A particle filtering approach for joint detection/estimation of multipath effects on GPS measurements

Multipath propagation causes major impairments to Global Positioning System (GPS) based navigation. Multipath results in biased GPS measurements, hence inaccurate position estimates. In this work, multipath effects are considered as abrupt changes affecting the navigation system. A multiple model formulation is proposed whereby the changes are represented by a discrete valued process. The detection of the errors induced by multipath is handled by a Rao-Blackwellized particle filter (RBPF). The RBPF estimates the indicator process jointly with the navigation states and multipath biases. The interest of this approach is its ability to integrate a priori constraints about the propagation environment. The detection is improved by using information from near future GPS measurements at the particle filter (PF) sampling step. A computationally modest delayed sampling is developed, which is based on a minimal duration assumption for multipath effects. Finally, the standard PF resampling stage is modified to include an hypothesis test based decision step

Artificial Intelligence-Assisted Inertial Geomagnetic Passive Navigation

In recent years, the integration of machine learning techniques into navigation systems has garnered significant interest due to their potential to improve estimation accuracy and system robustness. This doctoral dissertation investigates the use of Deep Learning combined with a Rao-Blackwellized Particle Filter for enhancing geomagnetic navigation in airborne simulated missions. A simulation framework is developed to facilitate the evaluation of the proposed navigation system. This framework includes a detailed aircraft model, a mathematical representation of the Earth\u27s magnetic field, and the incorporation of real-world magnetic field data obtained from online databases. The setup allows an accurate assessment of the performance and effectiveness of the proposed Geomagentic architecture in diverse and realistic geomagnetic scenarios. The results of this research demonstrate the potential of Machine Learning algorithms in improving the performance of the sensor fusion filter for geomagnetic navigation, and introduces a novel approach for resolution enhancing of available geomagnetic models, which provides a better description of the magnetic features within these models. The integration leads to more accurate and robust inertial guidance in airborne missions, thus paving the way for advanced, reliable navigation systems for a variety of aerial vehicles. Overall, this dissertation contributes to the state-of-the-art in geomagnetic navigation research by offering a novel approach to integrating machine learning techniques with traditional estimation methods, with a novel technique to obtain more accurate geomagnetic models required within these navigation architectures. The findings of this work hold promise for the development of advanced, adaptive navigation systems for both civilian and military aviation applications

Nonlinear bayesian filtering with applications to estimation and navigation

In principle, general approaches to optimal nonlinear filtering can be described in a unified way from the recursive Bayesian approach. The central idea to this recur- sive Bayesian estimation is to determine the probability density function of the state vector of the nonlinear systems conditioned on the available measurements. However, the optimal exact solution to this Bayesian filtering problem is intractable since it requires an infinite dimensional process. For practical nonlinear filtering applications approximate solutions are required. Recently efficient and accurate approximate non- linear filters as alternatives to the extended Kalman filter are proposed for recursive nonlinear estimation of the states and parameters of dynamical systems. First, as sampling-based nonlinear filters, the sigma point filters, the unscented Kalman fil- ter and the divided difference filter are investigated. Secondly, a direct numerical nonlinear filter is introduced where the state conditional probability density is calcu- lated by applying fast numerical solvers to the Fokker-Planck equation in continuous- discrete system models. As simulation-based nonlinear filters, a universally effective algorithm, called the sequential Monte Carlo filter, that recursively utilizes a set of weighted samples to approximate the distributions of the state variables or param- eters, is investigated for dealing with nonlinear and non-Gaussian systems. Recentparticle filtering algorithms, which are developed independently in various engineer- ing fields, are investigated in a unified way. Furthermore, a new type of particle filter is proposed by integrating the divided difference filter with a particle filtering framework, leading to the divided difference particle filter. Sub-optimality of the ap- proximate nonlinear filters due to unknown system uncertainties can be compensated by using an adaptive filtering method that estimates both the state and system error statistics. For accurate identification of the time-varying parameters of dynamic sys- tems, new adaptive nonlinear filters that integrate the presented nonlinear filtering algorithms with noise estimation algorithms are derived. For qualitative and quantitative performance analysis among the proposed non- linear filters, systematic methods for measuring the nonlinearities, biasness, and op- timality of the proposed nonlinear filters are introduced. The proposed nonlinear optimal and sub-optimal filtering algorithms with applications to spacecraft orbit es- timation and autonomous navigation are investigated. Simulation results indicate that the advantages of the proposed nonlinear filters make these attractive alterna- tives to the extended Kalman filter

