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Reference for ultralytics/trackers/utils/kalman_filter.py

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ultralytics.trackers.utils.kalman_filter.KalmanFilterXYAH

KalmanFilterXYAH()

A KalmanFilterXYAH class for tracking bounding boxes in image space using a Kalman filter.

Implements 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, and bounding box location (x, y, a, h) is taken as a direct observation of the state space (linear observation model).

Attributes:

Name Type Description
_motion_mat ndarray

The motion matrix for the Kalman filter.

_update_mat ndarray

The update matrix for the Kalman filter.

_std_weight_position float

Standard deviation weight for position.

_std_weight_velocity float

Standard deviation weight for velocity.

Methods:

Name Description
initiate

Creates a track from an unassociated measurement.

predict

Runs the Kalman filter prediction step.

project

Projects the state distribution to measurement space.

multi_predict

Runs the Kalman filter prediction step (vectorized version).

update

Runs the Kalman filter correction step.

gating_distance

Computes the gating distance between state distribution and measurements.

Examples:

Initialize the Kalman filter and create a track from a measurement

>>> kf = KalmanFilterXYAH()
>>> measurement = np.array([100, 200, 1.5, 50])
>>> mean, covariance = kf.initiate(measurement)
>>> print(mean)
>>> print(covariance)

The Kalman filter is initialized with an 8-dimensional state space (x, y, a, h, vx, vy, va, vh), where (x, y) represents the bounding box center position, 'a' is the aspect ratio, 'h' is the height, and their respective velocities are (vx, vy, va, vh). The filter uses a constant velocity model for object motion and a linear observation model for bounding box location.

Examples:

Initialize a Kalman filter for tracking:

>>> kf = KalmanFilterXYAH()
Source code in ultralytics/trackers/utils/kalman_filter.py
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def __init__(self):
    """
    Initialize Kalman filter model matrices with motion and observation uncertainty weights.

    The Kalman filter is initialized with an 8-dimensional state space (x, y, a, h, vx, vy, va, vh), where (x, y)
    represents the bounding box center position, 'a' is the aspect ratio, 'h' is the height, and their respective
    velocities are (vx, vy, va, vh). The filter uses a constant velocity model for object motion and a linear
    observation model for bounding box location.

    Examples:
        Initialize a Kalman filter for tracking:
        >>> kf = KalmanFilterXYAH()
    """
    ndim, dt = 4, 1.0

    # 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
    self._std_weight_position = 1.0 / 20
    self._std_weight_velocity = 1.0 / 160

gating_distance

gating_distance(
    mean: ndarray,
    covariance: ndarray,
    measurements: ndarray,
    only_position: bool = False,
    metric: str = "maha",
) -> np.ndarray

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:

Name Type Description Default
mean ndarray

Mean vector over the state distribution (8 dimensional).

required
covariance ndarray

Covariance of the state distribution (8x8 dimensional).

required
measurements ndarray

An (N, 4) 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.

required
only_position bool

If True, distance computation is done with respect to box center position only.

False
metric str

The metric to use for calculating the distance. Options are 'gaussian' for the squared Euclidean distance and 'maha' for the squared Mahalanobis distance.

'maha'

Returns:

Type Description
ndarray

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

Examples:

Compute gating distance using Mahalanobis metric:

>>> kf = KalmanFilterXYAH()
>>> mean = np.array([0, 0, 1, 1, 0, 0, 0, 0])
>>> covariance = np.eye(8)
>>> measurements = np.array([[1, 1, 1, 1], [2, 2, 1, 1]])
>>> distances = kf.gating_distance(mean, covariance, measurements, only_position=False, metric="maha")
Source code in ultralytics/trackers/utils/kalman_filter.py
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def gating_distance(
    self,
    mean: np.ndarray,
    covariance: np.ndarray,
    measurements: np.ndarray,
    only_position: bool = False,
    metric: str = "maha",
) -> np.ndarray:
    """
    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.

    Args:
        mean (np.ndarray): Mean vector over the state distribution (8 dimensional).
        covariance (np.ndarray): Covariance of the state distribution (8x8 dimensional).
        measurements (np.ndarray): An (N, 4) 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 (bool): If True, distance computation is done with respect to box center position only.
        metric (str): The metric to use for calculating the distance. Options are 'gaussian' for the squared
            Euclidean distance and 'maha' for the squared Mahalanobis distance.

