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[MINIMUM,FVAL,EXITFLAG,OUTPUT] = fminkalman(FUN,PARS,[OPTIONS],[CONSTRAINTS], ...) unscented Kalman filter optimizer


function [pars,fval,exitflag,output] = fminkalman(varargin)


 [MINIMUM,FVAL,EXITFLAG,OUTPUT] = fminkalman(FUN,PARS,[OPTIONS],[CONSTRAINTS], ...) unscented Kalman filter optimizer

 Unconstrained optimization using the unscented Kalman filter.
 The Kalman filter is actually a feedback approach to minimize the estimation 
 error in terms of sum of square. This approach can be generalized to general 
 nonlinear optimization. This function shows a way using the extended Kalman 
 filter to solve some unconstrained nonlinear optimization problems.
 The objective function has syntax: criteria = objective(p)
   fminkalman(fun, pars) asks to minimize the 'fun' objective function with starting
     parameters 'pars' (vector)
   fminkalman(fun, pars, options) same as above, with customized options (optimset)
   fminkalman(fun, pars, options, fixed) 
     is used to fix some of the parameters. The 'fixed' vector is then 0 for
     free parameters, and 1 otherwise.
   fminkalman(fun, pars, options, lb, ub) 
     is used to set the minimal and maximal parameter bounds, as vectors.
   fminkalman(fun, pars, options, constraints) 
     where constraints is a structure (see below).
   fminkalman(problem) where problem is a structure with fields
     problem.objective:   function to minimize
     problem.x0:          starting parameter values
     problem.options:     optimizer options (see below)
     problem.constraints: optimization constraints
   fminkalman(..., args, ...)
     sends additional arguments to the objective function
       criteria = FUN(pars, args, ...))

   banana = @(x)100*(x(2)-x(1)^2)^2+(1-x(1))^2;
   [x,fval] = fminkalman(banana,[-1.2, 1])

  FUN is the function to minimize (handle or string): criteria = FUN(PARS)
  It needs to return a single value or vector.

  PARS is a vector with initial guess parameters. You must input an
  initial guess. PARS can also be given as a single-level structure.

  OPTIONS is a structure with settings for the simulated annealing, 
  compliant with optimset. Default options may be obtained with
  options.MinFunEvals sets the minimum number of function evaluations to reach
  An empty OPTIONS sets the default configuration.

  CONSTRAINTS may be specified as a structure
   constraints.min=   vector of minimal values for parameters
   constraints.max=   vector of maximal values for parameters
   constraints.fixed= vector having 0 where parameters are free, 1 otherwise
   constraints.step=  vector of maximal parameter changes per iteration
   constraints.eval=  expression making use of 'p', 'constraints', and 'options' 
                        and returning modified 'p'
                      or function handle p=@constraints.eval(p)
  An empty CONSTRAINTS sets no constraints.

  Additional arguments are sent to the objective function.

          MINIMUM is the solution which generated the smallest encountered
            value when input into FUN.
          FVAL is the value of the FUN function evaluated at MINIMUM.
          EXITFLAG return state of the optimizer
          OUTPUT additional information returned as a structure.

  Kalman, R. E. "A New Approach to Linear Filtering and Prediction Problems,
    Transactions of the ASME - J. of Basic Engineering Vol. 82: pp. 35 (1960)
   By Yi Cao at Cranfield University, 08 January 2008 [ukfopt, ukf]

 Version: Nov. 26, 2018
 See also: fminsearch, optimset
 (c) E.Farhi, ILL. License: EUPL.


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