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Reference for ultralytics/trackers/utils/kalman_filter.py

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Full source code for this file is available at https://github.com/ultralytics/ultralytics/blob/main/ultralytics/trackers/utils/kalman_filter.py. Help us fix any issues you see by submitting a Pull Request 🛠️. Thank you 🙏!


ultralytics.trackers.utils.kalman_filter.KalmanFilterXYAH

For bytetrack. A simple Kalman filter for tracking bounding boxes in image space.

The 8-dimensional state space (x, y, a, h, vx, vy, va, vh) contains the bounding box center position (x, y), aspect ratio a, height h, and their respective velocities.

Object motion follows a constant velocity model. The bounding box location (x, y, a, h) is taken as direct observation of the state space (linear observation model).

Source code in ultralytics/trackers/utils/kalman_filter.py
class KalmanFilterXYAH:
    """
    For bytetrack. A simple Kalman filter for tracking bounding boxes in image space.

    The 8-dimensional state space (x, y, a, h, vx, vy, va, vh) contains the bounding box center position (x, y),
    aspect ratio a, height h, and their respective velocities.

    Object motion follows a constant velocity model. The bounding box location (x, y, a, h) is taken as direct
    observation of the state space (linear observation model).
    """

    def __init__(self):
        """Initialize Kalman filter model matrices with motion and observation uncertainty weights."""
        ndim, dt = 4, 1.

        # Create Kalman filter model matrices.
        self._motion_mat = np.eye(2 * ndim, 2 * ndim)
        for i in range(ndim):
            self._motion_mat[i, ndim + i] = dt
        self._update_mat = np.eye(ndim, 2 * ndim)

        # Motion and observation uncertainty are chosen relative to the current state estimate. These weights control
        # the amount of uncertainty in the model. This is a bit hacky.
        self._std_weight_position = 1. / 20
        self._std_weight_velocity = 1. / 160

    def initiate(self, measurement):
        """
        Create track from unassociated measurement.

        Parameters
        ----------
        measurement : ndarray
            Bounding box coordinates (x, y, a, h) with center position (x, y),
            aspect ratio a, and height h.

        Returns
        -------
        (ndarray, ndarray)
            Returns the mean vector (8 dimensional) and covariance matrix (8x8
            dimensional) of the new track. Unobserved velocities are initialized
            to 0 mean.
        """
        mean_pos = measurement
        mean_vel = np.zeros_like(mean_pos)
        mean = np.r_[mean_pos, mean_vel]

        std = [
            2 * self._std_weight_position * measurement[3], 2 * self._std_weight_position * measurement[3], 1e-2,
            2 * self._std_weight_position * measurement[3], 10 * self._std_weight_velocity * measurement[3],
            10 * self._std_weight_velocity * measurement[3], 1e-5, 10 * self._std_weight_velocity * measurement[3]]
        covariance = np.diag(np.square(std))
        return mean, covariance

    def predict(self, mean, covariance):
        """
        Run Kalman filter prediction step.

        Parameters
        ----------
        mean : ndarray
            The 8 dimensional mean vector of the object state at the previous time step.
        covariance : ndarray
            The 8x8 dimensional covariance matrix of the object state at the previous time step.

        Returns
        -------
        (ndarray, ndarray)
            Returns the mean vector and covariance matrix of the predicted state. Unobserved velocities are
            initialized to 0 mean.
        """
        std_pos = [
            self._std_weight_position * mean[3], self._std_weight_position * mean[3], 1e-2,
            self._std_weight_position * mean[3]]
        std_vel = [
            self._std_weight_velocity * mean[3], self._std_weight_velocity * mean[3], 1e-5,
            self._std_weight_velocity * mean[3]]
        motion_cov = np.diag(np.square(np.r_[std_pos, std_vel]))

        # mean = np.dot(self._motion_mat, mean)
        mean = np.dot(mean, self._motion_mat.T)
        covariance = np.linalg.multi_dot((self._motion_mat, covariance, self._motion_mat.T)) + motion_cov

        return mean, covariance

    def project(self, mean, covariance):
        """
        Project state distribution to measurement space.

