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.
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