting conventional leveling and vertical networks (together with a vertical datum), whereas their Cartesian coordinates in a new frame are measured/estimated by adjusting modern 3D Global Navigation Satellite System (GNSS) networks. To...

In this paper, a nonlinear dynamic errors-in-variables (DEIV) model which considers all of the random errors in both system equations and observation equations is presented. The nonlinear DEIV model is more general in the structure, which is an extension of the existing DEIV model. A generalized total Kalman filter (GTKF) algorithm that is capable...

Analysis centers (ACs) for global navigation satellite systems (GNSSs) cannot accurately obtain real-time Earth rotation parameters (ERPs). Thus, the prediction of ultra-rapid orbits in the international terrestrial reference system (ITRS) has to utilize the predicted ERPs issued by the International Earth Rotation and Reference Systems Service (IE...

The 3D similarity coordinate transformation with the Gauss-Helmert error model is investigated. The first-order error analysis of an analytical least-squares solution to this problem is developed in detail. While additive errors are assumed in the translation and scale estimates, a 3×1 multiplicative error vector is defined to effectively parameter...

Determining the attitude using GNSS carrier signals is studied. It features an analytical approach to get an estimate as initial guess for iterative algorithms, in three steps. First, baseline vectors are estimated by least-squares method. Second, the constraint of the direction cosine matrix (DCM) is ignored and the least-squares estimates of its...

The M-estimator for the 3D symmetric Helmert coordinate transformation problem is developed. Small-angle rotation assumption is abandoned. The direction cosine matrix or the quaternion is used to represent the rotation. The 3×1 multiplicative error vector is defined to represent the rotation estimation error. An analytical solution can be employed...

The similarity transformation between two coordinate frames, is widely adopted in science and engineering. The transformation parameters are estimated using coordinate determinations of a set of common points in both frames. The quaternion is employed to represent the rotation transformation; and a 3×1 error vector is defined to represent the quate...

The symmetric Helmert transformation model is widely used in geospatial science and engineering. Using an analytical least-squares solution to the problem, a simple and approximate error analysis is developed. This error analysis follows the Pope procedure solving nonlinear problems, but no iteration is needed here. It is simple because it is not b...

3D rotation estimation using vector measurements is investigated. A general stochastic model is employed in which no specific structure is assumed about the variance-covariance matrix of the measurement errors, or in other words, different elements of the same vector, and/or different vectors can have different variances and can be arbitrarily corr...

The GNSS attitude determination using carrier phase measurements with 4 antennas is studied on condition that the integer ambiguities have been resolved. The solution to the nonlinear least-squares is often obtained iteratively, however analytical solution can exist for specific baselines configurations. The main aim of this work is to design this...

The iterated version of a family of non-linear Kalman filters, named the unscented transform (UT) based unscented Kalman filters (UKF), are revisited. Two existing frameworks of the iterated UKF are analysed and some shortcomings of them are pointed out. A new framework is proposed based on the statistical linear regression (SLR) perspective of the...

In the Helmert transformation model, the rotation is more difficult to be treated in terms of representation, estimation, and error analysis. First, two classes of representations of the rotation, i.e. the redundant class including the direction cosine matrix and the unit quaternion, and the minimum class including the rotation vector, the Gibbs ve...

The integration of Global Positioning System (GPS) with Inertial Navigation System (INS) has been very intensively developed and widely applied in multiple areas. To further enhance the reliability and availability of GPS/INS integrated navigation in GPS challenging environment, range observation through ultra-wideband (UWB) is introduced in GPS/IN...

The Wahba's problem is widely recognised as a least-square problem in three-axis attitude estimation from vector measurements. However, both the observation and the reference vectors can be corrupted by errors, so a total least-square problem considering both errors should be formulated to be rigorous. It is found that for errors with heteroscedast...

A robust Kalman filter based on Chi square test with sequential measurement update is proposed. This approach can not only handle outliers in part or even individual measurement channel, but can also further improve the accuracy especially when a novel ordering strategy in processing the measurement elements is adopted. The accuracy improvement can...

An improved two-position initial alignment model for strapdown inertial navigation system is proposed. In addition to the velocity, angular rates are incorporated as measurements. The measurement equations in full three channels are derived in both navigation and body frames and the latter of which is found to be preferred. The cross-correlation be...

This paper addresses the numerical and statistical stability in the integration of inertial navigation system and global navigation satellite system (GNSS) using Kalman filter (KF). Due to the different units used in horizontal and vertical components of the geodetic (curvilinear) coordinates in the vicinity of the earth’s surface, i.e. radians in...

Least-squares (LS) solutions to the 3D Helmert and symmetric Helmert transformations with rotational invariant covariance structure are studied in a unified framework. This is an extension of the 3D Helmert transformation with naïve identity covariance and the counterpart of the 2D symmetric Helmert transformation with rotational invariant covarian...

In this note, the 3D similarity datum transformation problem with Gauss–Helmert model, also known as the 3D symmetric Helmert transformation, is studied. The closed-form least-squares solution, i.e., without iteration, to this problem is derived. It is found that the rotation parameters in this solution are the same to that for the transformation w...

The aim of this paper was to develop a robust version of the Kalman filter (KF) to address process modeling errors in linear system with rank deficient measurement models. An important infinitesimal robustness metric, called the influence function, which is widely used in location, scale, and regression models, is introduced into KF. After recastin...

This paper is concerned with the topic of gravity matching aided inertial navigation technology using Kalman filter. The dynamic state space model for Kalman filter is constructed as follows: the error equation of the inertial navigation system is employed as the process equation while the local gravity model based on 9-point surface interpolation...

In inertial navigation system (INS) and global positioning system (GPS) integrated system, GPS antennas are usually not located at the same location as the inertial measurement unit (IMU) of the INS, so the lever arm effect exists, which makes the observation equation highly nonlinear. The INS/GPS integration with constant lever arm effect is studi...

The Kalman filter for linear systems with colored measurement noises is revisited. Besides two well-known approaches, i.e., Bryson's and Petovello's, another measurement time difference-based approach is introduced. This approach is easy to be implemented and generalized to nonlinear system, and can provide filtering solutions directly. A unified v...

In the paper by Wu et al, an interesting method was proposed to calculate the calibration parameters of a three-axis magnetometer based on the constrained total least-squares method. It is claimed in this comment that in order to construct the error of the design matrix A in equation (13) in that paper, it is the unknown magnetic field strength rat...

The Kalman filter for linear system with cross-correlated process and observation noises at the same epoch is revisited. As the process noise is correlated with the observation noise, the probability of the former conditioned on the latter should have a higher concentration than its original probability, implying that the conditional one becomes mo...