# Iterated Extended Kalman Smoother-based Variable Splitting for L1-Regularized State Estimation

arXiv: https://arxiv.org/abs/1903.08605 · HTML: https://mlsanity.com/paper/1903.08605/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Mar 2019.

## Built on by (most cited first, 3 of 3)

- [Sparse Graphical Linear Dynamical Systems](https://mlsanity.com/paper/2307.03210/) (2023)
- [Parallel-in-Time Probabilistic Numerical ODE Solvers](https://mlsanity.com/paper/2310.01145/) (2023)
- [Hierarchical Non-Stationary Temporal Gaussian Processes With L1-Regularization](https://mlsanity.com/paper/2105.09695/) (2021)

## Abstract (arXiv)

In this paper, we propose a new framework for solving state estimation problems with an additional sparsity-promoting L1-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.