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Posted to dev@commons.apache.org by lu...@apache.org on 2007/03/13 21:02:57 UTC
svn commit: r517838 -
/jakarta/commons/proper/math/trunk/xdocs/userguide/estimation.xml
Author: luc
Date: Tue Mar 13 13:02:56 2007
New Revision: 517838
URL: http://svn.apache.org/viewvc?view=rev&rev=517838
Log:
added a section for the estimation package in the user guide
Added:
jakarta/commons/proper/math/trunk/xdocs/userguide/estimation.xml (with props)
Added: jakarta/commons/proper/math/trunk/xdocs/userguide/estimation.xml
URL: http://svn.apache.org/viewvc/jakarta/commons/proper/math/trunk/xdocs/userguide/estimation.xml?view=auto&rev=517838
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--- jakarta/commons/proper/math/trunk/xdocs/userguide/estimation.xml (added)
+++ jakarta/commons/proper/math/trunk/xdocs/userguide/estimation.xml Tue Mar 13 13:02:56 2007
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+<?xml version="1.0"?>
+
+<!--
+ Licensed to the Apache Software Foundation (ASF) under one or more
+ contributor license agreements. See the NOTICE file distributed with
+ this work for additional information regarding copyright ownership.
+ The ASF licenses this file to You under the Apache License, Version 2.0
+ (the "License"); you may not use this file except in compliance with
+ the License. You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+ Unless required by applicable law or agreed to in writing, software
+ distributed under the License is distributed on an "AS IS" BASIS,
+ WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ See the License for the specific language governing permissions and
+ limitations under the License.
+ -->
+
+<?xml-stylesheet type="text/xsl" href="./xdoc.xsl"?>
+<!-- $Revision: 480435 $ $Date: 2006-11-29 08:06:35 +0100 (mer., 29 nov. 2006) $ -->
+<document url="estimation.html">
+
+ <properties>
+ <title>The Commons Math User Guide - Parametric Estimation</title>
+ </properties>
+
+ <body>
+ <section name="12 Parametric Estimation">
+ <subsection name="12.1 Overview" href="overview">
+ <p>
+ The estimation package provides classes to fit some non-linear model
+ to available observations depending on it. These problems are commonly
+ called estimation problems.
+ </p>
+ <p>
+ The estimation problems considered here are parametric problems where
+ a user-provided model depends on initially unknown scalar parameters and
+ several measurements made on values that depend on the model are available.
+ As examples, one can consider the center and radius of a circle given
+ points approximately lying on a ring, or a satellite orbit given range,
+ range-rate and angular measurements from various ground stations.
+ </p>
+ <p>
+ One important class of estimation problems is weighted least squares problems.
+ They basically consist in finding the values for some parameters p<sub>k</sub>
+ such that a cost function J = ∑(w<sub>i</sub> r<sub>i</sub><sup>2</sup>)
+ is minimized. The various r<sub>i</sub> terms represent the deviation
+ r<sub>i</sub> = mes<sub>i</sub> - mod<sub>i</sub> between the measurements and
+ the parameterized models. The w<sub>i</sub> factors are the measurements weights,
+ they are often chosen either all equal to 1.0 or proportional to the inverse of
+ the variance of the measurement type. The solver adjusts the values of the
+ estimated parameters p<sub>k</sub> which are not bound (i.e. the free parameters).
+ It does not touch the parameters which have been put in a bound state by the user.
+ </p>
+ <p>
+ The aim of this package is similar to the aim of the optimization package, but the
+ algorithms are entirely differents as:
+ <ul>
+ <li>
+ they need the partial derivatives of the measurements
+ with respect to the free parameters
+ </li>
+ <li>
+ they are residuals based instead of generic cost functions based
+ </ul>
+ </p>
+
+ </subsection>
+ <subsection name="12.2 Models" href="models">
+ The <a href="../apidocs/org/apache/commons/math/estimation/EstimationProblem.html">
+ org.apache.commons.math.estimation.EstimationProblem</a> interface is a very
+ simple container packing together parameters and measurements.
+ </subsection>
+ <subsection name="12.3 Parameters" href="parameters">
+ <p>
+ The <a href="../apidocs/org/apache/commons/math/estimation/EstimatedParameter.html">
+ org.apache.commons.math.estimation.EstimatedParameter</a> class to represent each
+ estimated parameter. The parameters are set up with a guessed value which will be
+ adjusted by the solver until a best fit is achieved. It is possible to change which
+ parameters are modified and which are preserved thanks to a bound property. Such
+ settings are often needed by expert users to handle contingency cases with very
+ low observability.
+ </p>
+ </subsection>
+ <subsection name="12.4 Measurements" href="measurements">
+ <p>
+ The user extends the <a href="../apidocs/org/apache/commons/math/estimation/WeightedMeasurement.html">
+ org.apache.commons.math.estimation.WeightedMeasurement</a> abstract class to define its
+ own measurements. Each measurement types should have its own implementing class, for
+ example in the satellite example above , the user should define three classes, one
+ for range measurements, one for range-rates measurements and one for angular measurements.
+ Each measurement would correspond to an instance of the appropriate class, set up with
+ the date, a reference to the ground station, the weight and the measured value.
+ </p>
+ </subsection>
+ <subsection name="12.5 Solvers" href="solvers">
+ <p>
+ The package provides two common <a href="../apidocs/org/apache/commons/math/estimation/Estimator.html">
+ org.apache.commons.math.estimation.Estimator</a> implementations to solve weighted
+ least squares problems. The first one is based on the
+ <a href="../apidocs/org/apache/commons/math/estimation/GaussNewtonEstimator.html">Gauss-Newton</a> method.
+ The second one is based on the
+ <a href="../apidocs/org/apache/commons/math/estimation/LevenbergMarquardtEstimator.html">Levenberg-Marquardt</a>
+ method. The first one is best suited when a good approximation of the parameters is known while the second one
+ is more robust and can handle starting points far from the solution.
+ </p>
+ </subsection>
+ </section>
+ </body>
+</document>
Propchange: jakarta/commons/proper/math/trunk/xdocs/userguide/estimation.xml
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