Evaluation of Matrix Square Root Operations for UKF within a UAV GPS/INS Sensor Fusion Application

Matthew Rhudy,Marcello R Napolitano,Yu Gu,Jason Gross

doi:10.1155/2011/416828

Abstract

Using an Unscented Kalman Filter (UKF) as the nonlinear estimator within a Global Positioning System/Inertial Navigation System (GPS/INS) sensor fusion algorithm for attitude estimation, various methods of calculating the matrix square root were discussed and compared. Specifically, the diagonalization method, Schur method, Cholesky method, and five different iterative methods were compared. Additionally, a different method of handling the matrix square root requirement, the square-root UKF (SR-UKF), was evaluated. The different matrix square root calculations were compared based on computational requirements and the sensor fusion attitude estimation performance, which was evaluated using flight data from an Unmanned Aerial Vehicle (UAV). The roll and pitch angle estimates were compared with independently measured values from a high quality mechanical vertical gyroscope. This manuscript represents the first comprehensive analysis of the matrix square root calculations in the context of UKF. From this analysis, it was determined that the best overall matrix square root calculation for UKF applications in terms of performance and execution time is the Cholesky method.

Highlights

The improvement of microprocessors and sensors has increased civilian use of Unmanned Aerial Vehicles (UAVs) for various applications, many of which requiring an accurate estimate of the aircraft attitude [1, 2]
This paper aims to expand upon the existing matrix square root comparison studies through an example application of the matrix square root within a Unscented Kalman Filter (UKF)-based Global Positioning System/Inertial Navigation System (GPS/Inertial Navigation System (INS)) sensor fusion algorithm for attitude estimation that relies on experimentally collected flight data
To analyze the sensitivity of this formulation of Global Positioning System (GPS)/INS sensor fusion to the matrix square root operation, the UKF algorithm was executed for each set of flight data using different methods of calculating the matrix square root

Summary

Introduction

The improvement of microprocessors and sensors has increased civilian use of Unmanned Aerial Vehicles (UAVs) for various applications, many of which requiring an accurate estimate of the aircraft attitude [1, 2]. Attitude estimation algorithms that rely only on low-cost sensors have become essential for civilian applications. A popular approach to the attitude estimation problem involves fusing together information from a low-cost Inertial Navigation System (INS) with information from a Global Positioning System (GPS) receiver [8, 9]. Various formulations and analyses of GPS/INS sensor fusion exist in the literature [10,11,12], including a detailed comparison by the authors with respect to attitude estimation performance and computational cost [13]

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Conclusion