User`s guide

5 ODE P ara meter Estimation (Grey-Box Modeling)

1 Create the M-ﬁle mynoise that computes the state-space matrices as a

function of the ﬁve unknown parameters and the auxiliary variable that

represents the known variance

R2.

Note R2 is treated as an a ux il iary variable rather than assigned a value

in the M-ﬁle to let you change this value directly at the comma n d line

and avoid editing the M-ﬁle.

function [A,B, C,D, K,x0] = mynoise(par,T,aux)

R2 = aux(1); % Known measurement noise variance

A = [par(1) par(2);1 0];

B = [1;0];

C = [par(3) par(4)];

D=0;

R1 = [par(5) 0;0 0];

[est,K] = kalman(ss(A,eye(2),C,0,T),R1,R2);

% Uses Control System Toolbox product

%u=[]

x0 = [0;0];

2 Specify initial guesses for the unknown parameter values and the auxiliary

parameter value

R2:

par1 = 0.1; % Initial guess for A(1,1)

par2 = -2; % Initial guess for A(1, 2)

par3 = 1; % Initial guess for C(1, 1)

par4 = 3; % Initial guess for C(1, 2)

par5 = 0.2; % Initial guess for R1(1,1)

Pvec = [par1; par2; par3; par4; par5]

auxVal = 1; % R2=1

3 Construct an idgrey model using the m ynoi se M-ﬁle:

Minit = idgrey('mynoise',Pvec,'d',auxVal);

The third input argum ent 'd' speciﬁes a discrete-time system.

4 Estimate the model parameter values from data:

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