Sequential Importance Resampling Particle Filter for Ambiguity Resolution

In this thesis the sequential importance resampling particle filter for estimating the full geometry-based float solution state vector for Global Navigation Satellite System (GNSS) ambiguity resolution is implemented. The full geometry-based state vector, consisting on position, velocity, acceleration, and float ambiguities, is estimated using a particle filter in RTK mode. In contrast to utilizing multi-frequency and multi-constellation GNSS measurements, this study employed solely L1 GPS code and carrier phase observations. This approach simulates scenarios wherein the signal reception environment is suboptimal and only a restricted number of satellites are visible. However, it should be noted that the methodology outlined in this thesis can be expanded for cases involving multiple frequencies and constellations. The distribution of particles after the resampling step is used to compute an empirical covariance matrix Pk based on the incorporated observations at each epoch. This covariance matrix is then used to transform the distribution using the decorrelating Z transformation of the LAMBDA method [1]. The performance of a float solution based on point mass representation is compared to the typically used extended Kalman filter (EKF) for searching the integer ambiguities using the three common search methods described in [2]: Integer Rounding, Integer Bootstrapping, and Integer Least Squares with and without the Z transformation. As Bayesian estimators are able to include highly non-linear elements and accurately describe non-Gaussian posterior densities, the particle filter outperforms the EKF when a constraint leading to highly non-Gaussian distributions is added to the estimator. Such is the case of the map-aiding constraint, which integrates digital road maps with GPS observations to compute a more accurate position state. The comparison between the position accuracy of the particle filter solution with and without the map-aiding constraint to the solution estimated with the EKF is made. The algorithm is tested in different segments of data and shows how the position convergence improves when adding digital road map information within the first thirty seconds of initializing the Particle Filter in different scenarios that include driving in a straight line, turning, and changing lanes. The assessment of the effect of the map-aiding algorithm on the ambiguity domain is carried out as well and it is shown how the convergence time of the float ambiguities improves when the position accuracy is improved by the constraint. The particle filter is able to weight the measurements according to any kind of distribution, unlike the EKF which always assumes a Gaussian distribution. The performance of the PF when having non-Gaussian measurements is assessed, such as when the measurements are distorted by multipath. Two additional steps are implemented, an outlier detection technique based on the predicted set of particles, and the use of a mixture of Gaussians to weight the measurements detected as outliers. The implemented outlier detection algorithm is based on the residual (or innovation) testing technique which is commonly applied into the EKF. The innovation and its covariance matrix are estimated from a predicted set of residuals using the transitional prior distribution and the measurement model. Then, the innovation is compared against the critical value of N (0, 1) at a level of significance α. The mixture of Gaussians is the weighted sum of two Gaussians, one from the measurement noise matrix, and the second being a scaled version of the first one describing the multipath error. This procedure de-weights the measurements with multipath, and reduces the bias in the position estimate. The proposed map-aiding algorithm improves the ambiguity convergence time by approximately 80%, while the deweighting process enhances it by around 25% for the segments of the vehicle dataset that were analyzed. This work serves as a demonstration of cases wherein the particle filter addresses the limitations of the EKF in estimating the float solution in ambiguity resolution. Such limitations include constraints that give rise to non-Gaussian probability density functions and the utilization of a distinct likelihood function for outlier measurements, as opposed to the Gaussian assumption made by the EKF. The proposed map-aided particle filter can be implemented in real-time to enhance the float ambiguity during the initial epochs after the filter has been initialized. This implementation proves beneficial in urban environments where there is a loss or complete obstruction of the GNSS signal

A Survey of Positioning Systems Using Visible LED Lights

© 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.As Global Positioning System (GPS) cannot provide satisfying performance in indoor environments, indoor positioning technology, which utilizes indoor wireless signals instead of GPS signals, has grown rapidly in recent years. Meanwhile, visible light communication (VLC) using light devices such as light emitting diodes (LEDs) has been deemed to be a promising candidate in the heterogeneous wireless networks that may collaborate with radio frequencies (RF) wireless networks. In particular, light-fidelity has a great potential for deployment in future indoor environments because of its high throughput and security advantages. This paper provides a comprehensive study of a novel positioning technology based on visible white LED lights, which has attracted much attention from both academia and industry. The essential characteristics and principles of this system are deeply discussed, and relevant positioning algorithms and designs are classified and elaborated. This paper undertakes a thorough investigation into current LED-based indoor positioning systems and compares their performance through many aspects, such as test environment, accuracy, and cost. It presents indoor hybrid positioning systems among VLC and other systems (e.g., inertial sensors and RF systems). We also review and classify outdoor VLC positioning applications for the first time. Finally, this paper surveys major advances as well as open issues, challenges, and future research directions in VLC positioning systems.Peer reviewe

