Use of Gravity Sensors for Free Space Orientation

Abstract: This thesis deals with different approaches to filtering the signal output of a three axis accelerometerfor free space orientation, that is, finding the orientation of a sensor relative to gravity. Theplatform this orientation system is to be developed for is a low-power, high-efficiency fixed-pointmath microprocessor, therefore efficiency and mathematical operation precision are factors thatalso need to be taken into consideration in this work.This is an exploratory work which goals are to analize potential filtering solutions for free spaceorientation with a three-axis accelerometer, develop a tool to validate the theorical analysis, studythe repercusions of limited precision math on those algorithms and implement a filtering solutionas versatile as possible.The goal of finding the orientation with the output of an accelerometer and without a prioriinformation is deceptively simple: while in relaxed state and within inertial systems the outputof a three axis accelerometer and the direction of gravity is the same, when that hypothesis istaken away measurements output by the accelerometer include both gravity and acceleration dueto external forces applied to the system.The contributions of this thesis are a discussion of potential solutions for free space orientationwith unrestrictive preconditions by use of an accelerometer, and an implementation of such solutionfor the MSP430, popular platform of choice for digital signal processing. The main purposeof such a solution is to improve the precision with which gravity is estimated from the outputof the accelerometer. Potential applications of this work are relative position tracking, mapping,positioning systems (for example, within buildings or vehicles, where any other existing positioningsystem cannot work, such as tunnels for GPS).Instead of just low-pass filtering the output of the accelerometer, estimations to the state ofexternal forces applied to the system and tracking of changes to those forces are presented. Tomodel that system, the Kalman filter and the Particle filter are introduced and analyzed as potentialsolutions.This document includes a discussion of both Kalman and Particle filters, implementation ofa tool to compare and validate the models to estimate gravity, a discussion of the effect of fixedpoint math to those models and an implementation of a gravity estimation algorithm that is typeand plattform agnosic based on the output of a 3-axis accelerometer.All relevant code has been included as an appendix to this work This thesis deals with di_erent approaches to _ltering the signal output of a three axis accelerometer for free space orientation, that is, _nding the orientation of a sensor relative to gravity. The plattform this orientation system is to be developed for is a low-power, high-e_ciency _xed-point math microprocessor, therefore e_ciency and mathematical operation precision are factors that also need to be taken into consideration in this work. This is an exploratory work which goals are to analize potential _ltering solutions for free space orientation with a three-axis accelerometer, develop a tool to validate the theorical analysis, study the repercusions of limited precision math on those algorithms and implement a _ltering solution as versatile as possible. The goal of _nding the orientation with the output of an accelerometer and without a priori information is deceptively simple: while in relaxed state and within inertial systems the output of a three axis accelerometer and the direction of gravity is the same, when that hypothesis is taken away measurements output by the accelerometer include both gravity and acceleration due to external forces applied to the system. The contributions of this thesis are a discussion of potential solutions for free space orientation with unrestrictive preconditions by use of an accelerometer, and an implementation of such solution for the MSP430, popular platform of choice for digital signal processing. The main purpose of such a solution is to improve the precision with which gravity is estimated from the output of the accelerometer. Potential applications of this work are relative position tracking, mapping, positioning systems (for example, within buildings or vehicles, where any other existing positioning system cannot work, such as tunnels for GPS). Instead of just low-pass _ltering the output of the accelerometer, estimations to the state of external forces applied to the system and tracking of changes to those forces are presented. To model that system, the Kalman _lter and the Particle _lter are introduced and analyzed as potential solutions. This document includes a discussion of both Kalman and Particle _lters, implementation of a tool to compare and validate the models to estimate gravity, a discussion of the e_ect of _xed point math to those models and an implementation of a gravity estimation algorithm that is type and plattform agnosic based on the output of a 3-axis accelerometer. All relevant code has been included as an appendix to this work.