Houses the parameters required for performing Bayesian filtering. More...

#include <filter.h>

Public Attributes
unsigned short	id

unsigned short	barcode

state_t	state_estimate = state_t::Zero()
	Estimated robot state - x coordinate [m], y-coordinate [m], and orientation (heading) [rad]: 3x1 matrix.

measurement_t	measurement = measurement_t::Zero()
	Recieved range and bearing measurement: 2x1 matrix.

measurement_t	innovation = measurement_t::Zero()
	The difference between the measurement recieved by the sensor and the predicted measurement based on the vehicles' states.

measurementCovariance_t	innovation_covariance
	Measurement innovation covariance matrix: 2x2 matrix.

augmentedState_t	estimation_residual = augmentedState_t::Zero()
	The difference between the prior and posterior state estimtes.

covariance_t	error_covariance = covariance_t::Identity() * 0.001
	Estimation Error Covariance: 3x3 matrix.

kalmanGain_t	kalman_gain = kalmanGain_t::Zero()
	Kalman gain: 5x2 matrix.

processCovariance_t	process_noise = processCovariance_t::Zero()
	Odometry process noise covariance matrix: 2x2 matrix.

measurementCovariance_t	measurement_noise = measurementCovariance_t::Zero()
	Measurement noise covariance matrix: 2x2 matrix.

motionJacobian_t	motion_jacobian = motionJacobian_t::Zero()
	Jacobian matrix of the motion model evaluated in terms of the systems states: x, y and orientation.

processJacobian_t	process_jacobian = processJacobian_t::Zero()
	Jacobian matrix of the motion model evaluated in terms of the process inputs.

measurementJacobian_t	measurement_jacobian = measurementJacobian_t::Zero()
	Jacobian of the measurement model: 2 x 6 matrix.

state_t	information_vector = state_t::Zero()
	Information vector: 3x1 matrix.

precision_t	precision_matrix = error_covariance.inverse()
	Precision matrix: 3x3 matrix.

Detailed Description

Houses the parameters required for performing Bayesian filtering.

Member Data Documentation

◆ barcode

unsigned short Filter::EstimationParameters::barcode

◆ error_covariance

covariance_t Filter::EstimationParameters::error_covariance = covariance_t::Identity() * 0.001

Estimation Error Covariance: 3x3 matrix.

There is a high certainty in the prior value of system state, therefore the prior estimation error covariance is initialised to a small value.

◆ estimation_residual

augmentedState_t Filter::EstimationParameters::estimation_residual = augmentedState_t::Zero()

The difference between the prior and posterior state estimtes.

The estimation residual is defined by the expresssion:

\[\delta \mathbf{x}_k = \mathbf{x}_{k\mid k-1} - \mathbf{x}_{k\mid k} \]

.

◆ id

unsigned short Filter::EstimationParameters::id

◆ information_vector

state_t Filter::EstimationParameters::information_vector = state_t::Zero()

Information vector: 3x1 matrix.

Used by the information form of the (Extended) Kalman Filter. The expression of the information vector take the form:

\[\begin{align}\nabla &= \Sigma^{-1}\mathbf{x} \\ &= \Lambda \mathbf{x}\end{align}\]

, where \(\Sigma\) denotes the estimation error covariance matrix (Filter::EstimationParameters.error_covariance); \(\Lambda\) denotes the information matrix (Filter::EstimationParameters.information_vector) \(\mathbf{x}\) denotes the state of the system (Filter::EstimationParameters.state_estimate).

◆ innovation

measurement_t Filter::EstimationParameters::innovation = measurement_t::Zero()

The difference between the measurement recieved by the sensor and the predicted measurement based on the vehicles' states.

The measurement residual is defined by the expression:

\[ \tilde{\mathbf{y}}_k = \mathbf{z}_k - h(\hat{\mathbf{x}}_{k\mid k-1})\]

, where \(\mathbf{z}\) is the measurement taken, and \(x_{k\mid k-1}\) is the estimated state of the robot.

◆ innovation_covariance

measurementCovariance_t Filter::EstimationParameters::innovation_covariance

Initial value:

=

measurementCovariance_t::Zero()

Measurement innovation covariance matrix: 2x2 matrix.

◆ kalman_gain

kalmanGain_t Filter::EstimationParameters::kalman_gain = kalmanGain_t::Zero()

Kalman gain: 5x2 matrix.

Note: The reason the Kalman gain matrix has 5 elements is because the cooperative localisation (positioning) requires the estimation covariances of both the ego and measured robots position [3+2]. See EKF::correction.

◆ measurement

measurement_t Filter::EstimationParameters::measurement = measurement_t::Zero()

Recieved range and bearing measurement: 2x1 matrix.

◆ measurement_jacobian

measurementJacobian_t Filter::EstimationParameters::measurement_jacobian = measurementJacobian_t::Zero()

Jacobian of the measurement model: 2 x 6 matrix.

◆ measurement_noise

measurementCovariance_t Filter::EstimationParameters::measurement_noise = measurementCovariance_t::Zero()

Measurement noise covariance matrix: 2x2 matrix.

The matrix for the measurement noise covariance matrix take the form

\[ v = \begin{bmatrix} q_r & 0 \\ 0 & q_\phi \end{bmatrix}, \]

where \(q_r\) denotes the range noise variance; and \(\phi_r\) denotes the bearing noise variance.

Note: The measurement noise is assumed to be uncorrelated and therefore the covariance between the range and bearing is assumed to be zero.

◆ motion_jacobian

motionJacobian_t Filter::EstimationParameters::motion_jacobian = motionJacobian_t::Zero()

Jacobian matrix of the motion model evaluated in terms of the systems states: x, y and orientation.

◆ precision_matrix

precision_t Filter::EstimationParameters::precision_matrix = error_covariance.inverse()

Precision matrix: 3x3 matrix.

Used by the information form of the (Extended) Kalman Filter. The expression for the information matrix takes the form

\[\Lambda = \Sigma^{-1}\]

, where \(\Sigma\) denotes the estimation error covariance matrix (Filter::EstimationParameters.error_covariance).

◆ process_jacobian

processJacobian_t Filter::EstimationParameters::process_jacobian = processJacobian_t::Zero()

Jacobian matrix of the motion model evaluated in terms of the process inputs.

◆ process_noise

processCovariance_t Filter::EstimationParameters::process_noise = processCovariance_t::Zero()

Odometry process noise covariance matrix: 2x2 matrix.

The process noise covariance matrix is defined by the expression:

\[ w = \begin{bmatrix} q_v & 0 \\ 0 & q_\omega \end{bmatrix}, \]

where \(q_v\) denotes the forward velocity noise variance; and \(q_\omega\) denotes the angular velocity noise variance.

Note: The process noise is assumed to be uncorrelated and therefore the covariance between the forward velocity and the angular velocity is assumed to be zero.

◆ state_estimate

state_t Filter::EstimationParameters::state_estimate = state_t::Zero()

Estimated robot state - x coordinate [m], y-coordinate [m], and orientation (heading) [rad]: 3x1 matrix.

The state vector of the robot take the form

\[\begin{bmatrix} x & y & \theta \end{bmatrix}^\top, \]

where \(x\) and \(y\) denotes the robots 2D coordinates; and \(\theta \) denotes the robots heading.

The documentation for this struct was generated from the following file:

/home/dan/Code/UTIAS-Multi-Robot/Filters/include/filter.h

Public Attributes