SINS制导工具误差补偿研究
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摘要
随着计算机技术的不断发展和制导技术的不断完善,捷联制导工具误差成为当前影响导弹制导精度的主要因素。而受加工水平和制造工艺的限制,单纯依靠提高陀螺仪和加速度计的加工精度来减小捷联制导工具误差的代价变得愈发昂贵。相比之下,采用仪表级或者系统级的捷联制导工具误差补偿方法,则是一种更为经济而有效的途径。但是,捷联制导工具误差补偿的有效性主要取决于惯性仪表误差模型的准确性、误差系数的稳定性和补偿方法的完善性。因此,本文从理论和实际两个方面深入系统地研究了捷联制导工具误差分离与补偿中的一系列问题,在试验设计、模型结构确定、辨识算法、天地检验、误差补偿等几个方面做出了一系列细致而富有成效的工作:
首先,建立了捷联制导工具误差模型。根据干扰力拒的类型和刚体转动的动力学原理,推导了陀螺仪和加速度计的静态和动态误差模型。基于捷联导航原理,推导出捷联制导工具误差模型。该模型物理意义明确,可根据仿真研究和工程应用的需要进行扩充或简化处理;
其次,为了提供高精度的遥、外测速度差数据以作为捷联制导工具误差模型估计的观测量,本文结合载体具有高动态、高过载的飞行特性,深入研究了高动态环境下的捷联导航算法,重点考虑位置解算中的涡卷效应补偿算法、速度解算中的划桨效应补偿算法和姿态解算中的圆锥效应补偿算法,从而大大减小了捷联导航算法误差。考虑到在对导航数据的野值鉴别过程中容易出现“误判”和“漏判”的情形,本文提出了利用基于模糊聚类和神经网络的模糊预测系统来检测野值和滤除野值的方法,该方法能够克服常用野值识别和剔除方法效果差的缺点。这样,根据靶场提供的惯性测量元件脉冲输出能够进行真实弹道复现,从而为误差系数分离提供精确的遥测数据;
接着,考虑到SINS制导工具误差模型阶次高、复共线性严重的特点,本文采用先结构辨识、后参数估计的序贯辨识方案。在结构辨识中,常用的方法由于将模型中的强相关项全部剔除而给工程应用带来损失,因此,本文提出了新的有益思想,即在保留一定相关性的基础上进行辨识:将输出向量ΔW与环境函数矩阵S构成增广矩阵A,然后采用“比定阶行列式”来剔除相关向量的方法,这样既可以尽可能多地保留了对落点影响大的强相关参数,又可以对落点影响小的强相关参数给予剔除;在参数估计中,改进了特征根估计中特征根和特征向量的筛选方法,提出“近零”准则,从而大大提高了参数估计的精度;
再者,鉴于天地模型“一致性”检验是飞行试验和SINS制导工具误差系数分离的主要目的,因此,本文又深入分析了造成天地模型不一致的原因,提出了采用基于F统计的线性回归模型假设检验方法来进行捷联制导工具误差模型的天地“一致性”检验;
最后,鉴于飞行环境剧烈变化可能会对惯性仪表误差系数稳定性带来一定的影响,因此本文深入地分析了SINS制导工具误差系数与外界环境的关系,提出了基于过载变化大小的分段辨识和分段实时补偿的算法。这不仅能够降低捷联制导工具误差模型的复共线性程度、减小计算量,从而有利于误差模型估计精度的提高,而且能够大大提高SINS制导精度。
With the developnent of computer technology and the guidance technology, SINS guidance instrument errors become the key factors to influence the homing precision of missile. Limited by the processing and manufacturing level, however, the improvement of inertial navigation system accuracy merely by increasing the machining accuracy of inertial devices such as gyroscopes and accelerometers has become more and more costly. By contrast , a more economic method is the system level or the instrument level guidance instrument compensation based on the inertial instruments. The effectiveness of compensation depends on the accuracy of inertial instrument error model, the stability of the error coefficients and the perfection of compensation method. Therefore, many problems in SINS guidance instrument error separation and compensation are deeply and systematically investigated from both theory and practical aspects. A series of research work have been done in the respects of experimental design, model structure identification, identification algorithm, consistence check between the flight and the ground, error compensation.
