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ICASSP
2011
IEEE

Estimation and dynamic updating of time-varying signals with sparse variations

12 years 7 months ago
Estimation and dynamic updating of time-varying signals with sparse variations
This paper presents an algorithm for an 1-regularized Kalman filter. Given observations of a discrete-time linear dynamical system with sparse errors in the state evolution, we estimate the state sequence by solving an optimization algorithm that balances fidelity to the measurements (measured by the standard 2 norm) against the sparsity of the innovations (measured using the 1 norm). We also derive an efficient algorithm for updating the estimate as the system evolves. This dynamic updating algorithm uses a homotopy scheme that tracks the solution as new measurements are slowly worked into the system and old measurements are slowly removed. The effective cost of adding new measurements is a number of low-rank updates to the solution of a linear system of equations that is roughly proportional to the joint sparsity of all the innovations in the time interval of interest.
Muhammad Salman Asif, Adam Charles, Justin K. Romb
Added 20 Aug 2011
Updated 20 Aug 2011
Type Journal
Year 2011
Where ICASSP
Authors Muhammad Salman Asif, Adam Charles, Justin K. Romberg, Christopher Rozell
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