On robust estimation of the location parameter

[1] Changes in regional groundwater storage in North China were estimated from the Gravity Recovery and Climate Experiment (GRACE) satellites data and ground-based measurements collected from 2003 to 2010. The study area (∼370,000 km2) included the Beijing and Tianjin municipality, the Hebei and Shanxi province, which is one of the largest irrigation areas in the world and is subjected to intensive groundwater-based irrigation. Groundwater depletion in North China was estimated by removing the simulated soil moisture changes from the GRACE-derived terrestrial water storage changes. The rate of groundwater depletion in North China based on GRACE was 2.2 ± 0.3 cm/yr from 2003 to 2010, which is equivalent to a volume of 8.3 ± 1.1 km3/yr. The groundwater depletion rate estimated from monitoring well stations during the same time period was between 2.0 and 2.8 cm/yr, which is consistent with the GRACE-based result. However, the estimated groundwater depletion rate in shallow plain aquifers according to the Groundwater Bulletin of China Northern Plains (GBCNP) for the same time period was only approximately 2.5 km3/yr. The difference in groundwater depletion rates estimated from GRACE and GBCNP data indicates the important contribution of groundwater depletion from deep aquifers in the plain and piedmont regions of North China.

Evaluation of groundwater depletion in North China using the Gravity Recovery and Climate Experiment (GRACE) data and ground-based measurements (EI)

The central task of GPS/INS integration is to effectively blend GPS and INS data together to generate an optimal solution. The present data fusion algorithms, which are mostly based on Kalman filtering (KF), have several limitations. One of those limitations is the stringent requirement on precise a priori knowledge of the system models and noise properties. Uncertainty in the covariance parameters of the process noise (Q) and the observation errors (R) may significantly degrade the filtering performance. The conventional way of determining Q and R relies on intensive analysis of empirical data. However, the noise levels may change in different applications. Over the past few decades adaptive KF algorithms have been intensively investigated with a view to reducing the influence of the Q and R definition errors. The covariance matching method has been shown to be one of the most promising techniques. This paper first investigates the utilization of an online stochastic modelling algorithm with regards to its parameter estimation stability, convergence, optimal window size, and the interaction between Q and R estimations. Then a new adaptive process noise scaling algorithm is proposed. Without artificial or empirical parameters being used, the proposed adaptive mechanism has demonstrated the capability of autonomously tuning the process noise covariance to the optimal magnitude, and hence improving the overall filtering performance.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0373463307004316

Improving Adaptive Kalman Estimation in GPS/INS Integration

The core performance elements of global navigation satellite system include availability, continuity, integrity and accuracy, all of which are particularly important for the developing BeiDou global navigation satellite system (BDS-3). This paper describes the basic performance of BDS-3 and suggests some methods to improve the positioning, navigation and timing (PNT) service. The precision of the BDS-3 post-processing orbit can reach centimeter level, the average satellite clock offset uncertainty of 18 medium circular orbit satellites is 1.55 ns and the average signal-in-space ranging error is approximately 0.474 m. The future possible improvements for the BeiDou navigation system are also discussed. It is suggested to increase the orbital inclination of the inclined geostationary orbit (IGSO) satellites to improve the PNT service in the Arctic region. The IGSO satellite can perform part of the geostationary orbit (GEO) satellite’s functions to solve the southern occlusion problem of the GEO satellite service in the northern hemisphere (namely the “south wall effect”). The space-borne inertial navigation system could be used to realize continuous orbit determination during satellite maneuver. In addition, high-accuracy space-borne hydrogen clock or cesium clock can be used to maintain the time system in the autonomous navigation mode, and stability of spatial datum. Furthermore, the ionospheric delay correction model of BDS-3 for all signals should be unified to avoid user confusion and improve positioning accuracy. Finally, to overcome the vulnerability of satellite navigation system, the comprehensive and resilient PNT infrastructures are proposed for the future seamless PNT services.

/pdf/basic-performance-and-future-developments-of-beidou-global-18ysrcaj1o.pdf

Basic performance and future developments of BeiDou global navigation satellite system

In order to better understand the differential code biases (DCBs) of global navigation satellite system, the IGGDCB method is extended to estimate the intra- and inter-frequency biases of the global positioning system (GPS), GLONASS, BeiDou navigation satellite system (BDS), and Galileo based on observations collected by the multi-GNSS experiment (MGEX) of the international GNSS service (IGS). In the approach of IGGDCB, the local ionospheric total electronic content is modeled with generalized triangular series (GTS) function rather than using a global ionosphere model or a priori ionospheric information. The DCB estimated by the IGGDCB method is compared with the DCB products from the Center for Orbit Determination in Europe (CODE) and German Aerospace Center (DLR), as well as the broadcast timing group delay (TGD) parameters over a 2-year span (2013 and 2014). The results indicate that GPS and GLONASS intra-frequency biases obtained in this work show the same precision levels as those estimated by DLR (about 0.1 and 0.2–0.4 ns for the two constellations, respectively, with respect to the products of CODE). The precision levels of IGGDCB-based inter-frequency biases estimated over the 24-month period are about 0.29 ns for GPS, 0.56 ns for GLONASS, 0.36 ns for BDS, and 0.24 ns for Galileo, respectively. Here, the accuracies of GPS and GLONASS biases are assessed relative to the products of CODE, while those of BDS and Galileo are compared with the estimates of DLR. In addition, the monthly stability indices of IGGDCB-based DCBs are 0.11 (GPS), 0.18 (GLONASS), 0.17 (BDS), and 0.14 (Galileo) ns for the individual constellation.

