# How to Train Your Differentiable Filter

arXiv: https://arxiv.org/abs/2012.14313 · HTML: https://mlsanity.com/paper/2012.14313/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Dec 2020.

## Built on by (most cited first, 23 of 23)

- [Differentiable Particle Filtering via Entropy-Regularized Optimal Transport](https://mlsanity.com/paper/2102.07850/) (2021)
- [An overview of differentiable particle filters for data-adaptive sequential Bayesian inference](https://mlsanity.com/paper/2302.09639/) (2023)
- [Safe Output Feedback Motion Planning from Images via Learned Perception Modules and Contraction Theory](https://mlsanity.com/paper/2206.06553/) (2022)
- [Differentiable Particle Filters through Conditional Normalizing Flow](https://mlsanity.com/paper/2107.00488/) (2021)
- [Probabilistic 3D Multi-Object Cooperative Tracking for Autonomous Driving via Differentiable Multi-Sensor Kalman Filter](https://mlsanity.com/paper/2309.14655/) (2023)
- [Normalizing Flow-based Differentiable Particle Filters](https://mlsanity.com/paper/2403.01499/) (2024)
- [Efficient Learning of the Parameters of Non-Linear Models using Differentiable Resampling in Particle Filters](https://mlsanity.com/paper/2111.01409/) (2021)
- [Neural Extended Kalman Filters for Learning and Predicting Dynamics of Structural Systems](https://mlsanity.com/paper/2210.04165/) (2022)
- [Conditional Measurement Density Estimation in Sequential Monte Carlo via Normalizing Flow](https://mlsanity.com/paper/2203.08617/) (2022)
- [Streaming Motion Forecasting for Autonomous Driving](https://mlsanity.com/paper/2310.01351/) (2023)
- [Particle-Based Score Estimation for State Space Model Learning in Autonomous Driving](https://mlsanity.com/paper/2212.06968/) (2022)
- [Differentiable Bootstrap Particle Filters for Regime-Switching Models](https://mlsanity.com/paper/2302.10319/) (2023)
- [DiffPF: Differentiable Particle Filtering with Generative Sampling via Conditional Diffusion Models](https://mlsanity.com/paper/2507.15716/) (2025)
- [Differentiable Filtering for Learning Hidden Markov Models](https://mlsanity.com/paper/2511.10571/) (2025)
- [Optimization Algorithm for Feedback and Feedforward Policies towards Robot Control Robust to Sensing Failures](https://mlsanity.com/paper/2104.00385/) (2021)
- [DnD Filter: Differentiable State Estimation for Dynamic Systems using Diffusion Models](https://mlsanity.com/paper/2503.01274/) (2025)
- [Mitigating Error Accumulation in Continuous Navigation via Memory-Augmented Kalman Filtering](https://mlsanity.com/paper/2602.11183/) (2026)
- [E-3DPSM: A State Machine for Event-Based Egocentric 3D Human Pose Estimation](https://mlsanity.com/paper/2604.08543/) (2026)
- [Differentiable Particle Filtering using Optimal Placement Resampling](https://mlsanity.com/paper/2402.16639/) (2024)
- [Inverse Particle Filter](https://mlsanity.com/paper/2407.16623/) (2024)
- [Denoising Particle Filters: Learning State Estimation with Single-Step Objectives](https://mlsanity.com/paper/2602.19651/) (2026)
- [FW-NKF: Frequency-Weighted Neural Kalman Filters](https://mlsanity.com/paper/2606.02251/) (2026)
- [Online Learning via Learned Latent Bayesian Tracking](https://mlsanity.com/paper/2609.31559/) (2026)

## Abstract (arXiv)

In many robotic applications, it is crucial to maintain a belief about the state of a system, which serves as input for planning and decision making and provides feedback during task execution. Bayesian Filtering algorithms address this state estimation problem, but they require models of process dynamics and sensory observations and the respective noise characteristics of these models. Recently, multiple works have demonstrated that these models can be learned by end-to-end training through differentiable versions of recursive filtering algorithms. In this work, we investigate the advantages of differentiable filters (DFs) over both unstructured learning approaches and manually-tuned filtering algorithms, and provide practical guidance to researchers interested in applying such differentiable filters. For this, we implement DFs with four different underlying filtering algorithms and compare them in extensive experiments. Specifically, we (i) evaluate different implementation choices and training approaches, (ii) investigate how well complex models of uncertainty can be learned in DFs, (iii) evaluate the effect of end-to-end training through DFs and (iv) compare the DFs among each other and to unstructured LSTM models.