        Parameters
        ----------
        mean : ndarray
            The state's mean vector (8 dimensional array).
        covariance : ndarray
            The state's covariance matrix (8x8 dimensional).

        Returns
        -------
        (ndarray, ndarray)
            Returns the projected mean and covariance matrix of the given state estimate.
        """
        std = [
            self._std_weight_position * mean[3], self._std_weight_position * mean[3], 1e-1,
            self._std_weight_position * mean[3]]
        innovation_cov = np.diag(np.square(std))

        mean = np.dot(self._update_mat, mean)
        covariance = np.linalg.multi_dot((self._update_mat, covariance, self._update_mat.T))
        return mean, covariance + innovation_cov

    def multi_predict(self, mean, covariance):
        """
        Run Kalman filter prediction step (Vectorized version).

        Parameters
        ----------
        mean : ndarray
            The Nx8 dimensional mean matrix of the object states at the previous time step.
        covariance : ndarray
            The Nx8x8 dimensional covariance matrix of the object states at the previous time step.

        Returns
        -------
        (ndarray, ndarray)
            Returns the mean vector and covariance matrix of the predicted state. Unobserved velocities are
            initialized to 0 mean.
        """
        std_pos = [
            self._std_weight_position * mean[:, 3], self._std_weight_position * mean[:, 3],
            1e-2 * np.ones_like(mean[:, 3]), self._std_weight_position * mean[:, 3]]
        std_vel = [
            self._std_weight_velocity * mean[:, 3], self._std_weight_velocity * mean[:, 3],
            1e-5 * np.ones_like(mean[:, 3]), self._std_weight_velocity * mean[:, 3]]
        sqr = np.square(np.r_[std_pos, std_vel]).T

        motion_cov = [np.diag(sqr[i]) for i in range(len(mean))]
        motion_cov = np.asarray(motion_cov)

        mean = np.dot(mean, self._motion_mat.T)
        left = np.dot(self._motion_mat, covariance).transpose((1, 0, 2))
        covariance = np.dot(left, self._motion_mat.T) + motion_cov

        return mean, covariance

    def update(self, mean, covariance, measurement):
        """
        Run Kalman filter correction step.

        Parameters
        ----------
        mean : ndarray
            The predicted state's mean vector (8 dimensional).
        covariance : ndarray
            The state's covariance matrix (8x8 dimensional).
        measurement : ndarray
            The 4 dimensional measurement vector (x, y, a, h), where (x, y) is the center position, a the aspect
            ratio, and h the height of the bounding box.

        Returns
        -------
        (ndarray, ndarray)
            Returns the measurement-corrected state distribution.
        """
        projected_mean, projected_cov = self.project(mean, covariance)

        chol_factor, lower = scipy.linalg.cho_factor(projected_cov, lower=True, check_finite=False)
        kalman_gain = scipy.linalg.cho_solve((chol_factor, lower),
                                             np.dot(covariance, self._update_mat.T).T,
                                             check_finite=False).T
        innovation = measurement - projected_mean

        new_mean = mean + np.dot(innovation, kalman_gain.T)
        new_covariance = covariance - np.linalg.multi_dot((kalman_gain, projected_cov, kalman_gain.T))
        return new_mean, new_covariance

    def gating_distance(self, mean, covariance, measurements, only_position=False, metric='maha'):
        """
        Compute gating distance between state distribution and measurements. A suitable distance threshold can be
        obtained from `chi2inv95`. If `only_position` is False, the chi-square distribution has 4 degrees of
        freedom, otherwise 2.

        Parameters
        ----------
        mean : ndarray
            Mean vector over the state distribution (8 dimensional).
        covariance : ndarray
            Covariance of the state distribution (8x8 dimensional).
        measurements : ndarray
            An Nx4 dimensional matrix of N measurements, each in format (x, y, a, h) where (x, y) is the bounding box
            center position, a the aspect ratio, and h the height.
        only_position : Optional[bool]
            If True, distance computation is done with respect to the bounding box center position only.

