Wavelet transform adapted to an approximate Kalman filter system Original Research Article

Wavelets are constructed as a class of orthonormal functions with compact support and multi-resolution. Wavelet transforms can effectively compress data and extract key features in frequencies and locations. Wavelets can also be used as a base of spectral representation in solving PDEʹs. This work demonstrates an effort to apply wavelet methods to a simple data assimilation system. The multi-resolution wavelet transform is applied to one dimensional convection diffusion equation, and a propagator in wavelet space is constructed. The wavelet transform is also applied to the error covariance matrix. The matrix is then compressed and then truncated, so as to reduce the cost of covariance propagation. The results show that the characteristic and localized features in the flow and error covariance are resolved and captured in this approximated Kalman filter system.