Novel Process Noise Model for GNSS Kalman Filter Based on Sensitivity Analysis of Covariance with Poor Satellite Geometry

One of the great unsolved GNSS problems is inaccuracy in urban canyons due to Non-Line-Of-Sight (NLOS) signal reception. Owing to several studies about the NLOS signal rejection method, almost all NLOS signals can be excluded from the calculation of the position. However, such precise NLOS rejection would make satellite geometry poor, especially in dense urban environments. This paper points out, through numerical simulations and theoretical analysis, that poor satellite geometry leads to unintentional performance degradation of the Kalman filter with a conventional technique to prevent filter divergence. The conventional technique is to bump up process noise covariance, and causes unnecessary inflation of estimation-error covariance when satellite geometry is poor. We propose a novel choice of process noise covariance based on satellite geometry that can reduce such unnecessary inflation. Numerical and experimental results demonstrate that performance improvement can be achieved by the choice of process noise covariance even for a poor satellite geometry.

Using Galileo and BDS-3 Quad-Frequency Signals for Long-Baseline Instantaneous Decimeter-Level Positioning

As the signals of Galileo and the global BDS-3 navigation satellite system have been accessible, positioning users can use quad-frequency even five-frequency signals nowadays. With multifrequency signals, one can form some useful combinations to improve the positioning performance, e.g., the widely used extra-wide-lane (EWL)/wide-lane (WL) in triple-frequency cases. For quad-frequency or five-frequency cases, better positioning performance can be expected since additional frequencies are introduced. In this study, we systematically analyse the benefits of Galileo and BDS-3 quad-frequency signals on long-baseline instantaneous positioning. First, the theoretical analysis of EWL/WL ambiguity resolution (AR) and satellite-station range estimation with a single-satellite geometry-free and ionosphere-free model is studied, along with the comparison with triple-frequency cases. Second, using the quad-frequency advantages, an instantaneous decimeter-level positioning model is proposed, where the geometry-free model is adopted for the first two EWL AR and the geometry-based model is adopted for the third WL AR. In the end, the AR and positioning performance are evaluated using real long-baseline date containing Galileo and BDS-3 quad-frequency observations. The results indicate that, with quad-frequency observations, both Galileo and BDS-3 EWL/WL ambiguities can be fixed reliably with a single epoch. Contributed by the resolved EWL/WL ambiguities, instantaneous decimeter-level positioning can be obtained, with the accuracies of 0.116 m/0.126 m/0.351 m in north, east, and up directions, respectively.

Sampling theorem of satellite gravimetry from the perspective of the Bender configuration

<p>Satellites in different orbital configurations acquire gravity signals differently. Thus, a difference in admissible spectral coefficients can be expected when the orbital geometry changes. A simple illustration of this phenomenon is seen in the Bender configuration of two GRACE-like satellite pairs - polar and inclined. In the Bender configuration, the polar pair covers the entire globe. In contrast, the inclined pair does not cover the higher latitudes leaving a local discontinuity around the poles in the acquired signal (better known as the <em>Polar Gap problem</em>). Similarly, due to its north-south orientation, the polar pair can capture the features that are predominantly oriented in the east-west direction. Trying to understand better the relationship between satellite geometry and signal acquisition led us to take our first steps in the direction of a unified sampling theory in satellite gravimetry. To this end, we employed the concepts behind the rotation of spherical harmonic coefficients built upon Inclination functions to express the geopotential functionals. Our work utilizes the Lomb-Scargle Periodogram based approach to ascertain limiting frequencies from the systemic quasi-regular sampling net formed on the satellite torus contrary to interpolation and FFT based techniques used in earlier such research endeavors. Through our work, we aim at improving our understanding of how the transformation of the geopotential occurs from the global to the spectral domain. We hope that this will help design future satellite missions with geometries best suited for their objective based on the precise determination of essential spectral coefficients.</p>

Estimation of the scale lengths of turbulence from GPS single difference phase observations

