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 matrics 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 = []
        for i in range(len(mean)):
            motion_cov.append(np.diag(sqr[i]))
        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
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 matrics 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.
        
trackers/motdt_tracker/kalman_filter.py