Code covered by the BSD License

### Highlights from UD Factorization & Kalman Filtering

5.0
5.0 | 2 ratings Rate this file 9 Downloads (last 30 days) File Size: 73 KB File ID: #32537 Version: 1.7

# UD Factorization & Kalman Filtering

### Gerard Van Willigenburg (view profile)

15 Aug 2011 (Updated )

UD and LD factorization of nonnegative matrices and associated Kalman filter implementations.

File Information
Description

Description:

To enhance the efficiency and accuracy of Kalman filter computations, in particular the time and measurement updates, UD factorization is employed.
An interesting feature of the current implementation is the extension to semi-positive (nonnegative) matrices and systems with a time-varying state dimension. The matlab implementation is through both m files and mex files written in c. The mex files speed up the computations which contain several for loops. Use the function mexudu to compile all .c mex files in the current folder

As a complete mirror image of UD factorization, LD factorization may be employed. Depending on the application, one may have an advantage over the other.
Or, to obtain computational symmetry, both may be required. Therefore dual to each UD function a dual LD version is provided.

References:
Factorization methods for discrete sequential estimation, 1977, Gerald J. Bierman

L.G. van Willigenburg, W.L. De Koning, 2004, "UDU factored discrete-time Lyapunov recursions solve optimal reduced-order LQG problems", European Journal of Control, 10, pp. 588-601

http://www.gvw007.yolasite.com/resources/EJC2005_1.pdf

MATLAB release MATLAB 7.5 (R2007b)
23 Aug 2012 BILL XUE

### BILL XUE (view profile)

06 Jan 2012 afu2007 ??

### afu2007 ?? (view profile)

sounds very good, let me check carefully

16 Aug 2011 1.1

In sym2ut.m the 3rd output argument inz has been added. In the readme.m file utinv is now correctly mentioned to compute the inverse of u.

31 Aug 2011 1.3

The application to systems with time-varying state-dimension has been implemented.
The efficiency of sym2ud, sym2ut and psdr has been improved.

23 Sep 2011 1.4

LDL mirror images of each function are added.
The comments of several functions are corrected or improved.

17 Jan 2012 1.5

kmudu and kmldl are updated to also produce a Kalman gain for vector updates.
Functions ud2ut, ld2lt, ut2ud, lt2ld are added. uduex and ldlex are updated. Code and comments of several functions are corrected or improved.

03 Mar 2012 1.6

UDU is replaced with UD in the title and some desciptions, notably in the readme.m and modifications.txt file. The internet link to one reference is updated.

14 Apr 2013 1.7

The internet link in the description has been updated. No changes to the files.