        Returns
        -------
        ndarray
            Returns an array of length N, where the i-th element contains the squared Mahalanobis distance between
            (mean, covariance) and `measurements[i]`.
        """
        mean, covariance = self.project(mean, covariance)
        if only_position:
            mean, covariance = mean[:2], covariance[:2, :2]
            measurements = measurements[:, :2]

        d = measurements - mean
        if metric == 'gaussian':
            return np.sum(d * d, axis=1)
        elif metric == 'maha':
            cholesky_factor = np.linalg.cholesky(covariance)
            z = scipy.linalg.solve_triangular(cholesky_factor, d.T, lower=True, check_finite=False, overwrite_b=True)
            return np.sum(z * z, axis=0)  # square maha
        else:
            raise ValueError('invalid distance metric')

__init__()

Initialize Kalman filter model matrices with motion and observation uncertainty weights.

Source code in ultralytics/trackers/utils/kalman_filter.py
def __init__(self):
    """Initialize Kalman filter model matrices with motion and observation uncertainty weights."""
    ndim, dt = 4, 1.

    # Create Kalman filter model matrices.
    self._motion_mat = np.eye(2 * ndim, 2 * ndim)
    for i in range(ndim):
        self._motion_mat[i, ndim + i] = dt
    self._update_mat = np.eye(ndim, 2 * ndim)

    # Motion and observation uncertainty are chosen relative to the current state estimate. These weights control
    # the amount of uncertainty in the model. This is a bit hacky.
    self._std_weight_position = 1. / 20
    self._std_weight_velocity = 1. / 160

gating_distance(mean, covariance, measurements, only_position=False, metric='maha')

Compute gating distance between state distribution and measurements. A suitable distance threshold can be obtained from chi2inv95. If only_position is False, the chi-square distribution has 4 degrees of freedom, otherwise 2.

Parameters

mean : ndarray Mean vector over the state distribution (8 dimensional). covariance : ndarray Covariance of the state distribution (8x8 dimensional). measurements : ndarray An Nx4 dimensional matrix of N measurements, each in format (x, y, a, h) where (x, y) is the bounding box center position, a the aspect ratio, and h the height. only_position : Optional[bool] If True, distance computation is done with respect to the bounding box center position only.

Returns

ndarray Returns an array of length N, where the i-th element contains the squared Mahalanobis distance between (mean, covariance) and measurements[i].

Source code in ultralytics/trackers/utils/kalman_filter.py
def gating_distance(self, mean, covariance, measurements, only_position=False, metric='maha'):
    """
    Compute gating distance between state distribution and measurements. A suitable distance threshold can be
    obtained from `chi2inv95`. If `only_position` is False, the chi-square distribution has 4 degrees of
    freedom, otherwise 2.

    Parameters
    ----------
    mean : ndarray
        Mean vector over the state distribution (8 dimensional).
    covariance : ndarray
        Covariance of the state distribution (8x8 dimensional).
    measurements : ndarray
        An Nx4 dimensional matrix of N measurements, each in format (x, y, a, h) where (x, y) is the bounding box
        center position, a the aspect ratio, and h the height.
    only_position : Optional[bool]
        If True, distance computation is done with respect to the bounding box center position only.

    Returns
    -------
    ndarray
        Returns an array of length N, where the i-th element contains the squared Mahalanobis distance between
        (mean, covariance) and `measurements[i]`.
    """
    mean, covariance = self.project(mean, covariance)
    if only_position:
        mean, covariance = mean[:2], covariance[:2, :2]
        measurements = measurements[:, :2]

    d = measurements - mean
    if metric == 'gaussian':
        return np.sum(d * d, axis=1)
    elif metric == 'maha':
        cholesky_factor = np.linalg.cholesky(covariance)
        z = scipy.linalg.solve_triangular(cholesky_factor, d.T, lower=True, check_finite=False, overwrite_b=True)
        return np.sum(z * z, axis=0)  # square maha
    else:
        raise ValueError('invalid distance metric')

initiate(measurement)

Create track from unassociated measurement.

Parameters

measurement : ndarray Bounding box coordinates (x, y, a, h) with center position (x, y), aspect ratio a, and height h.

