用于MEMS陀螺阵列信号处理的OBE平滑算法(英文)
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收稿日期：2016-11-04；修回日期：2017-01-20 基金项目：国家自然科学基金（61503390，61503392） 作者简介：沈强（1989—） ，男，博士研究生，从事MEMS惯性技术研究。E-mail: shenq110@163.com 联 系 人：刘洁瑜（1970—） ，女，教授，博士生导师。E-mail: liujieyu128@163.com
OBE smoother for signal processing of MEMS gyroscope array
SHEN Qiang, LIU Jie-yu, WANG Qi, QIN Wei-wei
(Department of Control Engineering, Rocket Force University of Engineering, Xi’an 710025, China) Abstract: To improve the accuracy of the MEMS gyroscopes, a novel smoother based on the optimal bounding ellipsoid (OBE) algorithms is proposed for signal processing of the gyroscope array. Firstly, several gyroscopes measuring the same angular rate signal are used to construct an array, and then a data fusion model is established. For traditional fusion methods, the uncertainty of noises statistical characters may lead to accuracy degeneration. To solve this problem, the set-membership (SM) methods, in which errors are assumed only to be bounded, can be used as a substitute. The proposed SM method is a Rauch-Tung-Striebel (RTS)-type smoother, which is constructed by a forward pass and a backward one. The forward pass estimates the angular rate with the OBE filter, while the backward pass updates the estimates by using the OBE algorithm in the backward direction. Experiment results indicate that the method can significantly improve the accuracy of MEMS gyroscopes, with the static drift of the estimated rate signal being reduced to 0.1368 (°)/s from 0.5130 (°)/s. Under dynamic condition, the drift can be reduced to 0.1704 (°)/s from 0.5343 (°)/s. Key words: MEMS gyroscope array; data fusion; set-membership estimate; Rauch-Tung-Striebel smoother; optimal bounding ellipsoid algorithm
第 25 卷第 1 期 2017 年 02 月 文章编号： 1005-6734(2017)01-0109-06
中国惯性技术学报 Journal of Chinese Inertial Technology
Vol.25 No.1 Feb. 2017 doi: 10.13695/j.cnki.12-1222/o3.2017.01.022
用于 MEMS 陀螺阵列信号处理的 OBE 平滑算法
沈 强，刘洁瑜，王 琪，秦伟伟
（பைடு நூலகம்箭军工程大学 控制工程系，西安 710025）
摘要：为提高 MEMS 陀螺的精度，提出了一种基于最优定界椭球（OBE）的平滑算法，并将其用于陀 螺阵列信号的处理。首先，利用多个相同型号的 MEMS 陀螺构成阵列，测量同一角速率信号，并建立 数据融合模型。对于融合问题而言，噪声统计特性的不确定会导致传统融合方法精度下降。为解决该 问题，引入仅要求噪声未知但有界的集员估计理论，结合 RTS 平滑思想，提出一种新的平滑算法作为 融合方法，它由前向滤波和反向平滑两个过程构成：前者采用集员估计理论中的 OBE 滤波估计角速 率， 后者则逆序执行 OBE 算法进一步提高估计精度。 实验表明： 该方法能够将陀螺的静态漂移由 0.5130 (°)/s 降低到 0.1368 (°)/s；动态条件下，在有效跟踪载体角度变化的同时，将漂移由 0.5343 (°)/s 降低到 0.1704 (°)/s，显著提高了陀螺的使用精度。 关 键 词：MEMS 陀螺阵列；数据融合；集员估计；RTS 平滑；OBE 算法 文献标志码：A MEMS devices has been improved a lot. The MEMS gyroscopes, however, are still not sufficiently accurate for many applications such as space vehicle. To enlarge the application field of the MEMS gyroscope and give full play to its advantages, it is necessary to improve its accuracy further without hardware break 中图分类号：V241.5 The micro-electrical-mechanical systems (MEMS) gyroscopes have many excellent properties including lightweight, compact size, low power consumption, low cost and ease of mass production. Thus they have been widely used in various applications[1-2]. With recent developments in MEMS technology, the accuracy of the
- 110 [3]
中国惯性技术学报
第 25 卷
through . With the development of the data fusion technique, the gyroscopes array is used to achieve higher performance. The gyroscope array technique was first proposed by Bayard and Ploen[4], which integrated the outputs of several MEMS gyroscopes to obtain an optimal estimated rate signal by data fusion method. This rate estimate is sometimes known as a “virtual gyro” since it is different from the rate signal of a single physical gyroscope. Ji and Wang presented complete error model and measurement model of the gyroscope array and used the Kalman filter (KF) to process their signals[5]. Xue and Jiang took six separate MEMS gyroscopes to form a gyroscope array and proposed a novel KF to implement the virtual gyro system[6-7]. The key of gyroscope array technique lies in the estimate method. The KF and its variants and extensions are used in above approaches, which have been proven effective to some extent. However, the Gaussian noise assumption in these classical techniques may render them invalid in some practical application. When the Kalman filters are used for gyroscope array, the uncertainty of noises statistical character may lead to accuracy degeneration. An innovative alternative is to use the set-membership (SM) estimation approach, in which noises are assumed only to be bounded[8]. In addition, by using the filter algorithms, the angular rate estimates are obtained using the present and historic measurements. The estimate accuracy can be improved further by smoothing because it uses observations both before and after the current estimation time[9]. As an important subclass of SM algorithms, optimal bounding ellipsoid (OBE) algorithms are widely adopted in the estimation problems[10-11]. Thus, in this paper, a new SM smoothing method based on OBE algorithm is presented and used for array signal processing to improve the accuracy of MEMS gyroscopes. This method is a RTS-type algorithm, which updates each state twice: once during its forward OBE filter, and second during its backward smoothing with an OBE recursion. Therefore, the proposed method can be called an OBE smoother. The minimum-volume and minimum-trace bounding ellipsoids containing the feasible state set are derived from this algorithm.
