# ITE / code / IPA / demos / estimate_ARX_IPA.m

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55``` ```function [e_hat,de_hat,Fs_hat,Bs_hat,W_hat,Fx_hat,Bx_hat,s_hat] = estimate_ARX_IPA(Fx,Bx,Ae,Dx,Du,u_size,ICA,ISA,unknown_dimensions,de,ARX) %Estimates the ARX-IPA model. Method: ARX identification + ISA on the estimated innovation. % %INPUT: % Fx: matrix describing the AR evolution of observation x. % Bx: matrix describing the effect of the control on observation x. % Ae: driving noise of observation x, =A*e. % Dx: dimension of the observation. % Du: dimension of the control. % u_size: size of the control; box constraint, i.e., |u_i| <= u_size % ICA: solver for independent component analysis, see 'estimate_ICA.m'. % ISA: solver for independent subspace analysis (=clustering of the ICA elements). ISA.cost_type, ISA.cost_name, ISA.opt_type: cost type, cost name, optimization type. Example: ISA.cost_type = 'sumH', ISA.cost_name = 'Renyi_kNN_1tok', ISA.opt_type = 'greedy' means that we use an entropy sum ISA formulation ('sumH'), where the entropies are estimated Renyi entropies via kNN methods ('Renyi_kNN_1tok') and the optimization is greedy; see also 'demo_ISA.m' % unknown_dimensions: '0' means 'the subspace dimensions are known'; '1' means 'the number of the subspaces are known' (but the individual dimensions are unknown). % de: % 1)in case of 'unknown_dimensions = 0': 'de' contains the subspace dimensions. % 2)in case of 'unknown_dimensions = 1': the length of 'de' must be equal to the number of subspaces, but the coordinates of the vector can be arbitrary. % ARX: ARX estimator, see 'estimate_ARX.m'. %OUTPUT: % e_hat: e_hat(:,t) is the estimated driving noise at time t. % de_hat: in case of known subspace dimensions ('unknown_dimensions = 0') de_hat = de; else it contains the estimated subspace dimensions; ordered increasingly. % Fs_hat: estimated matrix describing the AR evolution of source s. % Bs_hat: estimated matrix describing the effect of the control on source s. % W_hat: estimated inverse of the mixing matrix. % Fx_hat: estimated matrix describing the AR evolution of observation x. % Bx_hat: estimated matrix describing the effect of the control on observation x. % s_hat: estimated source. % %REFERENCE: % Zoltan Szabo and Andras Lorincz. Towards Independent Subspace Analysis in Controlled Dynamical Systems. ICA Research Network International Workshop (ICARN), pages 9-12, 2008. %NOTE: % Fx,Bx, and Ae are used for observation generation only. % %Copyright (C) 2012 Zoltan Szabo ("http://nipg.inf.elte.hu/szzoli", "szzoli (at) cs (dot) elte (dot) hu") % %This file is part of the ITE (Information Theoretical Estimators) Matlab/Octave toolbox. % %ITE is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by %the Free Software Foundation, either version 3 of the License, or (at your option) any later version. % %This software is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of %MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. % %You should have received a copy of the GNU General Public License along with ITE. If not, see . %ARX-identification = estimate dynamics (Fx_hat, Bx_hat) and innovation (x_innov_hat): [x_innov_hat,Fx_hat,Bx_hat,observation] = estimate_ARX(Fx,Bx,Ae,Dx,Du,u_size,ARX);%the observation is generated online %ISA on the estimation innovation: [e_hat,W_hat,de_hat] = estimate_ISA(x_innov_hat,ICA,ISA,unknown_dimensions,de,size(x_innov_hat,1)); %basis tranformation (x->s): Fs_hat,Bs_hat, s_hat: %Fs_hat,Bs_hat: invW_hat = inv(W_hat); [Fs_hat,Bs_hat] = basis_transformation_ARX(Fx_hat,Bx_hat,W_hat,invW_hat); s_hat = W_hat * observation; ```
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