Returns

(ndarray, ndarray) Returns the mean vector (8 dimensional) and covariance matrix (8x8 dimensional) of the new track. Unobserved velocities are initialized to 0 mean.

Source code in ultralytics/trackers/utils/kalman_filter.py
def initiate(self, measurement):
    """
    Create track from unassociated measurement.

    Parameters
    ----------
    measurement : ndarray
        Bounding box coordinates (x, y, a, h) with center position (x, y),
        aspect ratio a, and height h.

    Returns
    -------
    (ndarray, ndarray)
        Returns the mean vector (8 dimensional) and covariance matrix (8x8
        dimensional) of the new track. Unobserved velocities are initialized
        to 0 mean.
    """
    mean_pos = measurement
    mean_vel = np.zeros_like(mean_pos)
    mean = np.r_[mean_pos, mean_vel]

    std = [
        2 * self._std_weight_position * measurement[3], 2 * self._std_weight_position * measurement[3], 1e-2,
        2 * self._std_weight_position * measurement[3], 10 * self._std_weight_velocity * measurement[3],
        10 * self._std_weight_velocity * measurement[3], 1e-5, 10 * self._std_weight_velocity * measurement[3]]
    covariance = np.diag(np.square(std))
    return mean, covariance

multi_predict(mean, covariance)

Run Kalman filter prediction step (Vectorized version).

Parameters

mean : ndarray The Nx8 dimensional mean matrix of the object states at the previous time step. covariance : ndarray The Nx8x8 dimensional covariance matrix of the object states at the previous time step.

Returns

(ndarray, ndarray) Returns the mean vector and covariance matrix of the predicted state. Unobserved velocities are initialized to 0 mean.

Source code in ultralytics/trackers/utils/kalman_filter.py
def multi_predict(self, mean, covariance):
    """
    Run Kalman filter prediction step (Vectorized version).

    Parameters
    ----------
    mean : ndarray
        The Nx8 dimensional mean matrix of the object states at the previous time step.
    covariance : ndarray
        The Nx8x8 dimensional covariance matrix of the object states at the previous time step.

    Returns
    -------
    (ndarray, ndarray)
        Returns the mean vector and covariance matrix of the predicted state. Unobserved velocities are
        initialized to 0 mean.
    """
    std_pos = [
        self._std_weight_position * mean[:, 3], self._std_weight_position * mean[:, 3],
        1e-2 * np.ones_like(mean[:, 3]), self._std_weight_position * mean[:, 3]]
    std_vel = [
        self._std_weight_velocity * mean[:, 3], self._std_weight_velocity * mean[:, 3],
        1e-5 * np.ones_like(mean[:, 3]), self._std_weight_velocity * mean[:, 3]]
    sqr = np.square(np.r_[std_pos, std_vel]).T

    motion_cov = [np.diag(sqr[i]) for i in range(len(mean))]
    motion_cov = np.asarray(motion_cov)

    mean = np.dot(mean, self._motion_mat.T)
    left = np.dot(self._motion_mat, covariance).transpose((1, 0, 2))
    covariance = np.dot(left, self._motion_mat.T) + motion_cov

    return mean, covariance

predict(mean, covariance)

Run Kalman filter prediction step.

Parameters

mean : ndarray The 8 dimensional mean vector of the object state at the previous time step. covariance : ndarray The 8x8 dimensional covariance matrix of the object state at the previous time step.

Returns

(ndarray, ndarray) Returns the mean vector and covariance matrix of the predicted state. Unobserved velocities are initialized to 0 mean.

Source code in ultralytics/trackers/utils/kalman_filter.py
def predict(self, mean, covariance):
    """
    Run Kalman filter prediction step.

    Parameters
    ----------
    mean : ndarray
        The 8 dimensional mean vector of the object state at the previous time step.
    covariance : ndarray
        The 8x8 dimensional covariance matrix of the object state at the previous time step.

