Strapdown inertial navigation system algorithms based on dual quaternions

The design of strapdown inertial navigation system (INS) algorithms based on dual quaternions is addressed. Dual quaternion is a most concise and efficient mathematical tool to represent rotation and translation simultaneously, i.e., the general displacement of a rigid body. The principle of strapdown inertial navigation is represented using the tool of dual quaternion. It is shown that the principle can be expressed by three continuous kinematic equations in dual quaternion. These equations take the same form as the attitude quaternion rate equation. Subsequently, one new numerical integration algorithm is structured to solve the three kinematic equations, utilizing the traditional two-speed approach originally developed in attitude integration. The duality between the coning and sculling corrections, raised in the recent literature, can be essentially explained by splitting the new algorithm into the corresponding rotational and translational parts. The superiority of the new algorithm over conventional ones in accuracy is analytically derived. A variety of simulations are carried out to support the analytic results. The numerical results agree well with the analyses. The new algorithm turns out to be a better choice than any conventional algorithm for high-precision navigation systems and high-maneuver applications. Several guidelines in choosing a suitable navigation algorithm are also provided.     

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     

Comparison of strapdown inertial navigation algorithm based on rotation vector and dual quaternion

 For the navigation algorithm of the strapdown inertial navigation system, by comparing to the equations of the dual quaternion and quaternion, the superiority of the attitude algorithm based on dual quaternion over the ones based on rotation vector in accuracy is analyzed in the case of the rotation of navigation frame. By comparing the update algorithm of the gravitational velocity in dual quaternion solution with the compensation algorithm of the harmful acceleration in traditional velocity solution, the accuracy advantage of the gravitational velocity based on dual quaternion is addressed. In view of the idea of the attitude and velocity algorithm based on dual quaternion, an improved navigation algorithm is proposed, which is as much as the rotation vector algorithm in computational complexity. According to this method, the attitude quaternion does not require compensating as the navigation frame rotates. In order to verify the correctness of the theoretical analysis, simulations are carried out utilizing the software, and the simulation results show that the accuracy of the improved algorithm is approximately equal to the dual quaternion algorithm.     

平台惯导系统飞行试验性能误差分析

针对某型平台式惯导系统试飞中存在的性能超差现象,对惯导系统误差机理和飞行数据进行了分析,提出了影响飞行性能的误差因素。根据分析结果,从提高惯性元件精度和对相关误差进行标定和补偿两方面采取措施对惯导系统进行改进。改进后的惯导系统经过试飞验证,其性能满足设计指标,表明所采取的改进措施有效可行。     

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     

捷联惯导系统误差特点分析

对捷联惯导系统的误差源进行了深入分析,结果表明当陀螺仪刻度系数误差较大时,捷联惯导系统定位误差闭合现象较明显,即飞机返场时,误差有明显减小的现象;分析了舒拉调谐周期对惯导系统位置误差的影响并进行仿真,仿真结果验证了舒拉调谐对误差的调制作用,即在舒拉周期振荡分量的影响下,惯导系统的累积误差在某段时间内存在误差减小现象。     

Observability analysis of piece-wise constant systems. II.Application to inertial navigation in-flight alignment [militaryapplications]

For pt.I see ibid., vol.28, no.4, p.1056-67, Oct. 1992. The method of analyzing the observability of time-varying linear systems as piecewise constant systems (PWCS) is applied to the analysis of in-flight alignment (IFA) of inertial navigation systems (INS) whose estimability is known to be enhanced by maneuvers. The validity of this approach to the analysis of IFA is proven. The analysis lays the theoretical background to, and clearly demonstrates the observability enhancement of, IFA. The analytic conclusions are confirmed by covariance simulations. Although INS IFA was handled to various degrees in the past, a comprehensive control theoretic approach to the problem is introduced. The analysis yields practical conclusions and a procedure previously unknown     

Linear parametrically varying systems with brief instabilities: an application to vision/inertial navigation

This paper addresses the problem of nonlinear filter design to estimate the relative position and velocity of an unmanned air vehicle (UAV) with respect to a point on a ship using infrared (IR) vision, inertial, and air data sensors. Sufficient conditions are derived for the existence of a particular type of complementary filters with guaranteed stability and performance in the presence of so-called out-of-frame events that arise when the vision system loses its target temporarily. The results obtained build upon new developments in the theory of linear parametrically varying systems (LPVs) with brief instabilities - also reported in the paper - and provide the proper framework to deal with out-of-frame events. Field tests with a prototype UAV illustrate the performance of the filter and the scope of applications of the new theory developed.     

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.     

燃气分析法测试燃气轮机主燃烧室燃烧效率、气态污染物误差分析

介绍了测量燃气涡轮发动机主燃烧室燃烧效率、气态污染物排放的燃气分析系统,从取样、摆动测量方式、过程温度控制、仪器测量4方面分析了燃烧效率、气态污染物的误差.结果表明:采用混合式取样器以摆动测量方式得到的燃烧效率误差在0.21%以内,余气系数的误差在1.11％以内,气态污染物误差在2.24%以内.此外还对燃烧室不同工况下的燃烧效率和污染物组分体积分数分布进行了统计分析,确认了除较高油气比状态的燃烧效率分布较为均匀,可适当减少取样点数量外,足够的取样点数量是保证燃气分析测试结果准确性的必要条件.      

Geometric error analysis of an over-constrained parallel tracking mechanism using the screw theory

This paper deals with geometric error modeling and sensitivity analysis of an overconstrained parallel tracking mechanism. The main contribution is the consideration of overconstrained features that are usually ignored in previous research. The reciprocal property between a motion and a force is applied to tackle this problem in the framework of the screw theory. First of all, a nominal kinematic model of the parallel tracking mechanism is formulated. On this basis, the actual twist of the moving platform is computed through the superposition of the joint twist and geometric errors. The actuation and constrained wrenches of each limb are applied to exclude the joint displacement. After eliminating repeated errors brought by the multiplication of wrenches, a geometric error model of the parallel tracking mechanism is built. Furthermore,two sensitivity indices are defined to select essential geometric errors for future kinematic calibration. Finally, the geometric error model with minimum geometric errors is verified by simulation with SolidWorks software. Two typical poses of the parallel tracking mechanism are selected, and the differences between simulation and calculation results are very small. The results confirm the correctness and accuracy of the geometric error modeling method for over-constrained parallel mechanisms.     

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.     

Passive localization by a single moving observer using TOA only with unknown SRI: Observability analysis and algorithm

Passive localization by a single moving observer using Time of Arrival (TOA) only with an unknown Signal Repetition Interval (SRI) is investigated in this paper. Observability analysis is performed first. The observability condition for uniquely determining the emitter position and SRI is derived. The conditional Cramer-Rao Lower Bound (CRLB) is also analyzed. It is found that the ambiguity of the SRI integer of the first TOA does not affect the theoretical estimation precision of the emitter position and SRI. A Reference-Fixed Differential TOA (RFDTOA)-based Iterative Maximum Likelihood Estimator (IMLE) is proposed, which only needs O(M) computational operations. Theoretical analysis and simulation results show that the Mean Square Error (MSE) of the proposed algorithm could attain the CRLB with moderate Gaussian measurement noise.