A Kalman Filter for Nonlinear Attitude Estimation Using Time Variable Matrices and Quaternions.

Álvaro Deibe,Jesús Cardenal,José Augusto Antón Nacimiento,Fernando López Peña

doi:10.3390/s20236731

Abstract

The nonlinear problem of sensing the attitude of a solid body is solved by a novel implementation of the Kalman Filter. This implementation combines the use of quaternions to represent attitudes, time-varying matrices to model the dynamic behavior of the process and a particular state vector. This vector was explicitly created from measurable physical quantities, which can be estimated from the filter input and output. The specifically designed arrangement of these three elements and the way they are combined allow the proposed attitude estimator to be formulated following a classical Kalman Filter approach. The result is a novel estimator that preserves the simplicity of the original Kalman formulation and avoids the explicit calculation of Jacobian matrices in each iteration or the evaluation of augmented state vectors.

Highlights

Inertial sensors are among the most common types of devices used for estimating the orientation of a solid body
The inherent bias and drift of the sensor introduce errors that increase throughout the integration process. This problem is more serious for low-cost Microelectromechanical System (MEMS) gyroscopes, which are more prone to drift and bias than larger and more expensive gyroscopes [1]
As discussed in previous sections, the proposed new filter formulation is simpler and computationally less demanding than other common Kalman Filters (KF) implementations for nonlinear estimation. This feature will be of interest in many implementations, those related to AHRS

Summary

Introduction

Inertial sensors (in particular, accelerometers and gyroscopes) are among the most common types of devices used for estimating the orientation of a solid body. The inherent bias and drift of the sensor introduce errors that increase throughout the integration process This problem is more serious for low-cost Microelectromechanical System (MEMS) gyroscopes, which are more prone to drift and bias than larger and more expensive gyroscopes [1]. Quaternions can be used to perform changes in attitude or system of reference through simple scalar addition and multiplication operations. This property allows writing these changes as matrix–vector products, which turns out to be essential for the particular formulation of the present method. That is taken advantage of in the present approach, it is not an essential factor in its operation

Objectives

Results

Conclusion