卡尔曼滤波(Kalman)Matlab工具箱使用说明书.pdf-资料库

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KALMTOOL Version 2 for Use with MATLAB State Estimation for Nonlinear Systems Technical Report IMM-REP-2000-6 (Revised edition, Dec. 2001) Department of Mathematical Modelling & Department of Automation Technical University of Denmark Magnus Nørgaard December 17, 2002

RELEASE NOTES This note contains important information on how the present toolbox is to be installed, and the conditions under which it may be used. Please read it carefully before use. Before You Start Using the Toolbox After installation, all toolbox functions will be located in one directory, and the ﬁles associated with the demonstration programs will be located in a subdirectory under this. The user should make a path to these directories with the MATLAB function path: >> path(path,’/xx/.../xx/Kalmtool’); >> path(path,’/xx/.../xx/Kalmtool/Demo’); If the toolbox is going to be used on a regular basis, it is recommended to include this statement in the ﬁle startup.m, which is invoked during the start of MATLAB. If a C compiler is available, and the MATLAB mex command has been set up, the MEX functions in the demonstration directory are compiled as follows: >> cd /xx/xx/.../Kalmtool/Demo >> demomex This script invokes the mex command for each of the MEX functions in the demonstra- tion directory. Conditions/Disclaimer By using the toolbox the user agrees to all of the following: • If one is going to publish any work where this toolbox has been used, please include a reference to the article: M. Nørgaard, N.K. Poulsen, O. Ravn: New Developments in State Estimation for Nonlinear Systems, Automatica, (36:11), Nov. 2000, pp. 1627–1638. • Magnus Nørgaard does not provide any support for this product whatsoever. i

ii • The Kalmtool toolbox is shareware. The limited version, which is the one available from the internet, does not include the C source code for the mex-ﬁles. The full version is the same as the limited version, but it includes the source code. The conditions for use are the same for the two versions. The full license can currently be obtained for 85USD/95EUR (single-user license) or 150USD/170EUR (multi- user license). The price does not include support. Please contact the author by e-mail for registration details. The registration requirements are the following: For education and research at the Technical University of Denmark (DTU): Limited and full versions are free. For full-time registered undergraduate and graduate students and for university researchers: The limited version is free. Others: Everyone else are free to download and evaluate the toolbox for a 30 day period but are required to obtain a full license for use beyond 30 days. Exceptions: None. Requests for free access to the source code will not be an- swered. • It is not permitted to utilize any part of the software in commercial products without prior written consent of Magnus Nørgaard. • THE TOOLBOX IS PROVIDED ”AS-IS” WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE IMPLIED WARRANTIES OR CONDITIONS OF MERCHANTABIL- ITY OR FITNESS FOR A PARTICULAR PURPOSE. IN NO EVENT SHALL MAGNUS NØRGAARD BE LIABLE FOR ANY SPECIAL, INCIDENTAL, IN- DIRECT, OR CONSEQUENTIAL DAMAGES OF ANY KIND, OR DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA, OR PROFITS, WHETHER OR NOT MAGNUS NØRGAARD HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES, AND/OR ON ANY THEORY OF LIA- BILITY ARISING OUT OF OR IN CONNECTION WITH THE USE OR PER- FORMANCE OF THIS SOFTWARE. Trademarks of companies and/or organizations mentioned in this documentation ap- pear for identiﬁcation purposes only and are the property of their respective companies and/or organizations. Magnus Nørgaard toolbox@magnusnorgaard.dk