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

    Examples:
        Compute gating distance using Mahalanobis metric:
        >>> kf = KalmanFilterXYAH()
        >>> mean = np.array([0, 0, 1, 1, 0, 0, 0, 0])
        >>> covariance = np.eye(8)
        >>> measurements = np.array([[1, 1, 1, 1], [2, 2, 1, 1]])
        >>> distances = kf.gating_distance(mean, covariance, measurements, only_position=False, metric="maha")
    """
    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

initiate(measurement: ndarray)

Create a track from an unassociated measurement.

Parameters:

Name Type Description Default
measurement ndarray

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

required

Returns:

Type Description
ndarray

Mean vector (8-dimensional) of the new track. Unobserved velocities are initialized to 0 mean.

ndarray

Covariance matrix (8x8 dimensional) of the new track.

Examples:

>>> kf = KalmanFilterXYAH()
>>> measurement = np.array([100, 50, 1.5, 200])
>>> mean, covariance = kf.initiate(measurement)
Source code in ultralytics/trackers/utils/kalman_filter.py
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def initiate(self, measurement: np.ndarray):
    """
    Create a track from an unassociated measurement.

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

    Returns:
        (np.ndarray): Mean vector (8-dimensional) of the new track. Unobserved velocities are initialized to 0 mean.
        (np.ndarray): Covariance matrix (8x8 dimensional) of the new track.

    Examples:
        >>> kf = KalmanFilterXYAH()
        >>> measurement = np.array([100, 50, 1.5, 200])
        >>> mean, covariance = kf.initiate(measurement)
    """
    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

multi_predict(mean: ndarray, covariance: ndarray)

Run Kalman filter prediction step for multiple object states (Vectorized version).

Parameters:

Name Type Description Default
mean ndarray

The Nx8 dimensional mean matrix of the object states at the previous time step.

required
covariance ndarray

The Nx8x8 covariance matrix of the object states at the previous time step.

required

Returns:

Type Description
ndarray

Mean matrix of the predicted states with shape (N, 8).

ndarray

Covariance matrix of the predicted states with shape (N, 8, 8).

Examples:

>>> mean = np.random.rand(10, 8)  # 10 object states
>>> covariance = np.random.rand(10, 8, 8)  # Covariance matrices for 10 object states
>>> predicted_mean, predicted_covariance = kalman_filter.multi_predict(mean, covariance)
Source code in ultralytics/trackers/utils/kalman_filter.py
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def multi_predict(self, mean: np.ndarray, covariance: np.ndarray):
    """
    Run Kalman filter prediction step for multiple object states (Vectorized version).

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

    Returns:
        (np.ndarray): Mean matrix of the predicted states with shape (N, 8).
        (np.ndarray): Covariance matrix of the predicted states with shape (N, 8, 8).

    Examples:
        >>> mean = np.random.rand(10, 8)  # 10 object states
        >>> covariance = np.random.rand(10, 8, 8)  # Covariance matrices for 10 object states
        >>> predicted_mean, predicted_covariance = kalman_filter.multi_predict(mean, covariance)
    """
    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

predict(mean: ndarray, covariance: ndarray)

Run Kalman filter prediction step.

Parameters:

Name Type Description Default
mean ndarray

The 8-dimensional mean vector of the object state at the previous time step.

required
covariance ndarray

The 8x8-dimensional covariance matrix of the object state at the previous time step.

required

Returns:

Type Description
ndarray

Mean vector of the predicted state. Unobserved velocities are initialized to 0 mean.

ndarray

Covariance matrix of the predicted state.

Examples:

>>> kf = KalmanFilterXYAH()
>>> mean = np.array([0, 0, 1, 1, 0, 0, 0, 0])
>>> covariance = np.eye(8)
>>> predicted_mean, predicted_covariance = kf.predict(mean, covariance)
Source code in ultralytics/trackers/utils/kalman_filter.py
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def predict(self, mean: np.ndarray, covariance: np.ndarray):
    """
    Run Kalman filter prediction step.

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

    Returns:
        (np.ndarray): Mean vector of the predicted state. Unobserved velocities are initialized to 0 mean.
        (np.ndarray): Covariance matrix of the predicted state.

    Examples:
        >>> kf = KalmanFilterXYAH()
        >>> mean = np.array([0, 0, 1, 1, 0, 0, 0, 0])
        >>> covariance = np.eye(8)
        >>> predicted_mean, predicted_covariance = kf.predict(mean, covariance)
    """
    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(mean, self._motion_mat.T)
    covariance = np.linalg.multi_dot((self._motion_mat, covariance, self._motion_mat.T)) + motion_cov

    return mean, covariance

project

project(mean: ndarray, covariance: ndarray)

Project state distribution to measurement space.

