Daniel@0: function [A,B,C,Q,R,Qbig,Rbig,init_x,init_V,robot_block,landmark_block,...
Daniel@0: 	  true_landmark_pos, true_robot_pos, true_data_assoc, ...
Daniel@0: 	  obs_rel_pos, ctrl_signal] = mk_linear_slam(varargin)
Daniel@0: 
Daniel@0: % We create data from a linear system for testing SLAM algorithms.
Daniel@0: % i.e. , new robot pos = old robot pos + ctrl_signal, which is just a displacement vector.
Daniel@0: % and  observation = landmark_pos - robot_pos, which is just a displacement vector.
Daniel@0: %
Daniel@0: % The behavior is determined by the following optional arguments:
Daniel@0: %
Daniel@0: % 'nlandmarks' - num. landmarks
Daniel@0: % 'landmarks' - 'rnd' means random locations in the unit sqyare
Daniel@0: %               'square' means at [1 1], [4 1], [4 4] and [1 4]
Daniel@0: % 'T' - num steps to run
Daniel@0: % 'ctrl' - 'stationary' means the robot remains at [0 0],
Daniel@0: %          'leftright' means the robot receives a constant contol of [1 0],
Daniel@0: %          'square' means we navigate the robot around the square
Daniel@0: % 'data-assoc' - 'rnd' means we observe landmarks at random
Daniel@0: %                'nn' means we observe the nearest neighbor landmark
Daniel@0: %                'cycle' means we observe landmarks in order 1,2,.., 1, 2, ...
Daniel@0: 
Daniel@0: args = varargin;
Daniel@0: % get mandatory params
Daniel@0: for i=1:2:length(args)
Daniel@0:   switch args{i},
Daniel@0:    case 'nlandmarks', nlandmarks = args{i+1};
Daniel@0:    case 'T', T = args{i+1};
Daniel@0:   end
Daniel@0: end
Daniel@0: 
Daniel@0: % set defaults
Daniel@0: true_landmark_pos = rand(2,nlandmarks);
Daniel@0: true_data_assoc = [];
Daniel@0: 
Daniel@0: % get args
Daniel@0: for i=1:2:length(args)
Daniel@0:   switch args{i},
Daniel@0:    case 'landmarks',
Daniel@0:     switch args{i+1},
Daniel@0:      case 'rnd',   true_landmark_pos = rand(2,nlandmarks);
Daniel@0:      case 'square',   true_landmark_pos = [1 1; 4 1; 4 4; 1 4]';
Daniel@0:     end
Daniel@0:    case 'ctrl',
Daniel@0:     switch args{i+1},
Daniel@0:      case 'stationary', ctrl_signal = repmat([0 0]', 1, T);
Daniel@0:      case 'leftright', ctrl_signal = repmat([1 0]', 1, T);
Daniel@0:      case 'square',   ctrl_signal = [repmat([1 0]', 1, T/4) repmat([0 1]', 1, T/4) ...
Daniel@0: 		    repmat([-1 0]', 1, T/4) repmat([0 -1]', 1, T/4)];
Daniel@0:     end
Daniel@0:    case 'data-assoc', 
Daniel@0:     switch args{i+1},
Daniel@0:      case 'rnd', true_data_assoc  = sample_discrete(normalise(ones(1,nlandmarks)),1,T);
Daniel@0:      case 'cycle', true_data_assoc = wrap(1:T, nlandmarks);
Daniel@0:     end
Daniel@0:   end
Daniel@0: end
Daniel@0: if isempty(true_data_assoc)
Daniel@0:   use_nn = 1;
Daniel@0: else
Daniel@0:   use_nn = 0;
Daniel@0: end
Daniel@0: 
Daniel@0: %%%%%%%%%%%%%%%%%%%%%%%%
Daniel@0: % generate data
Daniel@0: 
Daniel@0: init_robot_pos = [0 0]';
Daniel@0: true_robot_pos = zeros(2, T);
Daniel@0: true_rel_dist = zeros(2, T);
Daniel@0: for t=1:T
Daniel@0:   if t>1
Daniel@0:     true_robot_pos(:,t) = true_robot_pos(:,t-1) + ctrl_signal(:,t);
Daniel@0:   else
Daniel@0:     true_robot_pos(:,t) = init_robot_pos + ctrl_signal(:,t);
Daniel@0:   end
Daniel@0:   nn = argmin(dist2(true_robot_pos(:,t)', true_landmark_pos'));
Daniel@0:   if use_nn
Daniel@0:     true_data_assoc(t) = nn;
