The Continuous-Time Smooth Variable Structure Filter

State and parameter estimation techniques are important tools which provide accurate estimates of system states. This is important for the reliable and safe control of mechanical and electrical systems. Most estimation techniques are derived in discrete-time, due to the wide use of digital computers. However, continuous-time derivations do exist, and are particularly useful for studying estimation problems with small sampling intervals. The smooth variable structure filter (SVSF) is a relatively new estimation strategy based on sliding mode theory, and has been shown to be robust to modeling uncertainties. In this paper, a formulation of the SVSF is presented in continuous-time. The continuous-time SVSF is applied on an estimation problem, and the results are compared with the popular Kalman filter (KF).