This course focuses on modern state-space filtering techniques and their applications. Topics include the fundamentals of discrete-time and continuous-time linear system modelling of random signals; state-space signal estimation; Kalman filtering and smoothing; the extended Kalman filter; introduction to advanced filtering techniques such as robust filtering and adaptive filtering; Matlab tools for state-space signal estimation and filtering; example applications from the following selection: channel equalisation, CDMA networks, estimation of wireless communication signals. The course offers a series of lectures and tutorials aimed at assisting students understand the idea and implementations of state-space filters. At the completion of the course students will have both theoretical knowledge and practical skills necessary to develop and implement modern signal estimation and filtering algorithms including the Kalman filter and the H-infinity filter.