COMP 145 UNC-Chapel Hill Maintenance Manual The Kalman
Contents
1. stq_F stq_S oe oe Run sim of level sensors ale o Input T truth struct with fields L actual levels struct w fields L C constant L F filling L S sloshing L FS filling and sloshing L SO slosh around 0 m measured values struct level linear fields m 1 C m 1 F m 1 S m 1 FS angle nonlinear fields m a C m a F m a S m a FS ts time steps second a bunch of other parameters that need to come from truth cda char specifying ACTUAL dynamics C F S FS cdm char specifying MODELED dynamics C F S FS cm char specifying the measurement type L A sr_scale meas noise factor to play 0 01 0 1 1 10 100 sq_scale process noise factor to play 0 01 0 1 1 10 100 ale o Ae ale Je lO ale A AP AP dP OS ole misc globals global d2r r2d d2r pi 180 0 constant to convert degree to radian r2d 180 0 pi constant to convert radian to degree temporal parameters stime T stime length of sim second mrate T mrate measurement rate 1 second dt 1 mrate water level limits L_min T L_min where start filling etc meter L_max T L_max full meter o Measurement device parameters global db df ka kl db T db Base for angular sensor just above the max water meter df T df Angular sensor arm w float long enough to hit bottom on empty meter ka T ka Angular non linear float scale constant kl2. F zeros 1 T nmeas L F 1 mf 1 T L_min L F mf T nmeas T L_min fmeas T L_max m 1 F T k1 L F n l level measured m a F T ka r2d asin T db L F T df n a angle measured signal angle non linear 3 Sloshing S see equation 3 in document models L SO T sm sin 2 pi T ts T sf T sp d2r L S T L_min L SO m 1 S T k1 L S n l level measured m a S T ka r2d asin T db L S T df n a angle measured signal angle non linear 4 Filling Sloshing FS ole A see equations 2 and 3 in document oe put true Level and measurement information L L m HH m return signal level linear noise noise around 0 signal level linear noise noise models L FS L F L S0 sum of filling and sloshing slosh around 0 not min m 1 FS T k1 L FS n l level measured signal level linear noise m a FS T ka r2d asin T db L FS T df n a angle measured signal angle non linear noise in struct Index actual dynamics in parameter window 6 setting 10 adding a file 7 applet version 4 application version 4 checking in a file 7 checking out a module 7 control buttons Edit 11 Help 11 Plot 11 Step 11 CVS 7 12 comment procedures 8 CVSROOT 7 data tab delimited saving to file 4 data repository 6 IDE initial project development 12 Implementation Manual updating 8 Jama module 4 Java API
3. bring it up to date with the files currently in the repository by doing the following 1 Goto your local workspace that you desire to update e g cd afs cs unc edu home parker kfcode 2 Update the module s e g cvs update kftool 4 2 Editing the source To modify an existing source code file for any module s 1 Checkout the source code see 84 1 2 Modify the file s in your local workspace as desired 3 Rebuild the project see 84 3 4 Checkin the modified file s 1 e cvs commit filename To create a new source code file for any module s 1 Checkout the source code see 84 1 2 Create the file s in your local workspace as desired 3 Rebuild the project modifying the build procedures as appropriate see 84 3 4 Add and checkin the new file s 1 e cvs add filename cvs commit filename 4 PROCEDURES 8 Note CVS allows you to provide a message anytime you add or commit a file The message is simply a comment added to the change log in which you can give some reason for modifying the code Using this feature is recommended to get the most out of version control To learn more about messaging type man cvs or see http www cvshome org docs manual cvs html 4 3 Building the project The Makefile in the kftool module is provided to facilitate the process of building an executable for The Kalman Filter On line Learning Tool Touse the Makefile do the following 1 Read and follow the directions in k
4. f_tool Makefile 2 Build the desired target e g make all 4 4 Testing the system Whenever The Kalman Filter On line Learning Tool source code is modified testing its output for correctness is recommended The following two methods of testing are suggested e The test_data module contains data files for every permutation of the input parameters to the Kalman filter simulation The tab delimited data output saved to file by the application version of The Kalman Filter On line Learning Tool should be identical to a data file in the test_data module according to the simulation parameters used as input The random number generator used will produce identical results for a given set of input parameters so long as the seed stays the same For more information see the java util Random class However if the random number generator and or its seed are modified comparison against these data files will not be a good test In fact if the random number generator is modified replacing the data files of the test_data module with new data files believed to be correct for the modified random number generator is recommended to facilitate testing of subsequent versions of The Kalman Filter On line Learning Tool e Comparison with output of the client s Matlab code see Appendix D is also a good way to test the accuracy of the simulation data and plots Note that output the Matlab implementation of the Kalman filter simulation will differ
