# Consensus+Innovations Distributed Kalman Filter with Optimized Gains

arXiv: https://arxiv.org/abs/1605.06096 · HTML: https://mlsanity.com/paper/1605.06096/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 May 2016.

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

- [A Regret Minimization Approach to Multi-Agent Control](https://mlsanity.com/paper/2201.13288/) (2022)
- [On observability and optimal gain design for distributed linear filtering and prediction](https://mlsanity.com/paper/2203.03521/) (2022)
- [An alternative approach for distributed parameter estimation under Gaussian settings](https://mlsanity.com/paper/2204.08317/) (2022)

## Abstract (arXiv)

In this paper, we address the distributed filtering and prediction of time-varying random fields represented by linear time-invariant (LTI) dynamical systems. The field is observed by a sparsely connected network of agents/sensors collaborating among themselves. We develop a Kalman filter type consensus+innovations distributed linear estimator of the dynamic field termed as Consensus+Innovations Kalman Filter. We analyze the convergence properties of this distributed estimator. We prove that the mean-squared error of the estimator asymptotically converges if the degree of instability of the field dynamics is within a pre-specified threshold defined as tracking capacity of the estimator. The tracking capacity is a function of the local observation models and the agent communication network. We design the optimal consensus and innovation gain matrices yielding distributed estimates with minimized mean-squared error. Through numerical evaluations, we show that, the distributed estimator with optimal gains converges faster and with approximately 3dB better mean-squared error performance than previous distributed estimators.