% GSSM_BOT  General state space model for Bearings-Only Tracking of a randomly maneuvering%           target relative to a stationary observer.%%   The following state space model is used :%%     X(k) = |1 1 0 0| X(k-1) + |0.5  0 | V(k-1)%            |0 1 0 0|          | 1   0 |%            |0 0 1 1|          | 0  0.5|%            |0 0 0 1|          | 0   1 |%%     O(k) = arctan(x3(k)/x1(k)) + n(k)%%   Where the state vector is defined as the 2D position and velocity vector of the target,%   relative to a fixed external reference frame, i.e.%%     X(k) = |x1(k)| = |x-position at time k|%            |x2(k)|   |x-velocity at time k|%            |x3(k)|   |y-position at time k|%            |x4(k)|   |y-velocity at time k|%%   and the observation at time k, O(k) is the bearing angle (in radians) from the fixed%   observer towards the target.%%   The state dynamics are driven by a 2 dimensional white Gaussian noise source and the%   observations are corrupted by additive scalar white Gaussian noise.%%   See :  Gordon, Salmond & Ewing, "Bayesian State Estimation for Tracking and Guidance Using%   the Bootstrap Filter", Journal of Guidance, Control and Dynamics, 1995.%%   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_Bearings_Only_Tracking';  % ID tag  model.statedim   = 4;                      %   state dimension  model.obsdim     = 1;                      %   observation dimension  model.paramdim   = 10;                     %   parameter dimension                                             %   parameter estimation will be done)  model.U1dim      = 0;                      %   exogenous control input 1 dimension  model.U2dim      = 0;                      %   exogenous control input 2 dimension  model.Vdim       = 2;                      %   process noise dimension  model.Ndim       = 1;                      %   observation noise dimension  model.ffun_type = 'lti';                   % state transition function type  : linear time invariant  model.hfun_type = 'nla';                   % state observation function type : nonlinear, aditive noise  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.setparams  = @setparams;             % file handle to SETPARAMS  model.obsAngleCompIdxVec = [1];            % indicate that the first (and only component) of the observation                                             % vector is an angle measured in radians. This is needed so that the                                             % SPKF based algorithms can correctly deal with the angular discontinuity                                             % at +- pi radians.  Arg.type = 'gaussian';  Arg.cov_type = 'sqrt';  Arg.dim = model.Vdim;  Arg.mu  = zeros(Arg.dim,1);  Arg.cov   = 0.01*eye(Arg.dim);  model.pNoise = gennoiseds(Arg);            % process noise : zero mean white Gaussian noise, cov = 0.001^2  Arg.type = 'gaussian';  Arg.cov_type = 'sqrt';  Arg.dim = model.Ndim;  Arg.mu = 0;  Arg.cov  = 0.01;  model.oNoise = gennoiseds(Arg);            % observation noise : zero mean white Gaussian noise, cov=0.01^2  model.params = zeros(model.paramdim,1);  model.A = zeros(model.statedim, model.statedim);  model.G = zeros(model.statedim, model.Vdim);  model = setparams(model,[1 1 1 1 1 1 0.5 1 0.5 1]');%===============================================================================================%-- Unpack and update model internal parameters from parameter vector, 'params'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  model.A([1 5 6 11 15 16]) = params(1:6);  model.G([1 2 7 8]) = params(7:10);  G = model.G;  model.convFact1 = (G'*G)\G';    % conversion matrix needed to calculate state transition prior%===============================================================================================%-- State transition function (vehicle dynamic model)function new_state = ffun(model, state, V, U1)  if isempty(V)      new_state = model.A*state;  else      new_state = model.A*state + model.G*V;  end%===============================================================================================%-- State observation functionfunction observ = hfun(model, state, N, U2)  observ = atan2(state(3,:),state(1,:));  % Now add the process noise... taking care with the discontinueties at +-pi radians  if ~isempty(N),      observ = observ + N;      idx = find(abs(observ) > pi);      temp = rem(observ(idx),2*pi);      observ(idx) = temp - sign(temp).*(2*pi);  end%===============================================================================================function tranprior = prior(model, nextstate, state, U1, pNoiseDS)  V = model.convFact1 * (nextstate - model.A*state);  tranprior = feval(pNoiseDS.likelihood, pNoiseDS, V);%===============================================================================================function llh = likelihood(model, obs, state, U2, oNoiseDS)  observ = hfun(model, state, [], U2);  N = subangle(obs, observ);  llh = feval(oNoiseDS.likelihood, oNoiseDS, N);%===============================================================================================function innov = innovation(model, obs, observ)  innov = subangle(obs,observ);