Firstly, the SINS guidance instrument error model is built. Static and dynamic error models of inertial sensors are deduced from the types of interferential torque and dynamic principle. The SINS guidance instrument error model is deduced based on the principle of SINS. The physical meaning of error model is very explicit. And the dimension of it is easy to be augmented or reduced according to the need of simulation study or engineering application.
Then the algorithm of SINS in high dynamic circumstance is deeply investigated in order to provide the high-precision velocity error between the telemetric velocity and tracking velocity as the observation of the SINS guidance instrument error model. The scrolling compensation in position solution, sculling compensation in velocity solution and the coning compensation in attitude solution are emphasized so that the algorithmic error is decreased. On the other hand, because of false-negative judgments and miss judgments of outlier values, the fuzzy forecasting system based on fuzzy cluster analysis and neural network is brought out to detect and delete the abnormal values. The ballistic is reconstructed accurately based on the pulse outputs of inertial instruments.
Next, considering the characteristics of high grades and serious multiliearity of SINS guidance instrument error model, the scheme of structure identification first and parameters identification later is applied. The common method, that all strong-correlation terms of the model are eliminated, can bring the loss in the engineering application, so the new method is proposed that the identified model reserves some correlation. The augmented matrix A is constructed by the outputΔW and the matrix S. The“determinating order based on ratio of determinant”is brought out to screen the strong-correlation terms in the structure identification. The latent root estimation is improved in screening the eigenvalues and eigenvectors. Thus the estimation precision is improved greatly.
The consistence check of guidance instrument error coefficients of flight test and ground test is the purpose of flight experiment. The causes of inconsistency of the two models are analyzed. The hypothesis test of linear regression model based on F statistics is proposed to check the consistence.
Finally, the instability of error coefficients is probably caused by the change of the flight environments, therefore, the relation between the error coefficients and flight environment is analyzed. The approach is presented to identify SINS guidance instrument error models and compensate the error in the segmented sections corresponding to the change of vertical acceleration of aircraft. It can decrease the multiliearity of model and computational complexity greatly so that the identification accuracy of error model and guidance precision is improved greatly.
首先,建立了捷联制导工具误差模型。根据干扰力拒的类型和刚体转动的动力学原理,推导了陀螺仪和加速度计的静态和动态误差模型。基于捷联导航原理,推导出捷联制导工具误差模型。该模型物理意义明确,可根据仿真研究和工程应用的需要进行扩充或简化处理;
其次,为了提供高精度的遥、外测速度差数据以作为捷联制导工具误差模型估计的观测量,本文结合载体具有高动态、高过载的飞行特性,深入研究了高动态环境下的捷联导航算法,重点考虑位置解算中的涡卷效应补偿算法、速度解算中的划桨效应补偿算法和姿态解算中的圆锥效应补偿算法,从而大大减小了捷联导航算法误差。考虑到在对导航数据的野值鉴别过程中容易出现“误判”和“漏判”的情形,本文提出了利用基于模糊聚类和神经网络的模糊预测系统来检测野值和滤除野值的方法,该方法能够克服常用野值识别和剔除方法效果差的缺点。这样,根据靶场提供的惯性测量元件脉冲输出能够进行真实弹道复现,从而为误差系数分离提供精确的遥测数据;
接着,考虑到SINS制导工具误差模型阶次高、复共线性严重的特点,本文采用先结构辨识、后参数估计的序贯辨识方案。在结构辨识中,常用的方法由于将模型中的强相关项全部剔除而给工程应用带来损失,因此,本文提出了新的有益思想,即在保留一定相关性的基础上进行辨识:将输出向量ΔW与环境函数矩阵S构成增广矩阵A,然后采用“比定阶行列式”来剔除相关向量的方法,这样既可以尽可能多地保留了对落点影响大的强相关参数,又可以对落点影响小的强相关参数给予剔除;在参数估计中,改进了特征根估计中特征根和特征向量的筛选方法,提出“近零”准则,从而大大提高了参数估计的精度;
再者,鉴于天地模型“一致性”检验是飞行试验和SINS制导工具误差系数分离的主要目的,因此,本文又深入分析了造成天地模型不一致的原因,提出了采用基于F统计的线性回归模型假设检验方法来进行捷联制导工具误差模型的天地“一致性”检验;
最后,鉴于飞行环境剧烈变化可能会对惯性仪表误差系数稳定性带来一定的影响,因此本文深入地分析了SINS制导工具误差系数与外界环境的关系,提出了基于过载变化大小的分段辨识和分段实时补偿的算法。这不仅能够降低捷联制导工具误差模型的复共线性程度、减小计算量,从而有利于误差模型估计精度的提高,而且能够大大提高SINS制导精度。