    Returns
    -------
    (ndarray, ndarray)
        Returns the mean vector and covariance matrix of the predicted state. Unobserved velocities are
        initialized to 0 mean.
    """
    std_pos = [
        self._std_weight_position * mean[3], self._std_weight_position * mean[3], 1e-2,
        self._std_weight_position * mean[3]]
    std_vel = [
        self._std_weight_velocity * mean[3], self._std_weight_velocity * mean[3], 1e-5,
        self._std_weight_velocity * mean[3]]
    motion_cov = np.diag(np.square(np.r_[std_pos, std_vel]))

    # mean = np.dot(self._motion_mat, mean)
    mean = np.dot(mean, self._motion_mat.T)
    covariance = np.linalg.multi_dot((self._motion_mat, covariance, self._motion_mat.T)) + motion_cov

    return mean, covariance

project(mean, covariance)

Project state distribution to measurement space.

Parameters

mean : ndarray The state's mean vector (8 dimensional array). covariance : ndarray The state's covariance matrix (8x8 dimensional).

Returns

(ndarray, ndarray) Returns the projected mean and covariance matrix of the given state estimate.

Source code in ultralytics/trackers/utils/kalman_filter.py
def project(self, mean, covariance):
    """
    Project state distribution to measurement space.

    Parameters
    ----------
    mean : ndarray
        The state's mean vector (8 dimensional array).
    covariance : ndarray
        The state's covariance matrix (8x8 dimensional).

    Returns
    -------
    (ndarray, ndarray)
        Returns the projected mean and covariance matrix of the given state estimate.
    """
    std = [
        self._std_weight_position * mean[3], self._std_weight_position * mean[3], 1e-1,
        self._std_weight_position * mean[3]]
    innovation_cov = np.diag(np.square(std))

    mean = np.dot(self._update_mat, mean)
    covariance = np.linalg.multi_dot((self._update_mat, covariance, self._update_mat.T))
    return mean, covariance + innovation_cov

update(mean, covariance, measurement)

Run Kalman filter correction step.

Parameters

mean : ndarray The predicted state's mean vector (8 dimensional). covariance : ndarray The state's covariance matrix (8x8 dimensional). measurement : ndarray The 4 dimensional measurement vector (x, y, a, h), where (x, y) is the center position, a the aspect ratio, and h the height of the bounding box.

Returns

(ndarray, ndarray) Returns the measurement-corrected state distribution.

Source code in ultralytics/trackers/utils/kalman_filter.py
def update(self, mean, covariance, measurement):
    """
    Run Kalman filter correction step.

    Parameters
    ----------
    mean : ndarray
        The predicted state's mean vector (8 dimensional).
    covariance : ndarray
        The state's covariance matrix (8x8 dimensional).
    measurement : ndarray
        The 4 dimensional measurement vector (x, y, a, h), where (x, y) is the center position, a the aspect
        ratio, and h the height of the bounding box.

    Returns
    -------
    (ndarray, ndarray)
        Returns the measurement-corrected state distribution.
    """
    projected_mean, projected_cov = self.project(mean, covariance)

    chol_factor, lower = scipy.linalg.cho_factor(projected_cov, lower=True, check_finite=False)
    kalman_gain = scipy.linalg.cho_solve((chol_factor, lower),
                                         np.dot(covariance, self._update_mat.T).T,
                                         check_finite=False).T
    innovation = measurement - projected_mean

    new_mean = mean + np.dot(innovation, kalman_gain.T)
    new_covariance = covariance - np.linalg.multi_dot((kalman_gain, projected_cov, kalman_gain.T))
    return new_mean, new_covariance




ultralytics.trackers.utils.kalman_filter.KalmanFilterXYWH

Bases: KalmanFilterXYAH

For BoT-SORT. A simple Kalman filter for tracking bounding boxes in image space.

The 8-dimensional state space (x, y, w, h, vx, vy, vw, vh) contains the bounding box center position (x, y), width w, height h, and their respective velocities.

Object motion follows a constant velocity model. The bounding box location (x, y, w, h) is taken as direct observation of the state space (linear observation model).

Source code in ultralytics/trackers/utils/kalman_filter.py
class KalmanFilterXYWH(KalmanFilterXYAH):
    """
    For BoT-SORT. A simple Kalman filter for tracking bounding boxes in image space.

    The 8-dimensional state space (x, y, w, h, vx, vy, vw, vh) contains the bounding box center position (x, y),
    width w, height h, and their respective velocities.

