unscented_transform

Copyright 2015 Roger R Labbe Jr.

FilterPy library. http://github.com/rlabbe/filterpy

Documentation at: https://filterpy.readthedocs.org

Supporting book at: https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python

This is licensed under an MIT license. See the readme.MD file for more information.

filterpy.kalman.unscented_transform(sigmas, Wm, Wc, noise_cov=None, mean_fn=None, residual_fn=None)[source]

Computes unscented transform of a set of sigma points and weights. returns the mean and covariance in a tuple.

Parameters:

sigmas: ndarray [#sigmas per dimension, dimension]

2D array of sigma points.

Wm : ndarray [# sigmas per dimension]

Weights for the mean. Must sum to 1.

Wc : ndarray [# sigmas per dimension]

Weights for the covariance. Must sum to 1.

noise_cov : ndarray, optional

noise matrix added to the final computed covariance matrix.

mean_fn : callable (sigma_points, weights), optional

Function that computes the mean of the provided sigma points and weights. Use this if your state variable contains nonlinear values such as angles which cannot be summed.

def state_mean(sigmas, Wm):
    x = np.zeros(3)
    sum_sin, sum_cos = 0., 0.

    for i in range(len(sigmas)):
        s = sigmas[i]
        x[0] += s[0] * Wm[i]
        x[1] += s[1] * Wm[i]
        sum_sin += sin(s[2])*Wm[i]
        sum_cos += cos(s[2])*Wm[i]
    x[2] = atan2(sum_sin, sum_cos)
    return x

residual_fn : callable (x, y), optional

Function that computes the residual (difference) between x and y. You will have to supply this if your state variable cannot support subtraction, such as angles (359-1 degreees is 2, not 358). x and y are state vectors, not scalars.

def residual(a, b):
    y = a[0] - b[0]
    y = y % (2 * np.pi)
    if y > np.pi:
        y -= 2*np.pi
    return y
Returns:

x : ndarray [dimension]

Mean of the sigma points after passing through the transform.

P : ndarray

covariance of the sigma points after passing throgh the transform.