geninfds.m

Matlab toolbox that contains functions of Kalman filter and random system simulation.

    % loop over all input vectors
    for k=1:nov,

        % set model parameter vector
        InferenceDS.model = feval(InferenceDS.model.setparams, InferenceDS.model, state(:,k), InferenceDS.paramParamIdxVec);

        % FFUN part of likelihood
        llh_f = feval(InferenceDS.model.prior, InferenceDS.model, ext_nextstate(:,k), ext_state_1(:,k), oNoiseDS.noiseSources{1});

        % HFUN part of likelihood
        llh_h = feval(InferenceDS.model.likelihood, InferenceDS.model, ext_obs(:,k), ext_state_2(:,k), ext_U2(:,k), oNoiseDS.noiseSources{2});

        llh(k) = llh_f * llh_h;       % we assume independence

    end


%-------------------------------------------------------------------------------------
function observ = hfun_parameter_f(InferenceDS, state, N, U2)

    %  HFUN_PARAMETER_F   State observation function of meta system for parameter estimation using only ffun
    %                     from the underlying GSSM.
    %
    %    observ = hfun_parameter_f(InferenceDS, state, N, U2)
    %
    %    INPUT
    %         InferenceDS     : (InferenceDS) Inference data structure
    %         state           : (c-vector) meta system state vector
    %         N               : (c-vector) meta system observation noise vector
    %         U2              : (c-vector) meta system exogenous input 2
    %    OUTPUT
    %         observ          : (c-vector) meta system observation vector
    %
    % Relationship between arguments and external model (GSSM) variables
    %
    %   state  -> external model parameters or a subset (specified by InferenceDS.paramParamIdxVec) thereof
    %   U2     -> [external_state(k-1) external_U1(k-1)]'
    %   N      -> [external_process_noise(k-1)]'
    %   observ -> [external_state(k)]'

    [dim,nov] = size(state);

    observ = zeros(InferenceDS.obsdim,nov);

    dimX  = InferenceDS.model.statedim;
    dimV  = InferenceDS.model.Vdim;
    dimU1 = InferenceDS.model.U1dim;

    ext_state_1     = U2(1:dimX,:);
    ext_proc_noise  = N(1:dimV,:);
    ext_U1          = U2(dimX+1:dimX+dimU1,:);

    ffun_idx = InferenceDS.paramFFunOutIdxVec;

    dimFO = length(ffun_idx);

    % loop over all input vectors
    for k=1:nov,
        % set model parameter vector
        InferenceDS.model = feval(InferenceDS.model.setparams, InferenceDS.model, state(:,k), InferenceDS.paramParamIdxVec);
        FFunOut  = feval(InferenceDS.model.ffun, InferenceDS.model, ext_state_1(:,k), ext_proc_noise(:,k), ext_U1(:,k));
        observ(:,k) = FFunOut(ffun_idx);
    end

%-------------------------------------------------------------------------------------
function observ = hfun_parameter_h(InferenceDS, state, N, U2)

    %  HFUN_PARAMETER_H   State observation function of meta system for parameter estimation using only hfun
    %                     from the underlying GSSM.
    %
    %    observ = hfun_parameter_h(InferenceDS, state, N, U2)
    %
    %    INPUT
    %         InferenceDS     : (InferenceDS) Inference data structure
    %         state           : (c-vector) system state vector
    %         N               : (c-vector) observation noise vector
    %         U2              : (c-vector) exogenous input 2
    %    OUTPUT
    %         observ          : (c-vector) observation vector
    %
    % Relationship between input arguments and external model (GSSM) variables
    %
    %   state  -> external model parameters or a subset (specified by InferenceDS.paramParamIdxVec) thereof
    %   U2     -> [external_state(k) external_U2(k)]'
    %   N      -> [external_observation_noise(k)]'
    %   observ -> [external_observation(k)]'

    [dim,nov] = size(state);

    observ = zeros(InferenceDS.obsdim,nov);

    dimX  = InferenceDS.model.statedim;
    dimO  = InferenceDS.model.obsdim;
    dimN  = InferenceDS.model.Ndim;
    dimU2 = InferenceDS.model.U2dim;

    ext_state_2     = U2(1:dimX,:);
    ext_U2          = U2(dimX+1:dimX+dimU2,:);
    ext_obs_noise   = N(1:dimN,:);

    hfun_idx = InferenceDS.paramHFunOutIdxVec;

    dimHO = length(hfun_idx);

