Performance assessment of a low-complexity autoregressive Kalman filter for GNSS carrier tracking using real scintillation time series

AbstractIonospheric scintillation is one of the most challenging sources of errors in global navigation satellite systems (GNSS). It is an effect of space weather that introduces rapid amplitude and phase fluctuations to transionospheric signals and, as a result, it severely degrades the tracking performance of receivers, particularly carrier tracking. It can occur anywhere on the earth during intense solar activity, but the problem aggravates in equatorial and high-latitude regions, thus posing serious concerns to the widespread deployment of GNSS in those areas. One of the most promising approaches to address this problem is the use of Kalman filter-based techniques at the carrier tracking level, incorporating some a priori knowledge about the statistics of the scintillation to be dealt with. These techniques aim at dissociating the carrier phase dynamics of interest from phase scintillation by modeling the latter through some correlated Gaussian function, such as the case of autoregressive processes. However, besides the fact that the optimality of these techniques is still to be reached, their applicability for dealing with scintillation in real-world environments also remains to be confirmed. We carry out an extensive analysis and experimentation campaign on the suitability of these techniques by processing real data captures of scintillation at low and high latitudes. We first evaluate how well phase scintillation can be modeled through an autoregressive process. Then, we propose a novel adaptive, low-complexity autoregressive Kalman filter intended to facilitate the implementation of the approach in practice. Last, we provide an analysis of the operational region of the proposed technique and the limits at which a performance gain over conventional tracking architectures is obtained. The results validate the excellence of the proposed approach for GNSS carrier tracking under scintillation conditions.

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Generalised DOPs with Consideration of the Influence Function of Signal-in-Space Errors

Journal of Navigation ◽

10.1017/s0373463311000415 ◽

2011 ◽

Vol 64 (S1) ◽

pp. S3-S18 ◽

Cited By ~ 20

Author(s):

Yuanxi Yang ◽

Jinlong Li ◽

Junyi Xu ◽

Jing Tang

Keyword(s):

Least Squares ◽

Stochastic Models ◽

Influence Function ◽

A Priori ◽

Functional Model ◽

Global Navigation Satellite Systems ◽

Parameter Estimates ◽

Model Parameters ◽

Integrated Navigation ◽

Satellite Systems

Integrated navigation using multiple Global Navigation Satellite Systems (GNSS) is beneficial to increase the number of observable satellites, alleviate the effects of systematic errors and improve the accuracy of positioning, navigation and timing (PNT). When multiple constellations and multiple frequency measurements are employed, the functional and stochastic models as well as the estimation principle for PNT may be different. Therefore, the commonly used definition of “dilution of precision (DOP)” based on the least squares (LS) estimation and unified functional and stochastic models will be not applicable anymore. In this paper, three types of generalised DOPs are defined. The first type of generalised DOP is based on the error influence function (IF) of pseudo-ranges that reflects the geometry strength of the measurements, error magnitude and the estimation risk criteria. When the least squares estimation is used, the first type of generalised DOP is identical to the one commonly used. In order to define the first type of generalised DOP, an IF of signal–in-space (SIS) errors on the parameter estimates of PNT is derived. The second type of generalised DOP is defined based on the functional model with additional systematic parameters induced by the compatibility and interoperability problems among different GNSS systems. The third type of generalised DOP is defined based on Bayesian estimation in which the a priori information of the model parameters is taken into account. This is suitable for evaluating the precision of kinematic positioning or navigation. Different types of generalised DOPs are suitable for different PNT scenarios and an example for the calculation of these DOPs for multi-GNSS systems including GPS, GLONASS, Compass and Galileo is given. New observation equations of Compass and GLONASS that may contain additional parameters for interoperability are specifically investigated. It shows that if the interoperability of multi-GNSS is not fulfilled, the increased number of satellites will not significantly reduce the generalised DOP value. Furthermore, the outlying measurements will not change the original DOP, but will change the first type of generalised DOP which includes a robust error IF. A priori information of the model parameters will also reduce the DOP.