The Estimation Methods for an Integrated INS/GPS UXO Geolocation System

This work was supported by a project funded by the US Army Corps of Engineers, Strategic Environment Research and Development Program, contract number W912HQ- 08-C-0044.This report was also submitted to the Graduate School of the Ohio State University in partial fulfillment of the PhD degree in Geodetic Science.Unexploded ordnance (UXO) is the explosive weapons such as mines, bombs, bullets, shells and grenades that failed to explode when they were employed. In North America, especially in the US, the UXO is the result of weapon system testing and troop training by the DOD. The traditional UXO detection method employs metal detectors which measure distorted signals of local magnetic fields. Based on detected magnetic signals, holes are dug to remove buried UXO. However, the detection and remediation of UXO contaminated sites using the traditional methods are extremely inefficient in that it is difficult to distinguish the buried UXO from the noise of geologic magnetic sources or anthropic clutter items. The reliable discrimination performance of UXO detection system depends on the employed sensor technology as well as on the data processing methods that invert the collected data to infer the UXO. The detection systems require very accurate positioning (or geolocation) of the detection units to detect and discriminate the candidate UXO from the non-hazardous clutter, greater position and orientation precision because the inversion of magnetic or EMI data relies on their precise relative locations, orientation, and depth. The requirements of position accuracy for MEC geolocation and characterization using typical state-of-the-art detection instrumentation are classified according to levels of accuracy outlined in: the screening level with position tolerance of 0.5 m (as standard deviation), area mapping (less than 0.05 m), and characterize and discriminate level of accuracy (less than 0.02m). The primary geolocation system is considered as a dual-frequency GPS integrated with a three dimensional inertial measurement unit (IMU); INS/GPS system. Selecting the appropriate estimation method has been the key problem to obtain highly precise geolocation of INS/GPS system for the UXO detection performance in dynamic environments. For this purpose, the Extended Kalman Filter (EKF) has been used as the conventional algorithm for the optimal integration of INS/GPS system. However, the newly introduced non-linear based filters can deal with the non-linear nature of the positioning dynamics as well as the non-Gaussian statistics for the instrument errors, and the non-linear based estimation methods (filtering/smoothing) have been developed and proposed. Therefore, this study focused on the optimal estimation methods for the highly precise geolocation of INS/GPS system using simulations and analyses of two Laboratory tests (cart-based and handheld geolocation system). First, the non-linear based filters (UKF and UKF) have been shown to yield superior performance than the EKF in various specific simulation tests which are designed similar to the UXO geolocation environment (highly dynamic and small area). The UKF yields 50% improvement in the position accuracy over the EKF particularly in the curved sections (medium-grade IMUs case). The UKF also performed significantly better than EKF and shows comparable improvement over the UKF when the IMU noise probability iii density function is symmetric and non-symmetric. Also, since the UXO detection survey does not require the real-time operations, each of the developed filters was modified to accommodate the standard Rauch-Tung-Striebel (RTS) smoothing algorithms. The smoothing methods are applied to the typical UXO detection trajectory; the position error was reduced significantly using a minimal number of control points. Finally, these simulation tests confirmed that tactical-grade IMUs (e.g. HG1700 or HG1900) are required to bridge gaps of high-accuracy ranging solution systems longer than 1 second. Second, these result of the simulation tests were validated from the laboratory tests using navigation-grade and medium-grade accuracy IMUs. To overcome inaccurate a priori knowledge of process noise of the system, the adaptive filtering methods have been applied to the EKF and UKF and they are called the AEKS and AUKS. The neural network aided adaptive nonlinear filtering/smoothing methods (NN-EKS and NN-UKS) which are augmented with RTS smoothing method were compared with the AEKS and AUKS. Each neural network-aided, adaptive filter/smoother improved the position accuracy in both straight and curved sections. The navigation grade IMU (H764G) can achieve the area mapping level of accuracy when the gap of control points is about 8 seconds. The medium grade IMUs (HG1700 and HG1900) with NN-AUKS can maintain less than 10cm under the same conditions as above. Also, the neural network aiding can decrease the difference of position error between the straight and the curved section. Third, in the previous simulation test, the UPF performed better than the other filters. However since the UPF needs a large number of samples to represent the a posteriori statistics in high-dimensional space, the RBPF can be used as an alternative to avoid the inefficiency of particle filter. The RBPF is tailored to precise geolocation for UXO detection using IMU/GPS system and yielded improved estimation results with a small number of samples. The handheld geolocation system using HG1900 with a nonlinear filter-based smoother can achieve the discrimination level of accuracy if the update rate of control points is less than 0.5Hz and 1Hz for the sweep and swing respectively. Also, the sweep operation is more preferred than the swing motion because the position accuracy of the sweep test was better than that of the swing test