News in version 2 of KALMTOOL Version 2 looks much like version 1 on the surface as there are no new functions. Nev- ertheless, inside all major functions the changes are substantial. Linear Terms in the Equations The DD1 and DD2 ﬁltering functions in the ﬁrst version of the toolbox were written in a very general fashion in the sense that there was no possibility to take advantage of particularly simple terms in the model equations. This has been changed in version 2 so that linear terms can be speciﬁed upon call of the functions. This has a particulaly strong impact on the DD2 ﬁlters as the speed increase here will be very signiﬁcant. The downside of these extensions is that the toolbox code is no longer quite as short, clean and simple as it used to be. In Section 2.6 it will be explained how to call the functions when the equations contain linear terms. Mean Values In version 1 it was possible to specify mean values of the noise processes when calling the functions. I have decided to remove this feature for various reasons. I believe it was rarely needed and to most people it was plainly confusing. If needed, mean values can easily be hard coded or simply passed to the equation functions through the optional initialization matrix optpar.init. Mex functions Starting from Matlab 6, the Windows version now ships with the C compiler lcc (it was shipped even with some versions of Matlab 5.3). Thus, I have not found it necessary to provide compilations of the kalmlib library for all major Windows compilers but only for the lcc compiler. Linux users can still use gcc compiler for their mex-functions. iii

Chapter 1 Introduction This manual is a user’s guide for the KALMTOOL toolbox; a MATLAB toolbox con- taining functions for state estimation for nonlinear systems. The toolbox contains the well-known Extended Kalman Filter (EKF) and two new ﬁlters called the DD1 ﬁlter and the DD2 ﬁlter. The toolbox will run under MATLAB 5.3 and higher, and it is independent of other MATLAB toolboxes. All functions exist as m-ﬁles but for faster execution of the com- putationally intensive functions these have also been written in C and are provided as CMEX-functions. The user will have to add some problem speciﬁc C code and compile the functions with the mex command in order to run the CMEX-functions. Generally, it will require only superﬁcial knowledge about the C programming language to work with the MEX functions. If you run MATLAB under Linux, you can use the gcc compiler. Under Windows you can use the lcc compiler, which now ships with MATLAB. See the External Interfaces manual for MATLAB (formerly known as the Application Program Interface Guide) on how to set up the mex command for these compilers. 1.1 Why this Toolbox? The purpose of this toolbox is to make implementations of the new DD1 and DD2 ﬁl- ters available for solving nonlinear state estimation problems and to enable a comparison with a conventional method like the extended Kalman ﬁlter. So what’s the deal with these ﬁlters? If you are familiar with the EKF, or one of its ‘relatives’, you will quickly ﬁnd out about the advantage of the new ﬁlters. First of all, they are easier to use. Secondly, you can expect a similar (DD1) or better (DD2) performance than with the EKF. On the downside, the new ﬁlters tend to require more computations than the EKF. 1

2 CHAPTER 1. INTRODUCTION What exactly is diﬀerent about the new ﬁlters? To make a short story long, we found that the extended Kalman ﬁlter was somewhat inconvenient to use in some of our appli- cations. A small modiﬁcation of the application sometimes had serious implications on the EKF implementation. Moreover, it was often diﬃcult to implement. Our problem was that the EKF requires a linearization of the system model. Sometimes this is easy to ﬁnd but sometimes it can be pretty hard. In any case, it makes things inﬂexible. If a small change is made in the model, one has to work out a new set of derivatives. This is particularly inconvenient in model calibration where certain model parameters are tem- porarily included in the state vector and estimated simultaneously with the actual states. So where can I read about these ﬁlters? Three publications are available so far. The short introduction: M. Nørgaard, N.K. Poulsen, O. Ravn: Easy and Accurate State Estimation for Nonlinear Systems, 14th IFAC World Conference in Beijing, China, July 5-9, 1999, pp. 343–348. An expanded version: M. Nørgaard, N.K. Poulsen, O. Ravn: New Developments in State Estimation for Non- linear Systems, Automatica, (36:11), Nov. 2000, pp. 1627–1638. The most thorough description (is shipped with the toolbox): M. Nørgaard, N.K. Poulsen, O. Ravn: Advances in Derivative-Free State Estimation for Nonlinear Systems, Technical Report IMM-REP-1998-15, Department of Mathematical Modelling, DTU, 1998 (revised Apr. 2000).

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