5. in The Kalman Filter On line Learning Tool project package 3 SYSTEM OVERVIEW 4 3 System Overview 3 1 Project modules All project files are stored in a CVS repository see 84 1 and belong to one of the following project modules kftool This module contains the source code for The Kalman Filter On line Learning Tool application and applet Sections 3 2 and 3 3 are devoted to the discussion of this module Note The appli cation version of The Kalman Filter On line Learning Tool includes an option for saving tab delimited simulation data to file The applet version does not include this option because Java s secu rity features forbid applets from accessing the local file system Otherwise the two versions of the tool are the same ptplot3 1p1 This module contains source code for the plot software used in this project and is included for archival purposes Jama The module contains source code for the Java matrix package used in this project and is included for archival purposes matlab_code This module contains source code for a Matlab implementation of the Kalman filter sim ulation see Appendix D manuals This module contains files for the Maintenance Manual Implementation Manual and Java API Documentation for The Kalman Filter On line Learning Tool latex_doclet This module contains software for generating the Java API Documentation for The Kalman Filter On line Learning Tool docum
6. slightly from the Java implementation since a different random number generator is used and the source code is not identical However the Matlab output of data and plots should certainly be similar to thatof The Kalman Filter On line Learning Tool 4 5 Updating the documentation Updates to the documentation are recommended as The Kalman Filter On line Learning Tool source code is modified Of course these procedures are optional and have no effect on the functionality of the tool The Implementation Manual and Maintenance Manual should be updated as necessary i e when sig nificant changes are made to the source code Both documents are written in IEX and the tex files are located in the manuals module For more information on I4TpX type man latex 4 PROCEDURES 9 The Java API Documentation for The Kalman Filter On line Learning Tool doc ument should be regenerated whenever changes to the source code affect its documentation e g dele tion addition of project classes deletion addition of class methods deletion addition of method parameters etc The software for generating the Java doclet is located in the latex doclet module The following two steps are suggestions for updating the Java API Documentation for The Kalman Filter On line Learning Tool document 1 Add delete edit Javadoc comments in the source code The general form of a Javadoc comment is the following This is
7. the description part of a doc comment tag Comment for the tag 7 For more information on how to write Javadoc comments see http java sun com j2se javadoc writingdoccomments 2 Generate the Java doclet using the following suggested steps a Go to your local workspace where you have previously checked out the source code e g cd afs cs unc edu home parker kfcode b Make certain the latex doclet module has been checked out e g cvs checkout latex doclet c Go to the kftool module 1 e cd kftool d Use the Makefile to execute the Java doclet software 1 e make latex _docs e A file doclet tex will be written to the latex_doc subdirectory of kftool so go to that subdirectory 1 e cd latex_doc Send doclet tex to the IATEX interpreter to produce the postscript document doclet ps 1 latex doclet tex dvips o doclet ps doclet A APPENDIX THE USER MANUAL 10 A Appendix The User Manual The User Manual is provided to give the reader some context for how the The Kalman Filter On line Learning Tool is to be used as well as to document a set of instructions should they ever be needed A l 1 A 2 Quick Start Gotohttp www cs unc edu parker comp145 kalman html Click on Use The Kalman Filter On line Learning Tool Leave the controls in their default settings Click on the Plot button View the plots Close the plot window Desc