Parameters:

Name Type Description Default
mean ndarray

The state's mean vector (8 dimensional array).

required
covariance ndarray

The state's covariance matrix (8x8 dimensional).

required

Returns:

Type Description
ndarray

Projected mean of the given state estimate.

ndarray

Projected covariance matrix of the given state estimate.

Examples:

>>> kf = KalmanFilterXYAH()
>>> mean = np.array([0, 0, 1, 1, 0, 0, 0, 0])
>>> covariance = np.eye(8)
>>> projected_mean, projected_covariance = kf.project(mean, covariance)
Source code in ultralytics/trackers/utils/kalman_filter.py
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def project(self, mean: np.ndarray, covariance: np.ndarray):
    """
    Project state distribution to measurement space.

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

    Returns:
        (np.ndarray): Projected mean of the given state estimate.
        (np.ndarray): Projected covariance matrix of the given state estimate.

    Examples:
        >>> kf = KalmanFilterXYAH()
        >>> mean = np.array([0, 0, 1, 1, 0, 0, 0, 0])
        >>> covariance = np.eye(8)
        >>> projected_mean, projected_covariance = kf.project(mean, covariance)
    """
    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

update(mean: ndarray, covariance: ndarray, measurement: ndarray)

Run Kalman filter correction step.

Parameters:

Name Type Description Default
mean ndarray

The predicted state's mean vector (8 dimensional).

required
covariance ndarray

The state's covariance matrix (8x8 dimensional).

required
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.

required

Returns:

Type Description
ndarray

Measurement-corrected state mean.

ndarray

Measurement-corrected state covariance.

Examples:

>>> kf = KalmanFilterXYAH()
>>> mean = np.array([0, 0, 1, 1, 0, 0, 0, 0])
>>> covariance = np.eye(8)
>>> measurement = np.array([1, 1, 1, 1])
>>> new_mean, new_covariance = kf.update(mean, covariance, measurement)
Source code in ultralytics/trackers/utils/kalman_filter.py
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def update(self, mean: np.ndarray, covariance: np.ndarray, measurement: np.ndarray):
    """
    Run Kalman filter correction step.

    Args:
        mean (np.ndarray): The predicted state's mean vector (8 dimensional).
        covariance (np.ndarray): The state's covariance matrix (8x8 dimensional).
        measurement (np.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:
        (np.ndarray): Measurement-corrected state mean.
        (np.ndarray): Measurement-corrected state covariance.

    Examples:
        >>> kf = KalmanFilterXYAH()
        >>> mean = np.array([0, 0, 1, 1, 0, 0, 0, 0])
        >>> covariance = np.eye(8)
        >>> measurement = np.array([1, 1, 1, 1])
        >>> new_mean, new_covariance = kf.update(mean, covariance, measurement)
    """
    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

KalmanFilterXYWH()

Bases: KalmanFilterXYAH

A KalmanFilterXYWH class for tracking bounding boxes in image space using a Kalman filter.

Implements a Kalman filter for tracking bounding boxes with state space (x, y, w, h, vx, vy, vw, vh), where (x, y) is the center position, w is the width, h is the height, and vx, vy, vw, vh are their respective velocities. The object motion follows a constant velocity model, and the bounding box location (x, y, w, h) is taken as a direct observation of the state space (linear observation model).

Attributes:

Name Type Description
_motion_mat ndarray

The motion matrix for the Kalman filter.

_update_mat ndarray

The update matrix for the Kalman filter.

_std_weight_position float

Standard deviation weight for position.

_std_weight_velocity float

Standard deviation weight for velocity.

Methods:

Name Description
initiate

Creates a track from an unassociated measurement.

predict

Runs the Kalman filter prediction step.

project

Projects the state distribution to measurement space.

multi_predict

Runs the Kalman filter prediction step in a vectorized manner.

update

Runs the Kalman filter correction step.

Examples:

Create a Kalman filter and initialize a track

>>> kf = KalmanFilterXYWH()
>>> measurement = np.array([100, 50, 20, 40])
>>> mean, covariance = kf.initiate(measurement)
>>> print(mean)
>>> print(covariance)
Source code in ultralytics/trackers/utils/kalman_filter.py
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def __init__(self):
    """
    Initialize Kalman filter model matrices with motion and observation uncertainty weights.