<p>Signals from the Global Navigation Satellite System (GNSS) travel through the whole atmosphere and encounter fluctuations of the index of refraction. The long-term variations of the tropospheric refractive index delay the signals, whereas its random variations correlate with the phase measurements. The power spectral density of microwave phase difference can be derived from physical considerations by combining results from the Kolmogorov theory and electromagnetic wave propagation. Four different dominant noise regimes are expected. Their cutoff frequencies can be estimated with the unbiased Whittle Maximum Likelihood estimator; They provide information about the scale lengths of turbulence which are directly linked with the size of the eddies or swirling motion present in the free atmosphere. Dependencies of these parameters with the satellite geometry or the time of the day pave the way for a better comprehension of how tropospheric turbulence acts as correlating GNSS phase observations. The result is less empirical modeling of GNSS phase correlations to improve the positioning results and avoid an overestimation of their precision. We use GPS single differences from 290 m distant antenna positions recorded during two days in 2013 in a common clock experiment at the Physikalisch Technische Bundesanstalt in Braunschweig Germany to explain our methodology, based on adequate filtering of the residuals to mitigate multipath effects.</p>

Prediction of RTK positioning integrity for journey planning

Positioning integrity is crucial for Intelligent Transport Systems (ITS) applications. In this article, a method is presented for prediction of GNSS positioning integrity for ITS journey planning. This information, in addition to other route information, such as distance and time, can be utilized to choose the safest and economical route. We propose to combine the Advanced Receiver Autonomous Integrity Monitoring (ARAIM) technique, tailored for ITS, with 3D city models. Positioning is performed by GNSS Real-Time Kinematic (RTK) method, which can provide the accuracy required for ITS. A new threat model employed for computation of the protection levels (PLs) for RTK positioning is discussed. Demonstration of the proposed approach is performed through a kinematic test in an urban area in Tokyo. The comparison between the prediction method and the actual observations show that the two estimate close satellite geometry and PLs. The method produced PLs that bounds the actual position errors all the time and they were less than the preset alert limit.

Enabling robust and accurate navigation for UAVs using real-time GNSS precise point positioning and IMU integration

ABSTRACTAccurate navigation is required in many Unmanned Aerial Vehicle (UAV) applications. In recent years, GNSS Precise Point Positioning (PPP) has been recognised as an efficient approach for providing precise positioning services. In contrast to the widely used Real-Time Kinematic (RTK), PPP is independent of reference stations, which greatly broadens its scope of application. However, the accuracy and reliability of PPP can be significantly decreased by poor GNSS satellite geometry and outage. In response, a real-time four-constellation GNSS PPP is applied to improve the geometry in this work, and PPP is tightly coupled with an Inertial Measurement Unit (IMU) to smooth the position and velocity output, thus improving the robustness of the navigation solution. Experimental flight tests are carried out using a UAV in an open-sky area, and GNSS-challenged environments are simulated. The results show that the four-constellation GNSS PPP/IMU integration reduces the Root-Mean-Square (RMS) Three-Dimensional (3D) positioning and velocity error by 76.4% and 67.1%, respectively, in open sky with respect to the one-GNSS PPP. Under scenarios where GNSS measurements are insufficient, the coupled system can still provide continuous solutions. Moreover, the coupled PPP/IMU system can also maintain the convergence of PPP during GNSS-challenged periods and can greatly shorten the re-convergence period of PPP when the UAV returns to the open sky.

