SigmaPoints

class SigmaPoints(alpha=1, kappa=0, beta=2, **kwargs)[source]

Helper class that defines sigma points.

Notes

This can be interpretted as a speacial case of the Quadrature points. See [20] for details.

alpha

Tunig parameter, influences the spread of sigma points about the mean. In range (0, 1]. The default is 1.

kappa

Tunig parameter, influences the spread of sigma points about the mean. In range [0, inf]. The default is 0.

beta

Tunig parameter for distribution type. In range [0, Inf]. Defaults to 2 which is ideal for Gaussians.

Methods

`__init__`
`init_weights`	Initializes the weights based on other parameters.
`plot_points`	Plots the weighted points.
`update_points`	Updates the sigma points given some initial point and covariance.

Attributes

`cov`	Covariance of the points, accounting for the weights.
`lam`	Read only derived parameter of the sigma points.
`mean`	Mean of the points, accounting for the weights.
`num_points`	Read only expected number of points.
`weights_cov`	Wights for calculating the covariance.
`weights_mean`	Wights for calculating the mean.

init_weights()[source]

Initializes the weights based on other parameters.

This should be called to setup the weight vectors after setting alpha, kappa, beta, and n.

plot_points(inds, x_lbl='X Position', y_lbl='Y Position', ttl='Weighted Positions', size_factor=10000, **kwargs)

Plots the weighted points.

Keywrod arguments are processed with gncpy.plotting.init_plotting_opts(). This function implements

f_hndl

Any title/axis/text options

Parameters:

inds (list or int) – Indices of the point vector to plot. Can be a list of at most 2 elements. If only 1 is given a bar chart is created.
x_lbl (string, optional) – Label for the x-axis. The default is ‘X Position’.
y_lbl (string, optional) – Label for the y-axis. The default is ‘Y Position’.
ttl (string, optional) – Title of the plot. The default is ‘Weighted positions’.
size_factor (int, optional) – Factor to multiply the weight by when determining the marker size. Only used if plotting 2 indices. The default is 100**2.
**kwargs (dict) – Additional standard plotting options.

Returns:

fig – Handle to the figure used.

Return type:

matplotlib figure handle

update_points(x, scale, have_sqrt=False)[source]

Updates the sigma points given some initial point and covariance.

Parameters:

x (N x 1 numpy array) – Point to represent by sigma points.
scale (N x N numpy array) – Covariance or square root of the covariance matrix of the given point.
have_sqrt (bool) – Optional flag indicating if the square root of the matrix was supplied. The default is False.

Return type:

None.