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 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.

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 Distributed Robust Kalman Filtering with Unknown and Noisy Parameters in Sensor Networks

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Donghua Chen ◽  
Ya Zhang ◽  
Cheng-Lin Liu ◽  
Yangyang Chen
Keyword(s):  
Kalman Filter ◽  
Sensor Networks ◽  
Kalman Filtering ◽  
Estimation Error ◽  
Measuring System ◽  
Mean Square ◽  
System Matrix ◽  
Estimation Errors ◽  
System Parameters ◽  
The Mean

This paper investigates the distributed filtering for discrete-time-invariant systems in sensor networks where each sensor’s measuring system may not be observable, and each sensor can just obtain partial system parameters with unknown coefficients which are modeled by Gaussian white noises. A fully distributed robust Kalman filtering algorithm consisting of two parts is proposed. One is a consensus Kalman filter to estimate the system parameters. It is proved that the mean square estimation errors for the system parameters converge to zero if and only if, for any one system parameter, its accessible node subset is globally reachable. The other is a consensus robust Kalman filter to estimate the system state based on the system matrix estimations and covariances. It is proved that the mean square estimation error of each sensor is upper-bounded by the trace of its covariance. An explicit sufficient stability condition of the algorithm is further provided. A numerical simulation is given to illustrate the results.

Kalman Filtering Error Due to Inaccuracy in Filter’s Initial Condition

1997 ◽  
Vol 119 (1) ◽  
pp. 119-122 ◽  
Author(s):  
Z. Gajic ◽  
J. Boka
Keyword(s):  
Kalman Filter ◽  
Discrete Time ◽  
Kalman Filtering ◽  
Time Domain ◽  
Mean Value ◽  
Initial Condition ◽  
Initial State ◽  
Optimal Linear ◽  
The Mean

It is a very well known fact that the initial condition of the optimal linear Kalman filter has to be set at the mean value of the system initial state. In this paper, we have derived an expression for the filtering error in the case when this condition is not satisfied. Both continuous- and discrete-time domain filters are considered. The obtained results are simple and elegant and clearly indicate the effect of the erroneous filter’s initial condition. An example is included in order to demonstrate the results obtained.

scholarly journals Attitude and Heading Estimation for Indoor Positioning Based on the Adaptive Cubature Kalman Filter

Micromachines ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 79
Author(s):  
Jijun Geng ◽  
Linyuan Xia ◽  
Dongjin Wu
Keyword(s):  
Kalman Filter ◽  
Angular Rate ◽  
Indoor Positioning ◽  
Location Based Services ◽  
Statistical Characteristics ◽  
Fading Memory ◽  
Limited Memory ◽  
Cubature Kalman Filter ◽  
The Mean ◽  
Heading Estimation

The demands for indoor positioning in location-based services (LBS) and applications grow rapidly. It is beneficial for indoor positioning to combine attitude and heading information. Accurate attitude and heading estimation based on magnetic, angular rate, and gravity (MARG) sensors of micro-electro-mechanical systems (MEMS) has received increasing attention due to its high availability and independence. This paper proposes a quaternion-based adaptive cubature Kalman filter (ACKF) algorithm to estimate the attitude and heading based on smart phone-embedded MARG sensors. In this algorithm, the fading memory weighted method and the limited memory weighted method are used to adaptively correct the statistical characteristics of the nonlinear system and reduce the estimation bias of the filter. The latest step data is used as the memory window data of the limited memory weighted method. Moreover, for restraining the divergence, the filter innovation sequence is used to rectify the noise covariance measurements and system. Besides, an adaptive factor based on prediction residual construction is used to overcome the filter model error and the influence of abnormal disturbance. In the static test, compared with the Sage-Husa cubature Kalman filter (SHCKF), cubature Kalman filter (CKF), and extended Kalman filter (EKF), the mean absolute errors (MAE) of the heading pitch and roll calculated by the proposed algorithm decreased by 4–18%, 14–29%, and 61–77% respectively. In the dynamic test, compared with the above three filters, the MAE of the heading reduced by 1–8%, 2–18%, and 2–21%, and the mean of location errors decreased by 9–22%, 19–31%, and 32–54% respectively by using the proposed algorithm for three participants. Generally, the proposed algorithm can effectively improve the accuracy of heading. Moreover, it can also improve the accuracy of attitude under quasistatic conditions.