On Improving the Accuracy and Reliability of GPS/INS-Based Direct Sensor Georeferencing

Due to the complementary error characteristics of the Global Positioning System (GPS) and Inertial Navigation System (INS), their integration has become a core positioning component, providing high-accuracy direct sensor georeferencing for multi-sensor mobile mapping systems. Despite significant progress over the last decade, there is still a room for improvements of the georeferencing performance using specialized algorithmic approaches. The techniques considered in this dissertation include: (1) improved single-epoch GPS positioning method supporting network mode, as compared to the traditional real-time kinematic techniques using on-the-fly ambiguity resolution in a single-baseline mode; (2) customized random error modeling of inertial sensors; (3) wavelet-based signal denoising, specially for low-accuracy high-noise Micro-Electro-Mechanical Systems (MEMS) inertial sensors; (4) nonlinear filters, namely the Unscented Kalman Filter (UKF) and the Particle Filter (PF), proposed as alternatives to the commonly used traditional Extended Kalman Filter (EKF). The network-based single-epoch positioning technique offers a better way to calibrate the inertial sensor, and then to achieve a fast, reliable and accurate navigation solution. Such an implementation provides a centimeter-level positioning accuracy independently on the baseline length. The advanced sensor error identification using the Allan Variance and Power Spectral Density (PSD) methods, combined with a wavelet-based signal de-noising technique, assures reliable and better description of the error characteristics, customized for each inertial sensor. These, in turn, lead to a more reliable and consistent position and orientation accuracy, even for the low-cost inertial sensors. With the aid of the wavelet de-noising technique and the customized error model, around 30 percent positioning accuracy improvement can be found, as compared to the solution using raw inertial measurements with the default manufacturer’s error models. The alternative filters, UKF and PF, provide more advanced data fusion techniques and allow the tolerance of larger initial alignment errors. They handle the unknown nonlinear dynamics better, in comparison to EKF, resulting in a more reliable and accurate integrated system. For the high-end inertial sensors, they provide only a slightly better performance in terms of the tolerance to the losses of GPS lock and orientation convergence speed, whereas the performance improvements are more pronounced for the low-cost inertial sensors

Statistical Orbit Determination using the Particle Filter for Incorporating Non-Gaussian Uncertainties

The tracking of space objects requires frequent and accurate monitoring for collision avoidance. As even collision events with very low probability are important, accurate prediction of collisions require the representation of the full probability density function (PDF) of the random orbit state. Through representing the full PDF of the orbit state for orbit maintenance and collision avoidance, we can take advantage of the statistical information present in the heavy tailed distributions, more accurately representing the orbit states with low probability. The classical methods of orbit determination (i.e. Kalman Filter and its derivatives) provide state estimates based on only the second moments of the state and measurement errors that are captured by assuming a Gaussian distribution. Although the measurement errors can be accurately assumed to have a Gaussian distribution, errors with a non-Gaussian distribution could arise during propagation between observations. Moreover, unmodeled dynamics in the orbit model could introduce non-Gaussian errors into the process noise. A Particle Filter (PF) is proposed as a nonlinear filtering technique that is capable of propagating and estimating a more complete representation of the state distribution as an accurate approximation of a full PDF. The PF uses Monte Carlo runs to generate particles that approximate the full PDF representation. The PF is applied in the estimation and propagation of a highly eccentric orbit and the results are compared to the Extended Kalman Filter and Splitting Gaussian Mixture algorithms to demonstrate its proficiency