# Iterated Extended Kalman Smoother-based Variable Splitting for $L_1$-Regularized State Estimation

## TL;DR

This paper introduces a novel framework combining iterated extended Kalman smoothers with variable splitting techniques like ADMM to efficiently solve large-scale $L_1$-regularized state estimation problems, offering low complexity and promising results.

## Contribution

It develops a new algorithmic framework that integrates Kalman smoothing with variable splitting for $L_1$-regularized state estimation, enabling efficient large-scale problem solving.

## Key findings

- The proposed methods achieve significant speed-ups.
- The algorithms demonstrate convergence guarantees.
- Experiments show effective handling of high-dimensional problems.

## 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 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.