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Over the last few decades, Gyro-Free IMUs have been extensively researched toovercome the limitations of gyroscopes. This research presents a Non-coplanarAccelerometer Array (NAA) for estimating angular velocity with non-specificgeometric arrangement of four or more triaxial accelerometers withnon-coplanarity constraint. The presented proof of non-coplanar spacialarrangement also provides insights into propagation of the sensor noise andconstruction of the noise covariance matrices. The system noise depends on thesingular values of the relative displacement matrix (between the sensors). Adynamical system model with uncorrelated process and measurement noise isproposed where the accelerometer readings are used simultaneously as processand measurement inputs. The angular velocity is estimated using an EKF thatdiscretizes and linearizes the continuous-discrete time dynamical system. Thesimulations are performed on a Cube-NAA (Cu-NAA) comprising four accelerometersplaced at different vertices of a cube. They analyze the estimation error forstatic and dynamic movement as the distance between the accelerometers isvaried. Here, the system noise is observed to decrease inversely with thelength of the cube edge as the arrangement is kept identical. Consequently, thesimulation results indicate asymptotic decrease in the standard error ofestimation with edge length. The experiments are conducted on a Cu-NAA withfive reflective optical markers. The reflective markers are visually trackedusing VICON to construct the ground truth. This unique experimental setup,apart from providing three degrees of rotational freedom of movement, alsoallows for three degrees of spacial translation (linear acceleration of theCu-NAA in space). The simulation and experimental results indicate betterperformance of the proposed EKF as compared to one with correlated process andmeasurement noises.

Angular Velocity Estimation using Non-coplanar Accelerometer Array