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A statistical approach to estimate Global Navigation Satellite Systems (GNSS) receiver signal tracking performance in the presence of ionospheric scintillation

Journal of Space Weather and Space Climate ◽

10.1051/swsc/2018037 ◽

2018 ◽

Vol 8 ◽

pp. A51 ◽

Cited By ~ 4

Author(s):

Sreeja Vadakke Veettil ◽

Marcio Aquino ◽

Luca Spogli ◽

Claudio Cesaroni

Keyword(s):

Statistical Models ◽

Statistical Approach ◽

Global Navigation Satellite Systems ◽

Tracking Performance ◽

Ionospheric Scintillation ◽

Navigation Satellite ◽

Signal Tracking ◽

Satellite Systems ◽

Low Latitudes ◽

Global Navigation Satellite

Ionospheric scintillation can seriously impair the Global Navigation Satellite Systems (GNSS) receiver signal tracking performance, thus affecting the required levels of availability, accuracy and integrity of positioning that supports modern day GNSS based applications. We present results from the research work carried out under the Horizon 2020 European Commission (EC) funded Ionospheric Prediction Service (IPS) project. The statistical models developed to estimate the standard deviation of the receiver Phase Locked Loop (PLL) tracking jitter on the Global Positioning System (GPS) L1 frequency as a function of scintillation levels are presented. The models were developed following the statistical approach of generalized linear modelling on data recorded by networks in operation at high and low latitudes during the years of 2012–2015. The developed models were validated using data from different stations over varying latitudes, which yielded promising results. In the case of mid-latitudes, as the occurrence of strong scintillation is absent, an attempt to develop a dedicated model proved fruitless and, therefore, the models developed for the high and low latitudes were tested for two mid-latitude stations. The developed statistical models can be used to generate receiver tracking jitter maps over a region, providing users with the expected tracking conditions. The approach followed for the development of these models for the GPS L1 frequency can be used as a blueprint for the development of similar models for other GNSS frequencies, which will be the subject of follow on research.

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Performance Evaluation of GPS Auto-Surveying Techniques

Sensors ◽

10.3390/s21217374 ◽

2021 ◽

Vol 21 (21) ◽

pp. 7374

Author(s):

João Manito ◽

José Sanguino

Keyword(s):

Kalman Filter ◽

Least Squares ◽

Unscented Kalman Filter ◽

Weighted Least Squares ◽

Base Station ◽

Global Navigation Satellite Systems ◽

Precise Position ◽

Satellite Systems ◽

Global Navigation Satellite ◽

Position Estimate

With the increase in the widespread use of Global Navigation Satellite Systems (GNSS), increasing numbers of applications require precise position data. Of all the GNSS positioning methods, the most precise are those that are based in differential systems, such as Differential GNSS (DGNSS) and Real-Time Kinematics (RTK). However, for absolute positioning, the precision of these methods is tied to their reference position estimates. With the goal of quickly auto-surveying the position of a base station receiver, four positioning methods are analyzed and compared, namely Least Squares (LS), Weighted Least Squares (WLS), Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF), using only pseudorange measurements, as well as the Hatch Filter and position thresholding. The research results show that the EKF and UKF present much better mean errors than LS and WLS, with an attained precision below 1 m after about 4 h of auto-surveying. The methods that presented the best results are then tested against existing implementations, showing them to be very competitive, especially considering the differences between the used receivers. Finally, these results are used in a DGNSS test, which verifies a significant improvement in the position estimate as the base station position estimate improves.

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Validation of theα-μModel of the Power Spectral Density of GPS Ionospheric Amplitude Scintillation

International Journal of Antennas and Propagation ◽

10.1155/2014/573615 ◽

2014 ◽

Vol 2014 ◽

pp. 1-9 ◽

Cited By ~ 4

Author(s):

Kelias Oliveira ◽

Alison de Oliveira Moraes ◽

Emanoel Costa ◽

Marcio Tadeu de Assis Honorato Muella ◽

Eurico Rodrigues de Paula ◽

...

