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arXiv · 1808.06538

Some New Results on l1-Minimizing Nullspace Kalman Filtering for Remote Sensing Applications

Otmar Loffeld·Dunja Alexandra Hage·Miguel Heredia Conde·Ling Wang
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Abstract

This paper describes some new results on recursive l_1-minimizing by Kalman filtering. We consider the l_1-norm as an explicit constraint, formulated as a nonlinear observation of the state to be estimated. Interpretiing a sparse vector to be estimated as a state which is observed from erroneous (undersampled) measurements we can address time- and space-variant sparsity, any kind of a priori information and also easily address nonstationary error influences in the measurements available. Inherently in our approach we move slightly away from the classical RIP-based approaches to a more intuitive understanding of the structure of the nullspace which is implicitly related to the well understood engineering concepts of deterministic and stochastic observability in estimation theory

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Otmar Loffeld, Dunja Alexandra Hage, Miguel Heredia Conde, Ling Wang. 2018-08-16. Some New Results on l1-Minimizing Nullspace Kalman Filtering for Remote Sensing Applications. https://arxiv.org/abs/1808.06538

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