# The Kalman Evolve: Closing the Gap in Kalman Filtering via Interpretable Algorithm Discovery

arXiv: https://arxiv.org/abs/2605.26830 · HTML: https://mlsanity.com/paper/2605.26830/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 34 references that are in the map.
- First posted on arXiv 26 May 2026.

## Builds on (most cited first, 12 of 12)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [MOT20: A benchmark for multi object tracking in crowded scenes](https://mlsanity.com/paper/2003.09003/) (2020)
- [MOTChallenge 2015: Towards a Benchmark for Multi-Target Tracking](https://mlsanity.com/paper/1504.01942/) (2015)
- [KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamics](https://mlsanity.com/paper/2107.10043/) (2021)
- [FunBO: Discovering Acquisition Functions for Bayesian Optimization with FunSearch](https://mlsanity.com/paper/2406.04824/) (2024)
- [DANSE: Data-driven Non-linear State Estimation of Model-free Process in Unsupervised Learning Setup](https://mlsanity.com/paper/2306.03897/) (2023)
- [Optimization or Architecture: How to Hack Kalman Filtering](https://mlsanity.com/paper/2310.00675/) (2023)

## Abstract (arXiv)

State estimation is a fundamental problem in control and signal processing, for which the Kalman Filter provides an optimal solution under linear dynamics, Gaussian noise, and known noise covariances. However, these assumptions often fail in realistic sensing settings such as Doppler radar and LiDAR. In these cases, the optimal estimator is inherently nonlinear, which leads to systematic performance degradation. This creates a performance gap that cannot be eliminated by tuning the noise covariance parameters (i.e., the process and measurement noise in the Kalman Filter) alone. To address this limitation, we propose Kalman Evolve, a framework for discovering improved filtering algorithms by jointly optimizing both noise parameters and the update structure. Our approach leverages large language models (LLMs) as a structured prior over program space, enabling the generation of interpretable, non-affine modifications to the classical Kalman filter while preserving its recursive form. We provide analytical results establishing the suboptimality of affine estimators under common nonlinear sensing models, motivating the need for structure-aware updates. Across a range of synthetic and real-world tracking benchmarks, including Doppler radar, LiDAR-based localization, and pedestrian tracking, the discovered algorithms consistently improve over strong baselines such as the Optimized Kalman Filter, achieving up to 12% reduction in RMSE. These results suggest that optimizing the structure of the Kalman filter, rather than only its parameters, provides a practical and interpretable way to improve state estimation.