    Object motion follows a constant velocity model. The bounding box location (x, y, w, h) is taken as direct
    observation of the state space (linear observation model).
    """

    def initiate(self, measurement):
        """
        Create track from unassociated measurement.

        Parameters
        ----------
        measurement : ndarray
            Bounding box coordinates (x, y, w, h) with center position (x, y), width w, and height h.

        Returns
        -------
        (ndarray, ndarray)
            Returns the mean vector (8 dimensional) and covariance matrix (8x8 dimensional) of the new track.
            Unobserved velocities are initialized to 0 mean.
        """
        mean_pos = measurement
        mean_vel = np.zeros_like(mean_pos)
        mean = np.r_[mean_pos, mean_vel]

        std = [
            2 * self._std_weight_position * measurement[2], 2 * self._std_weight_position * measurement[3],
            2 * self._std_weight_position * measurement[2], 2 * self._std_weight_position * measurement[3],
            10 * self._std_weight_velocity * measurement[2], 10 * self._std_weight_velocity * measurement[3],
            10 * self._std_weight_velocity * measurement[2], 10 * self._std_weight_velocity * measurement[3]]
        covariance = np.diag(np.square(std))
        return mean, covariance

    def predict(self, mean, covariance):
        """
        Run Kalman filter prediction step.

        Parameters
        ----------
        mean : ndarray
            The 8 dimensional mean vector of the object state at the previous time step.
        covariance : ndarray
            The 8x8 dimensional covariance matrix of the object state at the previous time step.

        Returns
        -------
        (ndarray, ndarray)
            Returns the mean vector and covariance matrix of the predicted state. Unobserved velocities are
            initialized to 0 mean.
        """
        std_pos = [
            self._std_weight_position * mean[2], self._std_weight_position * mean[3],
            self._std_weight_position * mean[2], self._std_weight_position * mean[3]]
        std_vel = [
            self._std_weight_velocity * mean[2], self._std_weight_velocity * mean[3],
            self._std_weight_velocity * mean[2], self._std_weight_velocity * mean[3]]
        motion_cov = np.diag(np.square(np.r_[std_pos, std_vel]))

        mean = np.dot(mean, self._motion_mat.T)
        covariance = np.linalg.multi_dot((self._motion_mat, covariance, self._motion_mat.T)) + motion_cov

        return mean, covariance

    def project(self, mean, covariance):
        """
        Project state distribution to measurement space.

        Parameters
        ----------
        mean : ndarray
            The state's mean vector (8 dimensional array).
        covariance : ndarray
            The state's covariance matrix (8x8 dimensional).

        Returns
        -------
        (ndarray, ndarray)
            Returns the projected mean and covariance matrix of the given state estimate.
        """
        std = [
            self._std_weight_position * mean[2], self._std_weight_position * mean[3],
            self._std_weight_position * mean[2], self._std_weight_position * mean[3]]
        innovation_cov = np.diag(np.square(std))

        mean = np.dot(self._update_mat, mean)
        covariance = np.linalg.multi_dot((self._update_mat, covariance, self._update_mat.T))
        return mean, covariance + innovation_cov

    def multi_predict(self, mean, covariance):
        """
        Run Kalman filter prediction step (Vectorized version).

        Parameters
        ----------
        mean : ndarray
            The Nx8 dimensional mean matrix of the object states at the previous time step.
        covariance : ndarray
            The Nx8x8 dimensional covariance matrix of the object states at the previous time step.

        Returns
        -------
        (ndarray, ndarray)
            Returns the mean vector and covariance matrix of the predicted state. Unobserved velocities are
            initialized to 0 mean.
        """
        std_pos = [
            self._std_weight_position * mean[:, 2], self._std_weight_position * mean[:, 3],
            self._std_weight_position * mean[:, 2], self._std_weight_position * mean[:, 3]]
        std_vel = [
            self._std_weight_velocity * mean[:, 2], self._std_weight_velocity * mean[:, 3],
            self._std_weight_velocity * mean[:, 2], self._std_weight_velocity * mean[:, 3]]
        sqr = np.square(np.r_[std_pos, std_vel]).T

        motion_cov = [np.diag(sqr[i]) for i in range(len(mean))]
        motion_cov = np.asarray(motion_cov)

        mean = np.dot(mean, self._motion_mat.T)
        left = np.dot(self._motion_mat, covariance).transpose((1, 0, 2))
        covariance = np.dot(left, self._motion_mat.T) + motion_cov

        return mean, covariance

    def update(self, mean, covariance, measurement):
        """
        Run Kalman filter correction step.