Keyword(s):

Spectral Density ◽

Power Spectral Density ◽

Degrees Of Freedom ◽

Solar Flux ◽

Global Navigation Satellite Systems ◽

Ionospheric Scintillation ◽

Parameter Distribution ◽

Satellite Systems ◽

Amplitude Scintillation ◽

Power Spectral

Theα-μmodel has become widely used in statistical analyses of radio channels, due to the flexibility provided by its two degrees of freedom. Among several applications, it has been used in the characterization of low-latitude amplitude scintillation, which frequently occurs during the nighttime of particular seasons of high solar flux years, affecting radio signals that propagate through the ionosphere. Depending on temporal and spatial distributions, ionospheric scintillation may cause availability and precision problems to users of global navigation satellite systems. The present work initially stresses the importance of the flexibility provided byα-μmodel in comparison with the limitations of a single-parameter distribution for the representation of first-order statistics of amplitude scintillation. Next, it focuses on the statistical evaluation of the power spectral density of ionospheric amplitude scintillation. The formulation based on theα-μmodel is developed and validated using experimental data obtained in São José dos Campos (23.1°S; 45.8°W; dip latitude 17.3°S), Brazil, located near the southern crest of the ionospheric equatorial ionization anomaly. These data were collected between December 2001 and January 2002, a period of high solar flux conditions. The results show that the proposed model fits power spectral densities estimated from field data quite well.

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Kalman Filter-Based RAIM for Reliable Aircraft Positioning with GPS and NavIC Constellations

Sensors ◽

10.3390/s20226606 ◽

2020 ◽

Vol 20 (22) ◽

pp. 6606

Author(s):

Susmita Bhattacharyya ◽

Dinesh Mute

Keyword(s):

Kalman Filter ◽

Weighted Least Squares ◽

Unmanned Aircraft ◽

Global Navigation Satellite Systems ◽

Navigation Systems ◽

Satellite Systems ◽

Vector Tracking ◽

Receiver Autonomous Integrity Monitoring ◽

Global Navigation Satellite ◽

Computational Resources

This paper presents a novel Kalman filter (KF)-based receiver autonomous integrity monitoring (RAIM) algorithm for reliable aircraft positioning with global navigation satellite systems (GNSS). The presented method overcomes major limitations of the authors’ previous work, and uses two GNSS, namely, Navigation with Indian Constellation (NavIC) of India and the Global Positioning System (GPS). The algorithm is developed in the range domain and compared with two existing approaches—one each for the weighted least squares navigation filter and KF. Extensive simulations were carried out for an unmanned aircraft flight path over the Indian sub-continent for validation of the new approach. Although both existing methods outperform the new one, the work is significant for the following reasons. KF is an integral part of advanced navigation systems that can address frequent loss of GNSS signals (e.g., vector tracking and multi-sensor integration). Developing KF RAIM algorithms is essential to ensuring their reliability. KF solution separation (or position domain) RAIM offers good performance at the cost of high computational load. Presented range domain KF RAIM, on the other hand, offers satisfactory performance to a certain extent, eliminating a major issue of growing position error bounds over time. It requires moderate computational resources, and hence, shows promise for real-time implementations in avionics. Simulation results also indicate that addition of NavIC alongside GPS can substantially improve RAIM performance, particularly in poor geometries.

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Performance Analyses of a RAIM Algorithm for Kalman Filter with GPS and NavIC Constellations

Sensors ◽

10.3390/s21248441 ◽

2021 ◽

Vol 21 (24) ◽

pp. 8441

Author(s):

Susmita Bhattacharyya

Keyword(s):