Daniel@0:   end
Daniel@0:   true_rel_dist(:,t) = true_landmark_pos(:, nn) - true_robot_pos(:,t);
Daniel@0: end
Daniel@0: 
Daniel@0: 
Daniel@0: R = 1e-3*eye(2); % noise added to observation
Daniel@0: Q = 1e-3*eye(2); % noise added to robot motion
Daniel@0: 
Daniel@0: % Create data set
Daniel@0: obs_noise_seq = sample_gaussian([0 0]', R, T)';
Daniel@0: obs_rel_pos = true_rel_dist + obs_noise_seq;
Daniel@0: %obs_rel_pos = true_rel_dist;
Daniel@0: 
Daniel@0: %%%%%%%%%%%%%%%%%%
Daniel@0: % Create params
Daniel@0: 
Daniel@0: 
Daniel@0: % X(t) = A X(t-1) + B U(t) + noise(Q) 
Daniel@0: 
Daniel@0: % [L1]  = [1     ]  * [L1]       + [0]  * Ut  + [0   ]
Daniel@0: % [L2]    [  1   ]    [L2]         [0]          [ 0  ]
Daniel@0: % [R ]t   [     1]    [R ]t-1      [1]          [   Q]
Daniel@0: 
Daniel@0: % Y(t)|S(t)=s  = C(s) X(t) + noise(R)
Daniel@0: % Yt|St=1 = [1 0 -1]  * [L1]  + R
Daniel@0: %                       [L2]    
Daniel@0: %                       [R ]    
Daniel@0: 
Daniel@0: % Create indices into block structure
Daniel@0: bs = 2*ones(1, nlandmarks+1); % sizes of blocks in state space
Daniel@0: robot_block =  block(nlandmarks+1, bs);
Daniel@0: for i=1:nlandmarks
Daniel@0:   landmark_block(:,i) = block(i, bs)';
Daniel@0: end
Daniel@0: Xsz = 2*(nlandmarks+1); % 2 values for each landmark plus robot
Daniel@0: Ysz = 2; % observe relative location
Daniel@0: Usz = 2; % input is (dx, dy)
Daniel@0: 
Daniel@0: 
Daniel@0: % create block-diagonal trans matrix for each switch
Daniel@0: A = zeros(Xsz, Xsz);
Daniel@0: for i=1:nlandmarks
Daniel@0:   bi = landmark_block(:,i);
Daniel@0:   A(bi, bi) = eye(2);
Daniel@0: end
Daniel@0: bi = robot_block;
Daniel@0: A(bi, bi) = eye(2);
Daniel@0: A = repmat(A, [1 1 nlandmarks]); % same for all switch values
Daniel@0: 
Daniel@0: % create block-diagonal system cov
Daniel@0: 
Daniel@0: 
Daniel@0: Qbig = zeros(Xsz, Xsz);
Daniel@0: bi = robot_block;
Daniel@0: Qbig(bi,bi) = Q; % only add noise to robot motion
Daniel@0: Qbig = repmat(Qbig, [1 1 nlandmarks]);
Daniel@0: 
Daniel@0: % create input matrix
Daniel@0: B = zeros(Xsz, Usz);
Daniel@0: B(robot_block,:) = eye(2); % only add input to robot position
Daniel@0: B = repmat(B, [1 1 nlandmarks]);
Daniel@0: 
Daniel@0: % create observation matrix for each value of the switch node
Daniel@0: % C(:,:,i) = (0 ... I ... -I) where the I is in the i'th posn.
Daniel@0: % This computes L(i) - R
Daniel@0: C = zeros(Ysz, Xsz, nlandmarks);
Daniel@0: for i=1:nlandmarks
Daniel@0:   C(:, landmark_block(:,i), i) = eye(2); 
Daniel@0:   C(:, robot_block, i) = -eye(2);
Daniel@0: end
Daniel@0: 
Daniel@0: % create observation cov for each value of the switch node
Daniel@0: Rbig = repmat(R, [1 1 nlandmarks]);
Daniel@0: 
Daniel@0: % initial conditions
Daniel@0: init_x = zeros(Xsz, 1);
Daniel@0: init_v = zeros(Xsz, Xsz);
Daniel@0: bi = robot_block;
Daniel@0: init_x(bi) = init_robot_pos;
Daniel@0: %init_V(bi, bi) = 1e-5*eye(2); % very sure of robot posn
Daniel@0: init_V(bi, bi) = Q; % simualate uncertainty due to 1 motion step
Daniel@0: for i=1:nlandmarks
Daniel@0:   bi = landmark_block(:,i);
Daniel@0:   init_V(bi,bi)= 1e5*eye(2); % very uncertain of landmark psosns
Daniel@0:   %init_x(bi) = true_landmark_pos(:,i);
Daniel@0:   %init_V(bi,bi)= 1e-5*eye(2); % very sure of landmark psosns
Daniel@0: end