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研究一类动态多尺度系统的最优滤波,这类系统由具有不同分辨率的多个传感器独立观测,而系统具有已知的动态系统模型约束.假设传感器的信号采集带宽成倍递减,相应的采样频率也成倍递减.用Haar小波变换来拟合状态在各尺度空间的投影关系,给出该类多尺度系统的离散模型,并证明了其可以直接应用Kalman滤波的条件.基于线性时不变系统,研究了系统的可控可测性以及滤波的稳定性,并给出了一个判定定理,证明系统只要在最细尺度上可控可测,则Kalman滤波是稳定的.最后以匀速直线运动过程为例,验证了所提建模与估计方法的有效性.
The optimal filter for a class of dynamic multiscale systems is studied. These systems are independently observed by multiple sensors with different resolutions and the system has known dynamic system model constraints. Assuming that the signal acquisition bandwidth of the sensor decreases doubly, the corresponding The sampling frequency also decreases exponentially.Using Haar wavelet transform to fit the projection of the state in each scale space, the discrete model of this kind of multi-scale system is given and the conditions of Kalman filtering can be directly applied. Variable system, the controllable and testability of the system and the stability of the filter are studied, and a judgment theorem is given to prove that the Kalman filter is stable as long as the system is controllable and measurable at the smallest scale. Finally, As an example, the validity of the proposed modeling and estimation methods is verified.