MEMS陀螺阵列噪声相关性及其对融合信号漂移误差影响研究

How to improve the measurement precision of MEMS gyroscope is of great important significance to the development of micro inertial navigation system. The technology of homogeneous sensor multi-data fusion is becoming a promising and effective approach to reduce the stochastic drift of MEMS gyroscope. However, obtaining of correlation coefficient between the noises of a MEMS gyroscope array and its influencing mechanism on the drift error of the combined rate signal became a crucial technology that restrict the implement and practical application of the technology of MEMS gyroscope array. Thus, this project is focused on research of the noise correlation and multi-data fusion of MEMS gyroscope array. The study of the project is mainly contained the following three aspects: Firstly, a mathematical statistics method and numeric simulated method are established to analyze and obtain the noise correlation coefficient, the influence of geometry layout of the sensor array on the noise correlation is studied. Secondly, an optimal estimation algorithm for combining the output signals of a gyroscope array is studied and established, in which the MEMS gyroscope contains multiple noise parameters. Especially, analytical and numerical methods are used to solve the filter model respectively to design an optimal Kalman filter. Furthermore, a method for on-line monitoring, dynamically estimating and self-adaptive adjusting the designing parameters of optimal filter is studied to considerably improve the performance. Lastly, a mathematical model for the drift error of the combined rate signal is built through the analytical solution of filter model. Based on these analyses, the influencing mechanism of noise correlation on performance improvement is investigated. It could provide a theoretical basis for designing of an optimal correlated MEMS gyroscope array for greatly improving the accuracy. The results of this project has a better theoretical significance and military value for improving the accuracy of current MEMS gyroscope, which making it into the practical application of aviation and aerospace.

如何提高MEMS陀螺测量精度对于微惯性导航系统的发展具有重要意义，同类多传感器信号融合成为降低陀螺漂移的一种全新方法，而陀螺阵列噪声相关系数的获取及其对融合信号漂移的影响规律成为其技术实施和应用中亟待解决的关键问题。因此，本项目开展MEMS陀螺阵列噪声相关性分析和信号融合滤波研究。包含三方面内容：（1）提出一种基于数理统计和数值仿真的噪声相关系数求解算法，研究不同阵列几何结构对相关性的影响规律。（2）研究基于MEMS陀螺多噪声参数的阵列信号融合滤波，采用解析法和数值法求解滤波器模型，建立角速率信号最优估计卡尔曼滤波器，研究滤波参数的动态在线监测、估计及自适应调整方法。（3）建立合成角速率信号漂移误差的数学模型，以此研究相关性对精度提升的影响规律，为设计最优相关性的MEMS陀螺阵列提供理论依据。项目的研究成果对于提高当前MEMS陀螺精度水平，使其进入航空航天实际应用具有重要意义和应用前景。

MEMS 惯性器件展现出的优势非常适合于满足智能武器系统对于小型化、高精度、低成本的惯导系统的发展需求。如何降低MEMS 陀螺漂移误差是当前微惯性技术的研究热点。采用陀螺阵列信号融合的处理方法相比硬件方法具有更大的提升空间和前景意义。项目开展了MEMS陀螺阵列噪声相关性分析及阵列信号融合研究，包括四个方面：（1）建立了陀螺阵列Allan方差随机误差测量模型，提出了一种基于数理统计的陀螺阵列相关系数分析法，建立了其求解流程和执行算法，可用于遴选出最优相关性的陀螺单元组成阵列。进行了仿真分析和陀螺阵列不同几何布局下的相关系数测试，测试表明由单独的陀螺单元组成的阵列，几何布局不影响其相关性。（2）采用稳态滤波增益设计了陀螺阵列信号融合卡尔曼滤波器及角速率估计递推方程，通过陀螺噪声模型化，对阵列输出信号进行融合。（3）通过滤波器模型的解析求解，获取了合成角速率信号漂移误差的数学模型，建立了其与相关系数之间的关系，为探索相关性对合成角速率信号精度的影响规律、设计最优相关性的陀螺阵列提供了依据。进行了不同相关性陀螺阵列信号融合的仿真分析，结果表明，负相关性更有利于大幅降低漂移误差，在最优相关性的前提下，融合后陀螺漂移误差可降低一个数量级。（4）建立了滤波器带宽与角速率建模驱动噪声方差之间的函数关系，设计了噪声方差的模糊逻辑推理规则和在线自适应调整系统，并设计了陀螺阵列噪声方差多模自适应估计滤波器，建立了基于概率密度函数加权的滤波估计方程。采用6陀螺阵列和4陀螺阵列系统进行了信号融合处理，结果显示，不相关的6陀螺阵列其漂移误差降低近4倍，而具有正负相关系数的4陀螺阵列，漂移误差降低近5倍。本项目的研究可有效提高MEMS陀螺的测量精度，构建一种高性能的微惯导系统，应用于联合制导炸弹、制导炮弹等战术武器的精确打击中，以及用于战场侦察及态势感知的小型无人机系统的导航制导系统。