Steady-State Marginalized Particle Filter for Attitude Estimation

2014 ◽  
Author(s):  
Yizhou Wang ◽  
Dennis Wai ◽  
Masayoshi Tomizuka
Keyword(s):  
Kalman Filter ◽  
Steady State ◽  
Particle Filter ◽  
Stochastic Systems ◽  
Linear Part ◽  
Linear Structure ◽  
Attitude Estimation ◽  
Computational Time ◽  
Unit Quaternions ◽  
Linear Stochastic Systems

A marginalized particle filter (MPF) is designed for attitude estimation problem. Unit quaternions are used to parameterize rotations. The linear structure in the gyroscope bias dynamics enables us to completely decouple its evolution from quaternion particles. We further show that the linear part of the proposed MPF reaches a steady state, similar to what Kalman filter does for controllable and observable linear stochastic systems. Although the steady-state MPF is similar to the particle filter in structure, it has two advantages: (i) the theoretical superiority of marginalizing linear substructure, and (ii) the reduction in total computational time. Numerical simulations are performed to demonstrated the performance of the proposed filter.

scholarly journals Quaternion-Based Robust Attitude Estimation Using an Adaptive Unscented Kalman Filter

Sensors ◽  
2019 ◽  
Vol 19 (10) ◽  
pp. 2372 ◽  
Author(s):  
Antônio C. B. Chiella ◽  
Bruno O. S. Teixeira ◽  
Guilherme A. S. Pereira
Keyword(s):  
Kalman Filter ◽  
Unscented Kalman Filter ◽  
Ground Truth ◽  
Adaptive Strategy ◽  
Attitude Estimation ◽  
Covariance Matching ◽  
Adaptive Unscented Kalman Filter ◽  
Unit Quaternions ◽  
Abrupt Changes ◽  
Robust Adaptive

This paper presents the Quaternion-based Robust Adaptive Unscented Kalman Filter (QRAUKF) for attitude estimation. The proposed methodology modifies and extends the standard UKF equations to consistently accommodate the non-Euclidean algebra of unit quaternions and to add robustness to fast and slow variations in the measurement uncertainty. To deal with slow time-varying perturbations in the sensors, an adaptive strategy based on covariance matching that tunes the measurement covariance matrix online is used. Additionally, an outlier detector algorithm is adopted to identify abrupt changes in the UKF innovation, thus rejecting fast perturbations. Adaptation and outlier detection make the proposed algorithm robust to fast and slow perturbations such as external magnetic field interference and linear accelerations. Comparative experimental results that use an industrial manipulator robot as ground truth suggest that our method overcomes a trusted commercial solution and other widely used open source algorithms found in the literature.

scholarly journals Kalman Filtering for Attitude Estimation with Quaternions and Concepts from Manifold Theory

Sensors ◽  
2019 ◽  
Vol 19 (1) ◽  
pp. 149 ◽  
Author(s):  
Pablo Bernal-Polo ◽  
Humberto Martínez-Barberá
Keyword(s):  
Kalman Filter ◽  
Kalman Filtering ◽  
Attitude Estimation ◽  
Performance Metric ◽  
Unit Quaternions ◽  
The Mean ◽  
Correction Step ◽  
Manifold Theory ◽  
Multiplicative Update ◽  
Natural Way

The problem of attitude estimation is broadly addressed using the Kalman filter formalism and unit quaternions to represent attitudes. This paper is also included in this framework, but introduces a new viewpoint from which the notions of “multiplicative update” and “covariance correction step” are conceived in a natural way. Concepts from manifold theory are used to define the moments of a distribution in a manifold. In particular, the mean and the covariance matrix of a distribution of unit quaternions are defined. Non-linear versions of the Kalman filter are developed applying these definitions. A simulation is designed to test the accuracy of the developed algorithms. The results of the simulation are analyzed and the best attitude estimator is selected according to the adopted performance metric.

