(x_est, y_est, P, K) = DiscreteStateSpace.Design.UKF(x_pre, u_pre, y, P_pre, Q, R, alpha, beta, kappa, Ts)
Function UKF computes one recursion of the Unscented Kalman filter. Unscented Kalman filters are similar to Extended Kalman filters but using statistical linearization where extended Kalman filter apply the user-provided derivation of the system equation. Instead of explicit derivation linear regression between spcifically chosen sample points (sigma points). See [1] for more information.
See also UKF_SR, where the square root method to deal with positive definte matrices is applied to solve the mathematically identical problem.
function UKF
extends Modelica.Icons.Function;
import Modelica;
import Modelica_LinearSystems2;
import Modelica_LinearSystems2.DiscreteStateSpace;
input Real xpre[:] "State at instant k-1";
input Real upre[:] "Input at instant k-1";
input Real y[:] "Output at instant k";
input Real Ppre[size(xpre, 1), size(xpre, 1)] "Error covariance matrix at instant k-1";
input Real Q[size(xpre, 1), size(xpre, 1)] = identity(size(xpre, 1)) "Weighted covariance matrix of the associated process noise (F*Q*F')";
input Real R[size(y, 1), size(y, 1)] = identity(size(y, 1)) "Covariance matrix of the measurement noise";
input Real alpha = 0.1 "Spread of sigma points";
input Real beta = 2 "Characteristic of the distribution of x";
input Real kappa = 0 "Kurtosis scaling of sigma point distribution";
input Modelica.Units.SI.Time Ts "Sample time";
output Real x_est[size(xpre, 1)] "Estimated state vector";
output Real y_est[size(y, 1)] "Estimated output";
output Real P[size(Ppre, 1), size(Ppre, 1)] "Error covariance matrix";
output Real K[size(xpre, 1), size(y, 1)] "Kalman filter gain matrix";
replaceable function predict = DiscreteStateSpace.Internal.ukfPredict(redeclare Modelica_LinearSystems2.DiscreteStateSpace.Internal.fSigmaDummy fSigma) annotation(
Documentation(revisions = "<html>
<table border=\"1\" cellspacing=\"0\" cellpadding=\"2\">
<tr>
<th>Date</th>
<th>Author</th>
<th>Comment</th>
</tr>
<tr>
<td valign=\"top\">2010-06-11</td>
<td valign=\"top\">Marcus Baur, DLR-RM</td>
<td valign=\"top\">Realization</td>
</tr>
</table>
</html>"));
replaceable function update = DiscreteStateSpace.Internal.ukfUpdate(redeclare Modelica_LinearSystems2.DiscreteStateSpace.Internal.hSigmaDummy hSigma) annotation(
Documentation(revisions = "<html>
<table border=\"1\" cellspacing=\"0\" cellpadding=\"2\">
<tr>
<th>Date</th>
<th>Author</th>
<th>Comment</th>
</tr>
<tr>
<td valign=\"top\">2010-06-11</td>
<td valign=\"top\">Marcus Baur, DLR-RM</td>
<td valign=\"top\">Realization</td>
</tr>
</table>
</html>"));
replaceable function estimate = DiscreteStateSpace.Internal.ukfEstimate(redeclare Modelica_LinearSystems2.DiscreteStateSpace.Internal.hSigmaDummy yOut) annotation(
Documentation(revisions = "<html>
<table border=\"1\" cellspacing=\"0\" cellpadding=\"2\">
<tr>
<th>Date</th>
<th>Author</th>
<th>Comment</th>
</tr>
<tr>
<td valign=\"top\">2010-06-11</td>
<td valign=\"top\">Marcus Baur, DLR-RM</td>
<td valign=\"top\">Realization</td>
</tr>
</table>
</html>"));
end UKF;| Name | Description |
|---|---|
| predict | |
| update | |
| estimate |
| Date | Author | Comment |
|---|---|---|
| 2010-06-11 | Marcus Baur, DLR-RM | Realization |