    % loop over all input vectors
    for k=1:nov,
       % set model parameter vector
       InferenceDS.model = feval(InferenceDS.model.setparams, InferenceDS.model, state(:,k), InferenceDS.paramParamIdxVec);
       HFunOut = feval(InferenceDS.model.hfun, InferenceDS.model, ext_state_2(:,k), ext_obs_noise(:,k), ext_U2(:,k));
       observ(:,k) = HFunOut(hfun_idx);
    end

%-------------------------------------------------------------------------------------
function observ = hfun_parameter_both(InferenceDS, state, N, U2)

    %  HFUN_PARAMETER_BOTH   State observation function of meta system for parameter estimation using the full system
    %                        dynamics of the underlying GSSM as observation, i.e. observ=hfun(ffun(x))
    %
    %
    %    observ = hfun_parameter_both(InferenceDS, state, N, U2)
    %
    %    INPUT
    %         InferenceDS     : (InferenceDS) Inference data structure
    %         state           : (c-vector) system state vector
    %         N               : (c-vector) observation noise vector
    %         U2              : (c-vector) exogenous input 2
    %    OUTPUT
    %         observ          : (c-vector) observation vector
    %
    % Relationship between input arguments and external model (GSSM) variables
    %
    %   state  -> external model parameters or a subset (specified by InferenceDS.paramParamIdxVec) thereof
    %   U2     -> [external_state(k-1) external_U1(k-1) external_U2(k)]'
    %   N      -> [external_observation_noise(k)]'
    %   observ -> [external_observation(k)]'

    [dim,nov] = size(state);

    observ = zeros(InferenceDS.obsdim,nov);

    dimX  = InferenceDS.model.statedim;
    dimO  = InferenceDS.model.obsdim;
    dimN  = InferenceDS.model.Ndim;
    dimU1 = InferenceDS.model.U1dim;
    dimU2 = InferenceDS.model.U2dim;

    ext_state_1     = U2(1:dimX,:);
    ext_U1          = U2(dimX+1:dimX+dimU1,:);
    ext_U2          = U2(dimX+dimU1+1:dimX+dimU1+dimU2,:);
    ext_obs_noise   = N(1:dimN,:);

    hfun_idx = InferenceDS.paramHFunOutIdxVec;

    dimHO = length(hfun_idx);

    % loop over all input vectors
    for k=1:nov,
       % set model parameter vector
       InferenceDS.model = feval(InferenceDS.model.setparams, InferenceDS.model, state(:,k), InferenceDS.paramParamIdxVec);
       % calculate X(k)=ffun(X(k-1))
       ext_state_2 = feval(InferenceDS.model.ffun, InferenceDS.model, ext_state_1(:,k), [], ext_U1(:,k));
       HFunOut = feval(InferenceDS.model.hfun, InferenceDS.model, ext_state_2, ext_obs_noise(:,k), ext_U2(:,k));
       observ(:,k) = HFunOut(hfun_idx);
    end



%-------------------------------------------------------------------------------------
function llh = likelihood_parameter_f(InferenceDS, obs, state, U2, oNoiseDS)

    %  LIKELIHOOD_PARAMETER_F  Calculates the likelood of a real-world observation obs given
    %                           a realization of the predicted observation for a given state,
    %                           i.e. p(y|x) = p(obs|state)
    %
    %    llh = likelihood_parameter_f(InferenceDS, obs, observ)
    %
    %    INPUT
    %         InferenceDS     : (InferenceDS) Inference data structure
    %         obs             : (c-vector)  real-world observation vector
    %         state           : (c-vector)  meta system state vector
    %         U2              : (c-vector) meta system exogenous input 2
    %         oNoiseDS        : (NoiseDS)   observation noise data structure
    %    OUTPUT
    %         llh             : scalar  likelihood

