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