8. 12 design guidelines 12 Java doclet 12 updating 8 9 Javadoc comments 9 JDK requirements 12 jlfgr module 4 Kalman filter what is the 3 Kalman filter engine 6 kftool module 4 latex_doclet module 4 main window 5 Maintenance Manual updating 8 manuals module 4 Matlab code 8 14 matlab_code module 4 matrix package see Jama initial project development 12 measurement noise in parameter window 6 setting 10 measurement type in parameter window 6 setting 10 modeled dynamics in parameter window 6 setting 10 parameter window 6 plot window 6 plotting tool see ptplot3 1p1 initial project development 12 plug in requirements 12 project build procedures 8 ptplot3 1p1 module 4 step window 6 test_data module 4 8 testing the tool for correctness 4 8 The Kalman Filter On line Learning Tool what is the 3 truth see actual dynamics web browser requirements 12 web module 4
9. COMP 145 UNC Chapel Hill Maintenance Manual The Kalman Filter On line Learning Tool Greg Welch client May 1 2001 DOCUMENT CHANGE HISTORY Document Change History e March 8 2001 Annotated Outline e March 25 2001 Matlab code appendix e April 14 30 2001 Filled in annotated outline CONTENTS Contents 1 2 Document Change History Introduction 2 1 Statement of purpose 22 Document conventions 0 0 0 00000 ee ee System Overview 321 Projectmodules s s irai is Ba we Be ae Ae a A a ee S 3 2 High level view of the kftool module o 2 0 00 000000 3 3 Low level view of the kftool module o 0 2 a Procedures 4 1 Getting the Sourc eri 4 soe oot ee we ae par ed Re a OE ete A 4 2 Editing the Sotie ita wee Rae a ates ea Seow bape ee 4 3 Building the project ee 4 4 Testing the Systems loen d dae a A Bb a eee 4 5 Updating the documentation 20 000 000 eee eee eee Appendix The User Manual Av Quick Starts aora a bok wa a aan a aioe ak Gat dard eat ea de We wot A 2 Descriptions of the parameter settings and control buttons Appendix Development System Requirements and Information Appendix Contact Information Appendix Matlab Code for the Kalman Filter Delt ASMA A ack a ee ee ae Ad Go Se Ae ed DZ OUR shew ef th aa e a Shas ak a de Oh a ae lad Ra eel a Blas D3 ga ali back e 20 da Ao we a wee eo ae Sg Sean ee Sa Se an
10. T kl Level linear float parameters scale constant Sloshing sinusoidal parameters f T sf slosh sin frequency 1 second sp T sp slosh phase degree n 2 2 measurement noise magnitudes srl_m sr_scale T srl_m stdev of level linear sensor noise meter sra_d sr_scale T sra_d stdev of angule non linear sensor noise degree 2 2 D APPENDIX MATLAB CODE FOR THE KALMAN FILTER Set up filter parameters Four possibilities 1 Constant level C 2 Filling F 3 Sloshing S 4 Filling Sloshing FS JA P V dP y AP y a if nargin 6 normal situation stq_C 1 5 9609e 05 Tuned Constant w linear meas ale ole stq_C 2 3 5936e 05 Tuned Constant w angular meas sq_C mean stq_C avg of the two stq_F 1 1 9638 Tuned Filling w linear meas stq_F 2 2 027 Tuned Filling w angular meas sq_F mean stq_F avg of the two stq_sS 1 5 9609e 05 Tuned Sloshing w linear meas stq_S 2 5 9609e 05 Tuned Sloshing w angular meas 2 sq_S mean stq_S avg of the two special tune case for filling and sloshing if cdm FS stq_F 1 0 0028009 Tuned Filling w linear meas stq_F 2 0 0021271 Tuned Filling w angular meas sq_F mean stq_F avg of the two stq_S 1 0 0014462 Tuned Sloshing w linear meas stq_S 2 0 0010254 Tuned Sloshing w angular meas sq_S mean stq_S avg of the two end elseif nargin 9 tuning
11. as predict S Xp k A k S Xc k 1 SPD KI Att pty KY S P a SOFA A FE Oer ea KE ole measurement prediction and Jacobian S Zp k meas S Xp k mtype sd H measJacobian S Xp k mtype sd correct SKEGA S Pp k H inv H S Pp k H R Kalman gain S Xc k S Xp k S K k Za k S Zp k S Pc k eye sd S K k H S Pp k end 18 D APPENDIX MATLAB CODE FOR THE KALMAN FILTER return local subroutine for measurement model function Zp meas Xp mtype sd global db df ka r2d if mtype 1 Linear measurement model see Section 2 1 in document models A le H measJacobian Xp mtype sd Zp H Xp else 2 Angular measurement model see Section 2 2 and equation 13 in document models as db Xp 1 df if as gt 1 as 1 elseif as lt 1 as 1 end Zp r2d ka asin as end return local subroutine for measurement model Jacobian function H measJacobian Xp mtype sd global db df ka kl r2d if mtype 1 Linear measurement model see Section 2 1 in document models ae A H zeros 1 sd H 1 1 kl else Angular measurement model see Section 2 2 and equation 14 in document models H zeros 1 sd as2 db Xp 1 df 2 H 1 1 r2d ka df sqrt abs 1 as2 end return D 2 gui m da uicontrol Style Popup String Constant Fill Slosh Fill amp Sl
