Variable Splitting Methods for Constrained State Estimation in Partially Observed Markov Processes

Rui Gao*, Filip Tronarp, Simo Särkkä

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)


In this letter, we propose a class of efficient, accurate, and general methods for solving state-estimation problems with equality and inequality constraints. The methods are based on recent developments in variable splitting and partially observed Markov processes. We first present the generalized framework based on variable splitting, then develop efficient methods to solve the state-estimation subproblems arising in the framework. The solutions to these subproblems can be made efficient by leveraging the Markovian structure of the model as is classically done in so-called Bayesian filtering and smoothing methods. The numerical experiments demonstrate that our methods outperform conventional optimization methods in computation cost as well as the estimation performance.

Original languageEnglish
Article number9143395
Pages (from-to)1305-1309
Number of pages5
JournalIEEE Signal Processing Letters
Publication statusPublished - 2020
MoE publication typeA1 Journal article-refereed


  • Kalman filters
  • Optimization
  • Markov processes
  • State estimation
  • State-space methods
  • Minimization
  • Computational modeling
  • Constrained state estimation
  • inequality constraint
  • variable splitting
  • Kalman filtering and smoothing
  • Kalman smoother


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