Variational Bayesian Based Adaptive and Robust Filtering for Gnss Navigation Processing

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Project title

Code/計畫編號

MOST109-2221-E019-010

Translated Name/計畫中文名

基於變分貝氏自適應強健濾波器之衛星導航演算法

Project Coordinator/計畫主持人

Dah-Jing Jwo

Funding Organization/主管機關

National Science and Technology Council

Department/Unit

Department of Communications, Navigation and Control Engineering

Website

https://www.grb.gov.tw/search/planDetail?id=13540431

Year

2020

Start date/計畫起

01-08-2020

Expected Completion/計畫迄

31-10-2021

Bugetid/研究經費

1269千元

ResearchField/研究領域

航空工程

A research plan is proposed on the investigation of variational Bayesian (VB) learning algorithm based adaptive and robust filtering for the GNSS (Global Navigation Satellite System) navigation processing. The algorithm is utilized to solve for the problem of the time varying measurement noises for the GNSS navigation state estimation. The algorithm is also designed effectively for dealing with non-Gaussian errors or heavy-tailed outliers of the GNSS. GNSS navigation processing using the family of Kalman filter degrades severely since the statistics of the noise might usually be time-varying. The performance of the state estimation may be degraded due to the fact that in practical situations the statistics of measurement noise might change. In the proposed filtering algorithm, the adaptivity is achieved by estimating the time-varying noise covariance matrices based on VB approximation, where in each update step, both the system state and time-varying measurement noise were recognized as random variables to be estimated. Using the probabilistic approach, the VB learning possesses a recursive way to approximate the true posterior of the noise together with the states. The estimation is iterated at each time to approximate the real joint posterior distribution of state using the VB learning. The robustness is achieved by modifying the filter update based on Huber’s M-estimation and Gaussian-Newton iterated method in the filtering framework. The Gaussian ﬁltering based formulation of the non-linear state space model computation allows usage of efficient Gaussian integration methods such as unscented transform, and cubature integration along with the classical Taylor series approximations. The algorithms based on variational Bayes noise adaptive Gaussian filter filter (VB-GF) results in the cubature Kalman filter (VB-CKF), the unscented Kalman filter algorithm (VB-UKF), and the extended Kalman filter algorithm (VB-EKF). The inverse Gamma and inverse Wishart distributions were used to model the measurement noise parameters, and the nonlinear variational Bayes filter was utilized to estimate the joint posteriori probability of the state and the unknown measurement noise parameter. To resolve the problem of performance degradation caused by the outliers, the proposed algorithm took full account of the characteristics of the heavy-tailedness caused by outliers, and the measurement noise was modeled as Student’s t distribution to solve the problem of heavy tailed measurement noise. The adaptive variational Bayesian learning algorithm is adopted for the GNSS navigation processing. Performance evaluation will be conducted to compare the solutions based on various configurations and system designs. 本研究提出以變分貝氏(Variational Bayesian，VB)自適應強健濾波器進行全球導航衛星系統(GNSS)導航解算，解決濾波演算法在觀測雜訊參數未知或變化時出現的發散問題。變分貝氏學習是一種確定型逼近，將變分貝氏機器學習方法引入到濾波演算法中，設計了自適應高斯濾波器，實現對狀態和未知量測雜訊參數的聯合後驗機率的估測，在變分貝氏學習的框架下進行自適應強健濾波設計。GNSS接收機受到各方的雜訊和干擾，衛星導航濾波器因雜訊統計特性變化，量測存在離群值，導致雜訊分佈表現出厚尾特性，造成性能退化。變分貝氏自適應估測係利用基於變分貝氏學習的自適應濾波演算法，從機率角度將系統狀態與雜訊的統計矩同時作為待估測的隨機變數，反覆運算逼近得到雜訊變異數矩陣的後驗分佈，再根據該雜訊統計矩對狀態進行更新，實現了次優的狀態與量測雜訊變異數的同步估測。本計畫規劃執行三個主要的變分貝氏自適應濾波於GNSS導航技術之開發。包含(1)基於逆Gamma分佈之變分貝氏濾波，含變分貝氏自適應卡爾曼濾波器 (VB-KF)、變分貝氏自適應Ｍ估測強健濾波器(VB-HAKF)、變分貝氏自適應非線性高斯濾波器(VB-AGF)，包括變分貝氏無跡卡爾曼濾波(VB-UKF)以及變分貝氏平方根容積卡爾曼濾波器(VB-SRCKF)；(2)基於逆Wishart分佈之變分貝氏濾波，含變分貝氏強跟蹤卡爾曼濾波演算法(VB-STAKF)、變分貝氏自適應非線性高斯濾波，如變分貝氏容積卡爾曼濾波演算法(VB-CKF)；(3)技術發展三則發展基於Student’s t分佈之變分貝氏自適應卡爾曼濾波。本研究亦構造基於變分貝氏的自適應強健濾波算法，有效地解決自適應與強健濾波策略的矛盾，在變分貝氏的濾波框架內，利用變分貝氏近似估測量測雜訊，亦利用Huber濾波強健化方法處理連續離群值，兼顧自適應與強健性。另引入基於Student’s t分佈之變分貝氏自適應濾波，以克服定位量測雜訊中存在非高斯或重尾異常雜訊值下，具有良好的收斂性，保障濾波器的性能。本計畫結合非線性濾波器演算法，採用變分貝氏學習與修正，在變分貝氏學習的框架下進行自適應強健濾波演算法，對系統狀態和時變的量測雜訊變異數同步進行估測，亦對非高斯及重尾離群雜訊情形下濾波器的設計，提出了一種新的解決途徑。

Keyword(s)

衛星導航
變分貝氏
自適應
Huber M-估測
卡爾曼濾波器
無跡卡爾曼濾波器
容積卡爾曼濾波器
雜訊離群值
非高斯厚尾量測雜訊
逆威沙特分佈
Student's t 分佈
GNSS
Variational Bayesian
Adaptive
Huber M-estimation
Kalman filter
Unscented Kalman filter
Cubature Kalman filter
Outlier
Wishart
Heavy-tailed measurement noise
Student's t distribution

DSpace CRIS

Variational Bayesian Based Adaptive and Robust Filtering for Gnss Navigation Processing

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