非负矩阵和相关卡尔曼滤波器实现的UD和LDL分解Matlab代码.rar

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.sco.wur.nl/NR/rdonlyres/B575A290-A91F-4FB6-8A0C-AB7E4678BAC6/47048/EJC2005_1.pdf Modifications: 16 Aug 2011 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 The application to systems with time-varying state-dimension has been implemented. The efficiency of sym2ud, sym2ut and psdr has been improved. In uduex associated additional examples have been added. 23 Sep 2011 LD mirror images of each function are added. The comments of several functions are corrected or improved. 17 Jan 2012 The scalar measurement update functions kmudu and kmldl are updated to also produce a Kalman gain for vector updates. The output of kc and kwk has therefore been dropped. Conversion from UDU' to UU' and from LDL' to LL' are added: ud2ut, ld2lt, ut2ud, lt2ld. Errors in udinv.m, udinv.c, utinv.m, utinv.c, ldinv.m, ldinv.c, ltinv.m, ltinv.c are corrected. These only occurred for calls including tolerance specifications or rank output. The functions uduex and ldlex, containing tests of all UDU' and LDL' functions, have been modified to also test the modifications mentioned above. The comments of several functions are corrected or improved. 3 March 2012 Since UD factorization is a much more common name than UDU factorization the name of this toolbox and its description have been slightly modified. Also the internet link to one of the references was updated. This resulted in changes in the readme.m and modifications.txt file.