In this thesis the application of martingales in stochastic systems theory is studied. Modelling estimation and control aspects with an emphasis on jump processes are considered. In particular a simple and at the same time rather general way to model signals in jump-type observations are considered and the parameter estimation and the filtering problem for counting observations are discussed. Some implementable approximate estimation schemes obtained from theoretical consideration are also presented. The practical importance of the theoretical results is investigated in the context of the application of surveillance and control of traffic flow on motorways. Using the martingale concept a stochastic continuous time aggregate variable model for motorway traffic flow is presented. The results of a parameter identification and filtering study for counting observations using real traffic data are discussed. Finally the problem of traffic flow control by means of advisory speed signals is considered.
Abstract