Iterated Extended Kalman Smoother-Based Variable Splitting for L-1-Regularized State Estimation

Rui Gao*, Filip Tronarp, Simo Särkkä

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

11 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)5078-5092
Number of pages15
JournalIEEE Transactions on Signal Processing
Issue number19
Publication statusPublished - 1 Oct 2019
MoE publication typeA1 Journal article-refereed


  • State estimation
  • Sparsity
  • Variable splitting
  • Iterated extended Kalman smoother (IEKS)
  • Alternating direction method of multipliers (ADMM)
  • Alternating direction method
  • Algorithm
  • Frequency
  • Sigmals


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