12. d title sprintf Measurement Residual s cm return 21 D APPENDIX MATLAB CODE FOR THE KALMAN FILTER D5 truth m function T truth seed AP AIP AP P AP P AP AP AP AP AP AP AP PV AP OP AAP V OP x d2r pi 180 0 r2d 180 0 pi 2 Generate truth signals Input seed random number seed allows it to generate repeatable results Output T truth struct with fields L actual levels struct w fields L C constant L F filling L S sloshing L FS filling and sloshing L SO slosh around 0 m measured values struct level linear fields m 1 C m 1 F m 1 S m 1 FS angle nonlinear fields m a C m a F m a S m a FS ts time steps second misc globals constant to convert degree to radian constant to convert radian to degree 2 2 seed random number generator randn state seed ole 3 J ole 3 1 ole 3 1 ole J temporal parameters stime 5 length of sim second mrate 50 measurement rate 1 second nmeas T stime T mrate 1 water level limits L_min 0 3 where start filling etc meter L_max 1 0 full meter Angular non linear float parameters do T L_max 0 02 base for angular sensor just above the max water meter df 1 25 T db angular sensor arm w float long enough to hit bottom on empty meter ka 1 0 Level linear float parameters kl 1 0 measurement noise magnitudes s
13. e wh ne Ae ae DA PbO WSs Mt ea Abie Gee SG Bese Bs Sea ok ede ese a ee a eta Ss Gee See Sen DDD 9 tea Ty eee Se hi we a 3d Se ee dk ee ea Ge ee Se ai 10 10 10 12 13 2 INTRODUCTION 3 2 Introduction 2 1 Statement of purpose The purpose of this document is to provide instructions and guidance for the client or technical staff ap pointed by the client to use when extending modifying The Kalman Filter On line Learning Tool This manual does not attempt to anticipate every concern that may arise during the development of later versions of The Kalman Filter On line Learning Tool Instead it gives guidelines information and pointers that proved useful during the initial development of the tool The Kalman filter is a set of mathematical equations that provides an efficient computational esti mate of the state of a process e g the position and orientation of an airplane given a time varying se quence of noisy measurements e g air speed pressure temperature engine thrust The filter is a popular mathematical estimator due to its efficiency and robustness For more information on the Kalman filter see http www cs unc edu welch kalman index html The Kalman Filter On line Learning Tool is a web based tool to help develop the intuition and insight of novice users regarding the behavior of the Kalman filter Users have the ability to change various input parameters and then see how the Kalman filter responds for a given set o
14. ent a Java doclet The software reads Javadoc comments embedded in source code and conveniently produces a IATEX document which displays the in formation in an organized manner Refer to Section 4 5 for instructions on creating updating Javadoc comments and generating the Java doclet test_data This module contains simulation data generated by the application version of The Kalman Filter On line Learning Tool for every permutation of the input parameters These data files may be used to test the correctness of the tool in the case that it has been modified Refer to Section 4 4 for testing guidelines jlfgr This module contains a collection of toolbar button graphics The graphics have been designed specifically for use with the Java look and feel They conform to the Java look and feel Design Guide lines The step window s button icons use look and feel graphics For more information see http java sun com products jlf dg index htm web This module contains the files necessary for running The Kalman Filter On line Learn ing Tool applet The files should be copied to any space desiring to host the applet For more information see the README file in the web module 3 SYSTEM OVERVIEW 5 3 2 High level view of the kftool module The kftool module is largest and most important module of the project It contains source code for The Kalman Filter On line Learning Tool application and applet The module is divided into si
15. est in the simulation The buttons within the step window allow different time instances to be selected at which the behavior of the filter is most interesting B APPENDIX DEVELOPMENT SYSTEM REQUIREMENTS AND INFORMATION 12 B Appendix Development System Requirements and Information The following are requirements for extensions modifications to the project e Java Development Kit JDK 1 3 0 for Linux or Sun from Sun includes Java 2 RTE and Java Hotspot Client VM e Java Plug in 1 3 allows a browser to view web pages using Java 2 RTE available at http java sun com products plugin for more information see http java sun com products plugin 1 3 overview html The following is information about tools used in the initial project development provided in case they can be useful for further development of the project e Integrated Development Environment Forte for Java 2 0 from Sun available at http www sun com forte ff3 e Plotting Tool Ptplot 3 1 available athttp ptolemy eecs berkeley edu java ptplot3 1 ptolemy plot doc e Java Matrix Package Jama 1 0 1 available at http math nist gov Javanumerics jama e Version Control Software CVS 1 10 7 for more information see http www cvshome org docs manual cvs html or type man cvs e IATEX2 Generating Java doclet available at http www c2 tech com java TexDoclet This optional information proved to be helpful during