Determination of differential code biases with multi-GNSS observations

A new robust parameter estimator for the adjustment of correlated observations is developed based on a `bifactor reduction' model of weight elements. A shrinking factor for weight elements is proposed. The new equivalent weight matrix composed by the bifactor weight elements preserves the symmetry and keeps the original correlation coefficients unchanged. The new parameter estimator with its error influence function is derived. The robustness and efficiency of the new robust estimator is demonstrated with a simulated example and some conclusions are drawn.

Robust estimator for correlated observations based on bifactor equivalent weights

In this paper a brief review of Sage adaptive filtering is followed by an analysis of the shortcomings of covariance matrices formed by windowing residual vectors, innovation vectors and correction vectors of the dynamic states. A new adaptive Kalman filter is developed by combining the Sage filter and the variance components and its use tested against various other schemes.

An Adaptive Kalman Filter Based on Sage Windowing Weights and Variance Components

The Chinese BeiDou Navigation Satellite System (BDS) has completed its first milestone by providing coverage of the Asia---Pacific area navigation service since December 27, 2012. With the combination of BDS, the GNSS precise point positioning (PPP) can improve its positioning accuracy, availability and reliability. However, in order to achieve the best positioning solutions, the inter-system bias (ISB) between GPS and BDS must be resolved as precisely as possible. In this study, a 1-week period (GPS week 1810) of GPS/BDS observations for 18 distributed stations from the International GNSS Service Multi-GNSS Experiment are processed. Primarily, the ISB is estimated by an extended Kalman filter as a piece-wise parameter every 30 min. Then we generate a smoothed ISB series (ISB_s) with a sliding window median filter to reject the outliers from the original estimated ISB series (ISB_o). After analysing the characteristics of the ISB_s, a short-term station-dependent ISB model based on a 1-week period is proposed in this study. This model consists of a quadratic polynomial in time and two or three periodic functions with diurnal and semi-diurnal periods. Frequency spectrum analysis is used to determine the periods of the periodic functions, and the coefficients of the quadratic function and the periodic functions are estimated by least squares. For model verification, we compare the ISB derived from the model (ISB_m) with ISB_s (assumed the true values). The comparisons indicate an almost normal distribution. It is found that the proposed model is consistent with the true values: the root-mean-square (RMS) values being about 0.7 ns, and some stations are even better. This means that the short-term ISB model proposed has a high fitting accuracy. Hence, it can be used for ISB prediction. Comparing the prediction ISB series (ISB_p) with ISB_s in the following week (GPS week 1811), we can draw the conclusion that the accuracy of the prediction declines with an increase in the time period. The 1-day period precision can achieve 0.57---1.21 ns, while the accuracy of the 2-day prediction decreases to 0.77---1.72 ns. Hence, we recommend a predicting duration of 1 day. The proposed model will be beneficial for subsequent GPS/BDS PPP or precise orbit determination (POD) since the ISB derived from this model can be considered as a priori constraint in the PPP/POD solutions. With this a priori constraint, the convergence time can be shortened by 19.6, 16.1 and 2.4 % in N, E and U components, respectively. The accuracy of result in the E component is remarkably improved by 11.9 %.

/pdf/gps-bds-short-term-isb-modelling-and-prediction-4idlzokki5.pdf

GPS/BDS short-term ISB modelling and prediction

Orbit determination of the Next-Generation Beidou satellites with Intersatellite link measurements and a priori orbit constraints

Considering the contribution of the hardware biases to the estimated clock errors, an improved method for estimating the satellite inter-frequency clock bias (IFCB) is presented, i.e., the difference in the satellite clock error as computed from ionospheric-free pseudorange and carrier phase observations using L1/L2 and P1/P2 versus L1/L5 and P1/P5. The IFCB is composed of a constant and a variable part. The constant part is the inter-frequency hardware bias (IFHB). It contains the satellite and receiver hardware delays and can be expressed as a function of the DCBs [DCB (P1 ź P2) and DCB (P1 ź P5)]. When a reference satellite is selected, the satellite IFHB can be computed but is biased by a reference satellite IFHB. This bias will not affect the utilization of IFCB in positioning since it can be absorbed by the receiver clock error. Triple-frequency observations of 30 IGS stations between June 1, 2013, and May 31, 2014, were processed to show the variations of the IFHB. The IFHB values show a long-term variation with time. When a linear and a fourth-order harmonic function are used to model the estimated IFCB, which contains contributions of the hardware delays and clock errors, the results show that 89 % of the IFCB can be corrected given the current five triple-frequency GPS satellites with the averaged fitting RMS of 1.35 cm. Five days of data are processed to test the estimated satellite clock errors using the strategy presented. The residuals of P1/P5 and L1/L5 have a STD of <0.27 m and 0.97 cm, respectively. In addition, most predicted satellite IFCBs reach an accuracy of centimeter level and its mean accuracy of 5 days is better than 7 cm.

Tianhe Xu

Papers

Robust estimator for correlated observations based on bifactor equivalent weights

An Adaptive Kalman Filter Based on Sage Windowing Weights and Variance Components

GPS/BDS short-term ISB modelling and prediction

Orbit determination of the Next-Generation Beidou satellites with Intersatellite link measurements and a priori orbit constraints

Improved method for estimating the inter-frequency satellite clock bias of triple-frequency GPS