With the developnent of computer technology and the guidance technology, SINS guidance instrument errors become the key factors to influence the homing precision of missile. Limited by the processing and manufacturing level, however, the improvement of inertial navigation system accuracy merely by increasing the machining accuracy of inertial devices such as gyroscopes and accelerometers has become more and more costly. By contrast , a more economic method is the system level or the instrument level guidance instrument compensation based on the inertial instruments. The effectiveness of compensation depends on the accuracy of inertial instrument error model, the stability of the error coefficients and the perfection of compensation method. Therefore, many problems in SINS guidance instrument error separation and compensation are deeply and systematically investigated from both theory and practical aspects. A series of research work have been done in the respects of experimental design, model structure identification, identification algorithm, consistence check between the flight and the ground, error compensation.
Firstly, the SINS guidance instrument error model is built. Static and dynamic error models of inertial sensors are deduced from the types of interferential torque and dynamic principle. The SINS guidance instrument error model is deduced based on the principle of SINS. The physical meaning of error model is very explicit. And the dimension of it is easy to be augmented or reduced according to the need of simulation study or engineering application.
Then the algorithm of SINS in high dynamic circumstance is deeply investigated in order to provide the high-precision velocity error between the telemetric velocity and tracking velocity as the observation of the SINS guidance instrument error model. The scrolling compensation in position solution, sculling compensation in velocity solution and the coning compensation in attitude solution are emphasized so that the algorithmic error is decreased. On the other hand, because of false-negative judgments and miss judgments of outlier values, the fuzzy forecasting system based on fuzzy cluster analysis and neural network is brought out to detect and delete the abnormal values. The ballistic is reconstructed accurately based on the pulse outputs of inertial instruments.
Next, considering the characteristics of high grades and serious multiliearity of SINS guidance instrument error model, the scheme of structure identification first and parameters identification later is applied. The common method, that all strong-correlation terms of the model are eliminated, can bring the loss in the engineering application, so the new method is proposed that the identified model reserves some correlation. The augmented matrix A is constructed by the outputΔW and the matrix S. The“determinating order based on ratio of determinant”is brought out to screen the strong-correlation terms in the structure identification. The latent root estimation is improved in screening the eigenvalues and eigenvectors. Thus the estimation precision is improved greatly.
The consistence check of guidance instrument error coefficients of flight test and ground test is the purpose of flight experiment. The causes of inconsistency of the two models are analyzed. The hypothesis test of linear regression model based on F statistics is proposed to check the consistence.
Finally, the instability of error coefficients is probably caused by the change of the flight environments, therefore, the relation between the error coefficients and flight environment is analyzed. The approach is presented to identify SINS guidance instrument error models and compensate the error in the segmented sections corresponding to the change of vertical acceleration of aircraft. It can decrease the multiliearity of model and computational complexity greatly so that the identification accuracy of error model and guidance precision is improved greatly.
引文
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92方崇智,萧德云.过程辨识.清华大学出版社,1993.7:293-336
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103 W. Andreas and K. B. Fritz. Short Static GPS Sessions: Robust Estimation Results. GPS Solutions. 2002, 5(3): 70-79
104 Y. Yang, L. Song and T. Xu. Robust Estimator for Correlated Observations Based on Bifactor Equivalent Weights. Journal of Geodesy. 2002,7(6): 353-358
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108贺杰,黄显林.再入飞行器的捷联制导工具误差分段补偿研究.系统工程与电子技术. 2007, 29(1): 125-129