TY - GEN
T1 - Estimation and dynamic updating of time-varying signals with sparse variations
AU - Asif, M. Salman
AU - Charles, Adam
AU - Romberg, Justin
AU - Rozell, Christopher
PY - 2011
Y1 - 2011
N2 - This paper presents an algorithm for an ℓ1-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 ℓ2 norm) against the sparsity of the innovations (measured using the ℓ1 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.
AB - This paper presents an algorithm for an ℓ1-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 ℓ2 norm) against the sparsity of the innovations (measured using the ℓ1 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.
UR - http://www.scopus.com/inward/record.url?scp=80051660568&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=80051660568&partnerID=8YFLogxK
U2 - 10.1109/ICASSP.2011.5947206
DO - 10.1109/ICASSP.2011.5947206
M3 - Conference contribution
AN - SCOPUS:80051660568
SN - 9781457705397
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 3908
EP - 3911
BT - 2011 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 - Proceedings
T2 - 36th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011
Y2 - 22 May 2011 through 27 May 2011
ER -