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<div class="subTitle">org.apache.commons.math3.filter</div>
<h2 title="Class KalmanFilter" class="title">Class KalmanFilter</h2>
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<pre>public class <span class="strong">KalmanFilter</span>
extends <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></pre>
<div class="block">Implementation of a Kalman filter to estimate the state <i>x<sub>k</sub></i>
of a discrete-time controlled process that is governed by the linear
stochastic difference equation:
<pre>
<i>x<sub>k</sub></i> = <b>A</b><i>x<sub>k-1</sub></i> + <b>B</b><i>u<sub>k-1</sub></i> + <i>w<sub>k-1</sub></i>
</pre>
with a measurement <i>x<sub>k</sub></i> that is
<pre>
<i>z<sub>k</sub></i> = <b>H</b><i>x<sub>k</sub></i> + <i>v<sub>k</sub></i>.
</pre>
<p>
The random variables <i>w<sub>k</sub></i> and <i>v<sub>k</sub></i> represent
the process and measurement noise and are assumed to be independent of each
other and distributed with normal probability (white noise).
<p>
The Kalman filter cycle involves the following steps:
<ol>
<li>predict: project the current state estimate ahead in time</li>
<li>correct: adjust the projected estimate by an actual measurement</li>
</ol>
<p>
The Kalman filter is initialized with a <a href="../../../../../org/apache/commons/math3/filter/ProcessModel.html" title="interface in org.apache.commons.math3.filter"><code>ProcessModel</code></a> and a
<a href="../../../../../org/apache/commons/math3/filter/MeasurementModel.html" title="interface in org.apache.commons.math3.filter"><code>MeasurementModel</code></a>, which contain the corresponding transformation and
noise covariance matrices. The parameter names used in the respective models
correspond to the following names commonly used in the mathematical
literature:
<ul>
<li>A - state transition matrix</li>
<li>B - control input matrix</li>
<li>H - measurement matrix</li>
<li>Q - process noise covariance matrix</li>
<li>R - measurement noise covariance matrix</li>
<li>P - error covariance matrix</li>
</ul></div>
<dl><dt><span class="strong">Since:</span></dt>
<dd>3.0</dd>
<dt><span class="strong">Version:</span></dt>
<dd>$Id: KalmanFilter.java 1539676 2013-11-07 15:15:18Z tn $</dd>
<dt><span class="strong">See Also:</span></dt><dd><a href="http://www.cs.unc.edu/~welch/kalman/">Kalman filter
resources</a>,
<a href="http://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf">An
introduction to the Kalman filter by Greg Welch and Gary Bishop</a>,
<a href="http://academic.csuohio.edu/simond/courses/eec644/kalman.pdf">
Kalman filter example by Dan Simon</a>,
<a href="../../../../../org/apache/commons/math3/filter/ProcessModel.html" title="interface in org.apache.commons.math3.filter"><code>ProcessModel</code></a>,
<a href="../../../../../org/apache/commons/math3/filter/MeasurementModel.html" title="interface in org.apache.commons.math3.filter"><code>MeasurementModel</code></a></dd></dl>
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<th class="colOne" scope="col">Constructor and Description</th>
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<td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/filter/KalmanFilter.html#KalmanFilter(org.apache.commons.math3.filter.ProcessModel, org.apache.commons.math3.filter.MeasurementModel)">KalmanFilter</a></strong>(<a href="../../../../../org/apache/commons/math3/filter/ProcessModel.html" title="interface in org.apache.commons.math3.filter">ProcessModel</a>&nbsp;process,
<a href="../../../../../org/apache/commons/math3/filter/MeasurementModel.html" title="interface in org.apache.commons.math3.filter">MeasurementModel</a>&nbsp;measurement)</code>
<div class="block">Creates a new Kalman filter with the given process and measurement models.</div>
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</tr>
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<td class="colFirst"><code>void</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/filter/KalmanFilter.html#correct(double[])">correct</a></strong>(double[]&nbsp;z)</code>
<div class="block">Correct the current state estimate with an actual measurement.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>void</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/filter/KalmanFilter.html#correct(org.apache.commons.math3.linear.RealVector)">correct</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a>&nbsp;z)</code>
<div class="block">Correct the current state estimate with an actual measurement.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>double[][]</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/filter/KalmanFilter.html#getErrorCovariance()">getErrorCovariance</a></strong>()</code>
<div class="block">Returns the current error covariance matrix.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code><a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/filter/KalmanFilter.html#getErrorCovarianceMatrix()">getErrorCovarianceMatrix</a></strong>()</code>
<div class="block">Returns a copy of the current error covariance matrix.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>int</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/filter/KalmanFilter.html#getMeasurementDimension()">getMeasurementDimension</a></strong>()</code>
<div class="block">Returns the dimension of the measurement vector.</div>
</td>
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<tr class="rowColor">
<td class="colFirst"><code>int</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/filter/KalmanFilter.html#getStateDimension()">getStateDimension</a></strong>()</code>
<div class="block">Returns the dimension of the state estimation vector.</div>
</td>
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<td class="colFirst"><code>double[]</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/filter/KalmanFilter.html#getStateEstimation()">getStateEstimation</a></strong>()</code>
<div class="block">Returns the current state estimation vector.</div>
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<tr class="rowColor">
<td class="colFirst"><code><a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/filter/KalmanFilter.html#getStateEstimationVector()">getStateEstimationVector</a></strong>()</code>
<div class="block">Returns a copy of the current state estimation vector.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>void</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/filter/KalmanFilter.html#predict()">predict</a></strong>()</code>
<div class="block">Predict the internal state estimation one time step ahead.</div>
</td>
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<tr class="rowColor">
<td class="colFirst"><code>void</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/filter/KalmanFilter.html#predict(double[])">predict</a></strong>(double[]&nbsp;u)</code>
<div class="block">Predict the internal state estimation one time step ahead.</div>
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<tr class="altColor">
<td class="colFirst"><code>void</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/filter/KalmanFilter.html#predict(org.apache.commons.math3.linear.RealVector)">predict</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a>&nbsp;u)</code>
