comparison toolboxes/FullBNT-1.0.7/bnt/examples/dynamic/SLAM/Old/skf_data_assoc_gmux2.m @ 0:e9a9cd732c1e tip

first hg version after svn

+% This is like skf_data_assoc_gmux, except the objects don't move.
+% We are uncertain of their initial positions, and get more and more observations
+% over time. The goal is to test deterministic links (0 covariance).
+% This is like robot1, except the robot doesn't move and is always at [0 0],
+% so the relative location is simply L(s).
+
+nobj = 2;
+N = nobj+2;
+Xs = 1:nobj;
+S = nobj+1;
+Y = nobj+2;
+
+intra = zeros(N,N);
+inter = zeros(N,N);
+intra([Xs S], Y) =1;
+for i=1:nobj
+  inter(Xs(i), Xs(i))=1;
+end
+
+Xsz = 2; % state space = (x y)
+Ysz = 2;
+ns = zeros(1,N);
+ns(Xs) = Xsz;
+ns(Y) = Ysz;
+ns(S) = nobj;
+
+bnet = mk_dbn(intra, inter, ns, 'discrete', S, 'observed', [S Y]);
+
+% For each object, we have
+% X(t+1) = F X(t) + noise(Q)
+% Y(t) = H X(t) + noise(R)
+F = eye(2);
+H = eye(2);
+Q = 0*eye(Xsz); % no noise in dynamics
+R = eye(Ysz);
+
+init_state{1} = [10 10]';
+init_state{2} = [10 -10]';
+init_cov = eye(2);
+
+% Uncertain of initial state (position)
+for i=1:nobj
+  bnet.CPD{Xs(i)} = gaussian_CPD(bnet, Xs(i), 'mean', init_state{i}, 'cov', init_cov);
+end
+bnet.CPD{S} = root_CPD(bnet, S); % always observed
+bnet.CPD{Y} = gmux_CPD(bnet, Y, 'cov', repmat(R, [1 1 nobj]), 'weights', repmat(H, [1 1 nobj]));
+% slice 2
+eclass = bnet.equiv_class;
+for i=1:nobj
+  bnet.CPD{eclass(Xs(i), 2)} = gaussian_CPD(bnet, Xs(i)+N, 'mean', zeros(Xsz,1), 'cov', Q, 'weights', F);
+end
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Create LDS params 
+
+% X(t) = A X(t-1) + B U(t) + noise(Q)
+
+% [L11]  = [1  ]  * [L1]       +   [Q ]
+% [L2]     [  1]    [L2]           [ Q]
+
+% Y(t)|S(t)=s  = C(s) X(t) + noise(R)
+% Yt|St=1 = [1 0]  * [L1]  + R
+%                    [L2]    
+
+nlandmarks = nobj;
+
+% Create indices into block structure
+bs = 2*ones(1, nobj); % sizes of blocks in state space
+for i=1:nlandmarks
+  landmark_block(:,i) = block(i, bs)';
+end
+Xsz = 2*(nlandmarks); % 2 values for each landmark plus robot
+Ysz = 2; % observe relative location
+
+% create block-diagonal trans matrix for each switch
+A = zeros(Xsz, Xsz);
+for i=1:nlandmarks
+  bi = landmark_block(:,i);
+  A(bi, bi) = eye(2);
+end
+A = repmat(A, [1 1 nlandmarks]); % same for all switch values
+
+% create block-diagonal system cov
+Qbig = zeros(Xsz, Xsz);
+Qbig = repmat(Qbig, [1 1 nlandmarks]);
+
+
+% create observation matrix for each value of the switch node
+% C(:,:,i) = (0 ... I ...) where the I is in the i'th posn.
+C = zeros(Ysz, Xsz, nlandmarks);
+for i=1:nlandmarks
+  C(:, landmark_block(:,i), i) = eye(2);
+end
+
+% create observation cov for each value of the switch node
+Rbig = repmat(R, [1 1 nlandmarks]);
+
+% initial conditions
+init_x = [init_state{1}; init_state{2}];
+init_V = zeros(Xsz, Xsz);
+for i=1:nlandmarks
+  bi = landmark_block(:,i);
+  init_V(bi,bi) = init_cov;
+end
+
+
+
+%%%%%%%%%%%%%%%%
+% Observe objects at random
+T = 10;
+evidence = cell(N, T);
+data_assoc = sample_discrete(normalise(ones(1,nobj)), 1, T);
+evidence(S,:) = num2cell(data_assoc);
+evidence = sample_dbn(bnet, 'evidence', evidence);
+
+
+% Inference
+ev = cell(N,T);
+ev(bnet.observed,:) = evidence(bnet.observed, :);
+y = cell2num(evidence(Y,:));
+
+engine = pearl_unrolled_dbn_inf_engine(bnet);
+engine = enter_evidence(engine, ev);
+
+loopy_est_pos = zeros(2, nlandmarks);
+loopy_est_pos_cov = zeros(2, 2, nlandmarks);
+for i=1:nobj
+  m = marginal_nodes(engine, Xs(i), T);
+  loopy_est_pos(:,i) = m.mu;
+  loopy_est_pos_cov(:,:,i) = m.Sigma;
+end
+
+
+[xsmooth, Vsmooth] = kalman_smoother(y, A, C, Qbig, Rbig, init_x, init_V, 'model', data_assoc);
+
+kf_est_pos = zeros(2, nlandmarks);
+kf_est_pos_cov = zeros(2, 2, nlandmarks);
+for i=1:nlandmarks
+  bi = landmark_block(:,i);
+  kf_est_pos(:,i) = xsmooth(bi, T);
+  kf_est_pos_cov(:,:,i) = Vsmooth(bi, bi, T);
+end
+
+
+kf_est_pos
+loopy_est_pos
+
+kf_est_pos_time = zeros(2, nlandmarks, T);
+for t=1:T
+  for i=1:nlandmarks
+    bi = landmark_block(:,i);
+    kf_est_pos_time(:,i,t) = xsmooth(bi, t);
+  end
+end
+kf_est_pos_time % same for all t since smoothed