UnscentedTransform

class probnum.filtsmooth.UnscentedTransform(dimension, spread=0.0001, priorpar=2.0, special_scale=0.0)[source]

Bases: object

Used for unscented Kalman filter.

See also p. 7 (“Unscented transform:”) of 1.

Parameters
  • dimension (int) – Spatial dimensionality

  • spread (float) – Spread of the sigma points around mean

  • priorpar (float) – Incorporate prior knowledge about distribution of x. For Gaussians, 2.0 is optimal (see link below)

  • special_scale (float) – Secondary scaling parameter. The primary parameter is computed below.

References

1

Wan, E. A. and van der Merwe, R., The Unscented Kalman Filter, http://read.pudn.com/downloads135/ebook/574389/wan01unscented.pdf

Methods Summary

estimate_statistics(proppts, sigpts, covmat, …)

Computes predicted summary statistics, predicted mean/kernels/crosscovariance, from (propagated) sigmapoints.

propagate(time, sigmapts, modelfct)

Propagate sigma points.

sigma_points(mean, covar)

Sigma points.

Methods Documentation

estimate_statistics(proppts, sigpts, covmat, mpred)[source]

Computes predicted summary statistics, predicted mean/kernels/crosscovariance, from (propagated) sigmapoints.

Not to be confused with mean and kernels resulting from the prediction step of the Bayesian filter. Hence we call it “estimate_*” instead of “predict_*”.

propagate(time, sigmapts, modelfct)[source]

Propagate sigma points.

Parameters
  • time (float) – Time \(t\) which is passed on to the modelfunction.

  • sigmapts (np.ndarray, shape=(2 N+1, N)) – Sigma points (N is the spatial dimension of the dynamic model)

  • modelfct (callable, signature=(t, x, **kwargs)) – Function through which to propagate

Returns

M is the dimension of the measurement model

Return type

np.ndarray, shape=(2 N + 1, M),

sigma_points(mean, covar)[source]

Sigma points.

Parameters
  • mean (np.ndarray, shape (d,)) – mean of Gaussian distribution

  • covar (np.ndarray, shape (d, d)) – kernels of Gaussian distribution

Returns

Return type

np.ndarray, shape (2 * d + 1, d)