无陀螺捷联惯导系统若干关键技术研究
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摘要
由于传统的捷联惯导系统不太适合应用于大过载、大角速度的场合,而无陀螺捷联惯导系统(GFSINS)在具有大加速度、大角速度的情况下,仍然能正常工作。所以,近年来,无陀螺捷联惯导系统得到广泛研究,取得了许多研究成果,但仍然离工程化、实用化有一定差距。为了解决目前该研究领域存在的问题,本文针对系统构型、角速度解算、姿态估计和误差标定及补偿等几项关键技术来展开研究,为后续系统的研制打下基础。
首先,给出了GFSINS构型的可行性条件:构型矩阵J左可逆。针对系统构型的优劣,提出了一种基于几何精度扩散因子(GDOP)的评价指标,并通过三种典型构型方案验证了该指标的有效性。鉴于实用化的考虑,设计了一种基于旋转弹的十加速度计构型单元,当其中某一加速度计故障时,可以有四种不同的编排方式来保证系统正常工作且精度不变。通过GDOP指标的判断和对具体对象的分析表明,此设计很适合应用到旋转弹上。
其次,为了提高系统导航精度,针对角速度解算方法展开了研究。在分析了积分法、开方法、微分法等几种角速度算法优缺点的基础上,给出了一种运算简单、精度较高的对数算法。针对角速度代数公式算法解算误差达不到要求的情况,建立了一个三层BP神经网络模型来预测角速度,仿真结果表明,角速度预测精度比对数算法提高了将近两倍。为了消除加速度计随机噪声对角速度解算结果的影响,设计了一种H∞滤波器,并在改变噪声大小、噪声种类和初始状态估值大小的情况下进行了仿真,结果表明, H∞滤波比kalman滤波具有更好的鲁棒性和稳定精度,滤波后,角速度估计精度比对数法至少提高了1个数量级。
接着,对GFSINS姿态估计方法展开了研究。给出了基于四元数的四阶龙格库塔法和四子样旋转矢量法解算姿态,并在圆锥运动下完成了仿真,结果表明,四子样等效旋转矢量法姿态解算精度高于四阶龙格库塔法,而且当采用GFSINS独立确定姿态时,姿态角误差随时间而累积。基于重力矢量和三轴磁强计测量输出,给出了一种适合弹体在静止或匀速运动状态下的姿态确定方法,能避免误差积累。为了抑制弹体在不同运动环境下的姿态误差发散,提出了一种GFSINS/磁强计的组合定姿滤波方案,考虑到圆锥误差的影响,采用基于四子样等效旋转矢量法获得的四元数以及十加速度计输出中分解出的角速度作为状态量,加速度计组合输出的角速度交叉乘积项和三轴磁强计测量值作为量测量,构建了系统的状态方程和量测方程;然后设计了EKF和SUKF两种姿态估计器,并在圆锥运动下完成了仿真对比。结果表明,SUKF的性能要优于EKF,滤波后,姿态误差的发散能得到有效的抑制。
最后,对系统的主要误差源进行了标定及补偿技术的研究。针对加速度计静态和动态误差对GFSINS的显著影响,基于误差模型,利用线性神经网络技术完成了误差系数的辨识,通过给出的有效补偿算法将误差补偿到加速度计输出中,角速度解算精度均提高了一个数量级。针对加速度计安装误差对系统精度的影响,提出了一种十加速度计安装位置和方向误差系数的辨识方法,将转台上的系统构型在两种转速下各进行三次翻转,可以一次性标定出50个误差系数;在采用先计算补偿后的加速度计输出再解算角速度的方法补偿安装误差后,精度至少能提高一倍。
The common Strapdown Inertial Navigation System (SINS) isn’t suitable for high overload and angular velocity, but the Gyroscope Free Strapdown Inertial Navigation System (GFSINS) can work validly in the high acceleration and high angular velocity conditions. GFSINS is widely researched and effective in recent years, but still can’t meet the requirement of engineering application. To solve existing problems in this field, several key technologies are researched, such as GFSINS configuration, angular velocity calculation, attitude estimation and error calibration and compensation, and so on.
