Traffic matrix estimation based on a square root Kalman filtering algorithm

The traffic matrix (TM) is one of the crucial inputs for many network management and traffic engineering tasks. As it is usually impossible to directly measure traffic matrices, it becomes an important research topic to infer them by modeling incorporating measurable data and additional information. Many estimation methods have been proposed so far, but most of them are not sufficiently accurate or efficient. Researchers are therefore making efforts to seek better estimation methods. Of the proposed methods, the Kalman Filtering method is a very efficient and accurate method. However, the error covariance calculation components of Kalman filtering are difficult to implement in realistic network systems due to the existence of ill-conditioning problems. In this paper, we proposed a square root Kalman filtering traffic matrix estimation (SRKFTME) algorithm based on matrix decomposition to improve the Kalman filtering method. The SRKFTME algorithm makes use of the evolution equations of forecast and analysis error covariance square roots. In this way the SRKFTME algorithm can ensure the positive definiteness of the error covariance matrices, which can solve some ill-conditioning problems. Also, square root Kalman filtering will be less affected by numerical problems. Simulation and actual traffic testing results show superior accuracy and stability of SRKFTME algorithm compared with prior Kalman filtering methods.