scholarly journals Lightweight Extended Kalman Filter for MARG Sensors Attitude Estimation

2021 ◽  
Author(s):  
Lei Jing
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Process Model ◽  
Angular Rate ◽  
Measurement Model ◽  
Attitude Estimation ◽  
Human Motion ◽  
Computational Time ◽  
Orientation Estimation ◽  
Kinematic Equation

<div> <div> <div> <p>Low-power consumption of orientation estimation using low-cost inertial sensors are crucial for all the applications which are resource constrained critically. This paper presents a novel Lightweight quaternion-based Extended Kalman Filter (LEKF) for orientation estimation for magnetic, angular rate and gravity (MARG) sensors. In this filter, with employing the quaternion kinematic equation as the process model, we derived a simplified measurement model to create the lightweight system model for Kalman filtering, where the measurement model works efficiently and the involved computation of measurement model is reduced. It’s later proved that the proposed filter saves time consumption. Further, due to that no linearization is involved for the proposed measurement model, the good performance would be guaranteed in theory. For the experiments, a commercial sensor for data collection and an optical system to provide reference measurements of orientation, namely Vicon, are utilized to investigate the performance of the proposed filter. Evaluation for different application scenarios are considered, which primarily includes human motion capture and the drone application. Results indicate that the proposed filter provides reliable performance for both applications. What’s more, the comparison experiment shows that the proposed filter provides better performance in terms of either attitude estimation accu- racy or computational time. </p> </div> </div> </div>

Filtering for Linear Stochastic Systems With Small Measurement Noise

1995 ◽  
Vol 117 (3) ◽  
pp. 425-429 ◽  
Author(s):  
Z. Aganovic ◽  
Z. Gajic ◽  
X. Shen
Keyword(s):  
Kalman Filter ◽  
Riccati Equation ◽  
Stochastic Systems ◽  
Measurement Noise ◽  
Algebraic Riccati Equation ◽  
Reduced Order ◽  
Complete Decomposition ◽  
Algebraic Riccati Equations ◽  
Optimal Filters ◽  
Linear Stochastic Systems

In this paper we present a method which produces complete decomposition of the optimal global Kalman filter for linear stochastic systems with small measurement noise into exact pure-slow and pure-fast reduced-order optimal filters both driven by the system measurements. The method is based on the exact decomposition of the global small measurement noise algebraic Riccati equation into exact pure-slow and pure-fast algebraic Riccati equations. An example is included in order to demonstrate the proposed method.

scholarly journals Lightweight Extended Kalman Filter for MARG Sensors Attitude Estimation

2021 ◽  
Author(s):  
Lei Jing
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Process Model ◽  
Angular Rate ◽  
Measurement Model ◽  
Attitude Estimation ◽  
Human Motion ◽  
Computational Time ◽  
Orientation Estimation ◽  
Kinematic Equation

<div> <div> <div> <p>Low-power consumption of orientation estimation using low-cost inertial sensors are crucial for all the applications which are resource constrained critically. This paper presents a novel Lightweight quaternion-based Extended Kalman Filter (LEKF) for orientation estimation for magnetic, angular rate and gravity (MARG) sensors. In this filter, with employing the quaternion kinematic equation as the process model, we derived a simplified measurement model to create the lightweight system model for Kalman filtering, where the measurement model works efficiently and the involved computation of measurement model is reduced. It’s later proved that the proposed filter saves time consumption. Further, due to that no linearization is involved for the proposed measurement model, the good performance would be guaranteed in theory. For the experiments, a commercial sensor for data collection and an optical system to provide reference measurements of orientation, namely Vicon, are utilized to investigate the performance of the proposed filter. Evaluation for different application scenarios are considered, which primarily includes human motion capture and the drone application. Results indicate that the proposed filter provides reliable performance for both applications. What’s more, the comparison experiment shows that the proposed filter provides better performance in terms of either attitude estimation accu- racy or computational time. </p> </div> </div> </div>

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