The well-known Wahba Problem [1] is a non-linear, weighted least-squares problem that seeks to obtain the optimal attitude matrix from a set of at least two independent vector measurements. The most common technique used to solved the Wahba problem is the so-called q-method, developed by Davenport and documented in [2]. The q-method rearranges the Wahba performance index into a quadratic perfor...

Inertial orientation tracking is still an area of active research, especially in the context of out-door, real-time, human motion capture. Existing systems either propose loosely coupled tracking approaches where each segment is considered independently, taking the resulting drawbacks into account, or tightly coupled solutions that are limited to a fixed chain with few segments. Such solutions ...

In this chapter, we focused on the posture estimation problem of a body moving in 3D space. This study is devoted to the reconstruction of the body attitude and Dynamic Body Acceleration (DBA) in free ranging animal (application in Bio-logging) where the access to GPS locations is limited or impossible. A quaternion-based complementary filter is designed to provide a viable attitude estimation ...

Abstract Linear regression is a simple and widely used machine learning algorithm. It statistical approach for modeling the relationship between scalar variable one or more variables. In this paper, classification by principal component (CbPCR) strategy proposed. This depends on performing of each data class in terms its components. CbPCR formulation leads to new Regression Classification (LRC)...

Recently, quaternion collaborative representationbased classification (QCRC) and quaternion sparse representation-based classification (QSRC) have been proposed for color face recognition. They can obtain correlation information among different color channels. However, their performance is unstable in different conditions. For example, QSRC performs better than than QCRC on some situations but ...

This paper addresses the problem of integration of Inertial Navigation System (INS) and Global Navigation Satellite System (GNSS) for the purpose of developing a low-cost, robust and highly accurate navigation system for unmanned surface vehicles (USVs). A tightly-coupled integration approach is one of the most promising architectures to fuse the GNSS data with INS measurements. However, the re...

The integral octonions arise from the octonion XY-product. A parallel is shown to exist with the quaternion Z-product. Connections to the laminated lattices in dimensions 4, 8, 16 and 24 (Leech) are developed.

This article presents a generic motion model to capture mobile robots’ dynamic behaviors (translation and rotation). The is based on statistical models driven by white random processes formulated into full state estimation algorithm the error-state extended Kalman filtering framework (ESEKF). major benefits of this method are its versatility, being applicable different robotic systems without a...