        Parameters
        ----------
        mean : ndarray
            The predicted state's mean vector (8 dimensional).
        covariance : ndarray
            The state's covariance matrix (8x8 dimensional).
        measurement : ndarray
            The 4 dimensional measurement vector (x, y, w, h), where (x, y) is the center position, w the width,
            and h the height of the bounding box.

        Returns
        -------
        (ndarray, ndarray)
            Returns the measurement-corrected state distribution.
        """
        return super().update(mean, covariance, measurement)

initiate(measurement)

Create track from unassociated measurement.

Parameters

measurement : ndarray Bounding box coordinates (x, y, w, h) with center position (x, y), width w, and height h.

Returns

(ndarray, ndarray) Returns the mean vector (8 dimensional) and covariance matrix (8x8 dimensional) of the new track. Unobserved velocities are initialized to 0 mean.

Source code in ultralytics/trackers/utils/kalman_filter.py
def initiate(self, measurement):
    """
    Create track from unassociated measurement.

    Parameters
    ----------
    measurement : ndarray
        Bounding box coordinates (x, y, w, h) with center position (x, y), width w, and height h.

    Returns
    -------
    (ndarray, ndarray)
        Returns the mean vector (8 dimensional) and covariance matrix (8x8 dimensional) of the new track.
        Unobserved velocities are initialized to 0 mean.
    """
    mean_pos = measurement
    mean_vel = np.zeros_like(mean_pos)
    mean = np.r_[mean_pos, mean_vel]

    std = [
        2 * self._std_weight_position * measurement[2], 2 * self._std_weight_position * measurement[3],
        2 * self._std_weight_position * measurement[2], 2 * self._std_weight_position * measurement[3],
        10 * self._std_weight_velocity * measurement[2], 10 * self._std_weight_velocity * measurement[3],
        10 * self._std_weight_velocity * measurement[2], 10 * self._std_weight_velocity * measurement[3]]
    covariance = np.diag(np.square(std))
    return mean, covariance

multi_predict(mean, covariance)

Run Kalman filter prediction step (Vectorized version).

Parameters

mean : ndarray The Nx8 dimensional mean matrix of the object states at the previous time step. covariance : ndarray The Nx8x8 dimensional covariance matrix of the object states at the previous time step.

Returns

(ndarray, ndarray) Returns the mean vector and covariance matrix of the predicted state. Unobserved velocities are initialized to 0 mean.

Source code in ultralytics/trackers/utils/kalman_filter.py
def multi_predict(self, mean, covariance):
    """
    Run Kalman filter prediction step (Vectorized version).

    Parameters
    ----------
    mean : ndarray
        The Nx8 dimensional mean matrix of the object states at the previous time step.
    covariance : ndarray
        The Nx8x8 dimensional covariance matrix of the object states at the previous time step.

    Returns
    -------
    (ndarray, ndarray)
        Returns the mean vector and covariance matrix of the predicted state. Unobserved velocities are
        initialized to 0 mean.
    """
    std_pos = [
        self._std_weight_position * mean[:, 2], self._std_weight_position * mean[:, 3],
        self._std_weight_position * mean[:, 2], self._std_weight_position * mean[:, 3]]
    std_vel = [
        self._std_weight_velocity * mean[:, 2], self._std_weight_velocity * mean[:, 3],
        self._std_weight_velocity * mean[:, 2], self._std_weight_velocity * mean[:, 3]]
    sqr = np.square(np.r_[std_pos, std_vel]).T

    motion_cov = [np.diag(sqr[i]) for i in range(len(mean))]
    motion_cov = np.asarray(motion_cov)

    mean = np.dot(mean, self._motion_mat.T)
    left = np.dot(self._motion_mat, covariance).transpose((1, 0, 2))
    covariance = np.dot(left, self._motion_mat.T) + motion_cov

    return mean, covariance

predict(mean, covariance)

Run Kalman filter prediction step.

