Recursive KalmanNet (RKN)

About

We introduce Recursive KalmanNet (RKN), a Kalman filter-informed recurrent neural network, designed to estimate both the state variables and the error covariance of a stochastic dynamical system from noisy measurements, without requiring prior knowledge of the noise covariances. This estimator preserves the structure of the Kalman filter while learning the gain and estimation error covariance through deep learning. It propagates the error covariance using the recursive Joseph’s formula and optimizes the negative Gaussian log-likelihood.

Publications

• H. Mortada, C. Falcon, Y. Kahil, M. Clavaud, and J.-P. Michel, Recursive KalmanNet: Deep Learning-Augmented Kalman Filtering for State Estimation with Consistent Uncertainty Quantification, EUSIPCO 2025.

• C. Falcon, H. Mortada, M. Clavaud, and J.-P. Michel, Recursive KalmanNet : Analyse des capacités de généralisation d’un réseau de neurones récurrent guidé par un filtre de Kalman, GRETSI 2025.

Python Version and Dependencies

This project was developed and tested using Python 3.12.8.

Using the exact same version is not strictly necessary. You can check your Python version with:

python --version

To create an environment

python -m venv venv
venv\Scripts\activate # On Mac, use: source venv/bin/activate

To install all required dependencies, from the RecursiveKalmanNet folder:

pip install -r requirements.txt

Folder Architecture

• .data/: Stores all datasets used in the project.
• .models/: Contains saved trained models.
• .results/: Automatically saves training and validation loss curves, and may also include plots.
  • .results/loss_curves/: Saves loss curve values during training and validation.
  • .results/plot_saves/: Folder that can be specified to save generated plots.
• Algo/: Includes class definitions for dynamical systems, the Kalman filter, the Recursive KalmanNet, and loss functions.
• Tools/: Provides utility functions for data generation and plotting.

Entry point

The main_bimodal_noise.ipynb notebook offers a practical illustration of how to use this codebase.
The dynamical system is a one-dimensional constant-speed linear kinematic state-space model, with a position measurement. The measurement noise follows a gaussian bimodal distribution. The notebook covers:

• data generation according to the defined dynamical system
• demonstrates the use of the Kalman Filter
• demonstrates the instantiation, training, and usage of the Recursive Kalman Filter.

The notebook also includes several plots featured in the first paper listed above.