function?[xEstPEstxPredPPredzPredinovationSK]=ukf（xEstPEstUQffunzRhfundtalphabetakappa）;

%?title????:??UNSCENTED?KALMAN?FILTER??
%
%?PURPOSE??:??This?function?performs?one?complete?step?of?the?unscented?Kalman?filter.
%
%?SYNTAX???:??[xEstPEstxPredPPredzPredinovation]=ukf（xEstPEstUQffunzRhfundtalphabetakappa）
%
%?INPUTS???:??-?xEst?????????????:?state?mean?estimate?at?time?k??
%?????????????-?PEst?????????????:?state?covariance?at?time?k
%?????????????-?U????????????????:?vector?of?control?inputs
%?????????????-?Q????????????????:?process?noise?covariance?at?time?k??
%?????????????-?z????????????????:?observation?at?k+1??
%?????????????-?R????????????????:?measurement?noise?covariance?at?k+1??
%?????????????-?ffun?????????????:?process?model?function??
%?????????????-?hfun?????????????:?observation?model?function??
%?????????????-?dt???????????????:?time?step?（passed?to?ffun/hfun）???
%	??????-?alpha?（optional）?:?sigma?point?scaling?parameter.?Defaults?to?1.
%?????????????-?beta??（optional）?:?higher?order?error?scaling?parameter.?Default?to?0.??
%?????????????-?kappa?（optional）?:?scalar?tuning?parameter?1.?Defaults?to?0.??
%
%?OUTPUTS??:??-?xEst?????????????:?updated?estimate?of?state?mean?at?time?k+1
%	??????-?PEst?????????????:?updated?state?covariance?at?time?k+1
%?????????????-?xPred????????????:?prediction?of?state?mean?at?time?k+1
%?????????????-?PPred????????????:?prediction?of?state?covariance?at?time?k+1
%	??????-?inovation????????:?innovation?vector
%??
%
%?NOTES????:??The?process?model?is?of?the?form?x（k+1）?=?ffun[x（k）v（k）dtu（k）]
%?????????????where?v（k）?is?the?process?noise?vector.?The?observation?model?is?
%?????????????of?the?form?z（k）?=?hfun[x（k）w（k）dtu（k）]?where?w（k）?is?the?
%?????????????observation?noise?vector.
%
%?????????????This?code?was?written?to?be?readable.?There?is?significant
%?????????????scope?for?optimisation?even?in?Matlab.
%
??

%?Process?defaults

if?（nargin???alpha=1;
end;

if?（nargin???beta=0;
end;

if?（nargin???kappa=0;
end;


%?Calculate?the?dimensions?of?the?problem?and?a?few?useful
%?scalars

states???????=?size（xEst（:）1）;
observations?=?size（z（:）1）;
vNoise???????=?size（Q2）;
wNoise???????=?size（R2）;

noises???????=?vNoise+wNoise;

%?Augment?the?state?vector?with?the?noise?vectors.
%?Note:?For?simple?additive?noise?models?this?part
%?can?be?done?differently?to?save?on?c