% GSSM_N1  Generalized state space model for simple nonlinear system%% The model is a simple scalar nonlinear system with Gamma process and Gaussian observation noise.%   Copyright  (c) Rudolph van der Merwe (2002)%%   This file is part of the ReBEL Toolkit. The ReBEL Toolkit is available free for%   academic use only (see included license file) and can be obtained by contacting%   rvdmerwe@ece.ogi.edu.  Businesses wishing to obtain a copy of the software should%   contact ericwan@ece.ogi.edu for commercial licensing information.%%   See LICENSE (which should be part of the main toolkit distribution) for more%   detail.%=============================================================================================function [varargout] = model_interface(func, varargin)  switch func    %--- Initialize GSSM data structure --------------------------------------------------------    case 'init'      model = init(varargin);        error(consistent(model,'gssm'));               % check consistentency of initialized model      varargout{1} = model;    %--------------------------------------------------------------------------------------------    otherwise      error(['Function ''' func ''' not supported.']);  end%===============================================================================================function model = init(init_args)  model.type = 'gssm';                     % object type = generalized state space model  model.tag  = 'GSSM_N1';                  % ID tag  model.ffun_type = 'nla';                   % state transition function type  : nonlinear, aditive noise  model.hfun_type = 'nla';                   % state observation function type : " "        "    "  model.ffun      = @ffun;                   % file handle to FFUN  model.hfun      = @hfun;                   % file handle to HFUN  model.prior     = @prior;  model.likelihood = @likelihood;            % file handle to LIKELIHOOD  model.innovation = @innovation;            % file handle to INNOVATION  model.linearize  = @linearize;              % file handle to LINEARIZE  model.setparams  = @setparams;              % file handle to SETPARAMS  model.statedim   = 1;                      %   state dimension  model.obsdim     = 1;                      %   observation dimension  model.paramdim   = 2;                      %   parameter dimension  model.U1dim      = 1;                      %   exogenous control input 1 dimension  model.U2dim      = 1;                      %   exogenous control input 2 dimension  model.Vdim       = 1;                      %   process noise dimension  model.Ndim       = 1;                      %   observation noise dimension  Arg.type = 'gamma';  Arg.dim = model.Vdim;  Arg.alpha = 3;  Arg.beta  = 0.5;  model.pNoise = gennoiseds(Arg);   % process noise : Gamma(3,0.5) noise source  Arg.type = 'gaussian';  Arg.cov_type = 'full';  Arg.dim = model.Ndim;  Arg.mu = 0;  Arg.cov  = 1e-5;  Arg.cov_type = 'full';  model.oNoise = gennoiseds(Arg);     % observation noise : zero mean white Gaussian noise, cov=0.2  model.params = zeros(model.paramdim,1);  model = setparams(model,[4e-2 0.5]);   % [omega phi]%===============================================================================================function model = setparams(model, params, index_vector)  if (nargin==2)    model.params = params(:);  elseif (nargin==3)    model.params(index_vector) = params(:);  else    error('[ setparams ] Incorrect number of input arguments.');  end%===============================================================================================function new_state = ffun(model, state, V, U1)  new_state      = 1 + sin(model.params(1)*pi.*U1) + model.params(2)*state;  if ~isempty(V)    new_state = new_state + V;  end%===============================================================================================function observ = hfun(model, state, N, U2)  [dim,nop] = size(state);  observ = zeros(model.obsdim,nop);  for k=1:nop,    if (U2(k) <= 30),       observ(k) = model.params(2)*state(:,k).^2;    else       observ = model.params(2)*state - 2;    end  end  if ~isempty(N)    observ = observ + N;  end%===============================================================================================function tranprior = prior(model, nextstate, state, U1, pNoiseDS)  X = nextstate - ffun(model, state, [], U1);  tranprior = feval(pNoiseDS.likelihood, pNoiseDS, X);%===============================================================================================function llh = likelihood(model, obs, state, U2, oNoiseDS)  X = obs - hfun(model, state, [], U2);  llh = feval(oNoiseDS.likelihood, oNoiseDS, X);%===============================================================================================function innov = innovation(model, obs, observ)  innov = obs - observ;%===============================================================================================function out = linearize(model, state, V, N, U1, U2, term, index_vector)  if (nargin<7)    error('[ linearize ] Not enough input arguments!');  end  %--------------------------------------------------------------------------------------  switch (term)    case 'A'      %%%========================================================      %%%             Calculate A = df/dstate      %%%========================================================      out = model.params(2);    case 'B'      %%%========================================================      %%%             Calculate B = df/dU1      %%%========================================================      out = [];    case 'C'      %%%========================================================      %%%             Calculate C = dh/dx      %%%========================================================      if (U2 <= 30)        out = 2*model.params(2)*state;      else        out = model.params(2);      end    case 'D'      %%%========================================================      %%%             Calculate D = dh/dU2      %%%========================================================      out = [];    case 'G'      %%%========================================================      %%%             Calculate G = df/dv      %%%========================================================      out = 1;    case 'H'      %%%========================================================      %%%             Calculate H = dh/dn      %%%========================================================      out = 1;    case 'JFW'      %%%========================================================      %%%             Calculate  = dffun/dparameters      %%%========================================================      out = [cos(model.params(1)*pi*U1)*pi*U1 state];    case 'JHW'      %%%========================================================      %%%             Calculate  = dhfun/dparameters      %%%========================================================      if (U2 <= 30)        out = [0 state^2];      else        out = [0 state];      end    otherwise      error('[ linearize ] Invalid model term requested!');  end  if (nargin==8), out = out(:,index_vector); end  %--------------------------------------------------------------------------------------