Maximum likelihood estimation of position in GNSS

In this letter, we obtain the Maximum Likelihood Estimator of position in the framework of Global Navigation Satellite Systems. This theoretical result is the basis of a completely different approach to the positioning problem, in contrast to the conventional two-steps position estimation, consisting of estimating the synchronization parameters of the in-view satellites and then performing a position estimation with that information. To the authors’ knowledge, this is a novel approach which copes with signal fading and it mitigates multipath and jamming interferences. Besides, the concept of Position–based Synchronization is introduced, which states that synchronization parameters can be recovered from a user position estimation. We provide computer simulation results showing the robustness of the proposed approach in fading multipath channels. The Root Mean Square Error performance of the proposed algorithm is compared to those achieved with state-of-the-art synchronization techniques. A Sequential Monte–Carlo based method is used to deal with the multivariate optimization problem resulting from the ML solution in an iterative way.Peer Reviewe

GNSS Spoof Detection Based on Pseudoranges from Multiple Receivers

Spoofing is the common term used for describing the intentional broadcasting of false radio frequency signals intended to disrupt and mislead systems that depend on accurate position, navigation, and timing information provided by Global Navigation Satellite Systems (GNSS). Spoofing is an increasingly recognized threat garnering increased interest from researchers and users, both military and civilian. This paper presents a GNSS spoof detection algorithm that exploits the geometric distribution of a horizontal array of GNSS receiver antennae and the geometric configuration of visible navigation satellites. Using a Neyman-Pearson hypothesis testing formulation, a spatial correlation test is developed that can accurately and dependably detect a GNSS spoofing event. This paper develops the generalized likelihood ratio test using standard statistical models of the GNSS range measurements and maximum likelihood estimates of the unknown variables. An analysis is presented showing the performance effects of the number of receivers used, internal receiver clock bias estimation, unknown antenna array orientation, and temporal and spatial locations of the detector. Simulations were conducted using a GNSS simulator and receiver combination to further substantiate theoretical claims. Furthermore, comparisons to similar prior work using position solutions shows a marked improvement in performance

Comparison of SAGE and classical multi-antenna algorithms for multipath mitigation in real-world environment

The performance of the Space Alternating Generalized Expectation Maximisation (SAGE) algorithm for multipath mitigation is assessed in this paper. Numerical simulations have already proven the potential of SAGE in navigation context, but practical aspects of the implementation of such a technique in a GNSS receiver are the topic for further investigation. In this paper, we will present the first results of SAGE implementation in a real world environmen

Incrementally Learned Mixture Models for GNSS Localization

GNSS localization is an important part of today's autonomous systems, although it suffers from non-Gaussian errors caused by non-line-of-sight effects. Recent methods are able to mitigate these effects by including the corresponding distributions in the sensor fusion algorithm. However, these approaches require prior knowledge about the sensor's distribution, which is often not available. We introduce a novel sensor fusion algorithm based on variational Bayesian inference, that is able to approximate the true distribution with a Gaussian mixture model and to learn its parametrization online. The proposed Incremental Variational Mixture algorithm automatically adapts the number of mixture components to the complexity of the measurement's error distribution. We compare the proposed algorithm against current state-of-the-art approaches using a collection of open access real world datasets and demonstrate its superior localization accuracy.Comment: 8 pages, 5 figures, published in proceedings of IEEE Intelligent Vehicles Symposium (IV) 201

A new multipath mitigation method for GNSS receivers based on antenna array

the potential of small antenna array for multipath mitigation in GNSS systems is considered in this paper. To discriminate the different incoming signals (Line of sight and multipaths), a new implementation of the well known SAGE algorithm is proposed. This allows a significant complexity reduction and it is fully compatible with conventional GNSS receivers. Theoretical study thanks to the Cramer Rao Bound derivation and tracking simulation results (in static and dynamic scenarios) show that the proposed method is a very promising approach for the multipath mitigation problem in GNSS receivers

Simulation of Multi-element Antenna Systems for Navigation Applications

The application of user terminals with multiple antenna inputs for use with the global satellite navigation systems like GPS and Galileo becomes more and more attraction in last years. Multiple antennas may be spread over the user platform and provide signals required for the platform attitude estimation or may be arranged in an antenna array to be used together with array processing algorithms for improving signal reception, e.g. for multipath and interference mitigation. In order to generate signals for testing of receivers with multiple antenna inputs and corresponding receiver algorithms in a laboratory environment a unique HW signal simulation tool for wavefront simulation has been developed. The signals for a number of antenna elements in a flexible user defined geometry are first generated as digital signals in baseband and then mixed up to individual RF-outputs. The paper describes the principle function of the system and addresses some calibration issues. Measurement set-ups and results of data processing with simulated signals for different applications are shown and discussed

