State Estimation for Communication-Based Train Control Systems With CSMA Protocol

Train positioning is of critical importance for communication-based train control (CBTC) systems. The objective of this paper is to provide an algorithm to generate the precise estimates of the train position and velocity for CBTC systems with carrier-sense multiple access (CSMA) protocol scheduling, thereby improving the accuracy of train positioning as well as the availability of CBTC systems. First, the dynamics of a train with <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> cars linked by couplers is described based on Newton’s motion equations. Then, the transmission model reflecting the behaviors of <inline-formula> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula>-persistent CSMA protocol is presented by using a Bernoulli distributed sequence whose probability distribution is dependent on the number of trains sharing with one communication channel [i.e., <inline-formula> <tex-math notation="LaTeX">$N(k)$ </tex-math></inline-formula>]. Furthermore, the value of <inline-formula> <tex-math notation="LaTeX">$N(k)$ </tex-math></inline-formula> is assumed to be unknown but bounded by two known positive integers. The purpose of the problem addressed is to design an estimator, such that the estimation error is exponentially ultimately bounded (with a certain asymptotic upper bound) in mean square subject to the external resistive force. By utilizing the stochastic analysis approach, sufficient conditions are established to guarantee the ultimate boundedness of the estimation error in mean square. For the purpose of designing the desired estimator gains under different requirements (e.g., smallest ultimate bound and fastest decay rate), two optimization problems are solved in terms of linear matrix inequalities. Finally, a simulation example is given to illustrate the effectiveness of the estimator design scheme.