--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/m-toolbox/classes/@ssm/kalman.m	Wed Nov 23 19:22:13 2011 +0100
@@ -0,0 +1,327 @@
+% KALMAN applies Kalman filtering to a discrete ssm with given i/o
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+% DESCRIPTION: KALMAN applies Kalman filtering to a discrete ssm with
+%              given i/o.
+% CALL: [mat_out pl_out] = kalman(sys, plist_inputs)
+%
+% INPUTS:
+%         - sys, (array of) ssm object
+%
+% OUTPUTS:
+%          _ mat_out contains specified returned aos
+%          _ pl_out contains 'lastX', the last state position
+%
+% <a href="matlab:utils.helper.displayMethodInfo('ssm', 'kalman')">Parameters Description</a>
+% 
+% VERSION: $Id: kalman.m,v 1.51 2011/04/17 21:28:05 adrien Exp $
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+function varargout = kalman(varargin)
+  
+  %% starting initial checks
+  
+  % use the caller is method flag
+  callerIsMethod = utils.helper.callerIsMethod;
+
+  % Check if this is a call for parameters
+  if utils.helper.isinfocall(varargin{:})
+    varargout{1} = getInfo(varargin{3});
+    return
+  end
+  
+  utils.helper.msg(utils.const.msg.MNAME, ['running ', mfilename]);
+  
+  % Collect input variable names
+  in_names = cell(size(varargin));
+  for ii = 1:nargin,in_names{ii} = inputname(ii);end
+  
+  % Collect all SSMs and plists
+  [sys, ssm_invars, rest] = utils.helper.collect_objects(varargin(:), 'ssm', in_names);
+  [pl, invars2, rest]  = utils.helper.collect_objects(rest(:), 'plist');
+  if ~isempty(rest)
+    pl = combine(pl, plist(rest{:}));
+  end
+  pl = combine(pl, getDefaultPlist());
+  
+  %% retrieve system infos
+  if ~all(sys.isnumerical)
+    error(['error because system ', sys.name, ' is not numerical']);
+  end
+  timestep = sys.timestep;
+  if timestep==0
+    error('timestep should not be 0 in simulate!!')
+  end
+  if ~callerIsMethod
+    inhist  = sys(:).hist;
+  end
+  if pl.isparam('white noise variable names')
+    error('The noise option used must be split between "covariance" and "cpsd". "noise variable names" does not exist anymore!')
+  end
+  
+  %% display time ?
+  displayTime = find(pl, 'displayTime');
+  
+  %% initial state
+  ssini = find(pl,'ssini');
+  if isempty(ssini)
+    ssini = cell(sys.Nss,1);
+    for i=1:sys.Nss
+      ssini{i} = zeros(sys.sssizes(i),1);
+    end
+  end
+  ssSizesIni = sys.statesizes;
+  ssini = ssm.blockMatFusion(ssini,ssSizesIni,1);
+  
+  %% modifying system's ordering
+  if find(pl, 'reorganize')
+    sys = sys.reorganize(pl, 'set', 'for kalman', 'internal', 'internal');
+  end
+  sys_est = sys(1);
+  sys_exp = sys(2);
+  
+  %% getting system's i/o sizes
+  Naos_in = sys_est.inputsizes(1);
+  Nnoise = sys_est.inputsizes(2);
+  Nconstants = sys_est.inputsizes(3);
+  NstatesOut = sys_est.outputsizes(1);
+  NoutputsOut = sys_est.outputsizes(2);
+  Nknown = sys_exp.outputsizes(2);
+  
+  aos_in = find(pl, 'aos');
+  known_out = find(pl, 'known outputs');
+  constants_in = find(pl, 'constants');
+  cov_in = find(pl, 'covariance');
+  cpsd_in = find(pl, 'CPSD');
+  noise_in = blkdiag(cov_in, cpsd_in/(timestep*2));
+  
+  if numel(aos_in)~=Naos_in
+    error(['There are ' num2str(numel(aos_in)) ' input aos and ' num2str(Naos_in) ' corresponding inputs indexed.' ])
+  elseif numel(known_out)~=Nknown
+    error(['There are ' num2str(numel(known_out)) ' known output aos and ' num2str(Nknown) ' corresponding inputs indexed.' ])
+  elseif numel(diag(noise_in))~=Nnoise
+    error(['There are ' num2str(numel(noise_in)) ' input noise variances and ' num2str(Naos_in) ' corresponding inputs indexed.' ])
+  elseif numel(constants_in)~=Nconstants
+    error(['There are ' num2str(numel(constants_in)) ' input constants and ' num2str(Nconstants) ' corresponding inputs indexed.' ])
+  end
+  [U1,S1,V1] = svd(noise_in.'); %#ok<NASGU>
+  noise_mat = U1*sqrt(S1)/sqrt(timestep*2);
+  
+  A        = sys_est.amats{1,1};
+  Cstates  = sys_est.cmats{1,1};
+  Coutputs = sys_est.cmats{2,1};
+  Baos     = sys_est.bmats{1,1};
+  Daos     = sys_est.dmats{2,1};
+  Bnoise   = sys_est.bmats{1,2}*noise_mat;
+  %   Dnoise   = sys_est.dmats{1,2}*noise_mat;
+  Bcst     = sys_est.bmats{1,3};
+  Dcst     = sys_est.dmats{2,3};
+  
+  CoutputsK = sys_exp.cmats{2,1};
+  DaosK     = sys_exp.dmats{2,1};
+  DnoiseK   = sys_exp.dmats{2,2}*noise_mat;
+  DcstK     = sys_exp.dmats{2,3};
+  
+  %% getting correct number of samples
+  Nsamples = find(pl, 'Nsamples');
+  f0 = 1/timestep;
+  for i=1:Naos_in
+    Nsamples = min(Nsamples,length(aos_in(i).y));
+    try
+      if ~(f0==aos_in(i).fs)
+        str = ['WARNING : ssm frequency is ',num2str(f0),...