Kalman Filter ◽

Measurement Errors ◽

Weighted Least Squares ◽

Temporal Variations ◽

Global Navigation Satellite Systems ◽

Model Parameters ◽

Integrity Monitoring ◽

Satellite Systems ◽

Performance Analyses ◽

Global Navigation Satellite

This paper evaluates the performance of an integrity monitoring algorithm of global navigation satellite systems (GNSS) for the Kalman filter (KF), termed KF receiver autonomous integrity monitoring (RAIM). The algorithm checks measurement inconsistencies in the range domain and requires Schmidt KF (SKF) as the navigation processor. First, realistic carrier-smoothed pseudorange measurement error models of GNSS are integrated into KF RAIM, overcoming an important limitation of prior work. More precisely, the error covariance matrix for fault detection is modified to capture the temporal variations of individual errors with different time constants. Uncertainties of the model parameters are also taken into account. Performance of the modified KF RAIM is then analyzed with the simulated signals of the global positioning system and navigation with Indian constellation for different phases of aircraft flight. Weighted least squares (WLS) RAIM used for comparison purposes is shown to have lower protection levels. This work, however, is important because KF-based integrity monitors are required to ensure the reliability of advanced navigation methods, such as multi-sensor integration and vector receivers. A key finding of the performance analyses is as follows. Innovation-based tests with an extended KF navigation processor confuse slow ramp faults with residual measurement errors that the filter estimates, leading to missed detection. RAIM with SKF, on the other hand, can successfully detect such faults. Thus, it offers a promising solution to developing KF integrity monitoring algorithms in the range domain. The modified KF RAIM completes processing in time on a low-end computer. Some salient features are also studied to gain insights into its working principles.

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First Evidences of Ionospheric Plasma Depletions Observations Using GNSS-R Data from CYGNSS

Remote Sensing ◽

10.3390/rs12223782 ◽

2020 ◽

Vol 12 (22) ◽

pp. 3782

Author(s):

Carlos Molina ◽

Adriano Camps

Keyword(s):

Electromagnetic Waves ◽

Satellite Communications ◽

Study Data ◽

Global Navigation Satellite Systems ◽

Ionospheric Scintillation ◽

Electron Content ◽

Signal Delay ◽

Total Electron ◽

Satellite Systems ◽

Plasma Depletions

At some frequencies, Earth’s ionosphere may significantly impact satellite communications, Global Navigation Satellite Systems (GNSS) positioning, and Earth Observation measurements. Due to the temporal and spatial variations in the Total Electron Content (TEC) and the ionosphere dynamics (i.e., fluctuations in the electron content density), electromagnetic waves suffer from signal delay, polarization change (i.e., Faraday rotation), direction of arrival, and fluctuations in signal intensity and phase (i.e., scintillation). Although there are previous studies proposing GNSS Reflectometry (GNSS-R) to study the ionospheric scintillation using, for example TechDemoSat-1, the amount of data is limited. In this study, data from NASA CYGNSS constellation have been used to explore a new source of data for ionospheric activity, and in particular, for travelling equatorial plasma depletions (EPBs). Using data from GNSS ground stations, previous studies detected and characterized their presence at equatorial latitudes. This work presents, for the first time to authors’ knowledge, the evidence of ionospheric bubbles detection in ocean regions using GNSS-R data, where there are no ground stations available. The results of the study show that bubbles can be detected and, in addition to measure their dimensions and duration, the increased intensity scintillation (S4) occurring in the bubbles can be estimated. The bubbles detected here reached S4 values of around 0.3–0.4 lasting for some seconds to few minutes. Furthermore, a comparison with data from ESA Swarm mission is presented, showing certain correlation in regions where there is S4 peaks detected by CYGNSS and fluctuations in the plasma density as measured by Swarm.

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Measurement Signal Quality Assessment on All Available and New Signals of Multi-GNSS (GPS, GLONASS, Galileo, BDS, and QZSS) with Real Data

Journal of Navigation ◽

10.1017/s0373463315000624 ◽

2015 ◽

Vol 69 (2) ◽

pp. 313-334 ◽

Cited By ~ 23

Author(s):

Yiming Quan ◽

Lawrence Lau ◽

Gethin W. Roberts ◽

Xiaolin Meng

Keyword(s):

Attitude Determination ◽

Real Data ◽

Global Navigation Satellite Systems ◽

Double Difference ◽

Signal Quality ◽

Early Assessment ◽

Satellite Systems ◽

Agricultural Applications ◽

Short Baselines ◽

Global Navigation Satellite

Global Navigation Satellite Systems (GNSS) Carrier Phase (CP)-based high-precision positioning techniques have been widely used in geodesy, attitude determination, engineering survey and agricultural applications. With the modernisation of GNSS, multi-constellation and multi-frequency data processing is one of the foci of current GNSS research. The GNSS development authorities have better designs for the new signals, which are aimed for fast acquisition for civil users, less susceptible to interference and multipath, and having lower measurement noise. However, how good are the new signals in practice? The aim of this paper is to provide an early assessment of the newly available signals as well as assessment of the other currently available signals. The signal quality of the multi-GNSS (GPS, GLONASS, Galileo, BDS and QZSS) is assessed by looking at their zero-baseline Double Difference (DD) CP residuals. The impacts of multi-GNSS multi-frequency signals on single-epoch positioning are investigated in terms of accuracy, precision and fixed solution availability with known short baselines.

