Incorporating Transformer and LSTM to Kalman Filter with EM algorithm for state estimation (2105.00250v2)

Abstract: 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.

• The paper introduces a hybrid framework that integrates Transformer and LSTM with a Kalman Filter via the EM algorithm to improve state estimation under uncertain conditions.
• It leverages a seq2seq design where LSTM encodes sequential dependencies and Transformer employs self-attention to capture long-term relationships from noisy data.
• Experimental results show that the combined TL-KF model outperforms individual variants by more accurately estimating process noise covariance and the initial state parameters.

Incorporating Transformer and LSTM to Kalman Filter with EM Algorithm for State Estimation: A Review

The paper "Incorporating Transformer and LSTM to Kalman Filter with EM Algorithm for State Estimation" by Zhuangwei Shi introduces a hybrid architecture that integrates the Transformer and Long Short-Term Memory (LSTM) models into the classical Kalman Filter, enhanced with the Expectation Maximization (EM) algorithm. This synthesis aims to improve state estimation in systems where model parameters are initially unknown or imprecise, enhancing the precision and robustness of inference in sequential data processing contexts.

Core Contributions

The research addresses inherent challenges in Kalman Filters (KF), particularly when confronted with systems where model parameters are either known imprecisely or not at all. The two main drawbacks of Kalman Filters highlighted include:

1. The dependency on accurate model parameters, which are often estimated heuristically, can undermine the filter's efficacy.
2. The assumptions of Markovian state properties and conditional independence of observations, which do not always hold in real-world systems.

To mitigate these challenges, the paper extends the EM-KF framework by leveraging deep learning techniques, specifically LSTM and Transformers. The proposed method involves using a Sequence-to-Sequence (seq2seq) structure wherein LSTM serves as the encoder and Kalman Filter acts as the decoder. This architecture is designed to extract and encode salient state-related features from noisy observation data more effectively.

Key Methodologies

The paper explores several innovative approaches:

• LSTM-KF: An integration of LSTM as an encoder to pre-process observations, addressing sequential dependencies more effectively than traditional KFs.
• Transformer-KF: Utilizing the Transformer's capacity for capturing long-term dependencies through self-attention mechanisms, offering flexibility and robustness in processing complex sequences.
• TL-KF (Transformer-LSTM-KF): A novel combination where both Transformer and LSTM provide multi-layered encoding before KF processing, achieving superior parameter estimation.

The application of these models was tested through simulated experiments using a linear dynamical system, specifically a model of a mobile robot's motion in one degree of freedom. The experiments demonstrated improvements in the accuracy of state estimations when employing these neural network enhanced KFs over conventional methods.

Results and Implications

Experimental results indicate that the Transformer-KF variant yields the most accurate parameter estimations for the process noise covariance, while the LSTM-KF effectively estimates the initial state and its covariance. The TL-KF approach surpasses both individual variants, achieving enhancements across all parameter dimensions.

The outcomes of this work hold significant implications for fields where state estimation is critical under uncertain parameter settings, such as robotics, computer vision, and time-series forecasting. Moreover, the integration of deep learning models mitigates the limitations imposed by the Kalman Filter's assumptions, potentially broadening its applicability to more complex, non-linear, and non-Gaussian systems.

Directions for Future Research

The paper suggests several avenues for extending this research:

• Nonlinear System Applications: Expanding the methodology to handle nonlinear dynamics using Extended KF, Unscented KF, and Particle Filter.
• Advanced Initialization Techniques: Exploring alternative initialization techniques for the EM algorithm to address initial value dependency, such as variational Bayesian approaches or Gibbs sampling.
• Combining with Other Models: Investigating combinations of LSTM or Transformer with CNNs or GANs for enhanced feature extraction capabilities, especially for salient feature extraction.
• Bidirectional Mechanisms: Integrating bidirectional encoding (e.g., BERT) to further improve the filtering and smoothing of sequences.

This paper represents a step forward in state estimation accuracy by intertwining state-of-the-art deep learning techniques with classical filtering methods, offering a robust framework for dealing with uncertainty and complexity in modern signal processing applications.