Accuracy Estimating Algorithm for linear models based on Liapunov Limit Theorem

Due to the multi-scattering and the spectral difference between the covers and the selected end members, the solutions of Linear Models (LM) are not accurate enough. The accuracy estimating factors, namely the RMES (Residual Meaning Errors) of LM, are generally used to describe the regression status of two datasets. However, it can not be used to estimate the reasonableness of the LM solutions, even in some situations when the errors of the cover fractions are unbearably large. According to the comprehensive development status of mixing pixel techniques of LM, the main objective of the study was to explore the application of the Liapunov Limit Theorem (LLT) for the confidence level evaluation for the solution of LM. The data analysis results showed that although the correlative coefficient of a LM for artificial Moderate Mixing Pixel (MMP) was greater than that of the artificial Low Mixing Pixel (LMP), i.e., up to 0.96, its confidence level was not more than 0.05. The resulting value not more than 0.05 was generally considered as a small probability event and could hardly appear. Therefore, the Liapunov Accuracy Estimating Algorithm (LAEA) developed in this study has excellently overcome the drawback of the conventional LM which could not be used to determine the reasonableness of its solution to cover fractions in a mixing pixel.