+          ' but sampling frequency of ao named ',...
+          aos_in(i).name, ' is ', num2str(aos_in(i).fs) ];
+        utils.helper.msg(utils.const.msg.MNAME, str);
+      end
+    end
+    % maybe tdata should be retrieved and verified to be equal, rather than this.
+  end
+  for i=1:Nknown
+    Nsamples = min(Nsamples,length(known_out(i).y));
+    try
+      if ~(f0==known_out(i).fs)
+        str = ['WARNING : ssm frequency is ',num2str(f0),...
+          ' but sampling frequency of ao named ',...
+          aos_in(i).name, ' is ', num2str(aos_in(i).fs) ];
+        utils.helper.msg(utils.const.msg.MNAME, str);
+      end
+    end
+    % maybe tdata should be retrieved and verified to be equal, rather than this.
+  end
+  if Nsamples == inf % case there is no input!
+    display('warning : no input providing simulation duration is available!!')
+    Nsamples = 0;
+  end
+  
+  %% evaluating Kalman feedback K, innovation gain M, state covariance P, output covariance Z
+  % given Q and R (process and measurement noise covariances)
+  Qn = Bnoise*noise_in*transpose(Bnoise);
+  Qn = (Qn + 1e-10*norm(Qn)*eye(size(Qn)));
+  Rn = DnoiseK*noise_in*transpose(DnoiseK);
+  Rn = Rn + 1e-10*norm(Rn)*eye(size(Rn));
+  %   Nn = Bnoise*noise_in*transpose(Dnoise);
+  P = eye(size(A))*1e20;
+  for i=1:10000
+    P = A*P*A'+Qn;
+    K = P*CoutputsK'*(CoutputsK*P*CoutputsK'+Rn)^-1;
+    P = (eye(size(A)) - K*CoutputsK)*P;
+  end
+  Z = Coutputs*P*Coutputs' + Rn;
+  
+  %% constant vector
+  constants_vectX = Bcst*constants_in;
+  constants_vectY = Dcst*constants_in;
+  constants_vectYKnown = DcstK*constants_in;
+  
+  %% ao vector
+  aos_vect = zeros(Naos_in, Nsamples);
+  for j = 1:Naos_in
+    aos_vect(j,:) = aos_in(j).y(1:Nsamples).';
+  end
+  Y_in = zeros(Nknown, Nsamples);
+  for j=1:Nknown
+    Y_in(j,:) = reshape( known_out(j).y(1:Nsamples), 1, [] ).';
+  end
+  
+  %% rewriting fields to ssm/doSimulate
+  
+  A_kalman = A - K*Coutputs*A;
+  Baos_kalman = [ Baos - K*CoutputsK*Baos - K*DaosK   K];
+  aos_vect_kalman = [aos_vect; Y_in ];
+  Bcst_kalman = constants_vectX - K*constants_vectYKnown - K*CoutputsK*constants_vectX;
+  Coutputs_kalman = [Cstates ; Coutputs];
+  Dcst_kalman = [zeros(size(Cstates,1),1) ; constants_vectY];
+  Daos_kalman = [...
+    zeros(size(Cstates,1), size(Daos,2))   zeros(size(Cstates,1), size(K,2)) ;...
+    Daos                                   zeros(size(Daos,1), size(K,2))];
+  Cstates_kalman = zeros(0, size(A,2));
+  Bnoise_kalman = zeros(size(A,1), 0);
+  Dnoise_kalman = zeros(size(Coutputs_kalman,1), 0);
+  
+  %% call to doSimulate
+  doTerminate = false;
+  terminationCond = false;
+  forceComplete = false;
+  
+  [x, y, lastX] = ssm.doSimulate(ssini, Nsamples-1, ...
+    A_kalman, Baos_kalman, Coutputs_kalman, Cstates_kalman, Daos_kalman, Bnoise_kalman, Dnoise_kalman, ...