16. f noisy measurements It is assumed that the reader of this document has a general understanding of how The Kalman Fil ter On line Learning Tool works In particular it is strongly advised that the reader thoroughly review the User Manual see Appendix A and experiment with the tool before reading the rest of this document It is also advised that the reader have experience with the Java programming language 2 2 Document conventions e Command line instructions and URLs appear inthis font e CVS see 4 1 project modules appear in this font e The Kalman Filter On line Learning Tool always refers to the application to which this manual pertains 2 3 Other relevant documents e The client Greg Welch provides Matlab source code that executes the same simulation as The Kalman Filter On line Learning Tool see Appendix D e Detailed documentation of the project packages classes and interfaces is provided in Java API Documentation for The Kalman Filter On line Learning Tool The Implementation Manual is also helpful for navigating the source code Both are referenced in the remainder of this document and are included in The Kalman Filter On line Learning Tool project package e The Dynamic and Measurement Models document written by the client Greg Welch provides a de scription of the simulation performed by The Kalman Filter On line Learning Tool It is referenced in the remainder of this document and is included
17. for passing to the data repository The main window also passes formatted simulation data from the data repository to the plot window and the step window In the application version of the tool the main window also allows the user to save tab delimited simulation data to file receiving such data from the data repository 3 SYSTEM OVERVIEW 6 Parameter window The parameter window gives the user an opportunity to modify the default parameters of the Kalman filter simulation The user may select among several options for the actual dynamics the modeled dynamics the measurement type and the measurement noise For more information about the purpose of these parameters see the Dynamic and Measurement Models document Plot window The plot window displays three plots of simulation data to the user Plot 1 displays the values of truth and estimate for each time step Plot 2 displays the covariance values for each time step Plot 3 displays the residual values for each time step Step window The step window allows the user to step through the actual simulation data for a given time step Kalman filter engine The Kalman filter engine performs the simulation according to the parameters passed from the main window which are either the default parameters or the parameters specified by the user in the parameter window The Kalman filter engine generates raw simulation data and passes it to the main window which then passes it to the data repo
18. iance for m 1 T nmeas Q 1 1 m qce dt 3 3 0 Q 1 2 m qe dt 2 2 0 Q 2 1 m Q 1 2 m Q 2 2 m qce dt end oe Set aside space for results S Xp zeros sd T nmeas predicted state X S Xc zeros sd T nmeas corrected S Pp zeros sd sd T nmeas predicted covariance P S Pc zeros sd sd T nmeas corrected S Zp zeros 1 T nmeas predicted measurement Z S K zeros sd T nmeas Kalman gain Initialize filter L_init L_max 2 0 initial guess S Xp 1 1 L_init S Xc 1 1 L_init S Pp 1 L_max 2 0 0 L_max stime 2 S3Peey 1 L_max 2 0 0 L_max stime 2 case S Sloshing State dimension sd 2 Dynamic process model see Section 1 2 3 and equations 6 and 7 in document models ae ol A zeros sd sd T nmeas w 2 pi sf omega for m 1 T nmeas A 1 1 m 1 A 2 2 m 1 A 1 2 m w cos w T ts m sp d2r end Q zeros sd sd T nmeas qc sq_scale sq_S 2 scale qc then square for variance for m 1 T nmeas 0 1 1 m qc w 2 cos w T ts m 2 dt 3 T ts m 2 3 T ts m dt dt 2 3 0 Q 1 2 m w cos w T ts m qce dt 2 T ts m dt 2 0 Q 2 1 m Q 1 2 m 16 APPENDIX MATLAB CODE FOR THE KALMAN FILTER 0 2 2 m gc dt end Set aside space for results S Xp zeros sd T nmeas predicted state X S Xc zeros sd T nmeas corrected S Pp zeros sd sd T nmeas predicted covariance P S Pc zeros sd
19. nt Type The measurement type feature allows the user to select whether the device used to measure the water level in the tank is i the height of a float on top of the water or 11 the angle of a mechanical arm whose end sits on top of the water Mathematically this difference is significant because in the linear float case the state of the process the actual level of the water is a linear function of the measurements received In the angular case however the state of the process is a more sophisticated sine function with respect to the measurements received The Kalman filter equations must take this difference into account and are more complex in the angular case It is recommended that the user thoroughly understand the linear case before running simulations in the angular case Measurement Noise The measurement noise determines the accuracy of the measurements to which the filter has access Real systems using the Kalman filter will have different qualities of measurement as determined by the precision of the measurement instruments available and features of the environment A APPENDIX THE USER MANUAL 11 in which the system operates The The Kalman Filter On line Learning Tool allows the user to simulate these differences by inserting random noise in levels commensurate with the simulated environment system Edit The edit button in the main window allows the user to select the desired actual dynamics modeled dynamics measurement ty
