Driving safety can be achieved by better understanding critical situations which may require the knowledge of interaction between vehicle tyres and the road surfaces. It is thus essential to have a good estimation of the tyre/road friction parameters in real-time. The paper deals with the trust-region based method for on-line estimation of tyre/road friction parameters. This method provides an appropriate modeling (of a vehicle and the tyre/road contact) to observe the tyre/road friction coefficients directly using measurable signals in real-time. In this work, we present a new LuGre model-based nonlinear least squares (NLLS) parameter estimation algorithm using vehicle dynamic to obtain the parameters of LuGre model based on recursive nonlinear optimization of the curve fitting errors. The proposed estimation method can also be utilized in large-scale problems with similar conditions. Very promising results have been obtained in real-time simulations for most of the driving and road situations. (C) 2016, IFAC (International Federation of Antomatic Control) Hosting by Elsevier Ltd. All rights reserved.