EE Seminar: A Novel Efficient Outlier Rejection Technique for Kalman Filters
Speaker: Eitan Navon
M.Sc. student under the supervision of Prof. Ben Zion Bobrovsky
Wednesday, January 22, 2019 at 15:00
Room 011, Kitot Bldg., Faculty of Engineering
A Novel Efficient Outlier Rejection Technique for Kalman Filters
Accurate localization is a need of rising importance in modern times, often obtained by GNSS (Global Navigation Satellite Systems) receivers. Such receivers might suffer from multipath and/or non line-of-sight receptions, caused by reflections and blockage of the original GNSS signals. An example for such a situation is navigation in “urban canyon”, where high buildings might both reflect the original signals and block line-of-sight receptions, creating outlier measurements. The Kalman filter is an essential component in GNSS receivers, designed for optimal performance when the measurement noise is Gaussian. Small deviations from the Gaussian assumption are usually not devastating, but when outliers are present, the Kalman filter performance degrades sharply. Therefore, outlier rejection techniques must be used when outlier measurements might be present.
We review three common outlier rejection techniques used in a Kalman filter scheme - Innovation Filtering, Yang's robust Kalman and RANSAC. Through this review, basic concepts of outlier rejection techniques are presented.
We further introduce a novel outlier rejection technique, based on adapting the measurement’s noise conventional model to the case where outliers are present. The technique, which we call Outlier Rejecting Kalman Filter (ORKF), is based on detecting the outlier measurements and rejecting them by creating a penalty covariance matrix, which is based on the outlier offset statistics, and adding it to the originally assumed covariance matrix of the measurement’s noise. This alters the Kalman gain in a way that it handles efficiently the outlier measurements, mostly by reducing their weight in the filter's update step. Concerning the computation burden – it is well known that the popular RANSAC is rather demanding. In contrast, it turns out that our proposed ORKF's computational burden is of the same order of magnitude of the conventional Kalman filter.
Comparison among the above-mentioned techniques and the proposed ORKF was conducted by simulations in different conditions of outlier rates, outlier offset magnitudes, and trajectories - differ both in courses and dynamics. When the conditions were relaxed, i.e. the outliers rate was low and the dynamics was slow, all rejection methods exhibited good performance and the results were relatively close. It comes, however, that even under these relaxed conditions the conventional Kalman filters performance was poor. When the conditions were getting harsh, i.e. higher outlier rates and more rapid dynamics, considerable differences among the various techniques were observed: some techniques exhibited moderate or even poor performance, while the ORKF outperforms them all. Moreover, the ORKF estimates correctly the covariance matrices of the state vector estimations, even in harsh conditions where other techniques fail. By this it produces a valuable tool for real-time assessment of the estimation error.
Although the main purpose of this work is examining outlier rejection in GNSS receivers, which are characterized by outliers that can only increase the pseudo-ranges, an extension was added for the case of zero-symmetric outliers. This was done in order to examine the possible use and advantages of the various rejection techniques for other applications, such as visual odometery. In this symmetric outliers scenario, the ORKF performance was mostly superior or at least equal even to the RANSAC. Due to the computational considerable advantage of the proposed ORKF, it might be an interesting candidate for the above-mentioned applications.