The Generalized Method of Wavelet Moments with Exogenous Inputs: a Fast Approach for the Analysis of GNSS Position Time Series

The Global Navigation Satellite System (GNSS) daily position time series are often described as the sum of stochastic processes and geophysical signals which allow studying global and local geodynamical effects such as plate tectonics, earthquakes, or ground water variations. In this work we propose to extend the Generalized Method of Wavelet Moments (GMWM) to estimate the parameters of linear models with correlated residuals. This statistical inferential framework is applied to GNSS daily position time series data to jointly estimate functional (geophysical) as well as stochastic noise models. Our method is called GMWMX, with X standing for eXogeneous variable: it is semi-parametric, computationally efficient and scalable. Unlike standard methods such as the widely used Maximum Likelihood Estimator (MLE), our methodology offers statistical guarantees, such as consistency and asymptotic normality, without relying on strong parametric assumptions. At the Gaussian model, our results show that the estimated parameters are similar to the ones obtained with the MLE. The computational performances of our approach has important practical implications. Indeed, the estimation of the parameters of large networks of thousands of GNSS stations quickly becomes computationally prohibitive. Compared to standard methods, the processing time of the GMWMX is over $1000$ times faster and allows the estimation of large scale problems within minutes on a standard computer. We validate the performances of our method via Monte-Carlo simulations by generating GNSS daily position time series with missing observations and we consider composite stochastic noise models including processes presenting long-range dependence such as power-law or Mat\'ern processes. The advantages of our method are also illustrated using real time series from GNSS stations located in the Eastern part of the USA.Comment: 30 pages, 11 figures, 3 table

Analysis of Multipath Mitigation Techniques with Land Mobile Satellite Channel Model

Multipath is undesirable for Global Navigation Satellite System (GNSS) receivers, since the reception of multipath can create a significant distortion to the shape of the correlation function leading to an error in the receivers’ position estimate. Many multipath mitigation techniques exist in the literature to deal with the multipath propagation problem in the context of GNSS. The multipath studies in the literature are often based on optimistic assumptions, for example, assuming a static two-path channel or a fading channel with a Rayleigh or a Nakagami distribution. But, in reality, there are a lot of channel modeling issues, for example, satellite-to-user geometry, variable number of paths, variable path delays and gains, Non Line-Of-Sight (NLOS) path condition, receiver movements, etc. that are kept out of consideration when analyzing the performance of these techniques. Therefore, this is of utmost importance to analyze the performance of different multipath mitigation techniques in some realistic measurement-based channel models, for example, the Land Multipath is undesirable for Global Navigation Satellite System (GNSS) receivers, since the reception of multipath can create a significant distortion to the shape of the correlation function leading to an error in the receivers’ position estimate. Many multipath mitigation techniques exist in the literature to deal with the multipath propagation problem in the context of GNSS. The multipath studies in the literature are often based on optimistic assumptions, for example, assuming a static two-path channel or a fading channel with a Rayleigh or a Nakagami distribution. But, in reality, there are a lot of channel modeling issues, for example, satellite-to-user geometry, variable number of paths, variable path delays and gains, Non Line-Of-Sight (NLOS) path condition, receiver movements, etc. that are kept out of consideration when analyzing the performance of these techniques. Therefore, this is of utmost importance to analyze the performance of different multipath mitigation techniques in some realistic measurement-based channel models, for example, the Land Mobile Satellite (LMS) channel model [1]-[4], developed at the German Aerospace Center (DLR). The DLR LMS channel model is widely used for simulating the positioning accuracy of mobile satellite navigation receivers in urban outdoor scenarios. The main objective of this paper is to present a comprehensive analysis of some of the most promising techniques with the DLR LMS channel model in varying multipath scenarios. Four multipath mitigation techniques are chosen herein for performance comparison, namely, the narrow Early-Minus-Late (nEML), the High Resolution Correlator, the C/N0-based two stage delay tracking technique, and the Reduced Search Space Maximum Likelihood (RSSML) delay estimator. The first two techniques are the most popular and traditional ones used in nowadays GNSS receivers, whereas the later two techniques are comparatively new and are advanced techniques, recently proposed by the authors. In addition, the implementation of the RSSML is optimized here for a narrow-bandwidth receiver configuration in the sense that it now requires a significantly less number of correlators and memory than its original implementation. The simulation results show that the reduced-complexity RSSML achieves the best multipath mitigation performance in moderate-to-good carrier-to-noise density ratio with the DLR LMS channel model in varying multipath scenarios