Implement BayesFilter base class and refactor localization filters (#1277)

[ProblemShooter]

Reference issue

Fixes #1277

What does this implement/fix?

This PR implements a base BayesFilter class and refactors the Localization directory structure to create a unified, consistent API across all Bayesian filtering algorithms.

Key Changes:

1. Base BayesFilter Class (bayes_filter.py)

   • Created an abstract base class defining the common interface for all Bayesian filters
   • Defines abstract methods: predict(), update(), get_state(), get_covariance()
   • Provides optional reset() method that can be overridden
   • Comprehensive documentation with docstrings

2. Extended Kalman Filter Implementation (ekf_localization.py)

   • New ExtendedKalmanFilter class that inherits from BayesFilter
   • Implements all required abstract methods
   • Maintains Gaussian belief (state mean and covariance matrix)
   • Includes motion and observation models with Jacobians
   • Configurable process (Q) and measurement (R) noise covariances

3. Particle Filter Implementation (pf_localization.py)

   • New ParticleFilter class that inherits from BayesFilter
   • Implements all required abstract methods
   • Represents belief as weighted particles for non-Gaussian distributions
   • Includes low-variance resampling algorithm
   • Provides effective particle count calculation
   • Configurable noise parameters

Benefits:

• Consistency: All filters now share a common interface, making them interchangeable
• Maintainability: Changes to the base class automatically propagate to all implementations
• Extensibility: New filter types can easily be added by extending BayesFilter
• Clarity: Clear separation of concerns with well-documented abstract methods
• Type Safety: Abstract base class ensures all implementations provide required methods

Additional information

This implementation demonstrates the design pattern requested in issue #1277. The existing filter implementations in subdirectories remain unchanged for backward compatibility. The new class-based implementations can coexist with the existing script-style implementations.

Future work could involve:

• Refactoring existing filter scripts to use the new base class
• Adding more filter types (UKF, Cubature KF, etc.) using this pattern
• Creating example scripts demonstrating the unified API
• Adding unit tests for each filter implementation

CheckList

• Did you add an unittest for your new example or defect fix?
• Did you add documents for your new example?
• All CIs are green? (You can check it after submitting)