Firstly, feasibility of system configuration is given: matrix J is left invertible. For the performance of system configuration, a kind of assessment standard based on Geometric Dilution of Precision (GDOP) is put forward and demonstrated. Considering the engineering realization, a ten-accelerometer configuration unit based on spinning projectile is designed. When one of accelerometers is trouble, four different arranging ways can guarantee system to work normally. At the same time, the judgment for GDOP and analysis for real condition show that the design is suitable for spinning projectile.
Secondly, angular velocity calculation methods are studied for promoting navigation precision. Aiming at low precision of traditional algorithms, such as integral algorithm, extraction algorithm, differential algorithm, a lognormal algorithm with fast computation and high precision is given. Due to high calculation errors of traditional algebra algorithms, a three-layer BP network model is built to predict angular velocity, and the predicting precision is three times higher than that of lognormal algorithm. As eliminating the influence of random noises of accelerometer, a kind of H∞filter is designed. Simulation is complete under the different magnitude of noise, variety of noise and initial estimated value of state variable, and results show that H∞filter has a stronger robustness and stability than Kalman filter. Moreover, precision of angular velocity is improved by one order of magnitude higher than that of lognormal algorithm after H∞filter.
Thirdly, attitude estimation for GFSINS is studied. Through simulation and comparison, the four samples rotation vector method has higher precision of attitude estimation than fourth-order Runge-Kutta method under cone rotation condition. Based on gravitational vector and magnetometers output, an attitude estimation method is put forward when carrier is in the static or constant motion state. To restrain error accumulation for different motion enviorment, a GFSINS/magnetometer integrated system is put forward. considering the cone error, the quaternion got by four samples rotation vector method and angular velocity obtained by ten accelerometers output, are chosen as state variable, cross-multiply output of angular velocity and measurement value of magnetometer are chosen as measurement variable, then the state equation and measurement equation are built. Moreover, EKF and SUKF filter are designed. Simulation results show that SUKF is superior to EKF, and attitude error can be inhibited validly after filtering.
Finally, the calibration and compensation technologies for GFSINS are studied. Aiming at static and dynamic errors of accelerometer, all the error coefficients are calibrated using linear neural network based on error models, and the precision of angular velocity is improved by 1 order of magnitude after error compensation. An identification method for ten-accelerometer fixed position and direction errors is put forward, and 50 error coefficients can be calibrated at one time by system configuration completing three rolling under two rotating rates. After that, through using the method that firstly computes accelerometer output after compensation and then calculates angular velocity, the angular velocity precision is improved by more than one time.
首先,给出了GFSINS构型的可行性条件:构型矩阵J左可逆。针对系统构型的优劣,提出了一种基于几何精度扩散因子(GDOP)的评价指标,并通过三种典型构型方案验证了该指标的有效性。鉴于实用化的考虑,设计了一种基于旋转弹的十加速度计构型单元,当其中某一加速度计故障时,可以有四种不同的编排方式来保证系统正常工作且精度不变。通过GDOP指标的判断和对具体对象的分析表明,此设计很适合应用到旋转弹上。
其次,为了提高系统导航精度,针对角速度解算方法展开了研究。在分析了积分法、开方法、微分法等几种角速度算法优缺点的基础上,给出了一种运算简单、精度较高的对数算法。针对角速度代数公式算法解算误差达不到要求的情况,建立了一个三层BP神经网络模型来预测角速度,仿真结果表明,角速度预测精度比对数算法提高了将近两倍。为了消除加速度计随机噪声对角速度解算结果的影响,设计了一种H∞滤波器,并在改变噪声大小、噪声种类和初始状态估值大小的情况下进行了仿真,结果表明, H∞滤波比kalman滤波具有更好的鲁棒性和稳定精度,滤波后,角速度估计精度比对数法至少提高了1个数量级。
接着,对GFSINS姿态估计方法展开了研究。给出了基于四元数的四阶龙格库塔法和四子样旋转矢量法解算姿态,并在圆锥运动下完成了仿真,结果表明,四子样等效旋转矢量法姿态解算精度高于四阶龙格库塔法,而且当采用GFSINS独立确定姿态时,姿态角误差随时间而累积。基于重力矢量和三轴磁强计测量输出,给出了一种适合弹体在静止或匀速运动状态下的姿态确定方法,能避免误差积累。为了抑制弹体在不同运动环境下的姿态误差发散,提出了一种GFSINS/磁强计的组合定姿滤波方案,考虑到圆锥误差的影响,采用基于四子样等效旋转矢量法获得的四元数以及十加速度计输出中分解出的角速度作为状态量,加速度计组合输出的角速度交叉乘积项和三轴磁强计测量值作为量测量,构建了系统的状态方程和量测方程;然后设计了EKF和SUKF两种姿态估计器,并在圆锥运动下完成了仿真对比。结果表明,SUKF的性能要优于EKF,滤波后,姿态误差的发散能得到有效的抑制。