20. osh Position 20 320 100 50 dm uicontrol Style Popup String Constant Fill Slosh Fill amp Slosh Position 120 320 100 50 mm uicontrol Style Popup String Linear Angular Position 220 320 100 50 go uicontrol Style Pushbutton Position 20 150 100 70 Callback guiCallback String Go D 3 guiCallback m vda get da Value vdm get dm Value vmm get mm Value 19 D APPENDIX MATLAB CODE FOR THE KALMAN FILTER switch vda case 1 cda C Case 2 cda F Case 3 cda S case 4 cda FS otherwise error Unknown actual dynamic model type end switch vdm case 1 cdm C case 2 cdm F case 3 cdm S case 4 cdm FS otherwise error Unknown measured dynamic model type end switch vmm case cm case cm A otherwise error Unknown measurement model type end bh ied N Il meas_scale 100 process_scale 1 T truth 0 S dosim T cda cdm cm meas_scale process_scale plotSim T S cda cdm cm D 4 plotSim m function plotSim T S cda cdm cm scrsz get 0 ScreenSize h figure 2 set h Position 1 scrsz 4 2 scrsz 3 2 scrsz 4 Level pane 1 h subplot 3 1 pane switch cda case C plot T ts 5 XO Ll TES ToL C0 case F pl
21. ot T ts S Xc 1 T ts T L F case S plot TyvEs XC Ly Ts T LS case FS plot T ts S Xc 1 T ts T L FS otherwise error Unknown dynamic model type end min_x 0 max_x T stime 20 D APPENDIX MATLAB CODE FOR THE KALMAN FILTER min_y 0 max_y T L_max axis min_x max_x min_y max_y xlabel t second ylabel L meter title sprintf Actual s vs Estimated s cda cdm o Covariance pane 2 h subplot 3 1 pane semilogy T ts sqrt squeeze S Pc 1 1 min_x 0 max_x T stime min_y 0 max_y T L_max axis min_x max_x min_y max_y xlabel t second ylabel sqrt P meter title sprintf Process deviation cda cdm o Measurement residuals pane 3 h subplot 3 1 pane switch cda case C if cm L plot T ts T m 1 C S Zp else plot T ts T m a C S Zp end case F if cm L plot T ts T m 1 F S Zp else plot T ts T m a F S Zp end case S if cm L plot T ts T m 1 S S Zp else plot T ts T m a S S Zp end case FS if cm L plot T ts T m 1 FS S Zp else plot T ts T m a FS S Zp end otherwise error Unknown dynamic model type end min_x 0 max_x T stime min_y 0 max_y T L_max Saxis min_x max_x min_y max_y xlabel t second if cm L ylabel dL meter else ylabel Angle degree en
22. pe and measurement noise Plot The plot button performs the simulation for a fixed amount of time At each instant the actual level of the water is determined based on the user s choice of actual dynamics Noisy measurements are then available to the filter based on the measurement noise and measurement type selected by the user The Kalman filter then uses the modeling function selected by the user as a part of the Kalman filter equations to determine the filter s estimate of the state of the water These quantities are then plotted in a separate window If some part of the plot is of particular interest the mouse may be used to draw a rectangle around that region causing it to be shown in more detail Help The help button allows the user to see the help features built into The Kalman Filter On line Learning Tool Step After developing a general feel for how the Kalman filter behaves with different combinations of truth and estimate functions the stepping mode is designed to allow users to study exactly how this behavior is achieved via the actual Kalman filter equations The step function shows for a selected time step the decimal values that determine the true state predicted state corrected state actual measurement predicted measurement Kalman gain predicted covariance and corrected covariance These values are displayed for two adjacent time steps so that the user can see how the equations compute these quantities at points of inter
23. r L_init L_max 2 0 initial guess S Xp 1 1 L_init S Xc 1 1 L_init S Xp 3 1 T sm temp cheat S Xc 3 1 T sm S Pp 1 L_max 2 0 0 0 L_max stime 2 0 0 0 L_max 2 72 S Pc 1 L_max 2 0 0 0 L_max stime 2 0 0 0 L_max 2 2 otherwise D APPENDIX MATLAB CODE FOR THE KALMAN FILTER error Unknown dynamic model type end Choose the set of measurements based on the input selector cda actual dynamics switch cda case C Constant level 2 Measurement model a o if mtype 1 Za T m l C actual measurements else Za T m a C actual measurements end case F Filling level 9 Measurement model if mtype 1 Za T m 1 F actual measurements else Za T m a F actual measurements end case S Sloshing level 2 Measurement model if mtype 1 Za T m 1 S actual measurements else Za T m a S actual measurements end case FS Filling and Sloshing level 2 Measurement model if mtype 1 Za T m 1 FS actual measurements else Za T m a FS actual measurements end otherwise error Unknown dynamic model type end Measurement noise model if mtype 1 see Section 2 1 in document models srl_m k1 72 e see Section 2 2 in document models sra_d ka 2 ole U W el an en o Loop through all measurements for k 2 T nme
