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

TL;DR

This paper introduces new recursive l_1-minimizing Kalman filtering techniques for remote sensing, addressing sparsity, nonstationary errors, and moving beyond classical RIP-based methods with an emphasis on nullspace structure and observability.

Contribution

It presents novel recursive l_1-minimizing Kalman filtering methods that incorporate explicit constraints and nullspace analysis for improved remote sensing estimation.

Findings

Enhanced handling of time- and space-variant sparsity

Ability to address nonstationary measurement errors

Shift from RIP-based approaches to nullspace and observability concepts

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