Many applications require reliable, high precision state estimation while mitigating measurement outliers. This dissertation presents a novel state estimation approach to the challenge of preventing outlier measurements from affecting the accuracy and reliability of state estimation. Since outliers can degrade the performance of state estimation, outlier accommodation is critical. The most common method for outlier accommodation utilizes a Neyman-Pearson (NP) type threshold test in a (extended) Kalman filter (KF) to detect and remove residuals greater than a designer specified threshold. Such threshold based methods may use residuals arbitrarily close to the threshold, even when they are not needed to achieve an application's performance specification. Outlier measurements that pass the residual test (i.e., missed detections) results in incorrect information being incorporated into the state and error covariance estimates. Once the state and covariance are incorrect, subsequent outlier decisions may be incorrect, possibly causing divergence.

The major contribution of this dissertation is changing the focus from outlier detection, to looking for a subset of measurements which have minimum risk while achieving a lower bounded information for state estimation. Risk-averse performance-specified (RAPS) state estimation works within an optimization setting to choose a set of measurements that achieves a performance specification with minimum risk of outlier inclusion. This dissertation derives and formulates the RAPS solution for outlier accommodation which applies to both linear and nonlinear applications. The approach is also extended to moving horizon state estimation problem. Global Navigation Satellite Systems (GNSS) and inertial measurements for moving vehicle state estimation are used as an example to show the performance of the proposed approach.

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.