24. riptions of the parameter settings and control buttons Actual Dynamics The actual dynamics determine how the water level will actually behave in the simu lation The default is that the water will remain at a constant level The other options include filling and sloshing When filling is selected the actual level of the water tank will steadily increase over the time interval during which the simulation is run When sloshing is selected the actual level of the water tank will have a sinusoidal increase and decrease i e like waves in water Note that these two options filling and sloshing are orthogonal to each other in the sense that it is possible to select i only filling ii only sloshing iii both filling and sloshing or iv neither filling nor sloshing the default Modeled Dynamics The modeled dynamics setting determines the analytic function that the Kalman filter will use to model the level of water in the tank In other words the Kalman filter thinks that the actual behavior of the water is described by the estimate setting Naturally the Kalman filter will give the best estimate of the state of the water level when the modeling function matches the truth It is intended however that the user experiment with the behavior of the filter when the modeled function does not match that of the truth In such case note the relationship between the residual plot and discrepancy between the truth and model functions Measureme
25. rl_m 0 01 T L_max stdev of level linear sensor noise meter sra_d 0 01 90 stdev of angule non linear sensor noise degree Filling parameters delay 1 delay to start of filling second frate T L_max T L_min T stime T delay 1 T mrate fill rate meter second fmeas frate T mrate amount filled per measurement meter meas mf T delay T mrate meas of first fill motion ole HHH AP W Sloshing sinusoidal parameters sf 10 T stime slosh sin frequency 1 second sp 0 slosh phase degree sm 0 05 slosh magnitude meter Generate signals Four possibilities D APPENDIX MATLAB CODE FOR THE KALMAN FILTER Constant level C Filling F Sloshing S Filling Sloshing FS Ss UN RE ae Ae Je Ae lO ole sample times ES 0 1 T mrate T stime 4 ole noise signals for each sensor type 1 T srl_m randn 1 T nmeas a T sra_d randn 1 T nmeas 2 2 5 5 actual true levels AP oP ye 23 level linear noise angle non linear noise generate same number resolution as measurements signal level linear noise 1 Constant level C see equation 1 in document models L C repmat T L_min 1 T nmeas constant signal m 1 C T k1 L C n l level measured m a C T ka r2d asin T db L C T df n a angle measured signal angle non linear noise 2 Filling F o o see equation 2 in document models L
26. sd T nmeas corrected S Zp zeros 1 T nmeas predicted measurement Z S K zeros sd T nmeas Kalman gain Initialize filter L_init L_max 2 0 initial guess S Xp 1 1 L_init S Xc 1 1 L_init S Xp 2 1 T sm temp cheat S Xc 2 1 T sm S Pp 1 L_max 2 0 0 L_max 2 72 SPee 1 Lmax 2 07 0 L max 2 2 case FS Filling and Sloshing State dimension sd 3 oe Dynamic process model see Section 1 2 4 and equations 8 and 9 in document models A zeros sd sd T nmeas oe w 2 pi sf omega for m 1 T nmeas A 1 1 m 1 A 2 2 m 1 A 3 3 m 1 A 1 2 m dt A 1 2 m w cos w T ts m sp d2r end Q zeros sd sd T nmeas qcs sq_scale sq_S 2 scale qc then square for variance qcef sq_scale sq_F 2 scale qc then square for variance for m 1 T nmeas Ol Lym dt dh 243 T ts m 243 T tsm edt qcf w 2 cos w T ts m 2 gqcs 3 0 Q 1 2 m qcf dt 2 T ts m dt 2 0 Q 2 1 m Q 1 2 m Q 1 3 m w cos w T ts m qces dt 2 T ts m dt 2 0 Q 3 1 m Q 1 3 m Q 2 2 m qcf dt Q 3 3 m qcs dt end Set aside space for results S Xp zeros sd T nmeas predicted state X S Xc zeros sd T nmeas corrected S Pp zeros sd sd T nmeas predicted covariance P S Pc zeros sd sd T nmeas corrected S Zp zeros 1 T nmeas predicted measurement Z S K zeros sd T nmeas Kalman gain Initialize filte