+    Bcst_kalman, Dcst_kalman, aos_vect_kalman, doTerminate, terminationCond, displayTime, timestep, forceComplete);
+  
+  y = [Coutputs_kalman*lastX y];
+  
+  %% saving in aos
+  fs     = 1/timestep;
+  isysStr = sys.name;
+  tini = find(pl, 'tini');
+  if isa(tini,'double')
+    tini = time(tini);
+  end
+  
+  ao_out = ao.initObjectWithSize(1, NoutputsOut + NstatesOut);
+  for ii=1:NstatesOut
+    ao_out(ii).setData(tsdata( y(ii,:), fs ));
+    ao_out(ii).setName(['kalman estimate of ' sys_est.outputs(1).ports(ii).name]);
+    ao_out(ii).setXunits('s');
+    ao_out(ii).setYunits(sys_est.outputs(1).ports(ii).units);
+    ao_out(ii).setDescription(...
+      ['Kalman estimate for ' isysStr, ' : ',  sys_est.outputs(1).ports(ii).name,...
+      '    ' sys_est.outputs(1).ports(ii).description]);
+    ao_out(ii).setT0(tini);
+  end
+  for ii=1:NoutputsOut
+    ao_out(NstatesOut+ii).setData(tsdata( y(NstatesOut+ii,:), fs ));
+    ao_out(NstatesOut+ii).setName(['kalman estimate of ' sys_est.outputs(2).ports(ii).name]);
+    ao_out(NstatesOut+ii).setXunits('s');
+    ao_out(NstatesOut+ii).setYunits(sys_est.outputs(2).ports(ii).units);
+    ao_out(NstatesOut+ii).setDescription(...
+      ['Kalman estimate for ' isysStr, ' : ',  sys_est.outputs(2).ports(ii).name, ...
+      '    ' sys_est.outputs(2).ports(ii).description]);
+    ao_out(NstatesOut+ii).setT0(tini);
+  end
+  
+    %% construct output matrix object
+  out = matrix(ao_out);
+  if callerIsMethod
+    % do nothing
+  else
+    myinfo = getInfo('None');
+    out.addHistory(myinfo, pl , ssm_invars(1), inhist );
+  end
+  
+  %% construct output analysis object
+  plist_out = plist('process covariance', Qn, 'readout covariance', Rn, ...
+    'state covariance', P, 'output covariance', Z, 'Kalman gain', K );
+  
+  %% Set output depending on nargout
+  if nargout == 1;
+    varargout = {out};
+  elseif nargout == 2;
+    varargout = {out plist_out};
+  elseif nargout == 0;
+    iplot(ao_out);
+  else
+    error('Wrong number of outputs')
+  end
+end
+
+%--------------------------------------------------------------------------
+% Get Info Object
+%--------------------------------------------------------------------------
+function ii = getInfo(varargin)
+  
+  if nargin == 1 && strcmpi(varargin{1}, 'None')
+    sets = {};
+    pl   = [];
+  else
+    sets = {'Default'};
+    pl   = getDefaultPlist;
+  end
+  % Build info object
+  ii = minfo(mfilename, 'ssm', 'ltpda', utils.const.categories.op, '$Id: kalman.m,v 1.51 2011/04/17 21:28:05 adrien Exp $', sets, pl);
+end
+
+%--------------------------------------------------------------------------
+% Get Default Plist
+%--------------------------------------------------------------------------
+function pl = getDefaultPlist()
+  pl = ssm.getInfo('reorganize', 'for kalman').plists;
+  pl.remove('set');
+  
+  p = param({'covariance', 'The covariance of this noise between input ports for the <i>time-discrete</i> noise model.'}, []);
+  pl.append(p);
+  
+  p = param({'CPSD', 'The one sided cross-psd of the white noise between input ports.'}, []);
+  pl.append(p);
+  
+  p = param({'aos', 'An array of input AOs (experimental stimuli).'}, ao.initObjectWithSize(1,0));
+  pl.append(p);
+  
+  p = param({'constants', 'Array of DC values for the different corresponding inputs.'}, paramValue.DOUBLE_VALUE(zeros(0,1)));
+  pl.append(p);
+  
+  p = param({'known outputs', 'Array of AOs for the different corresponding outputs (experiment measurements).'}, ao.initObjectWithSize(1,0));
+  pl.append(p);
+  
+  p = param({'Nsamples', 'The maximum number of samples to simulate (AO length(s) overide this).'}, paramValue.DOUBLE_VALUE(inf));
+  pl.append(p);
+  
+  p = param({'ssini', 'A cell-array of vectors that give the initial position for simulation.'}, {});
+  pl.append(p);
+  
+  p = param({'tini', 'The initial filtering time (seconds).'}, paramValue.DOUBLE_VALUE(0) );
+  pl.append(p);
+  
+  p = param({'displayTime', 'Switch off/on the display'},  paramValue.TRUE_FALSE);
+  pl.append(p);
+  
+  p = param({'reorganize', 'When set to 0, this means the ssm does not need be modified to match the requested i/o. Faster but dangerous!'}, paramValue.TRUE_FALSE);
+  pl.append(p);
+  
+  p = param({'force complete', 'Force the use of the complete simulation code.'}, paramValue.FALSE_TRUE);
+  pl.append(p);
+  
+  
+end
+