O'Reilly logo

Modeling, Estimation and Optimal Filtration in Signal Processing by Mohamed Najim

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

Appendix K

The Unscented Kalman Filter (UKF)

The unscented Kalman filter (UKF) is based on the “unscented transformation” (UT). First proposed by Julier et al. [1] the UT allows for the estimation of the mean and the covariance of an arbitrary analytical transformation y = f(images) of a random Gaussian vector images with a mean value images and a covariance matrix images.

If L denotes the size of the vector images, the method put forth by Julier et al. runs in three steps:

1) 2L+1 particles or σ-points [1] are generated as follows:

images

where (M)i is the iith row or column of matrix M and λ = α2(L + κ)– L is a scaling factor. Element α is a parameter which allows us to control the dispersion of the σ-points around the mean images. κ is a secondary scaling factor.

2) The σ-points are transformed using function f:

3) The mean and ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required