# Incorporating Transformer and LSTM to Kalman Filter with EM algorithm for state estimation

arXiv: https://arxiv.org/abs/2105.00250 · HTML: https://mlsanity.com/paper/2105.00250/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 42 references that are in the map.
- First posted on arXiv 1 May 2021.

## Builds on (most cited first, 14 of 14)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [Self-Attention with Relative Position Representations](https://mlsanity.com/paper/1803.02155/) (2018)
- [Sequence-to-Sequence Learning as Beam-Search Optimization](https://mlsanity.com/paper/1606.02960/) (2016)
- [Combining Recurrent Neural Networks and Adversarial Training for Human Motion Synthesis and Control](https://mlsanity.com/paper/1806.08666/) (2018)
- [Deep learning algorithm for data-driven simulation of noisy dynamical system](https://mlsanity.com/paper/1802.08323/) (2018)
- [EM-like Learning Chaotic Dynamics from Noisy and Partial Observations](https://mlsanity.com/paper/1903.10335/) (2019)
- [Financial series prediction using Attention LSTM](https://mlsanity.com/paper/1902.10877/) (2019)
- [LSTM-Based Zero-Velocity Detection for Robust Inertial Navigation](https://mlsanity.com/paper/1807.05275/) (2018)
- [A Comparison of LSTMs and Attention Mechanisms for Forecasting Financial Time Series](https://mlsanity.com/paper/1812.07699/) (2018)

## Built on by (most cited first, 5 of 5)

- [Attention-based CNN-LSTM and XGBoost hybrid model for stock prediction](https://mlsanity.com/paper/2204.02623/) (2022)
- [Bidirectional LSTM-CRF Attention-based Model for Chinese Word Segmentation](https://mlsanity.com/paper/2105.09681/) (2021)
- [ChronosAD: Leveraging Time Series Foundation Models for Accurate Anomaly Detection](https://mlsanity.com/paper/2606.01300/) (2026)
- [Differential equation and probability inspired graph neural networks for latent variable learning](https://mlsanity.com/paper/2202.13800/) (2022)
- [DIMM: Decoupled Multi-hierarchy Kalman Filter for 3D Object Tracking](https://mlsanity.com/paper/2505.12340/) (2025)

## Abstract (arXiv)

Kalman Filter requires the true parameters of the model and solves optimal state estimation recursively. Expectation Maximization (EM) algorithm is applicable for estimating the parameters of the model that are not available before Kalman filtering, which is EM-KF algorithm. To improve the preciseness of EM-KF algorithm, the author presents a state estimation method by combining the Long-Short Term Memory network (LSTM), Transformer and EM-KF algorithm in the framework of Encoder-Decoder in Sequence to Sequence (seq2seq). Simulation on a linear mobile robot model demonstrates that the new method is more accurate. Source code of this paper is available at https://github.com/zshicode/Deep-Learning-Based-State-Estimation.