%IMM_UPDATE Interacting Multiple Model (IMM) Filter update step
%
% Syntax:
% [X_i,P_i,MU,X,P] = IMM_UPDATE(X_p,P_p,c_j,ind,dims,Y,H,h,R,param)
%
% In:
% X_p - Cell array containing N^j x 1 mean state estimate vector for
% each model j after prediction step
% P_p - Cell array containing N^j x N^j state covariance matrix for
% each model j after prediction step
% c_j - Normalizing factors for mixing probabilities
% ind - Indices of state components for each model as a cell array
% dims - Total number of different state components in the combined system
% Y - Dx1 measurement vector.
% H - Measurement matrices for each linear model and Jacobians of each
% non-linear model's measurement model function as a cell array
% h - Cell array containing function handles for measurement functions
% for each model having non-linear measurements
% R - Measurement noise covariances for each model as a cell array.
% param - Parameters of h
%
% Out:
% X_i - Updated state mean estimate for each model as a cell array
% P_i - Updated state covariance estimate for each model as a cell array
% MU - Estimated probabilities of each model
% X - Combined updated state mean estimate
% P - Combined updated covariance estimate
%
% Description:
% IMM-EKF filter measurement update step. If some of the models have linear
% measurements standard Kalman filter update step is used for those.
%
% See also:
% IMM_PREDICT, 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] = eimm_update(X_p,P_p,c_j,ind,dims,Y,H,h,R,param)
% Number of models
m = length(X_p);
% Construct empty cell arrays for ekf_update if h is not specified
if isempty(h)
h = cell(1,m);
end
% Same for h's parameters
if isempty(param)
param = cell(1,m);
end
% Space for update state mean, covariance and likelihood of measurements
X_i = cell(1,m);
P_i = cell(1,m);
lambda = zeros(1,m);
% Update for each model
for i = 1:m
% Update the state estimates
%[X_i{i}, P_i{i}, K, IM, IS, lambda(i)] = ekf_update1(X_p{i},P_p{i},Y,H{i},R{i},h{i},[],param{i});
[X_i{i}, P_i{i}, K, IM, IS, lambda(i)] = ekf_update1(X_p{i},P_p{i},Y,H{i},R{i},h{i},[],param{i});
%[X_i{i}, P_i{i}, K, IM, IS] = kf_update(X_p{i},P_p{i},Y,H{i},R{i});
% Calculate measurement likelihoods for each model
%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;
% In case lambda's happen to be zero
% if c == 0
if c == 0
MU = c_j;
%X_i = X_p;
%P_i = P_p;
end
% 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