Recovering Method of Missing Data Based on Proposed Modified Kalman Filter When Time Series of Mean Data is Known

Abstract

Recovering method of missing data based on the proposed modified Kalman filter for the case that the time series of mean data is know is proposed. There are some cases of which although a portion of data is missing, mean value of the time series of data is known. For instance, although coarse resolution of imagery data are acquired every day, fine resolution of imagery data are missing sometimes. In other words, coarse resolution of imaging sensor has wide swath width while fine resolution of imaging sensor has narrow swath, in general. Therefore, coarse resolution of sensor data can be acquired every day while fine resolution of sensor data can be acquired not so frequently. It would be nice to become able to create frequently acquired fine resolution of sensor data (every day) using the previously acquired fine resolution of sensor data together with the coarse resolution of sensor data. The proposed method allows creation of fine resolution sensor data with the aforementioned method based on a modified Kalman filter. As an example of the proposed method, prediction of missing ASTER/VNIR data based on Kalman filter using simultaneously acquired MODIS data as a mean value of time series data in revision of filter status is attempted together with a comparative study of prediction errors for both conventional Kalman filter and the proposed modified Kalman filter which utilizes mean value of time series data derived from the other sources. Experimental data shows that 4 to 111% of prediction error reduction can be achieved by the proposed modified Kalman filter in comparison to the conventional Kalman filter. It is found that the reduction rate depends on the mean value accuracy of time series data derived from the other data sources. The experimental results with remote sensing satellite imagery data show a validity of the proposed method