Iterated Extended Kalman Smoother-Based Variable Splitting for L1-Regularized State Estimation
(2019) In IEEE Transactions on Signal Processing 67(19). p.5078-5092- Abstract
In this paper, we propose a new framework for solving state estimation problems with an additional sparsity-promoting $L-1$-regularizer term. We first formulate such problems as minimization of the sum of linear or nonlinear quadratic error terms and an extra regularizer, and then present novel algorithms which solve the linear and nonlinear cases. The methods are based on a combination of the iterated extended Kalman smoother and variable splitting techniques such as alternating direction method of multipliers (ADMM). We present a general algorithmic framework for variable splitting methods, where the iterative steps involving minimization of the nonlinear quadratic terms can be computed efficiently by iterated smoothing. Due to the... (More)
In this paper, we propose a new framework for solving state estimation problems with an additional sparsity-promoting $L-1$-regularizer term. We first formulate such problems as minimization of the sum of linear or nonlinear quadratic error terms and an extra regularizer, and then present novel algorithms which solve the linear and nonlinear cases. The methods are based on a combination of the iterated extended Kalman smoother and variable splitting techniques such as alternating direction method of multipliers (ADMM). We present a general algorithmic framework for variable splitting methods, where the iterative steps involving minimization of the nonlinear quadratic terms can be computed efficiently by iterated smoothing. Due to the use of state estimation algorithms, the proposed framework has a low per-iteration time complexity, which makes it suitable for solving a large-scale or high-dimensional state estimation problem. We also provide convergence results for the proposed algorithms. The experiments show the promising performance and speed-ups provided by the methods.
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- author
- Gao, Rui ; Tronarp, Filip LU and Särkkä, Simo
- publishing date
- 2019
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- alternating direction method of multipliers (ADMM), iterated extended Kalman smoother (IEKS), sparsity, State estimation, variable splitting
- in
- IEEE Transactions on Signal Processing
- volume
- 67
- issue
- 19
- article number
- 8805100
- pages
- 15 pages
- publisher
- IEEE - Institute of Electrical and Electronics Engineers Inc.
- external identifiers
-
- scopus:85072080503
- scopus:85072080503
- ISSN
- 1053-587X
- DOI
- 10.1109/TSP.2019.2935868
- language
- English
- LU publication?
- no
- id
- f851a99a-ea16-4ada-a316-52ffd6ce1aa1
- date added to LUP
- 2023-08-20 22:43:50
- date last changed
- 2023-11-10 15:04:32
@article{f851a99a-ea16-4ada-a316-52ffd6ce1aa1,
abstract = {{<p>In this paper, we propose a new framework for solving state estimation problems with an additional sparsity-promoting $L-1$-regularizer term. We first formulate such problems as minimization of the sum of linear or nonlinear quadratic error terms and an extra regularizer, and then present novel algorithms which solve the linear and nonlinear cases. The methods are based on a combination of the iterated extended Kalman smoother and variable splitting techniques such as alternating direction method of multipliers (ADMM). We present a general algorithmic framework for variable splitting methods, where the iterative steps involving minimization of the nonlinear quadratic terms can be computed efficiently by iterated smoothing. Due to the use of state estimation algorithms, the proposed framework has a low per-iteration time complexity, which makes it suitable for solving a large-scale or high-dimensional state estimation problem. We also provide convergence results for the proposed algorithms. The experiments show the promising performance and speed-ups provided by the methods.</p>}},
author = {{Gao, Rui and Tronarp, Filip and Särkkä, Simo}},
issn = {{1053-587X}},
keywords = {{alternating direction method of multipliers (ADMM); iterated extended Kalman smoother (IEKS); sparsity; State estimation; variable splitting}},
language = {{eng}},
number = {{19}},
pages = {{5078--5092}},
publisher = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
series = {{IEEE Transactions on Signal Processing}},
title = {{Iterated Extended Kalman Smoother-Based Variable Splitting for L<sub>1</sub>-Regularized State Estimation}},
url = {{http://dx.doi.org/10.1109/TSP.2019.2935868}},
doi = {{10.1109/TSP.2019.2935868}},
volume = {{67}},
year = {{2019}},
}