# DANSE: Data-driven Non-linear State Estimation of Model-free Process in Unsupervised Learning Setup

arXiv: https://arxiv.org/abs/2306.03897 · HTML: https://mlsanity.com/paper/2306.03897/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 68 references that are in the map.
- First posted on arXiv 4 Jun 2023.

## Builds on (most cited first, 17 of 17)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [Structured Inference Networks for Nonlinear State Space Models](https://mlsanity.com/paper/1609.09869/) (2016)
- [Deep Variational Bayes Filters: Unsupervised Learning of State Space Models from Raw Data](https://mlsanity.com/paper/1605.06432/) (2016)
- [KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamics](https://mlsanity.com/paper/2107.10043/) (2021)
- [Dynamical Variational Autoencoders: A Comprehensive Review](https://mlsanity.com/paper/2008.12595/) (2020)
- [A Disentangled Recognition and Nonlinear Dynamics Model for Unsupervised Learning](https://mlsanity.com/paper/1710.05741/) (2017)
- [Recurrent Kalman Networks: Factorized Inference in High-Dimensional Deep Feature Spaces](https://mlsanity.com/paper/1905.07357/) (2019)
- [Light Gated Recurrent Units for Speech Recognition](https://mlsanity.com/paper/1803.10225/) (2018)
- [Long Short-Term Memory Kalman Filters:Recurrent Neural Estimators for Pose Regularization](https://mlsanity.com/paper/1708.01885/) (2017)
- [Combining Generative and Discriminative Models for Hybrid Inference](https://mlsanity.com/paper/1906.02547/) (2019)
- [Unsupervised Learned Kalman Filtering](https://mlsanity.com/paper/2110.09005/) (2021)
- [Joint Smoothing, Tracking, and Forecasting Based on Continuous-Time Target Trajectory Fitting](https://mlsanity.com/paper/1708.02196/) (2017)
- [From Target Tracking to Targeting Track: A Data-Driven Yet Analytical Approach to Joint Target Detection and Tracking](https://mlsanity.com/paper/2104.11122/) (2021)

## Built on by (most cited first, 19 of 19)

- [AI-Aided Kalman Filters](https://mlsanity.com/paper/2410.12289/) (2024)
- [Flow-based Bayesian filtering for high-dimensional nonlinear stochastic dynamical systems](https://mlsanity.com/paper/2502.16232/) (2025)
- [Efficient Transformed Gaussian Process State-Space Models for Non-Stationary High-Dimensional Dynamical Systems](https://mlsanity.com/paper/2503.18309/) (2025)
- [Semi-Supervised Model-Free Bayesian State Estimation from Compressed Measurements](https://mlsanity.com/paper/2407.07368/) (2024)
- [Kalman Filter Aided Federated Koopman Learning](https://mlsanity.com/paper/2507.04808/) (2025)
- [Learning Flock: Enhancing Sets of Particles for Multi~Sub-State Particle Filtering with Neural Augmentation](https://mlsanity.com/paper/2408.11348/) (2024)
- [DIMM: Decoupled Multi-hierarchy Kalman Filter for 3D Object Tracking](https://mlsanity.com/paper/2505.12340/) (2025)
- [Differentiable Adaptive Kalman Filtering via Optimal Transport](https://mlsanity.com/paper/2508.07037/) (2025)
- [pDANSE: Particle-based Data-driven Nonlinear State Estimation from Nonlinear Measurements](https://mlsanity.com/paper/2510.27503/) (2025)
- [Filtering Jump Markov Systems with Partially Known Dynamics: A Model-Based Deep Learning Approach](https://mlsanity.com/paper/2511.09569/) (2025)
- [Model-Free Neural Filtering: A Comparison with Classical Filters in Nonlinear Systems](https://mlsanity.com/paper/2601.21266/) (2026)
- [VSE: Variational state estimation of complex model-free process](https://mlsanity.com/paper/2601.21887/) (2026)
- [DNS: Data-driven Nonlinear Smoother for Complex Model-free Process](https://mlsanity.com/paper/2602.08560/) (2026)
- [Online Prediction of Stochastic Sequences with High Probability Regret Bounds](https://mlsanity.com/paper/2602.16236/) (2026)
- [The Kalman Evolve: Closing the Gap in Kalman Filtering via Interpretable Algorithm Discovery](https://mlsanity.com/paper/2605.26830/) (2026)
- [Learning to Distributedly Estimate under Partially Known Dynamics: A Covariance-Agnostic Neural Kalman Consensus Filter](https://mlsanity.com/paper/2606.28441/) (2026)
- [Ensemble Controlled-Flow Filtering for Implicit Data Assimilation](https://mlsanity.com/paper/2607.12975/) (2026)
- [Unscented KalmanNet: Structure-Preserving Deep Learning with Calibrated Posterior Uncertainty under Incomplete Physics and Unknown Noise](https://mlsanity.com/paper/2608.04201/) (2026)
- [Online Learning via Learned Latent Bayesian Tracking](https://mlsanity.com/paper/2609.31559/) (2026)

## Abstract (arXiv)

We address the tasks of Bayesian state estimation and forecasting for a model-free process in an unsupervised learning setup. For a model-free process, we do not have any a-priori knowledge of the process dynamics. In the article, we propose DANSE -- a Data-driven Nonlinear State Estimation method. DANSE provides a closed-form posterior of the state of the model-free process, given linear measurements of the state. In addition, it provides a closed-form posterior for forecasting. A data-driven recurrent neural network (RNN) is used in DANSE to provide the parameters of a prior of the state. The prior depends on the past measurements as input, and then we find the closed-form posterior of the state using the current measurement as input. The data-driven RNN captures the underlying non-linear dynamics of the model-free process. The training of DANSE, mainly learning the parameters of the RNN, is executed using an unsupervised learning approach. In unsupervised learning, we have access to a training dataset comprising only a set of measurement data trajectories, but we do not have any access to the state trajectories. Therefore, DANSE does not have access to state information in the training data and can not use supervised learning. Using simulated linear and non-linear process models (Lorenz attractor and Chen attractor), we evaluate the unsupervised learning-based DANSE. We show that the proposed DANSE, without knowledge of the process model and without supervised learning, provides a competitive performance against model-driven methods, such as the Kalman filter (KF), extended KF (EKF), unscented KF (UKF), a data-driven deep Markov model (DMM) and a recently proposed hybrid method called KalmanNet. In addition, we show that DANSE works for high-dimensional state estimation.