ukfPtsWts: UKF: sigma points and weights
In piotrek-orlowski/ukfRcpp: R and C++ Unscented Kalman Filter

Functions for generating sigma-points from original state and a Cholesky decomposition of the state variance-covariance matrix, and for generating weights for calculating mean and covariance via the Unscented Transformation.

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generateSigmaPoints(xMat, gam, PMatChol, L)

generateSigmaWeights(L, alpha, beta)

`xMat`	Original state matrix: each column is a value of state variables. If `ncol(xMat)==1`, the matrix is simply expanded with `+/- gam * PMatChol[,k]`. If `xMat` has more than one column, it's rewritten and an expansion of the first column is concatenated on the right.
`gam`	Numeric. `gamma` parameter for Unscented Transformations.
`PMatChol`	Cholesky decomposition (preferably lower) of the variance-covariance matrix of `xMat[,1]`. If past states are propagated, then the top-left block of `PMatChol` contains the decomposition and other entries are `0`.
`L`	Dimension of state expansion. Should be equal to the number of non-zero entries on `diag(PMatChol)`
`alpha`	Numeric in `[0,1]`: size of step in the Scaled Uncented Transformation.
`beta`	Numeric. Corrections in weights for calculating higher moments. Set to `0` unless you know what you're doing.

Matrix of size nrow(xMat) x (ncol(xMat) + 2*L).

Matrix of size (2*L+1) x 2. First column contains weights for the calculation of the non-linearly transformed mean; second column – for the variance-covariance matrix.

piotrek-orlowski/ukfRcpp documentation built on July 21, 2020, 11:51 a.m.