Recursive Least Square: RLS Method-Based Time Series Data Prediction for Many Missing Data

Kohei Arai,Kaname Seto

doi:10.14569/ijacsa.2020.0111109

Abstract

Prediction methods for time series data with many missing data based on Recursive Least Square (RLS) method are proposed. There are two parameter tuning algorithms, time update and measurement update algorithms for parameter estimation of Kalman filter. Two learning methods for parameter estimation of Kalman filter are proposed based on RLS method. One is the method without measurement update algorithm (RLS-1). The other one is the method without both time and measurement update algorithms (RLS-2). The methods are applied to the time series data of Defense Meteorological Satellite Program (DMSP) / Special Sensor Microwave/Imager (SSM/I) data with a plenty of missing data. It is found that the proposed RLS-2 method shows smooth and fast convergence in learning process in comparison to the RLS-1.

Highlights

Earth observation satellites observe arbitrary points on the earth at unequal time intervals based on their orbital conditions
Evaluation between Recursive Least Square (RLS) method 1 and RLS method 2 In the comparison of J2 (m), RLS method 2 shows almost the same characteristics of J2(m) with respect to rn in four cases, whereas the RLS method In some cases, 1 has drawbacks such as the behavior of J2 (m) with respect to rn causing vibration
We proposed a method based on the Kalman filter as a method for estimating missing data from a multidimensional time series including missing data, or for estimating data at any time

Summary

Introduction

Earth observation satellites observe arbitrary points on the earth at unequal time intervals based on their orbital conditions. When this observation data is regarded as time-series data at equal time intervals, it can be regarded as time-series data including many unobserved and missing data. One of the purposes of the time series analysis is to improve prediction accuracy of future data with the past data for the time series of data with a plenty of missing data. There is the famous method, so called, Kalman filter for future data prediction with the previously observed time series of data. There are the parameters for Kalman filter. It is difficult to estimate the parameters

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