PEM grey box using merged data.

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Mike
Mike 2012-8-27
I am trying to understand exactly the underlying theory that pem uses working with merged data. Specifically, I am using a grey box model where the initial conditions and Kalman gain is parameterized by me. Is it just performing the identification separately and then combining the result or is it estimated in one run with two sets of initial conditions. Code is included as an example.
%%Define system
A = [0.8 0.1; 0.1 0.7];
B = [0.2; 0.7];
C = [1 0];
D = 0;
Q = 0.1;
R = 0.1;
Ts = 1;
%%Simulate the system twice
n = 200;
y = cell(2, 1);
y{1} = zeros(1, n);
y{2} = y{1};
u = [0*ones(1, 20), 1*ones(1, 30), 2*ones(1, 20), -1*ones(1, 20), 0*ones(1, 30), 2*ones(1, 20), 0*ones(1, 30), -2*ones(1, 30)];
x = zeros(2, n + 1);
for i = 1:2;
if( i == 1 )
x(:, 1) = [4; 4];
else
x(:, 1) = [-1; -1];
end
for k = 1:n;
y{i}(k) = C*x(:, k) + D*u(:, k) + sqrt(R)*randn;
x(:, k + 1) = A*x(:, k) + B*u(:, k) + sqrt(Q)*randn;
end
end
%%plot output
plot([y{1}', y{2}']);
%%gather data
data1 = iddata(y{1}', u', Ts);
data2 = iddata(y{2}', u', Ts);
data_all = merge(data1, data2);
%%identify
model1 = idgrey('sysmodel', zeros(1, 6), 'd');
options = greyestOptions('Display', 'On', 'Focus', 'Prediction');
options.SearchOption.MaxIter = 1000;
model_out = pem(data_all, model1, options);%, 'OutputWeight', [1 0; 0 0]);
MODEL FUNCTION
function [A, B, C, D, K, X0] = sysmodel(phi, Ts, extra)
%SYSMODEL Summary of this function goes here
% Detailed explanation goes here
A = [phi(1) 0.1; 0.1 phi(2)];
B = [0.2; 0.7];
C = [1 0];
D = 0;
K = [phi(3); phi(4)];
X0 = [phi(5); phi(6)];
end
Bump.
  2 个评论
Walter Roberson
Walter Roberson 2012-8-27
Is "pem" the Prediction Error Method in this context?
Mike
Mike 2012-8-27
Yes, I was using pem to specifically mean the function in MATLAB which uses the prediction error method to perform system identification.

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采纳的回答

Rajiv Singh
Rajiv Singh 2012-9-7
编辑：Rajiv Singh 2012-9-7
It is the latter - one combined estimation using both sets of data. If you parametrize initial states x0 (like you do in your sysmdoel file), then you are forcing a joint estimation of initial conditions that somehow do justice to both datasets (in an average sense). To avoid this, you can set the estimation option "InitialState" to "estimate" (options.InitialState = 'estimate'). This causes the X0 returned by sysmodel to be ignored and initial states are estimated separately for each data experiment. The estimated values are stored in model_out.Report.Parameters.X0 (and can also be returned as the second output argument of GREYEST).

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