## 4 Experiments
### Application to Real Data  
The Pacific Sea Temperature (PST) data set, which can be obtained from the Climate Data Library at Columbia University ([[http://iridl.ldeo.columbia.edu/SOURCES/CAC/](http://iridl.ldeo.columbia.edu/SOURCES/CAC/)]([http://iridl.ldeo.columbia.edu/SOURCES/CAC/](http://iridl.ldeo.columbia.edu/SOURCES/CAC/)), accessed on 27 September 2021) [38], has 2520 sample temperature data points per month on the Pacific from January 1970 through March 2003. The sampling mode is grid (84 * 30), with a longitude and latitude interval of 2. In the PST data, the first 120 time-series were used for training, and the observation error was set as 0.5. The data of the subsequent 24 months were then predicted and described.The forecast period was 24 months, from January 1980 to December 1982. To estimate the PST, we first used data normalization to make the coordinates in the same grade interval, and each time was resampled on a regular \(21*10\) grid. We applied the Kriging filter with the data covariance function in Equation (47), drift functions as \(\mathbf{f}(x)=\left[1,x,y,xy,x^{2},y^{2}\right]^{T}\), and cubic exponential smoothing model parameters \(\zeta=0.45\), \(\tau=0.2\), \(\gamma=0.95\), and \(L=12\). The results are shown in Figure 8, while  
Figure 7: 2D sequence signal simulation (times 1, 6, 11, 16 and 21 are shown). (**a**) Original signal functions without white noise; (**b**) Fit by FUKSS; and (**c**) Fit by Smoothing thin-plate spline. Figure 9 shows a comparison of the temperature of a single coordinate over time. As can be seen from the two figures, our method achieved good results, could effectively predict the temperature value of unknown points in the training data, and can also effectively show the trend of change in the prediction process. It can be seen, from the experiment, that the training deviation was relatively small, mainly due to the accuracy of universal Kriging estimation and Kalman filter using the correction of the current observations. At this point, we introduce the dynamic linear model to introduce additional quasi-observable values. Experimentally, it was found that the introduction of such quasi-observable values in the multi-step prediction led to better results. The possible reasons for this are as follows: (1) Kalman filtering cleans and smooths the data in the time-series, by removing the possible noise or outliers, such that better results can be obtained in dynamic linear prediction of the smoothed data; and (2) during the simulation interpolation, universal Kriging also fitted the data with features and correlations, in order to make the data more consistent with the actual situation. Although we solved the multi-step prediction, to a certain extent, the error of the additional quasi-observable values obtained by the dynamic linear model increases as the step size of the prediction increased. At the same time, this quasi-observable value error is also transmitted to the gain matrix, thereby increasing the error. In our choice of May 1981, which is a five-step forecast relative to the time interval, we can clearly see the variation of this error. The temperature of the Pacific Ocean changes on an annual basis. Although the range of change in this cycle is not large, it is also shown in the single point chart. Generally, the annual period of change is about 5 \({}^{\circ}\)C, but that in some regions can also reach a range of more than 10 \({}^{\circ}\)C. This is something that we have not fully solved yet as, over time, these errors accumulate and the forecast starts to drift. However, we still obtain high accuracy in multi-step short-term forecasting. The considered grain warehouse temperature test system was a generally distributed system. The temperature sensor is stored in a cable, and fixed on the wall at one end. In this way, a rather warehouse impression of the locations of temperature sensors could be obtained.