最后,对系统的主要误差源进行了标定及补偿技术的研究。针对加速度计静态和动态误差对GFSINS的显著影响,基于误差模型,利用线性神经网络技术完成了误差系数的辨识,通过给出的有效补偿算法将误差补偿到加速度计输出中,角速度解算精度均提高了一个数量级。针对加速度计安装误差对系统精度的影响,提出了一种十加速度计安装位置和方向误差系数的辨识方法,将转台上的系统构型在两种转速下各进行三次翻转,可以一次性标定出50个误差系数;在采用先计算补偿后的加速度计输出再解算角速度的方法补偿安装误差后,精度至少能提高一倍。
The common Strapdown Inertial Navigation System (SINS) isn’t suitable for high overload and angular velocity, but the Gyroscope Free Strapdown Inertial Navigation System (GFSINS) can work validly in the high acceleration and high angular velocity conditions. GFSINS is widely researched and effective in recent years, but still can’t meet the requirement of engineering application. To solve existing problems in this field, several key technologies are researched, such as GFSINS configuration, angular velocity calculation, attitude estimation and error calibration and compensation, and so on.
Firstly, feasibility of system configuration is given: matrix J is left invertible. For the performance of system configuration, a kind of assessment standard based on Geometric Dilution of Precision (GDOP) is put forward and demonstrated. Considering the engineering realization, a ten-accelerometer configuration unit based on spinning projectile is designed. When one of accelerometers is trouble, four different arranging ways can guarantee system to work normally. At the same time, the judgment for GDOP and analysis for real condition show that the design is suitable for spinning projectile.
Secondly, angular velocity calculation methods are studied for promoting navigation precision. Aiming at low precision of traditional algorithms, such as integral algorithm, extraction algorithm, differential algorithm, a lognormal algorithm with fast computation and high precision is given. Due to high calculation errors of traditional algebra algorithms, a three-layer BP network model is built to predict angular velocity, and the predicting precision is three times higher than that of lognormal algorithm. As eliminating the influence of random noises of accelerometer, a kind of H∞filter is designed. Simulation is complete under the different magnitude of noise, variety of noise and initial estimated value of state variable, and results show that H∞filter has a stronger robustness and stability than Kalman filter. Moreover, precision of angular velocity is improved by one order of magnitude higher than that of lognormal algorithm after H∞filter.
Thirdly, attitude estimation for GFSINS is studied. Through simulation and comparison, the four samples rotation vector method has higher precision of attitude estimation than fourth-order Runge-Kutta method under cone rotation condition. Based on gravitational vector and magnetometers output, an attitude estimation method is put forward when carrier is in the static or constant motion state. To restrain error accumulation for different motion enviorment, a GFSINS/magnetometer integrated system is put forward. considering the cone error, the quaternion got by four samples rotation vector method and angular velocity obtained by ten accelerometers output, are chosen as state variable, cross-multiply output of angular velocity and measurement value of magnetometer are chosen as measurement variable, then the state equation and measurement equation are built. Moreover, EKF and SUKF filter are designed. Simulation results show that SUKF is superior to EKF, and attitude error can be inhibited validly after filtering.
Finally, the calibration and compensation technologies for GFSINS are studied. Aiming at static and dynamic errors of accelerometer, all the error coefficients are calibrated using linear neural network based on error models, and the precision of angular velocity is improved by 1 order of magnitude after error compensation. An identification method for ten-accelerometer fixed position and direction errors is put forward, and 50 error coefficients can be calibrated at one time by system configuration completing three rolling under two rotating rates. After that, through using the method that firstly computes accelerometer output after compensation and then calculates angular velocity, the angular velocity precision is improved by more than one time.
引文
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