A parameter estimation framework for Multiscale Kalman Smoother algorithm in precipitation data fusion. Issue 11 (12th November 2014) - Wang, Shugong; Liang, Xu
Abstract A new effective parameter estimation approach is presented for the Multiscale Kalman Smoother (MKS) algorithm. As demonstrated, it shows promising potentials in deriving better data products involving sources from different spatial scales and precisions. The proposed approach employs a multiobjective parameter estimation framework, which includes three multiobjective estimation schemes (MO schemes), rather than using the conventional maximum likelihood scheme (ML scheme), to estimate the MKS parameters. Unlike the ML scheme, the MO schemes are not built on strict statistical assumptions related to prediction errors and observation errors, rather, they directly associate the fused data of multiple scales with multiple objective functions. In the MO schemes, objective functions are defined to facilitate consistency among the fused data at multiple scales and the input data at their original scales as well in terms of spatial patterns and magnitudes. Merits of the new approach are evaluated through a Monte Carlo experiment and a series of comparison analyses using synthetic precipitation data that contain noises which follow either the multiplicative error model or the additive error model. Our results show that the MKS fused precipitation performs better using the MO framework. Improvements are particularly significant for the fused precipitation associated with fine spatial resolutions. This is due mainly to the adoption of more criteria and constraints in the MO framework. The weakness of the original ML scheme, arising from its blindly putting more weights into the data associated with finer resolutions, is circumvented in the proposed new MO framework.