mirror of
https://github.com/AtsushiSakai/PythonRobotics.git
synced 2026-01-14 09:08:01 -05:00
d34f3ca7fa
* clean up SLAM docs * clean up SLAM docs * clean up SLAM docs * clean up SLAM docs * clean up SLAM docs * clean up SLAM docs * clean up SLAM docs * clean up SLAM docs * clean up SLAM docs * clean up SLAM docs * clean up SLAM docs * clean up SLAM docs * clean up SLAM docs * clean up SLAM docs
92 lines
2.7 KiB
ReStructuredText
92 lines
2.7 KiB
ReStructuredText
.. _localization:
|
|
|
|
Localization
|
|
============
|
|
|
|
.. include:: extended_kalman_filter_localization.rst
|
|
|
|
|
|
Unscented Kalman Filter localization
|
|
------------------------------------
|
|
|
|
|2|
|
|
|
|
This is a sensor fusion localization with Unscented Kalman Filter(UKF).
|
|
|
|
The lines and points are same meaning of the EKF simulation.
|
|
|
|
References:
|
|
~~~~~~~~~~~
|
|
|
|
- `Discriminatively Trained Unscented Kalman Filter for Mobile Robot
|
|
Localization`_
|
|
|
|
Particle filter localization
|
|
----------------------------
|
|
|
|
|3|
|
|
|
|
This is a sensor fusion localization with Particle Filter(PF).
|
|
|
|
The blue line is true trajectory, the black line is dead reckoning
|
|
trajectory,
|
|
|
|
and the red line is estimated trajectory with PF.
|
|
|
|
It is assumed that the robot can measure a distance from landmarks
|
|
(RFID).
|
|
|
|
This measurements are used for PF localization.
|
|
|
|
How to calculate covariance matrix from particles
|
|
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
|
|
|
The covariance matrix :math:`\Xi` from particle information is calculated by the following equation:
|
|
|
|
.. math:: \Xi_{j,k}=\frac{1}{1-\sum^N_{i=1}(w^i)^2}\sum^N_{i=1}w^i(x^i_j-\mu_j)(x^i_k-\mu_k)
|
|
|
|
- :math:`\Xi_{j,k}` is covariance matrix element at row :math:`i` and column :math:`k`.
|
|
|
|
- :math:`w^i` is the weight of the :math:`i` th particle.
|
|
|
|
- :math:`x^i_j` is the :math:`j` th state of the :math:`i` th particle.
|
|
|
|
- :math:`\mu_j` is the :math:`j` th mean state of particles.
|
|
|
|
References:
|
|
~~~~~~~~~~~
|
|
|
|
- `PROBABILISTIC ROBOTICS`_
|
|
- `Improving the particle filter in high dimensions using conjugate artificial process noise`_
|
|
|
|
Histogram filter localization
|
|
-----------------------------
|
|
|
|
|4|
|
|
|
|
This is a 2D localization example with Histogram filter.
|
|
|
|
The red cross is true position, black points are RFID positions.
|
|
|
|
The blue grid shows a position probability of histogram filter.
|
|
|
|
In this simulation, x,y are unknown, yaw is known.
|
|
|
|
The filter integrates speed input and range observations from RFID for
|
|
localization.
|
|
|
|
Initial position is not needed.
|
|
|
|
References:
|
|
~~~~~~~~~~~
|
|
|
|
- `PROBABILISTIC ROBOTICS`_
|
|
|
|
.. _PROBABILISTIC ROBOTICS: http://www.probabilistic-robotics.org/
|
|
.. _Discriminatively Trained Unscented Kalman Filter for Mobile Robot Localization: https://www.researchgate.net/publication/267963417_Discriminatively_Trained_Unscented_Kalman_Filter_for_Mobile_Robot_Localization
|
|
.. _Improving the particle filter in high dimensions using conjugate artificial process noise: https://arxiv.org/pdf/1801.07000.pdf
|
|
|
|
.. |2| image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/Localization/unscented_kalman_filter/animation.gif
|
|
.. |3| image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/Localization/particle_filter/animation.gif
|
|
.. |4| image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/Localization/histogram_filter/animation.gif
|