Introduction.- LISA data processing chain.- Applying the Kalman filter to a simple case.- The inter-spacecraft measurements.- Design a hybrid extended Kalman filter for the entire LISA constellation.- Alternative Kalman filter models.- Broken laser links and robustness.- Optimal filtering for LISA with effective system models.- Clock noise and disordered measurements.- Octahedron configuration for a displacement noise-canceling gravitational wave detector in space.- EMRI data analysis with a phenomenological waveform.- Fast detection and automatic parameter estimation of a gravitational wave signal with a novel method.- Likelihood transform: making optimization and parameter estimation easier.
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