27. sitory Data repository The data repository receives raw simulation data from the main window and formats this data in the following three ways 1 Arrays of size of time steps target plot window 2 Single elements corresponding to a time step target step window 3 String of tab delimited values for each time step target file 3 3 Low level view of the kftool module For a more detailed look at the kftool project module refer to Java API Documentation for The Kalman Filter On line Learning Tool and the Implementation Manual 4 PROCEDURES 7 4 Procedures 4 1 Getting the source The Kalman Filter On line Learning Tool source code is in a CVS Concurrent Versions System v1 11 repository CVS is a version control system that allows old versions of program files to be systematically stored with corresponding explanations of when why and by whom the files were modified For more information on CVS see http www cvshome org docs manual cvs html To get a copy of the source code for any module s 1 Set the CVSROOT environment variable to the designated project space 1 e setenv CVSROOT afs cs unc edu project tracker kftutor 2 Goto your local workspace where you desire to put the source code e g cd afs cs unc edu home parker kfcode 3 Checkout the module s e g to checkout the kftool module cvs checkout kftool Once you have checked out source code to your local workspace it is easy to
28. the filters SE Sst ges sq_F stq_F sq_S stq_S else error Incorrect number of input arguments for dosim m end Measurement model if cm L mtype 1 elseif cm A mtype 2 else error Unkown measurement model end Set up the dynamic model parameters based on the input selector cdm switch cdm case C Constant level State dimension sd 1 Dynamic process model see Section 1 2 1 in document models zeros 1 1 T nmeas 1 1 1 c sq_scale sq_C 2 scale qc then square for variance zeros 1 1 T nmeas 1 1 qce dt O OQ PP ole Set aside space for results Xp zeros sd T nmeas predicted state X un APPENDIX MATLAB CODE FOR THE KALMAN FILTER S Xc zeros sd T nmeas corrected S Pp zeros sd sd T nmeas predicted covariance P S Pc zeros sd sd T nmeas corrected S Zp zeros 1 T nmeas predicted measurement Z S K zeros sd T nmeas Kalman gain Initialize filter L_init L_max 2 0 initial guess S Xp 1 1 L_init S Xc 1 1 L_init S Pp 1 1 1 1 1 L_max 2 S Pc 1 1 1 1 1 L_max 2 case F Filling State dimension sd 2 Dynamic process model see Section 1 2 2 and equations 4 and 5 in document models A zeros sd sd T nmeas for m 1 T nmeas ale ole A 1 1 m 1 A 1 2 m dt end Q zeros sd sd T nmeas qc sq_scale sq_F 2 scale qc then square for var
29. the initial project development e Java 2 API Specification available at http java sun com products jdk 1 2 docs api index html e Java Look and Feel Design Guidelines available at http java sun com products 31f dg index htm C APPENDIX CONTACT INFORMATION 13 C Appendix Contact Information The following students completed The Kalman Filter On line Learning Tool as a course project for COMP145 at the University of North Carolina at Chapel Hill e TEAM 18 DIRECTOR Christopher Riley cjriley cs unc edu PRODUCER Thomas Bodenheimer bodenhei cs unc edu ADMINISTRATIVE LEADER Erin Parker parker cs unc edu LIBRARIAN John Carpenter carpente cs unc edu The client for the project was Greg Welch a professor in the Department of Computer Science at UNC CH welch cs unc edu D APPENDIX MATLAB CODE FOR THE KALMAN FILTER 14 D Appendix Matlab Code for the Kalman Filter The following is Matlab source code written by the client Greg Welch for the Kalman filter simulation performed by The Kalman Filter On line Learning Tool The code may be checked out of the CVS repository see 4 1 as module matlab_code To run the simulation execute gui m in Matlab Note that the Matlab source code is not a direct translation of the Java source code of The Kalman Filter On line Learning Tool but both perform the same Kalman filter simulation D I dosim m function S dosim T cda cdm cm sr_scale sq_scale sta
30. x parts see Figure 1 each performing a distinct function PARAMETER PLOT STEPPER WINDOW WINDOW WINDOW Contains editable Display s plots of a Steps through the settings for the single simulation s data of a single simulation data simulation EDIT PHOT STEP MAIN WINDOW Allows the user to edit the parameters of plot or step through a Kalman filter simulation Visible to the user Invisible to the user DATA K FILTER REPOSITORY ENGINE Manages simulation Generates Kalman data filter simulation Input raw data data given the Output formatted specified parameters data for plot step Figure 1 High level view of the kftool project module Main window Primarily the main window serves to provide the user with choices that govern the execu tion of The Kalman Filter On line Learning Tool The user can choose to Edit Plot or Step through a Kalman filter simulation The Edit selection invokes the parameter window the Plot selection invokes the plot window and the Step selection invokes the stepper window The user is also given a Help option which displays web pages with instructions and useful information Secondarily the main window acts as the main controller for the system It passes parameters from the parameter window to the Kalman filter engine and collects simulation data
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