SUMMARYThe traffi c matrix (TM) is one of the crucial inputs for many network management and traffi c engineering tasks. As it is usually impossible to directly measure traffi c 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 suffi ciently accurate or effi cient. Researchers are therefore making efforts to seek better estimation methods. Of the proposed methods, the Kalman Filtering method is a very effi cient and accurate method. However, the error covariance calculation components of Kalman fi ltering are diffi cult to implement in realistic network systems due to the existence of ill-conditioning problems. In this paper, we proposed a square root Kalman fi ltering traffi c matrix estimation (SRKFTME) algorithm based on matrix decomposition to improve the Kalman fi ltering 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 defi niteness of the error covariance matrices, which can solve some ill-conditioning problems. Also, square root Kalman fi ltering will be less affected by numerical problems. Simulation and actual traffi c testing results show superior accuracy and stability of SRKFTME algorithm compared with prior Kalman fi ltering methods.