MATLAB CONTROL SYSTEM TOOLBOX 9 Specifikace stáhnout pdf (Strana 242)

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101

10 Design Case Studies

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For simplicity, we have dropped the subscripts indicating the time dependence

of the state-space matrices.

Given initial conditions and , you can iterate these equations to

perform the filtering. Note that you must update both the state estimates

and error covariance matrices at each time sample.

Time-Varying Design

Although the Control System Toolbox does not offer specific commands to

perform time-varying Kalman filtering, it is easy to implement the filter

recursions in MATLAB. This section shows how to do this for the stationary

plant considered above.

First generate noisy output measurements

% Use process noise w and measurement noise v generated above

sys = ss(A,B,C,0,-1);

y = lsim(sys,u+w); % w = process noise

yv = y + v; % v = measurement noise

Given the initial conditions

you can implement the time-varying filter with the following

for loop.

P = B*Q*B'; % Initial error covariance

x = zeros(3,1); % Initial condition on the state

ye = zeros(length(t),1);

ycov = zeros(length(t),1);

for i=1:length(t)

% Measurement update

Mn = P*C'/(C*P*C'+R);

x = x + Mn*(yv(i)-C*x); % x[n|n]

P = (eye(3)-Mn*C)*P; % P[n|n]

ye(i) = C*x;

errcov(i) = C*P*C';

% Time update

x 10

[]

P 10

[]

xn.

[]

Pn.

[]

x 10

[]

0,= P 10

[]

BQB

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