scholarly journals The Salted Kalman Filter: Kalman filtering on hybrid dynamical systems

Automatica ◽  
2021 ◽  
Vol 131 ◽  
pp. 109752
Author(s):  
Nathan J. Kong ◽  
J. Joe Payne ◽  
George Council ◽  
Aaron M. Johnson
Keyword(s):  
Kalman Filter ◽  
Dynamical Systems ◽  
Kalman Filtering ◽  
Hybrid Dynamical Systems

Integral based sliding mode stabilizing a camera platform using Kalman filter attitude estimation

Mechatronics ◽  
2017 ◽  
Vol 44 ◽  
pp. 42-51 ◽  
Author(s):  
Mohammad Sheikh Sofla ◽  
Mohammad Zareinejad ◽  
Mohsen Parsa ◽  
Hassan Sheibani
Keyword(s):  
Kalman Filter ◽  
Sliding Mode ◽  
Attitude Estimation

scholarly journals A DCM Based Attitude Estimation Algorithm for Low-Cost MEMS IMUs

2015 ◽  
Vol 2015 ◽  
pp. 1-18 ◽  
Author(s):  
Heikki Hyyti ◽  
Arto Visala
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Low Cost ◽  
Direction Cosine ◽  
Estimation Algorithm ◽  
Calibration Method ◽  
Attitude Estimation ◽  
Mems Sensors ◽  
Acceleration Sensors ◽  
Adaptive Extended Kalman Filter

An attitude estimation algorithm is developed using an adaptive extended Kalman filter for low-cost microelectromechanical-system (MEMS) triaxial accelerometers and gyroscopes, that is, inertial measurement units (IMUs). Although these MEMS sensors are relatively cheap, they give more inaccurate measurements than conventional high-quality gyroscopes and accelerometers. To be able to use these low-cost MEMS sensors with precision in all situations, a novel attitude estimation algorithm is proposed for fusing triaxial gyroscope and accelerometer measurements. An extended Kalman filter is implemented to estimate attitude in direction cosine matrix (DCM) formation and to calibrate gyroscope biases online. We use a variable measurement covariance for acceleration measurements to ensure robustness against temporary nongravitational accelerations, which usually induce errors when estimating attitude with ordinary algorithms. The proposed algorithm enables accurate gyroscope online calibration by using only a triaxial gyroscope and accelerometer. It outperforms comparable state-of-the-art algorithms in those cases when there are either biases in the gyroscope measurements or large temporary nongravitational accelerations present. A low-cost, temperature-based calibration method is also discussed for initially calibrating gyroscope and acceleration sensors. An open source implementation of the algorithm is also available.

scholarly journals Modeling of temporal groundwater level variations based on a Kalman filter adaptation algorithm with exogenous inputs

2016 ◽  
Vol 19 (2) ◽  
pp. 191-206 ◽  
Author(s):  
Emmanouil A. Varouchakis
Keyword(s):  
Kalman Filter ◽  
Groundwater Level ◽  
Auxiliary Information ◽  
Model Parameters ◽  
Adaptation Algorithm ◽  
Arx Model ◽  
Resources Management ◽  
Temporal Modelling ◽  
The Mean ◽  
First Time

Reliable temporal modelling of groundwater level is significant for efficient water resources management in hydrological basins and for the prevention of possible desertification effects. In this work we propose a stochastic method of temporal monitoring and prediction that can incorporate auxiliary information. More specifically, we model the temporal (mean annual and biannual) variation of groundwater level by means of a discrete time autoregressive exogenous variable (ARX) model. The ARX model parameters and its predictions are estimated by means of the Kalman filter adaptation algorithm (KFAA) which, to our knowledge, is applied for the first time in hydrology. KFAA is suitable for sparsely monitored basins that do not allow for an independent estimation of the ARX model parameters. We apply KFAA to time series of groundwater level values from the Mires basin in the island of Crete. In addition to precipitation measurements, we use pumping data as exogenous variables. We calibrate the ARX model based on the groundwater level for the years 1981 to 2006 and use it to predict the mean annual and biannual groundwater level for recent years (2007–2010). The predictions are validated with the available annual averages reported by the local authorities.

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