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Time-series analysis with small and faulty data: L1-norm decompositions of Hankel matrices

In the rapidly advancing field of autonomous systems, real-time operation and monitoring in non-stationary environments frequently relies on analysis (filtering/prediction) of short sequences of sensed data that may be partly unreliable, missing, or faulty. Hankel-matrix representation and decomposition is a model-free approach that is becoming increasingly popular for the analysis of time-series data taking advantage of the progress in linear algebra methods in past years. In this work, we establish that novel L1-norm decompositions of Hankel matrices offer sturdy resistance against partially faulty sensed sequences and, therefore, creates a strong new framework for robust real-time monitoring of autonomous systems. The findings in this paper are illustrated and supported by extensive experimentation on artificial data.