Parameters

mean : ndarray The 8 dimensional mean vector of the object state at the previous time step. covariance : ndarray The 8x8 dimensional covariance matrix of the object state at the previous time step.

Returns

(ndarray, ndarray) Returns the mean vector and covariance matrix of the predicted state. Unobserved velocities are initialized to 0 mean.

Source code in ultralytics/trackers/utils/kalman_filter.py
def predict(self, mean, covariance):
    """
    Run Kalman filter prediction step.

    Parameters
    ----------
    mean : ndarray
        The 8 dimensional mean vector of the object state at the previous time step.
    covariance : ndarray
        The 8x8 dimensional covariance matrix of the object state at the previous time step.

    Returns
    -------
    (ndarray, ndarray)
        Returns the mean vector and covariance matrix of the predicted state. Unobserved velocities are
        initialized to 0 mean.
    """
    std_pos = [
        self._std_weight_position * mean[2], self._std_weight_position * mean[3],
        self._std_weight_position * mean[2], self._std_weight_position * mean[3]]
    std_vel = [
        self._std_weight_velocity * mean[2], self._std_weight_velocity * mean[3],
        self._std_weight_velocity * mean[2], self._std_weight_velocity * mean[3]]
    motion_cov = np.diag(np.square(np.r_[std_pos, std_vel]))

    mean = np.dot(mean, self._motion_mat.T)
    covariance = np.linalg.multi_dot((self._motion_mat, covariance, self._motion_mat.T)) + motion_cov

    return mean, covariance

project(mean, covariance)

Project state distribution to measurement space.

Parameters

mean : ndarray The state's mean vector (8 dimensional array). covariance : ndarray The state's covariance matrix (8x8 dimensional).

Returns

(ndarray, ndarray) Returns the projected mean and covariance matrix of the given state estimate.

Source code in ultralytics/trackers/utils/kalman_filter.py
def project(self, mean, covariance):
    """
    Project state distribution to measurement space.

    Parameters
    ----------
    mean : ndarray
        The state's mean vector (8 dimensional array).
    covariance : ndarray
        The state's covariance matrix (8x8 dimensional).

    Returns
    -------
    (ndarray, ndarray)
        Returns the projected mean and covariance matrix of the given state estimate.
    """
    std = [
        self._std_weight_position * mean[2], self._std_weight_position * mean[3],
        self._std_weight_position * mean[2], self._std_weight_position * mean[3]]
    innovation_cov = np.diag(np.square(std))

    mean = np.dot(self._update_mat, mean)
    covariance = np.linalg.multi_dot((self._update_mat, covariance, self._update_mat.T))
    return mean, covariance + innovation_cov

update(mean, covariance, measurement)

Run Kalman filter correction step.

Parameters

mean : ndarray The predicted state's mean vector (8 dimensional). covariance : ndarray The state's covariance matrix (8x8 dimensional). measurement : ndarray The 4 dimensional measurement vector (x, y, w, h), where (x, y) is the center position, w the width, and h the height of the bounding box.

Returns

(ndarray, ndarray) Returns the measurement-corrected state distribution.

Source code in ultralytics/trackers/utils/kalman_filter.py
def update(self, mean, covariance, measurement):
    """
    Run Kalman filter correction step.

    Parameters
    ----------
    mean : ndarray
        The predicted state's mean vector (8 dimensional).
    covariance : ndarray
        The state's covariance matrix (8x8 dimensional).
    measurement : ndarray
        The 4 dimensional measurement vector (x, y, w, h), where (x, y) is the center position, w the width,
        and h the height of the bounding box.

    Returns
    -------
    (ndarray, ndarray)
        Returns the measurement-corrected state distribution.
    """
    return super().update(mean, covariance, measurement)




Created 2023-07-16, Updated 2023-08-07
Authors: glenn-jocher (5), Laughing-q (1)