# The Fragility of Noise Estimation in Kalman Filter: Optimization Can Handle Model-Misspecification

arXiv: https://arxiv.org/abs/2104.02372 · HTML: https://mlsanity.com/paper/2104.02372/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 65 references that are in the map.
- First posted on arXiv 6 Apr 2021.

## Builds on (most cited first, 18 of 18)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [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)
- [Simple Online and Realtime Tracking with a Deep Association Metric](https://mlsanity.com/paper/1703.07402/) (2017)
- [Simple Online and Realtime Tracking](https://mlsanity.com/paper/1602.00763/) (2016)
- [Deep Reinforcement Learning that Matters](https://mlsanity.com/paper/1709.06560/) (2017)
- [Exploring Generalization in Deep Learning](https://mlsanity.com/paper/1706.08947/) (2017)
- [MOT20: A benchmark for multi object tracking in crowded scenes](https://mlsanity.com/paper/2003.09003/) (2020)
- [Implementation Matters in Deep Policy Gradients: A Case Study on PPO and TRPO](https://mlsanity.com/paper/2005.12729/) (2020)
- [What Matters In On-Policy Reinforcement Learning? A Large-Scale Empirical Study](https://mlsanity.com/paper/2006.05990/) (2020)
- [Convergence rates for the stochastic gradient descent method for non-convex objective functions](https://mlsanity.com/paper/1904.01517/) (2019)
- [Long Short-Term Memory Kalman Filters:Recurrent Neural Estimators for Pose Regularization](https://mlsanity.com/paper/1708.01885/) (2017)
- [A systematic literature review on state-of-the-art deep learning methods for process prediction](https://mlsanity.com/paper/2101.09320/) (2021)
- [Online Learning of the Kalman Filter with Logarithmic Regret](https://mlsanity.com/paper/2002.05141/) (2020)
- [Adaptive Adjustment of Noise Covariance in Kalman Filter for Dynamic State Estimation](https://mlsanity.com/paper/1702.00884/) (2017)
- [Fitting a Kalman Smoother to Data](https://mlsanity.com/paper/1910.08615/) (2019)
- [Adam revisited: a weighted past gradients perspective](https://mlsanity.com/paper/2101.00238/) (2021)
- [DeepDA: LSTM-based Deep Data Association Network for Multi-Targets Tracking in Clutter](https://mlsanity.com/paper/1907.09915/) (2019)

## Built on by (most cited first, 3 of 3)

- [Low-rank extended Kalman filtering for online learning of neural networks from streaming data](https://mlsanity.com/paper/2305.19535/) (2023)
- [Learning IMM Filter Parameters from Measurements using Gradient Descent](https://mlsanity.com/paper/2307.06618/) (2023)
- [Data-Driven Approaches for Modelling Target Behaviour](https://mlsanity.com/paper/2410.10538/) (2024)

## Abstract (arXiv)

The Kalman Filter (KF) parameters are traditionally determined by noise estimation, since under the KF assumptions, the state prediction errors are minimized when the parameters correspond to the noise covariance. However, noise estimation remains the gold-standard regardless of the assumptions - even when it is not equivalent to errors minimization. We demonstrate that even seemingly simple problems may include multiple assumptions violations - which are sometimes hard to even notice. We show theoretically and empirically that even a minor violation may largely shift the optimal parameters. We propose a gradient-based method along with the Cholesky parameterization to explicitly optimize the state prediction errors. We show consistent improvement over noise estimation in tens of experiments in 3 different domains. Finally, we demonstrate that optimization makes the KF competitive with an LSTM model - even in non linear problems.