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Quaternion Space Anti-Wraparound Algorithm

IP.com Disclosure Number: IPCOM000244482D
Publication Date: 2015-Dec-16
Document File: 8 page(s) / 320K

Publishing Venue

The IP.com Prior Art Database

Related People

Allyce North Macon & William Pratt Mounfield, Jr.: INVENTOR

Abstract

Attitude estimation in aircraft and other objects in space are largely based on either direct attitude representation methods angles, such as Euler angles, or indirect attitude representation methods such as quaternions based upon angles. The direct methods are simple as they may use direct measurements and may not involve any type of conversion. The indirect methods do require conversion from measured parameters to a quaternion representation and, when properly formed, may present singularity free features. Quaternion conversion is popular because it provides flexibility in terms of complex computation. However, quaternions may have their own limitations when converting attitude parameters such as heading, pitch, and roll, resulting in discontinuities. The discontinuities can be observed when consumed in the systems used downstream from the quaternion conversion. The quaternion based angle representations when used in estimation filters may suffer from singularity issues as the attitude angles come full circle. The discontinuities present problems when estimation filters have time constants, such that the filter cannot properly react to large changes in their inputs. To address the issue of accurate representation of angular input in quaternion form, and provide reliable estimation systems, this paper discloses a quaternion anti-wraparound algorithm which converts the attitude parameters accurately into quaternion form while maintaining continuity and differentiability of the quaternion without any singularities. The quaternion anti-wraparound algorithm maintains continuity and differentiability by restricting the input angle(s) used by quaternion to the range of -360 degrees to +360 degrees.

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Quaternion Space Anti-Wraparound Algorithm

Allyce North Macon & William Pratt Mounfield, Jr.

ABSTRACT

Attitude estimation in aircraft and other objects in space are largely based on either direct attitude representation methods angles, such as Euler angles, or indirect attitude representation methods such as quaternions based upon angles. The direct methods are simple as they may use direct measurements and may not involve any type of conversion. The indirect methods do require conversion from measured parameters to a quaternion representation and, when properly formed, may present singularity free features. Quaternion conversion is popular because it provides flexibility in terms of complex computation. However, quaternions may have their own limitations when converting attitude parameters such as heading, pitch, and roll, resulting in discontinuities. The discontinuities can be observed when consumed in the systems used downstream from the quaternion conversion. The quaternion based angle representations when used in estimation filters may suffer from singularity issues as the attitude angles come full circle. The discontinuities present problems when estimation filters have time constants, such that the filter cannot properly react to large changes in their inputs. To address the issue of accurate representation of angular input in quaternion form, and provide reliable estimation systems, this paper discloses a quaternion anti-wraparound algorithm which converts the attitude parameters accurately into quaternion form while maintaining continuity and differentiability of the quaternion without any singularities. The quaternion anti-wraparound algorithm maintains continuity and differentiability by restricting the input angle(s) used by quaternion to the range of -360 degrees to +360 degrees.

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1. INTRODUCTION & BACKGROUND

The attitude of aircraft and other objects in space can be determined by various methods. For example, attitude estimation filters use quaternions which in one form consumes angles (such as heading, pitch and roll) and angle rates (such as yaw, pitch and roll rates). If the attitude estimation filter is formed in quaternions, the angles received from sensors are converted to a quaternion. However, the normal form of the received angles, whether restricted to the range from 0 to 360 degrees or from -180 to +180 degrees, may present a problem to downstream systems like estimation filters when these angles are directly converted to a quaternion. The problems arise because of the differentiability of the real and imaginary parts of the quaternion as the angles pass across the -180 to +180 or 0 to 360 boundary, respectively. When the quaternion is used in downstream systems like estimation filters to estimate attitude, the estimation filter uses the angle representation and angle rates along with time constants. The state of filter is not represented accurately due to discontinuities and representation...