森林资源的卡尔曼滤波

Application of Kalman Filter to Forest Resources Estimation

本文引入Kalman滤波理论中状态变量的概念,将森林资源看作一个系统,描述森林资源状况的随机变量是系统的待估状态,通过建立由生长方程和抽样观测方程组成的线性滤波模型,利用Kalman基本方程,对森林资源的现状、将来及过去分别作出滤波、预测和平滑估计.在给出森林资源滤波模型一般形式的基础上,根据观测信息的不同,将滤波模型分为:以样本均值为观测值的滤波模型(KFM-1)和直接以样本单元值为观测值的滤波模型(KFM-2).模型经福建省1983、1988年两期杉木资源清查材料验证表明:KFM-2优于KFM-1;动态估计优于静态估计;Kalman滤波优于SPR动态估计.尤其在样本量小、两期相关不紧密时,Kalman动态估计的相对效率更高.

The concept of state variables in Kalman Filter is introduced and forest resources are regarded as a system.Random variables which describe the state of forest resources are to be estimated.Through estabilishing a linear filter model,composed of a growth equation and a sampling measurement equation,the past,present and future states of forest resources can be estimated with Kalman basic equations.The general forest resources filter model is divided in two types according to the observed information,filter model with sampling means as observed values (KFM-1 ) and filter model with sampling unit values as observed values (KFM-2).The models are tested with data from a two-occasion China fir resources inventory (1983,1988) in Fujian province.Results show that KFM-2 is better than KFM-1,recursive estimation is better than static estimation and the variance of the filter is never greater than that of SPR recursive estimation,The relative efficiency of the KF estimation is high,especially when sample size and coefficient of two occasions are small.