# Fitting a Kalman Smoother to Data

arXiv: https://arxiv.org/abs/1910.08615 · HTML: https://mlsanity.com/paper/1910.08615/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Oct 2019.

## Built on by (most cited first, 9 of 9)

- [KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamics](https://mlsanity.com/paper/2107.10043/) (2021)
- [Model-Based Deep Learning: On the Intersection of Deep Learning and Optimization](https://mlsanity.com/paper/2205.02640/) (2022)
- [Optimization or Architecture: How to Hack Kalman Filtering](https://mlsanity.com/paper/2310.00675/) (2023)
- [The Fragility of Noise Estimation in Kalman Filter: Optimization Can Handle Model-Misspecification](https://mlsanity.com/paper/2104.02372/) (2021)
- [KARNet: Kalman Filter Augmented Recurrent Neural Network for Learning World Models in Autonomous Driving Tasks](https://mlsanity.com/paper/2305.14644/) (2023)
- [Low Rank Forecasting](https://mlsanity.com/paper/2101.12414/) (2021)
- [Learning IMM Filter Parameters from Measurements using Gradient Descent](https://mlsanity.com/paper/2307.06618/) (2023)
- [Beyond One Model Fits All: Ensemble Deep Learning for Autonomous Vehicles](https://mlsanity.com/paper/2312.05759/) (2023)
- [Data-Driven Approaches for Modelling Target Behaviour](https://mlsanity.com/paper/2410.10538/) (2024)

## Abstract (arXiv)

This paper considers the problem of fitting the parameters of a Kalman smoother to data. We formulate the Kalman smoothing problem with missing measurements as a constrained least squares problem and provide an efficient method to solve it based on sparse linear algebra. We then introduce the Kalman smoother tuning problem, which seeks to find parameters that achieve low prediction error on held out measurements. We derive a Kalman smoother auto-tuning algorithm, which is based on the proximal gradient method, that finds good, if not the best, parameters for a given dataset. Central to our method is the computation of the gradient of the prediction error with respect to the parameters of the Kalman smoother; we describe how to compute this at little to no additional cost. We demonstrate the method on population migration within the United States as well as data collected from an IMU+GPS system while driving. The paper is accompanied by an open-source implementation.