%IMM_FILTER Interacting Multiple Model (IMM) Filter prediction and update steps
%
% Syntax:
% [X_i,P_i,MU,X,P] = IMM_FILTER(X_ip,P_ip,MU_ip,p_ij,ind,dims,A,Q,Y,H,R)
%
% In:
% X_ip - Cell array containing N^j x 1 mean state estimate vector for
% each model j after update step of previous time step
% P_ip - Cell array containing N^j x N^j state covariance matrix for
% each model j after update step of previous time step
% MU_ip - Vector containing the model probabilities at previous time step
% p_ij - Model transition matrix
% ind - Indices of state components for each model as a cell array
% dims - Total number of different state components in the combined system
% A - State transition matrices for each model as a cell array.
% Q - Process noise matrices for each model as a cell array.
% Y - Dx1 measurement vector.
% H - Measurement matrices for each model as a cell array.
% R - Measurement noise covariances for each model as a cell array.
%
%
% Out:
% X_p - Updated state mean for each model as a cell array
% P_p - Updated state covariance for each model as a cell array
% MU - Model probabilities as vector
% X - Combined state mean estimate
% P - Combined state covariance estimate
%
% Description:
% IMM filter prediction and update steps. Use this instead
% of separate prediction and update functions, if you don't need
% the prediction estimates.
%
% See also:
% IMM_UPDATE, IMM_SMOOTH, IMM_FILTER
% History:
% 01.11.2007 JH The first official version.
%
% Copyright (C) 2007 Jouni Hartikainen
%
% $Id: imm_update.m 111 2007-11-01 12:09:23Z jmjharti $
%
% This software is distributed under the GNU General Public
% Licence (version 2 or later); please refer to the file
% Licence.txt, included with the software, for details.
function [X_i,P_i,MU,X,P] = imm_filter(X_ip,P_ip,MU_ip,p_ij,ind,dims,A,Q,Y,H,R)
% Number of models
m = length(X_ip);
% Default values for state mean and covariance
MM_def = zeros(dims,1);
PP_def = diag(20*ones(dims,1));
% Normalizing factors for mixing probabilities
c_j = zeros(1,m);
for j = 1:m
for i = 1:m
c_j(j) = c_j(j) + p_ij(i,j).*MU_ip(i);
end
end
% Mixing probabilities
MU_ij = zeros(m,m);
for i = 1:m
for j = 1:m
MU_ij(i,j) = p_ij(i,j) * MU_ip(i) / c_j(j);
end
end
% Calculate the mixed state mean for each filter
X_0j = cell(1,m);
for j = 1:m
X_0j{j} = zeros(dims,1);
for i = 1:m
X_0j{j}(ind{i}) = X_0j{j}(ind{i}) + X_ip{i}*MU_ij(i,j);
end
end
% Calculate the mixed state covariance for each filter
P_0j = cell(1,m);
for j = 1:m
P_0j{j} = zeros(dims,dims);
for i = 1:m
P_0j{j}(ind{i},ind{i}) = P_0j{j}(ind{i},ind{i}) + MU_ij(i,j)*(P_ip{i} + (X_ip{i}-X_0j{j}(ind{i}))*(X_ip{i}-X_0j{j}(ind{i}))');
end
end
% Space for estimates
X_p = cell(1,m);
P_p = cell(1,m);
X_i = cell(1,m);
P_i = cell(1,m);
lambda = zeros(1,m);
% Filter the estimates for each model
for i = 1:m
% Predict the estimates
[X_p{i}, P_p{i}] = kf_predict(X_0j{i}(ind{i}),P_0j{i}(ind{i},ind{i}),A{i},Q{i});
% Update the estimates
[X_i{i}, P_i{i}, K, IM, IS] = kf_update(X_p{i},P_p{i},Y,H{i},R{i});
% Calculate likelihoods
lambda(i) = kf_lhood(X_p{i},P_p{i},Y,H{i},R{i});
end
% Calculate the model probabilities
MU = zeros(1,m);
c = sum(lambda.*c_j);
MU = c_j.*lambda/c;
% Output the combined updated state mean and covariance, if wanted.
if nargout > 3
% Space for estimates
X = zeros(dims,1);
P = zeros(dims,dims);
% Updated state mean
for i = 1:m
X(ind{i}) = X(ind{i}) + MU(i)*X_i{i};
end
% Updated state covariance
for i = 1:m
P(ind{i},ind{i}) = P(ind{i},ind{i}) + MU(i)*(P_i{i} + (X_i{i}-X(ind{i}))*(X_i{i}-X(ind{i}))');
end
end