    The Kalman filter is initialized with an 8-dimensional state space (x, y, a, h, vx, vy, va, vh), where (x, y)
    represents the bounding box center position, 'a' is the aspect ratio, 'h' is the height, and their respective
    velocities are (vx, vy, va, vh). The filter uses a constant velocity model for object motion and a linear
    observation model for bounding box location.

    Examples:
        Initialize a Kalman filter for tracking:
        >>> kf = KalmanFilterXYAH()
    """
    ndim, dt = 4, 1.0

    # 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
    self._std_weight_position = 1.0 / 20
    self._std_weight_velocity = 1.0 / 160

initiate

initiate(measurement: ndarray)

Create track from unassociated measurement.

Parameters:

Name Type Description Default
measurement ndarray

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

required

Returns:

Type Description
ndarray

Mean vector (8 dimensional) of the new track. Unobserved velocities are initialized to 0 mean.

ndarray

Covariance matrix (8x8 dimensional) of the new track.

Examples:

>>> kf = KalmanFilterXYWH()
>>> measurement = np.array([100, 50, 20, 40])
>>> mean, covariance = kf.initiate(measurement)
>>> print(mean)
[100.  50.  20.  40.   0.   0.   0.   0.]
>>> print(covariance)
[[ 4.  0.  0.  0.  0.  0.  0.  0.]
 [ 0.  4.  0.  0.  0.  0.  0.  0.]
 [ 0.  0.  4.  0.  0.  0.  0.  0.]
 [ 0.  0.  0.  4.  0.  0.  0.  0.]
 [ 0.  0.  0.  0.  0.25  0.  0.  0.]
 [ 0.  0.  0.  0.  0.  0.25  0.  0.]
 [ 0.  0.  0.  0.  0.  0.  0.25  0.]
 [ 0.  0.  0.  0.  0.  0.  0.  0.25]]
Source code in ultralytics/trackers/utils/kalman_filter.py
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def initiate(self, measurement: np.ndarray):
    """
    Create track from unassociated measurement.

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

    Returns:
        (np.ndarray): Mean vector (8 dimensional) of the new track. Unobserved velocities are initialized to 0 mean.
        (np.ndarray): Covariance matrix (8x8 dimensional) of the new track.

    Examples:
        >>> kf = KalmanFilterXYWH()
        >>> measurement = np.array([100, 50, 20, 40])
        >>> mean, covariance = kf.initiate(measurement)
        >>> print(mean)
        [100.  50.  20.  40.   0.   0.   0.   0.]
        >>> print(covariance)
        [[ 4.  0.  0.  0.  0.  0.  0.  0.]
         [ 0.  4.  0.  0.  0.  0.  0.  0.]
         [ 0.  0.  4.  0.  0.  0.  0.  0.]
         [ 0.  0.  0.  4.  0.  0.  0.  0.]
         [ 0.  0.  0.  0.  0.25  0.  0.  0.]
         [ 0.  0.  0.  0.  0.  0.25  0.  0.]
         [ 0.  0.  0.  0.  0.  0.  0.25  0.]
         [ 0.  0.  0.  0.  0.  0.  0.  0.25]]
    """
    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

multi_predict(mean, covariance)

Run Kalman filter prediction step (Vectorized version).

Parameters:

Name Type Description Default
mean ndarray

The Nx8 dimensional mean matrix of the object states at the previous time step.

required
covariance ndarray

The Nx8x8 covariance matrix of the object states at the previous time step.

required

Returns:

Type Description
ndarray

Mean matrix of the predicted states with shape (N, 8).

ndarray

Covariance matrix of the predicted states with shape (N, 8, 8).

Examples:

>>> mean = np.random.rand(5, 8)  # 5 objects with 8-dimensional state vectors
>>> covariance = np.random.rand(5, 8, 8)  # 5 objects with 8x8 covariance matrices
>>> kf = KalmanFilterXYWH()
>>> predicted_mean, predicted_covariance = kf.multi_predict(mean, covariance)
Source code in ultralytics/trackers/utils/kalman_filter.py
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def multi_predict(self, mean, covariance):
    """
    Run Kalman filter prediction step (Vectorized version).

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

    Returns:
        (np.ndarray): Mean matrix of the predicted states with shape (N, 8).
        (np.ndarray): Covariance matrix of the predicted states with shape (N, 8, 8).