OBE smoother for signal processing of MEMS gyroscope array
SHEN Qiang, LIU Jie-yu, WANG Qi, QIN Wei-wei
(Department of Control Engineering, Rocket Force University of Engineering, Xi’an 710025, China) Abstract: To improve the accuracy of the MEMS gyroscopes, a novel smoother based on the optimal bounding ellipsoid (OBE) algorithms is proposed for signal processing of the gyroscope array. Firstly, several gyroscopes measuring the same angular rate signal are used to construct an array, and then a data fusion model is established. For traditional fusion methods, the uncertainty of noises statistical characters may lead to accuracy degeneration. To solve this problem, the set-membership (SM) methods, in which errors are assumed only to be bounded, can be used as a substitute. The proposed SM method is a Rauch-Tung-Striebel (RTS)-type smoother, which is constructed by a forward pass and a backward one. The forward pass estimates the angular rate with the OBE filter, while the backward pass updates the estimates by using the OBE algorithm in the backward direction. Experiment results indicate that the method can significantly improve the accuracy of MEMS gyroscopes, with the static drift of the estimated rate signal being reduced to 0.1368 (°)/s from 0.5130 (°)/s. Under dynamic condition, the drift can be reduced to 0.1704 (°)/s from 0.5343 (°)/s. Key words: MEMS gyroscope array; data fusion; set-membership estimate; Rauch-Tung-Striebel smoother; optimal bounding ellipsoid algorithm
第 25 卷第 1 期 2017 年 02 月 文章编号： 1005-6734(2017)01-0109-06
中国惯性技术学报 Journal of Chinese Inertial Technology
Vol.25 No.1 Feb. 2017 doi: 10.13695/j.cnki.12-1222/o3.2017.01.022
用于 MEMS 陀螺阵列信号处理的 OBE 平滑算法
沈 强，刘洁瑜，王 琪，秦伟伟
（பைடு நூலகம்箭军工程大学 控制工程系，西安 710025）
摘要：为提高 MEMS 陀螺的精度，提出了一种基于最优定界椭球（OBE）的平滑算法，并将其用于陀 螺阵列信号的处理。首先，利用多个相同型号的 MEMS 陀螺构成阵列，测量同一角速率信号，并建立 数据融合模型。对于融合问题而言，噪声统计特性的不确定会导致传统融合方法精度下降。为解决该 问题，引入仅要求噪声未知但有界的集员估计理论，结合 RTS 平滑思想，提出一种新的平滑算法作为 融合方法，它由前向滤波和反向平滑两个过程构成：前者采用集员估计理论中的 OBE 滤波估计角速 率， 后者则逆序执行 OBE 算法进一步提高估计精度。 实验表明： 该方法能够将陀螺的静态漂移由 0.5130 (°)/s 降低到 0.1368 (°)/s；动态条件下，在有效跟踪载体角度变化的同时，将漂移由 0.5343 (°)/s 降低到 0.1704 (°)/s，显著提高了陀螺的使用精度。 关 键 词：MEMS 陀螺阵列；数据融合；集员估计；RTS 平滑；OBE 算法 文献标志码：A MEMS devices has been improved a lot. The MEMS gyroscopes, however, are still not sufficiently accurate for many applications such as space vehicle. To enlarge the application field of the MEMS gyroscope and give full play to its advantages, it is necessary to improve its accuracy further without hardware break 中图分类号：V241.5 The micro-electrical-mechanical systems (MEMS) gyroscopes have many excellent properties including lightweight, compact size, low power consumption, low cost and ease of mass production. Thus they have been widely used in various applications[1-2]. With recent developments in MEMS technology, the accuracy of the
- 110 [3]
中国惯性技术学报
第 25 卷
through . With the development of the data fusion technique, the gyroscopes array is used to achieve higher performance. The gyroscope array technique was first proposed by Bayard and Ploen[4], which integrated the outputs of several MEMS gyroscopes to obtain an optimal estimated rate signal by data fusion method. This rate estimate is sometimes known as a “virtual gyro” since it is different from the rate signal of a single physical gyroscope. Ji and Wang presented complete error model and measurement model of the gyroscope array and used the Kalman filter (KF) to process their signals[5]. Xue and Jiang took six separate MEMS gyroscopes to form a gyroscope array and proposed a novel KF to implement the virtual gyro system[6-7]. The key of gyroscope array technique lies in the estimate method. The KF and its variants and extensions are used in above approaches, which have been proven effective to some extent. However, the Gaussian noise assumption in these classical techniques may render them invalid in some practical application. When the Kalman filters are used for gyroscope array, the uncertainty of noises statistical character may lead to accuracy degeneration. An innovative alternative is to use the set-membership (SM) estimation approach, in which noises are assumed only to be bounded[8]. In addition, by using the filter algorithms, the angular rate estimates are obtained using the present and historic measurements. The estimate accuracy can be improved further by smoothing because it uses observations both before and after the current estimation time[9]. As an important subclass of SM algorithms, optimal bounding ellipsoid (OBE) algorithms are widely adopted in the estimation problems[10-11]. Thus, in this paper, a new SM smoothing method based on OBE algorithm is presented and used for array signal processing to improve the accuracy of MEMS gyroscopes. This method is a RTS-type algorithm, which updates each state twice: once during its forward OBE filter, and second during its backward smoothing with an OBE recursion. Therefore, the proposed method can be called an OBE smoother. The minimum-volume and minimum-trace bounding ellipsoids containing the feasible state set are derived from this algorithm.