Overview

The Extend Kalman Filter Localizer estimates robust and less noisy robot pose and twist by integrating the 2D vehicle dynamics model with input ego-pose and ego-twist messages. The algorithm is designed especially for fast-moving robots such as autonomous driving systems.

Flowchart

The overall flowchart of the ekf_localizer is described below.

Features

This package includes the following features:

• Time delay compensation for input messages, which enables proper integration of input information with varying time delays. This is important especially for high-speed moving robots, such as autonomous driving vehicles. (see the following figure).
• Automatic estimation of yaw bias prevents modeling errors caused by sensor mounting angle errors, which can improve estimation accuracy.
• Mahalanobis distance gate enables probabilistic outlier detection to determine which inputs should be used or ignored.
• Smooth update, the Kalman Filter measurement update is typically performed when a measurement is obtained, but it can cause large changes in the estimated value, especially for low-frequency measurements. Since the algorithm can consider the measurement time, the measurement data can be divided into multiple pieces and integrated smoothly while maintaining consistency (see the following figure).

Launch

The ekf_localizer starts with the default parameters with the following command.

roslaunch ekf_localizer ekf_localizer.launch

The parameters and input topic names can be set in the ekf_localizer.launch file.

Node

Subscribed Topics

• measured_pose_with_covariance (geometry_msgs/PoseWithCovarianceStamped)

  Input pose source with the measurement covariance matrix.

• measured_twist_with_covariance (geometry_msgs/TwistWithCovarianceStamped)

  Input twist source with the measurement covariance matrix.

• initialpose (geometry_msgs/PoseWithCovarianceStamped)

  Initial pose for EKF. The estimated pose is initialized with zeros at the start. It is initialized with this message whenever published.

Published Topics

• ekf_odom (nav_msgs/Odometry)

  Estimated odometry.

• ekf_pose (geometry_msgs/PoseStamped)

  Estimated pose.

• ekf_pose_with_covariance (geometry_msgs/PoseWithCovarianceStamped)

  Estimated pose with covariance.

• ekf_pose_with_covariance (geometry_msgs/PoseStamped)

  Estimated pose without yawbias effect.

• ekf_pose_with_covariance_without_yawbias (geometry_msgs/PoseWithCovarianceStamped)

  Estimated pose with covariance without yawbias effect.

• ekf_twist (geometry_msgs/TwistStamped)

  Estimated twist.

• ekf_twist_with_covariance (geometry_msgs/TwistWithCovarianceStamped)

  The estimated twist with covariance.

Published TF

• base_link

  TF from “map” coordinate to estimated pose.

Functions

Predict

The current robot state is predicted from previously estimated data using a given prediction model. This calculation is called at a constant interval (predict_frequency [Hz]). The prediction equation is described at the end of this page.

Measurement Update

Before the update, the Mahalanobis distance is calculated between the measured input and the predicted state, the measurement update is not performed for inputs where the Mahalanobis distance exceeds the given threshold.

The predicted state is updated with the latest measured inputs, measured_pose, and measured_twist. The updates are performed with the same frequency as prediction, usually at a high frequency, in order to enable smooth state estimation.

Parameter description

The parameters are set in launch/ekf_localizer.launch .

For Node

For pose measurement

For twist measurement

For process noise

note: process noise for positions x & y are calculated automatically from nonlinear dynamics.

How to tune EKF parameters

0. Preliminaries

• Check header time in pose and twist message is set to sensor time appropriately, because time delay is calculated from this value. If it is difficult to set an appropriate time due to the timer synchronization problem, use twist_additional_delay and pose_additional_delay to correct the time.
• Check if the relation between measurement pose and twist is appropriate (whether the derivative of the pose has a similar value to twist). This discrepancy is caused mainly by unit error (such as confusing radian/degree) or bias noise, and it causes large estimation errors.

1. Tune sensor parameters

Set standard deviation for each sensor. The pose_measure_uncertainty_time is for the uncertainty of the header timestamp data. You can also tune a number of steps for smoothing for each observed sensor data by tuning *_smoothing_steps. Increasing the number will improve the smoothness of the estimation, but may have an adverse effect on the estimation performance.

• pose_measure_uncertainty_time
• pose_smoothing_steps
• twist_smoothing_steps

2. Tune process model parameters

• proc_stddev_vx_c : set to maximum linear acceleration
• proc_stddev_wz_c : set to maximum angular acceleration
• proc_stddev_yaw_c : This parameter describes the correlation between the yaw and yawrate. A large value means the change in yaw does not correlate to the estimated yawrate. If this is set to 0, it means the change in estimated yaw is equal to yawrate. Usually, this should be set to 0.
• proc_stddev_yaw_bias_c : This parameter is the standard deviation for the rate of change in yaw bias. In most cases, yaw bias is constant, so it can be very small, but must be non-zero.

Kalman Filter Model

kinematics model in update function

where b_k is the yawbias.

time delay model

The measurement time delay is handled by an augmented state [1] (See, Section 7.3 FIXED-LAG SMOOTHING).

Note that, although the dimension gets larger since the analytical expansion can be applied based on the specific structures of the augmented states, the computational complexity does not significantly change.

Test Result with Autoware NDT

Known issues

• In the presence of multiple inputs with yaw estimation, yaw bias b_k in the current EKF state would not make any sense, since it is intended to capture the extrinsic parameter’s calibration error of a sensor. Thus, future work includes introducing yaw bias for each sensor with yaw estimation.

reference

[1] Anderson, B. D. O., & Moore, J. B. (1979). Optimal filtering. Englewood Cliffs, NJ: Prentice-Hall.