Variational Based Estimation of Sea Surface Temperature from Split-Window Observations of INSAT-3D/3DR Imager

Infrared (IR) radiometers from geostationary (GEO) satellites have an advantage over low-earth orbiting (LEO) satellites as they provide continuous observations to monitor the diurnal variations in the sea surface temperature (SST), typically better than 30-minute interval. However, GEO satellite observations suffer from significant diurnal and seasonal biases arising due to varying sun-earth-satellite geometry, leading to biases in SST estimates from conventional non-linear regression-based algorithms (NLSST). The midnight calibration issue occurring in GEO sensors poses a different challenge altogether. To mitigate these issues, we propose SST estimation from split-window IR observations of INSAT-3D and 3DR Imagers using One-Dimensional Variational (1DVAR) scheme. Prior to SST estimation, the bias correction in Imager observations is carried out using cumulative density function (CDF) matching. Then NLSST and 1DVAR algorithms were applied on six months of INSAT-3D/3DR observations to retrieve the SST. For the assessment of the developed algorithms, the retrieved SST was validated against in-situ SST measurements available from in-situ SST Quality Monitor (iQuam) for the study period. The quantitative assessment confirms the superiority of the 1DVAR technique over the NLSST algorithm. However, both the schemes under-estimate the SST as compared to in-situ SST, which may be primarily due to the differences in the retrieved skin SST versus bulk in-situ SST. The 1DVAR scheme gives similar accuracy of SST for both INSAT-3D and 3DR with a bias of −0.36 K and standard deviation (Std) of 0.63 K. However, the NLSST algorithm provides slightly less accurate SST with bias (Std) of −0.18 K (0.87 K) for INSAT-3DR and −0.27 K (0.95 K) for INSAT-3D. Both the NLSST and 1DVAR algorithms are capable of producing the accurate thermal gradients from the retrieved SST as compared to the gradients calculated from daily Multiscale Ultrahigh Resolution (MUR) level-4 analysis SST acquired from Group for High-Resolution Sea Surface Temperature (GHRSST). Based on these spatial gradients, thermal fronts can be generated that are very useful for predicting potential fishery zones (PFZ), which is available from GEO satellites, INSAT-3D/3DR, in near real-time at 15-minute intervals. Results from the proposed 1DVAR and NLSST algorithms suggest a marked improvement in the SST estimates with reduced diurnal/seasonal biases as compared to the operational NLSST algorithm.

Optimal GPS Satellite Selection using Stochastic Optimization and Volumes of Tetrahedrons for High Precision Positioning

A possibility of utilizing the Global Positioning System (GPS) depends on the positioning accuracy. Two decisive factors of position accuracy are User Range Error (URE) value and dimensionless Dilution of Precision (DOP), related to number of visible satellites. Several error modeling and correction techniques are available to improve the accuracy by optimizing the errors. While finding the GDOP at every instant, satellite selection plays predominant role. Satellite geometry with more satellites gives the good GDOP. However, due to limited receiver tracking channels and smaller size memories and other problems, it may not be possible to use all satellites in view for positioning. In GPS navigation, position of user requires minimum of four visible satellites. The selection of four satellites has a considerable impact on the position accuracy and GDOP shows the order of this impact. By using the concept of relation between GDOP and volume of tetrahedron optimal four satellites are selected to improve the position accuracy. Genetic Algorithm is used to select best ten combinations based on GDOP. For experimental validation the data collected at Andhra University, Visakhapatnam, located at (706970.9093, 6035941.0226, 1930009.5821) (m) is used. It is observed that selected satellites which are arranged in tetrahedron by following the work done by M Kihara on satellite selection method and accuracy for the GPS, using GA gives the best position values.

Differential Kalman Filter Design for GNSS Open Loop Tracking

Global navigation satellite system (GNSS) positioning in an urban environment is in need for accurate, reliable and robust positioning. Unfortunately, conventional closed-loop tracking fails to meet the demand. The open loop tracking shows improved robustness, however, the precision is unsatisfactory. We propose a differential Kalman filter for open loop, of which the measurement vector contains the differential values of open loop navigation results between adjacent epochs. The differential Kalman filter makes use of the satellite geometry (i.e., spatial domain) and motion relationship (i.e., temporal domain) to filter frequency and code phase estimations of conventional open loop tracking. The improved performances of this architecture have been analyzed theoretically and demonstrated by road tests in an urban environment. The proposed architecture shows more than 50% accuracy improvement than the conventional open-loop tracking architecture.