Novel SINS Initial Alignment Method under Large Misalignment Angles and Uncertain Noise Based on Nonlinear Filter

Mathematical Problems in Engineering, Feb 2017

For the SINS initial alignment problem under large misalignment angles and uncertain noise, two novel nonlinear filters, referred to as transformed unscented quadrature Kalman filter (TUQKF) and robust transformed unscented quadrature Kalman filter (RTUQKF), are proposed in this paper, respectively. The TUQKF sets new deterministic sigma points to address the nonlocal sampling problem and improve the numerical accuracy. The RTUQKF is the combination of technique and TUQKF. It improves the accuracy and robustness of state estimation. Simulation results indicate that TUQKF performs better than traditional filters when misalignment angles are large. Turntable and vehicle experiments results indicate that, under the condition of uncertain noise, the performances of RTUQKF are better than other filters and more robust. These two methods can effectively further increase precision and convergence speed of SINS initial alignment.

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Novel SINS Initial Alignment Method under Large Misalignment Angles and Uncertain Noise Based on Nonlinear Filter

Novel SINS Initial Alignment Method under Large Misalignment Angles and Uncertain Noise Based on Nonlinear Filter Bo Yang, Xiaosu Xu, Tao Zhang, Jin Sun, and Xinyu Liu Key Laboratory of Micro-Inertial Instrument and Advanced Navigation Technology, Ministry of Education, School of Instrument Science and Engineering, Southeast University, Nanjing 210096, China Correspondence should be addressed to Xiaosu Xu; nc.ude.ues@sxx Received 4 August 2016; Revised 19 December 2016; Accepted 24 January 2017; Published 19 February 2017 Academic Editor: Jean-Christophe Ponsart Copyright © 2017 Bo Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract For the SINS initial alignment problem under large misalignment angles and uncertain noise, two novel nonlinear filters, referred to as transformed unscented quadrature Kalman filter (TUQKF) and robust transformed unscented quadrature Kalman filter (RTUQKF), are proposed in this paper, respectively. The TUQKF sets new deterministic sigma points to address the nonlocal sampling problem and improve the numerical accuracy. The RTUQKF is the combination of technique and TUQKF. It improves the accuracy and robustness of state estimation. Simulation results indicate that TUQKF performs better than traditional filters when misalignment angles are large. Turntable and vehicle experiments results indicate that, under the condition of uncertain noise, the performances of RTUQKF are better than other filters and more robust. These two methods can effectively further increase precision and convergence speed of SINS initial alignment. 1. Introduction Initial alignment is one of the critical and difficult problems for inertial navigation system (INS). The essential purpose of initial alignment for strapdown INS (SINS) is to determine the attitude matrix between body frame and navigation frame [1, 2]. The Kalman filter (KF) is the mostly used technique to solve the problem of initial alignment. However, it can only deal with initial alignment under small misalignment angles [3]. Large misalignment angles and uncertain noise are two main problems existing in initial alignment in different application environments [4, 5]. The nonlinear model of SINS and nonlinear methods are developed to solve the alignment problem. In [6], a modeling method of nonlinear model of SINS was proposed. The widely used nonlinear filtering method in engineering is extended KF (EKF). The principle of EKF is simple and it has high computationally efficient [7]. However, the performance of EKF would decrease if the system has strong nonlinear characters [8]. The unscented KF (UKF) and cubature KF (CKF) were developed to overcome this problem [9, 10]. These two algorithms were applied to SINS initial alignment and got better effects than EKF [11, 12]. Although the derivation method of CKF is different from standard UKF, it is virtually a special case of the UKF [13]. It has pointed out that CKF has better precisions than UKF for high-dimensional problem [10]. However, it has proved that CKF suffers from nonlocal sampling problem which will lead to estimation errors in high-dimensional and strong nonlinear situations [14]. From [6] and Section 5, it is shown that nonlinear model of SINS includes a lot of trigonometric operations and the state dimensions are more than 10, so the SINS initial alignment problem under large misalignment angles is the high-dimensional problem coupled with strong nonlinear model. Therefore, in [14], new set of sigma points was designed to solve this problem and the novel algorithm is known as transformed unscented KF (TUKF). In this paper, in order to further increase accuracy of SINS initial alignment, the transformed unscented quadrature KF (TUQKF) was proposed based on TUKF. TUQKF is an extended version of TUKF. It is proved that, under single Gauss-Laguerre quadrature rule, TUQKF degenerates to TUKF and TUQKF exhibits better numerical characteristics than TUKF when using high-order Gauss-Laguerre rule. For the other problem, SINS initial alignment with uncertain noise, if environment noise is not Gaussian white noise, the traditional nonlinear filtering method mentioned above will produce a greater estimation error. One solution for this problem is to use the technique to improve the robustness of filter. The filter is more robust and has better precision than standard KF under uncertain noise [15, 16]. However, standard filter can only fulfill the linear filtering problems. In the recent two decades, filter was extended to nonlinear problems by combing with nonlinear filters. In [17], the filter was combined with EKF and the new algorithm known as robust extended KF (REKF) was proposed. In this framework, the filter was combined with UKF and CKF. These two new algorithms are known as robust uns (...truncated)


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Bo Yang, Xiaosu Xu, Tao Zhang, Jin Sun, Xinyu Liu. Novel SINS Initial Alignment Method under Large Misalignment Angles and Uncertain Noise Based on Nonlinear Filter, Mathematical Problems in Engineering, 2017, 2017, DOI: 10.1155/2017/5917917