<div class="block">Predict the internal state estimation one time step ahead.</div>
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<pre>public&nbsp;KalmanFilter(<a href="../../../../../org/apache/commons/math3/filter/ProcessModel.html" title="interface in org.apache.commons.math3.filter">ProcessModel</a>&nbsp;process,
<a href="../../../../../org/apache/commons/math3/filter/MeasurementModel.html" title="interface in org.apache.commons.math3.filter">MeasurementModel</a>&nbsp;measurement)
throws <a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a>,
<a href="../../../../../org/apache/commons/math3/linear/NonSquareMatrixException.html" title="class in org.apache.commons.math3.linear">NonSquareMatrixException</a>,
<a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a>,
<a href="../../../../../org/apache/commons/math3/linear/MatrixDimensionMismatchException.html" title="class in org.apache.commons.math3.linear">MatrixDimensionMismatchException</a></pre>
<div class="block">Creates a new Kalman filter with the given process and measurement models.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>process</code> - the model defining the underlying process dynamics</dd><dd><code>measurement</code> - the model defining the given measurement characteristics</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if any of the given inputs is null (except for the control matrix)</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonSquareMatrixException.html" title="class in org.apache.commons.math3.linear">NonSquareMatrixException</a></code> - if the transition matrix is non square</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if the column dimension of the transition matrix does not match the dimension of the
initial state estimation vector</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/linear/MatrixDimensionMismatchException.html" title="class in org.apache.commons.math3.linear">MatrixDimensionMismatchException</a></code> - if the matrix dimensions do not fit together</dd></dl>
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<h4>getStateDimension</h4>
<pre>public&nbsp;int&nbsp;getStateDimension()</pre>
<div class="block">Returns the dimension of the state estimation vector.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>the state dimension</dd></dl>
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<pre>public&nbsp;int&nbsp;getMeasurementDimension()</pre>
<div class="block">Returns the dimension of the measurement vector.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>the measurement vector dimension</dd></dl>
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<pre>public&nbsp;double[]&nbsp;getStateEstimation()</pre>
<div class="block">Returns the current state estimation vector.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>the state estimation vector</dd></dl>
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<pre>public&nbsp;<a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a>&nbsp;getStateEstimationVector()</pre>
<div class="block">Returns a copy of the current state estimation vector.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>the state estimation vector</dd></dl>
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<pre>public&nbsp;double[][]&nbsp;getErrorCovariance()</pre>
<div class="block">Returns the current error covariance matrix.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>the error covariance matrix</dd></dl>
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<pre>public&nbsp;<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;getErrorCovarianceMatrix()</pre>
<div class="block">Returns a copy of the current error covariance matrix.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>the error covariance matrix</dd></dl>
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<pre>public&nbsp;void&nbsp;predict()</pre>
<div class="block">Predict the internal state estimation one time step ahead.</div>
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<pre>public&nbsp;void&nbsp;predict(double[]&nbsp;u)
throws <a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></pre>
<div class="block">Predict the internal state estimation one time step ahead.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>u</code> - the control vector</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if the dimension of the control vector does not fit</dd></dl>
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<pre>public&nbsp;void&nbsp;predict(<a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a>&nbsp;u)
throws <a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></pre>
<div class="block">Predict the internal state estimation one time step ahead.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>u</code> - the control vector</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if the dimension of the control vector does not match</dd></dl>
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<pre>public&nbsp;void&nbsp;correct(double[]&nbsp;z)
throws <a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a>,
<a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a>,
<a href="../../../../../org/apache/commons/math3/linear/SingularMatrixException.html" title="class in org.apache.commons.math3.linear">SingularMatrixException</a></pre>
<div class="block">Correct the current state estimate with an actual measurement.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>z</code> - the measurement vector</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if the measurement vector is <code>null</code></dd>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if the dimension of the measurement vector does not fit</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/linear/SingularMatrixException.html" title="class in org.apache.commons.math3.linear">SingularMatrixException</a></code> - if the covariance matrix could not be inverted</dd></dl>
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<h4>correct</h4>
<pre>public&nbsp;void&nbsp;correct(<a href="../../../../../org/apache/commons/math3/linear/RealVector.html" title="class in org.apache.commons.math3.linear">RealVector</a>&nbsp;z)
throws <a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a>,
<a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a>,
<a href="../../../../../org/apache/commons/math3/linear/SingularMatrixException.html" title="class in org.apache.commons.math3.linear">SingularMatrixException</a></pre>
<div class="block">Correct the current state estimate with an actual measurement.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>z</code> - the measurement vector</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if the measurement vector is <code>null</code></dd>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if the dimension of the measurement vector does not fit</dd>
<dd><code><a href="../../../../../org/apache/commons/math3/linear/SingularMatrixException.html" title="class in org.apache.commons.math3.linear">SingularMatrixException</a></code> - if the covariance matrix could not be inverted</dd></dl>
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