Angular Velocity Estimation using Non-coplanar Accelerometer Array

TL;DR

This paper introduces a non-coplanar accelerometer array and an EKF-based method for estimating angular velocity, demonstrating improved accuracy through simulations and experiments with a cube-shaped sensor setup.

Contribution

It proposes a novel non-coplanar accelerometer arrangement and a dynamical system model for angular velocity estimation using an EKF, with insights into noise propagation and covariance.

Findings

Estimation error decreases with increasing edge length of the accelerometer array.

System noise inversely proportional to the cube edge length.

EKF outperforms methods with correlated process and measurement noise.

Abstract

Over the last few decades, Gyro-Free IMUs have been extensively researched to overcome the limitations of gyroscopes. This research presents a Non-coplanar Accelerometer Array (NAA) for estimating angular velocity with non-specific geometric arrangement of four or more triaxial accelerometers with non-coplanarity constraint. The presented proof of non-coplanar spacial arrangement also provides insights into propagation of the sensor noise and construction of the noise covariance matrices. The system noise depends on the singular values of the relative displacement matrix (between the sensors). A dynamical system model with uncorrelated process and measurement noise is proposed where the accelerometer readings are used simultaneously as process and measurement inputs. The angular velocity is estimated using an EKF that discretizes and linearizes the continuous-discrete time dynamical system. The simulations are performed on a Cube-NAA (Cu-NAA) comprising four accelerometers placed at different vertices of a cube. They analyze the estimation error for static and dynamic movement as the distance between the accelerometers is varied. Here, the system noise is observed to decrease inversely with the length of the cube edge as the arrangement is kept identical. Consequently, the simulation results indicate asymptotic decrease in the standard error of estimation with edge length. The experiments are conducted on a Cu-NAA with five reflective optical markers. The reflective markers are visually tracked using VICON to construct the ground truth. This unique experimental setup, apart from providing three degrees of rotational freedom of movement, also allows for three degrees of spacial translation (linear acceleration of the Cu-NAA in space). The simulation and experimental results indicate better performance of the proposed EKF as compared to one with correlated process and measurement noises.