This series is home to publications and data sets from the Bourns College of Engineering at the University of California, Riverside.
This article is a tutorial describing the process and issues related to developing a state-space model for the stochastic errors affecting an Inertial Measurement Unit (IMU). The starting point is the instrument error characterization data sheet provided by the manufacturer, which is typically either an Allan Variance graph or the parameters extracted from that graph. Along with this tutorial, supplementary software is available for open source distribution that calculates and plots the Allan Variance for a given set of data; extracts optimal parameters (e.g., $Q_N$, $Q_B$, $Q_K$, and $T_B$) from Allan Variance data for a given model structure; and, computes and simulates of the discrete-time equivalent model.
This tech note extends the discussion of the numericalresults in . The main article should be read first. Thatarticle presents RAPS for nonlinear applications; therefore,linear systems are a special case. This technical note includesnumerical results specific to linear systems that did not fitwithin the journal page constraints. Section I briefly introduceslinear system mode model. Section III studies the performanceof the binary RAPS approach for vehicle state estimation. Thelinear application is referred to in the GNSS literature as a PVAmodel wherein the GNSS measurements are used to estimatethe position, velocity, and acceleration of the GNSS antenna.Such estimators are included in almost all GNSS receivers.
Many applications, including connected and autonomous vehicles, would benefit from navigation technologies reliablyachieving sub-meter position accuracy with high reliability on moving platforms. Commercial on-vehicle implementation ofEarth-referenced positioning at submeter accuracy with 99% probability would require widely and reliably available differentialcorrections; however, such corrections delivered on a nationwide or global scale via satellite systems will incur latency betweentheir time-of-applicability and their time-of-reception at the vehicle.Phase 1 of this project presented a differential correction computation methodology designed to be robust to latency andstudied position accuracy as a function of differential correction latency for stationary receivers –. The study showed thatsubmeter accuracy at 95% probability was achievable when a sufficient number and diversity of satellites were available.This report summarizes the conclusions of the Phase 2 of the work performed by University of California, Riverside (UCR).There were two main goals for this effort. For moving platforms, Phase 2 investigates:1) the feasibility of achieving meter-level positioning accuracy on at least 95% of epochs using Global Navigation SatelliteSystem (DGNSS) based state estimation; and,2) the sensitivity of that positioning accuracy to communication latency.The study uses the utilizes the local based station design presented in .The study presents and experimentally analyzes two state estimation approaches suitable for moving platforms. The Position,Velocity, Acceleration (PVA) approach uses DGNSS data only within a Kalman filter framework. The Inertial Navigation System(INS) approach uses DGNSS and inertial measurement data within an extended Kalman filter implementation. Section VIIshows that both approaches have performance exceeding the SAE J2945 specification (1.5 meter horizontal accuracy and 3.0meter vertical accuracy at 68%) with PVA achieving 1m horizontal at 90% and 2 m vertical accuracy at 95% while the INSapproach using a consumer-grade IMU achieves 1m horizontal at 98% and 2 m vertical accuracy at 95%.Section VIII presents an analysis of position estimation accuracy, for moving platforms, as a function of communicationlatency, which shows that, using the DGNSS correction computation approach presented in , position estimation accuracyis robust to correction latency exceeding 500 seconds.The results herein used a local base station approach. National or global implementations would be more efficient usingnetworks of base stations working collaboratively to estimate parameters usable by user receivers to reconstruct corrections.Such methods are the focus of Phase 3 of this study.This study focuses on single frequency, single constellation results. The availability of multiple constellations and multiplefrequencies per constellations will facilitate compensation of ionospheric error, accommodation of outliers, and accommodationof multipath, while still having a set of satellites with appropriate geometry to reliably achieve the performance specification.
This tech note extends the discussion of the numerical results in . The main article should be read first. This technical note includes numerical results that could not fitwithin the journal page constraints. It presents the statistics of the vertical error for the nonlinear (INS) model and discussesthe interplay between the error, risk, and GDOP metrics for portions of an experiment using the linear (PVA) model. The error, risk and PVA metrics are defined in Sections VIII-C and VIII-E of .Each table and figure herein considers five algorithms, as summarized in Section VIII-B of . Four of the algorithms are the NP-(E)KF with four different values of the decision parameter g. The final algorithm is the RAPS approach.
This Technical Note is supplied to explain the state and noise propagation for an inertial navigation system (INS), betweentwo aiding measurement times. The temporal propagation of the state error and noise is required for optimal state estimation.
Commercial on-vehicle implementation of Earth-referenced positioning at submeter accuracy with 99% probability wouldrequire widely and reliably available differential corrections; however, such corrections delivered on a nationwide or global scale via satellite systems will incur latency between their time-of-applicability and their time-of-reception at the vehicle.This report summarizes the conclusions of the first phase of work performed by University of California, Riverside (UCR).There were two main goals for this one-year effort.1) To investigate the sensitivity of differential Global Navigation Satellite System (DGNSS) corrections and positionestimation accuracy to communication latency.2) To investigate the feasibility of achieving meter-level positioning accuracy at least 95% of epochs.The first phase of this project was designed to study stationary receivers, to clearly define, demonstrate, and address thechallenging issues. In this study, all algorithms use identical data sets (i.e., measurements and corrections); therefore, the study compares the performance of different algorithms using the same data.
The first conclusion is that GNSS corrections can be designed such that position estimation accuracy is robust to correctionlatency up to 600 seconds. This is demonstrated via experiments that are described in Section VI. The method of GNSS correction calculation is described in Section IV with results of example computations in Appendix A.The second conclusion is that meter-level horizontal position accuracy is achievable in excess of 99% of the samples whena sufficient number of satellites are observable with appropriate geometry, both pseudorange and Doppler measurements areused, and outlier measurements are suitably accommodated. Since DGNSS is designed to remove the effects of common mode errors, this study pays special attention to accommodation of the non-common mode errors. A main issue is accommodating multipath. The importance of the Doppler measurement for addressing multipath is motivated in Section V-B and demonstrated in Fig. 4. Experimental demonstration results are included in Sections VI and VII.Many applications, including connected and autonomous vehicles, would benefit from navigation technologies reliablyachieving sub-meter position accuracy with high reliability for a moving receiver. The second phase of this project willstudy the feasibility of achieving the position accuracy specification for a moving receiver combined with a commercial gradeinertial measurement unit. The results herein used a local base station approach. National or global implementations wouldbe more efficient using networks of base stations working collaboratively to estimate parameters usable by user receivers toreconstruct corrections. Such methods are the focus of phase three of the study.