Error analysis of quaternion transformations [inertial navigation]

Three transformation formulas that relate the quaternions to the direction cosine matrix used in strapdown inertial systems are derived. An error model associated with the computed direction cosine matrix is briefly discussed. Error analysis is fully evaluated analytically and tabulated for comparison. Transformation errors associated with these formulas are analyzed. The drift errors evaluated under constant angular velocity are shown to vary slightly among three different transformations. It is shown that the skew errors in three transformation schemes are not all intrinsically zero. The scale errors may differ largely by two orders of magnitude among transformation schemes. This may become a criteria for selection of altitude transformation schemes     

Improvement of strapdown inertial navigation using PDAF

A new application of PDAF (probabilistic data association filter) for improving the accuracy of autonomous strapdown inertial navigation systems (SINS) is presented. The proposed method is a terrain-aided navigation (TAN) algorithm based on landmark detection combined with a classical SINS. It is shown via a set of simulations that the method can improve significantly the precision of autonomous navigation if the landmark spatial density and quality of landmark detectors are good enough. This new concept of navigation called PDANF (probabilistic data association navigation filter) can be integrated with a relatively low cost in existing operational TAN systems     

A study on dual quaternion based cooperative relative navigation of multiple UAVs with monocular vision-inertial integration

This paper addresses a cooperative relative navigation problem for multiple aerial agents, relying on visual tracking information between vehicles. The research aims to investigate a sensor fusion architecture and algorithm that leverages partially available absolute navigation knowledge while exploiting collaborative visual interaction between vehicles in mission flight areas,where satellite navigation-denied regions are irregularly located. To achieve this, the paper introduces a new approach to defining the relative poses of cameras and develops a corresponding process to secure the relative pose information. This contrasts with previous research, which simply linearized the relative pose information of aircraft cameras into navigation states defined in an absolute coordinate system. Specifically, the target pose in relative navigation is defined, and the pose of the camera and feature points are directly derived using dual quaternion representation,which compactly represents both translation and rotation. Furthermore, a mathematical model for the relative pose of the camera is derived through the dual quaternion framework, enabling an explicit pose formulation of relative navigation. The study investigates navigation performance in typical mission flight scenarios using an in-house high-fidelity simulator and quantitatively highlights the contributions of the proposed scheme by comparing the navigation error performance.Consequently, the proposed method demonstrates to have navigation accuracy in decimeter level even in GNSS-denied environments and an improved 3D Root Mean Square(RMS) error by30% smaller than the conventional absolute navigation framework.     

Real-time total system error estimation:Modeling and application in required navigation performance

In required navigation performance（RNP）, total system error（TSE） is estimated to provide a timely warning in the presence of an excessive error. In this paper, by analyzing the underlying formation mechanism, the TSE estimation is modeled as the estimation fusion of a fixed bias and a Gaussian random variable. To address the challenge of high computational load induced by the accurate numerical method, two efficient methods are proposed for real-time application, which are called the circle tangent ellipse method（CTEM） and the line tangent ellipse method（LTEM）,respectively. Compared with the accurate numerical method and the traditional scalar quantity summation method（SQSM）, the computational load and accuracy of these four methods are extensively analyzed. The theoretical and experimental results both show that the computing time of the LTEM is approximately equal to that of the SQSM, while it is only about 1/30 and 1/6 of that of the numerical method and the CTEM. Moreover, the estimation result of the LTEM is parallel with that of the numerical method, but is more accurate than those of the SQSM and the CTEM. It is illustrated that the LTEM is quite appropriate for real-time TSE estimation in RNP application.     

Moving scanning emitter tracking by a single observer using time of interception: Observability analysis and algorithm

The target motion analysis (TMA) for a moving scanning emitter with known fixed scan rate by a single observer using the time of interception (TOI) measurements only is investigated in this paper.By transforming the TOI of multiple scan cycles into the direction difference of arrival (DDOA) model,the observability analysis for the TMA problem is performed.Some necessary conditions for uniquely identifying the scanning emitter trajectory are obtained.This paper also proposes a weighted instrumental variable (WIV) estimator for the scanning emitter TMA,which does not require any initial solution guess and is closed-form and computationally attractive.More importantly,simulations show that the proposed algorithm can provide estimation mean square error close to the Cramer-Rao lower bound (CRLB) at moderate noise levels with significantly lower estimation bias than the conventional pseudo-linear least square (PLS) estimator.