    Examples:
        >>> mean = np.random.rand(5, 8)  # 5 objects with 8-dimensional state vectors
        >>> covariance = np.random.rand(5, 8, 8)  # 5 objects with 8x8 covariance matrices
        >>> kf = KalmanFilterXYWH()
        >>> predicted_mean, predicted_covariance = kf.multi_predict(mean, covariance)
    """
    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

predict(mean, covariance)

Run Kalman filter prediction step.

Parameters:

Name Type Description Default
mean ndarray

The 8-dimensional mean vector of the object state at the previous time step.

required
covariance ndarray

The 8x8-dimensional covariance matrix of the object state at the previous time step.

required

Returns:

Type Description
ndarray

Mean vector of the predicted state. Unobserved velocities are initialized to 0 mean.

ndarray

Covariance matrix of the predicted state.

Examples:

>>> kf = KalmanFilterXYWH()
>>> mean = np.array([0, 0, 1, 1, 0, 0, 0, 0])
>>> covariance = np.eye(8)
>>> predicted_mean, predicted_covariance = kf.predict(mean, covariance)
Source code in ultralytics/trackers/utils/kalman_filter.py
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def predict(self, mean, covariance):
    """
    Run Kalman filter prediction step.

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

    Returns:
        (np.ndarray): Mean vector of the predicted state. Unobserved velocities are initialized to 0 mean.
        (np.ndarray): Covariance matrix of the predicted state.

    Examples:
        >>> kf = KalmanFilterXYWH()
        >>> mean = np.array([0, 0, 1, 1, 0, 0, 0, 0])
        >>> covariance = np.eye(8)
        >>> predicted_mean, predicted_covariance = kf.predict(mean, covariance)
    """
    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

project(mean, covariance)

Project state distribution to measurement space.

Parameters:

Name Type Description Default
mean ndarray

The state's mean vector (8 dimensional array).

required
covariance ndarray

The state's covariance matrix (8x8 dimensional).

required

Returns:

Type Description
ndarray

Projected mean of the given state estimate.

ndarray

Projected covariance matrix of the given state estimate.

Examples:

>>> kf = KalmanFilterXYWH()
>>> mean = np.array([0, 0, 1, 1, 0, 0, 0, 0])
>>> covariance = np.eye(8)
>>> projected_mean, projected_cov = kf.project(mean, covariance)
Source code in ultralytics/trackers/utils/kalman_filter.py
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def project(self, mean, covariance):
    """
    Project state distribution to measurement space.

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

    Returns:
        (np.ndarray): Projected mean of the given state estimate.
        (np.ndarray): Projected covariance matrix of the given state estimate.

    Examples:
        >>> kf = KalmanFilterXYWH()
        >>> mean = np.array([0, 0, 1, 1, 0, 0, 0, 0])
        >>> covariance = np.eye(8)
        >>> projected_mean, projected_cov = kf.project(mean, covariance)
    """
    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

update(mean, covariance, measurement)

Run Kalman filter correction step.

Parameters:

Name Type Description Default
mean ndarray

The predicted state's mean vector (8 dimensional).

required
covariance ndarray

The state's covariance matrix (8x8 dimensional).

required
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.

required

Returns:

Type Description
ndarray

Measurement-corrected state mean.

ndarray

Measurement-corrected state covariance.

Examples:

>>> kf = KalmanFilterXYWH()
>>> mean = np.array([0, 0, 1, 1, 0, 0, 0, 0])
>>> covariance = np.eye(8)
>>> measurement = np.array([0.5, 0.5, 1.2, 1.2])
>>> new_mean, new_covariance = kf.update(mean, covariance, measurement)
Source code in ultralytics/trackers/utils/kalman_filter.py
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def update(self, mean, covariance, measurement):
    """
    Run Kalman filter correction step.

    Args:
        mean (np.ndarray): The predicted state's mean vector (8 dimensional).
        covariance (np.ndarray): The state's covariance matrix (8x8 dimensional).
        measurement (np.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:
        (np.ndarray): Measurement-corrected state mean.
        (np.ndarray): Measurement-corrected state covariance.

    Examples:
        >>> kf = KalmanFilterXYWH()
        >>> mean = np.array([0, 0, 1, 1, 0, 0, 0, 0])
        >>> covariance = np.eye(8)
        >>> measurement = np.array([0.5, 0.5, 1.2, 1.2])
        >>> new_mean, new_covariance = kf.update(mean, covariance, measurement)
    """
    return super().update(mean, covariance, measurement)





📅 Created 1 year ago ✏️ Updated 7 months ago