    [dim,nov] = size(state);

    llh = zeros(1,nov);

    dimX  = InferenceDS.model.statedim;
    dimO  = InferenceDS.model.obsdim;
    dimU1 = InferenceDS.model.U1dim;

    ext_state_1     = U2(1:dimX,:);
    ext_U1          = U2(dimX+1:dimX+dimU1,:);

    ffun_idx = InferenceDS.paramFFunOutIdxVec;

    dimFO = length(ffun_idx);
    dimHO = length(hfun_idx);

    ext_nextstate = obs(1:dimF0,:);
    ext_obs = obs(dimF0+1:dimF0+dimH0,:);

    % loop over all input vectors
    for k=1:nov,

        % set model parameter vector
        InferenceDS.model = feval(InferenceDS.model.setparams, InferenceDS.model, state(:,k), InferenceDS.paramParamIdxVec);

        % FFUN part of likelihood
        llh(k) = feval(InferenceDS.model.prior, InferenceDS.model, ext_nextstate(:,k), ext_state_1(:,k), oNoiseDS);

    end


%-------------------------------------------------------------------------------------
function llh = likelihood_parameter_h(InferenceDS, obs, state, U2, oNoiseDS)

    %  LIKELIHOOD_PARAMETER_H  Calculates the likelood of a real-world observation obs given
    %                           a realization of the predicted observation for a given state,
    %                           i.e. p(y|x) = p(obs|state)
    %
    %    llh = likelihood_parameter_h(InferenceDS, obs, observ)
    %
    %    INPUT
    %         InferenceDS     : (InferenceDS) Inference data structure
    %         obs             : (c-vector)  real-world observation vector
    %         state           : (c-vector)  meta system state vector
    %         U2              : (c-vector) meta system exogenous input 2
    %         oNoiseDS        : (NoiseDS)   observation noise data structure
    %    OUTPUT
    %         llh             : scalar  likelihood

    [dim,nov] = size(state);

    llh = zeros(1,nov);

    dimX  = InferenceDS.model.statedim;
    dimO  = InferenceDS.model.obsdim;
    dimU2 = InferenceDS.model.U2dim;

    ext_state_2     = U2(1:dimX,:);
    ext_U2          = U2(dimX+1:end,:);

    hfun_idx = InferenceDS.paramHFunOutIdxVec;

    dimHO = length(hfun_idx);

    % loop over all input vectors
    for k=1:nov,

        % set model parameter vector
        InferenceDS.model = feval(InferenceDS.model.setparams, InferenceDS.model, state(:,k), InferenceDS.paramParamIdxVec);

        llh(k) = feval(InferenceDS.model.likelihood, InferenceDS.model, obs(:,k), ext_state_2(:,k), ext_U2(:,k), oNoiseDS);

    end


%-------------------------------------------------------------------------------------
function llh = likelihood_parameter_both(InferenceDS, obs, state, U2, oNoiseDS)

    %  LIKELIHOOD_PARAMETER_BOTH  Calculates the likelood of a real-world observation obs given
    %                             a realization of the predicted observation for a given state,
    %                             i.e. p(y|x) = p(obs|state)
    %
    %    llh = likelihood_parameter_both(InferenceDS, obs, observ)
    %
    %    INPUT
    %         InferenceDS     : (InferenceDS) Inference data structure
    %         obs             : (c-vector)  real-world observation vector
    %         state           : (c-vector)  meta system state vector
    %         U2              : (c-vector) meta system exogenous input 2
    %         oNoiseDS        : (NoiseDS)   observation noise data structure
    %    OUTPUT
    %         llh             : scalar  likelihood

    [dim,nov] = size(state);

    llh = zeros(1,nov);

    dimX  = InferenceDS.model.statedim;
    dimO  = InferenceDS.model.obsdim;
    dimU1 = InferenceDS.model.U1dim;
    dimU2 = InferenceDS.model.U2dim;

    ext_state_1     = U2(1:dimX,:);
    ext_U1          = U2(dimX+1:dimX+dimU1,:);
    ext_U2          = U2(dimX+dimU1+1:end,:);

    hfun_idx = InferenceDS.paramHFunOutIdxVec;

    dimHO = length(hfun_idx);

        % loop over all input vectors
    for k=1:nov,