基于改进CKF算法的一类有色噪声污染的线性观测系统的状态估计

State Estimation of a Class of Linear Observation Systems Contaminated by Colored Noise Based on Modified CKF Algorithm

针对系统受有色噪声污染时容积卡尔曼滤波(CKF)算法滤波精度下降甚至发散的问题,提出了基于量测信息增广的改进CKF算法.改进算法采用量测信息增广方式,将有色噪声白噪声化,再将白化后的噪声和系统噪声去相关化,从而解决了一类有色噪声污染的线性观测系统的状态估计问题.将本文算法应用于生物地球化学仿真模型,对生物圈植被碳含量进行动态估计,仿真结果表明,改进算法具有较高的精度和鲁棒性.

Cubature Kalman filter (CKF) has good accuracy and numerical stability when dealing with the nonlinear filtering estimation. Especially, for high-dimensional nonlinear system, CKF can avoid the problem encountered in unscented Kalman filter (UKF), i.e., the weight of the center sampling point may be less than 0, which will make the covariance matrix be non-definite and cause the filter to diverge and abort. Nevertheless, CKF still has some defects. For example, its filtering accuracy may decrease or even diverge when the system is polluted by colored noise. Aiming at these shortcomings, this paper proposes a modified CKF (MCKF) algorithm based on measurement information. By utilizing the augmenting measurement information to whiten the colored noise and de-correlate the noise and system noise, the obtained equivalent system can meet the requirement of CKF algorithm and obtain the state estimation of the linear observation system with colored noise pollution. Finally, the proposed algorithm is applied to the biogeochemical model. In the actual geosphere, the carbon content of vegetation and soil can be briefly described as a biogeochemical model, which characterizes the response and the feedback process of terrestrial ecosystems to climate change. During the simulation, the carbon content of soil is observed to estimate the dynamical carbon content of the biosphere vegetation. It is shown from the simulation results that the modified algorithm can attain high accuracy and strong robustness.