Supplement. Demonstration of Kalman filtering smoothing and confidence interval calibration.

File List kf_algorithm.R Description This file contains R-code which demonstrates the Kalman filter and smoother and construction of CIC curves. No estimation of parameters is shown, however, the negative log-likelihood is calculated and so this code could be modified to be used for mMaximum-likelihood estimation of parameters. Note that estimation routines used in practice are best coded in a compiled language (e.g., C/Fortran) for optimal speed. Modifications to the code below will allow for parameter estimation, but it is likely to be quite slow. The function sim.track generates some simulated data from a bivariate random walk. For simplicity the simulation gives a regular time series of positions. Also demonstrated is the construction of confidence interval calibration (CIC) curves. In this case because the correct parameter values are used the CIC curve is the best possible case. By tinkering with the parameter values in the error covariance, the user will be able to see how the CIC curves change. To run the code open an R session and source the code then run the kfdemo function:<br> &gt; source('kfalgorithm.R')<br> &gt; kfdemo() <br>

文件kf_algorithm.R 说明：
本文件包含R代码，用于演示卡尔曼滤波（Kalman filter）、卡尔曼平滑器以及置信区间校准（Confidence Interval Calibration，CIC）曲线的构建。本示例未展示参数估计流程，但已计算负对数似然值，因此可对该代码进行修改，以实现参数的极大似然估计。
请注意，实际应用中的估计程序最优实现方式为使用编译型语言（如C/Fortran）编写，以获得最佳运行速度。若对下述代码进行修改以实现参数估计，运行速度可能会较为缓慢。
函数sim.track可基于二元随机游走生成模拟数据，为简化流程，该模拟会生成规则的位置时间序列。本代码同时演示了置信区间校准（CIC）曲线的构建：在此示例中，由于使用了正确的参数值，所得CIC曲线为理论最优情形。用户可通过调整误差协方差中的参数值，观察CIC曲线的变化规律。
运行该代码的步骤为：打开R会话，加载该代码文件后运行kfdemo函数：<br> > source('kfalgorithm.R')<br> > kfdemo()