Add comprehensive documentation for Ensemble Kalman Filter localization

[Copilot]

Overview

This PR adds comprehensive documentation for the Ensemble Kalman Filter (EnKF) localization algorithm under the docs/modules/2_localization/ directory, as requested in the issue.

Changes

Enhanced the existing minimal documentation file at docs/modules/2_localization/ensamble_kalman_filter_localization_files/ensamble_kalman_filter_localization_main.rst from 13 lines to 205 lines with complete mathematical and algorithmic details.

Documentation Sections Added

1. Algorithm Overview

• Detailed explanation of EnKF as a Monte Carlo approach to Kalman filtering
• Complete predict and update steps with mathematical formulations
• 9-step algorithm with ensemble mean calculations, covariance matrices, and Kalman gain

2. Filter Design

• State vector specification: [x, y, φ, v]ᵀ (position, orientation, velocity)
• Input vector: [v, ω]ᵀ (linear velocity, angular velocity)
• Observation vector: [d, θ, x_lm, y_lm] (distance, bearing, landmark positions)
• Noise covariance matrices R and Q

3. Motion Model

• Continuous-time robot dynamics equations
• Discretized motion model with state transition matrix F and control matrix B
• Complete matrix formulations matching the code implementation

4. Observation Model

• Landmark position estimation in global frame
• Distance and bearing measurements from RFID tags

5. Advantages of EnKF

• No Jacobian computation required (unlike EKF)
• Handles non-Gaussian distributions
• Computationally efficient for high-dimensional systems
• Easy to parallelize

6. References

• Links to key papers and Probabilistic Robotics book

Style Consistency

The documentation follows the same structure and formatting as other localization methods in the repository (Extended Kalman Filter, Particle Filter, etc.) to maintain consistency across the documentation.

Note

The original documentation directory is named "ensamble" (with a typo), but I maintained this naming to avoid breaking existing links and references. The documentation content itself uses the correct spelling "Ensemble".

Original prompt

ensemble_kalman_filter.pyのコードを見て、docディレクトリの下のensemble kalman filterのドキュメントを追加するPRを作成してください。

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[AtsushiSakai]

@codex review

[chatgpt-codex-connector]

Codex Review: Didn't find any major issues. You're on a roll.

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[AtsushiSakai]

@rsasaki0109 Can you review this PR?

[rsasaki0109]

@AtsushiSakai
Hello.
I’ve reviewed both the document and the code, and I don’t see any issues.
I don’t have permission to approve it, so I haven’t done the approval.