CS_CO_ObsModel

   CS_CO_ObsModel constructor.

   Defines an observation model (p(o|s)) on continuous state and 
   observation spaces.
   This kind of observation models are defined via kernel smoothing (see
   Section 6.2, pag 22 of the paper)

   The CS_CO_ObsModel defines p(o,s) via Kernel smoothing: using a double
   Gaussian on 's' and on 'o'. From here:
       p(o|s)=p(o,s)/p(s)
   Where we assume p(s) as uniform.
   For simplicity the 1/p(s) scale factor is integrated into the kernel
   weight.

   Parameters
      S: Continuous state space.
      O: Continuous observation space.
      w: weights of the double mixture.
      gS: Gaussians in 's'.
      gO: Gaussians in 'o'.

0001 function OM=CS_CO_ObsModel(varargin)
0002 %   CS_CO_ObsModel constructor.
0003 %
0004 %   Defines an observation model (p(o|s)) on continuous state and
0005 %   observation spaces.
0006 %   This kind of observation models are defined via kernel smoothing (see
0007 %   Section 6.2, pag 22 of the paper)
0008 %
0009 %   The CS_CO_ObsModel defines p(o,s) via Kernel smoothing: using a double
0010 %   Gaussian on 's' and on 'o'. From here:
0011 %       p(o|s)=p(o,s)/p(s)
0012 %   Where we assume p(s) as uniform.
0013 %   For simplicity the 1/p(s) scale factor is integrated into the kernel
0014 %   weight.
0015 %
0016 %   Parameters
0017 %      S: Continuous state space.
0018 %      O: Continuous observation space.
0019 %      w: weights of the double mixture.
0020 %      gS: Gaussians in 's'.
0021 %      gO: Gaussians in 'o'.
0022 
0023   switch nargin
0024     case 1
0025       if isa(varargin{1},'CS_CO_ObsModel')
0026         OM=varargin{1};
0027       else
0028         error('Wrong parameter type in CS_CO_ObsModel constructor');
0029       end
0030     case 5
0031       if isa(varargin{1},'CSpace')
0032         OM.S=varargin{1};
0033       else
0034         error('Wrong parameter type in CS_CO_ObsModel constructor');
0035       end
0036       if isa(varargin{2},'CSpace')
0037         OM.O=varargin{2};
0038       else
0039         error('Wrong parameter type in CS_CO_ObsModel constructor');
0040       end
0041       if isa(varargin{3},'double')
0042         OM.w=varargin{3}*(1/UniformProbability(OM.S));
0043       end
0044       if isa(varargin{4},'cell')
0045         OM.gS=varargin{4};
0046       end
0047       if isa(varargin{5},'cell')
0048         OM.gO=varargin{5};
0049       end
0050       
0051       % Scale factor to apply = What it should be (UniformProbability(OM.S))
0052       % vs. what actually is (Value(o,Center(OM.S)))
0053       % We estimate p(s) via sampling (small variations can occur)
0054       gS=GMixture(OM.w,OM.gS); % p(s)=int_o p(o,s)
0055       ps=0;
0056       % draw 10 sample on 's' to estimate p(s).
0057       for i=1:10
0058         ps=ps+Value(gS,rand(OM.S));
0059       end
0060       ps=ps/10;
0061       scale=UniformProbability(OM.S)/ps;
0062       OM.w=OM.w*scale;
0063       
0064       OMBase=ObsModel();
0065       
0066       OM=class(OM,'CS_CO_ObsModel',OMBase);
0067     otherwise
0068       error('Wrong number of parameters in CS_CO_ObsdModel constructor');
0069   end
0070