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A noise robust automatic radiolocation animal tracking system

Animal Biotelemetry ◽

10.1186/s40317-021-00248-w ◽

2021 ◽

Vol 9 (1) ◽

Author(s):

Liang Wang ◽

Foivos Diakogiannis ◽

Scott Mills ◽

Nigel Bajema ◽

Ian Atkinson ◽

...

Keyword(s):

Kalman Filter ◽

Standard Deviation ◽

Learning Algorithm ◽

Tracking System ◽

Sensor Arrays ◽

Semantic Segmentation ◽

Global Navigation Satellite Systems ◽

Localization Error ◽

Satellite Systems ◽

Deep Learning Algorithm

AbstractAgriculture is becoming increasingly reliant upon accurate data from sensor arrays, with localization an emerging application in the livestock industry. Ground-based time difference of arrival (TDoA) radio location methods have the advantage of being lightweight and exhibit higher energy efficiency than methods reliant upon Global Navigation Satellite Systems (GNSS). Such methods can employ small primary battery cells, rather than rechargeable cells, and still deliver a multi-year deployment. In this paper, we present a novel deep learning algorithm adapted from a one-dimensional implementing a convolutional neural network (CNN) model, originally developed for the task of semantic segmentation. The presented model () both converts TDoA sequences directly to positions and reduces positional errors introduced by sources such as multipathing. We have evaluated the model using simulated animal movements in the form of TDoA position sequences in combination with real-world distributions of TDoA error. These animal tracks were simulated at various step intervals to mimic potential TDoA transmission intervals. We compare to a Kalman filter to evaluate the performance of our algorithm to a more traditional noise reduction approach. On average, for simulated tracks having added noise with a standard deviation of 50 m, the described approach was able to reduce localization error by between 66.3% and 73.6%. The Kalman filter only achieved a reduction of between 8.0% and 22.5%. For a scenario with larger added noise having a standard deviation of 100 m, the described approach was able to reduce average localization error by between 76.2% and 81.9%. The Kalman filter only achieved a reduction of between 31.0% and 39.1%. Results indicate that this novel 1D CNN like encoder/decoder for TDoA location error correction outperforms the Kalman filter. It is able to reduce average localization errors to between 16 and 34 m across all simulated experimental treatments while the uncorrected average TDoA error ranged from 55 to 188 m.

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Context-Aware Sensor Uncertainty Estimation for Autonomous Vehicles

Vehicles ◽

10.3390/vehicles3040042 ◽

2021 ◽

Vol 3 (4) ◽

pp. 721-735

Author(s):

Mohammed Alharbi ◽

Hassan A. Karimi

Keyword(s):

Autonomous Vehicles ◽

Real Data ◽

Global Navigation Satellite Systems ◽

Learning Approach ◽

Context Aware ◽

Satellite Systems ◽

Sensor Performance ◽

Machine Learning Approach ◽

Global Navigation Satellite ◽

Data Acquisition Process

Sensor uncertainty significantly affects the performance of autonomous vehicles (AVs). Sensor uncertainty is predominantly linked to sensor specifications, and because sensor behaviors change dynamically, the machine learning approach is not suitable for learning them. This paper presents a novel learning approach for predicting sensor performance in challenging environments. The design of our approach incorporates both epistemic uncertainties, which are related to the lack of knowledge, and aleatoric uncertainties, which are related to the stochastic nature of the data acquisition process. The proposed approach combines a state-based model with a predictive model, where the former estimates the uncertainty in the current environment and the latter finds the correlations between the source of the uncertainty and its environmental characteristics. The proposed approach has been evaluated on real data to predict the uncertainties associated with global navigation satellite systems (GNSSs), showing that our approach can predict sensor uncertainty with high confidence.

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