Fault detection can be used to improve the reliability and safety of industrial system. An important component of fault detection is filtering for parameter and state estimation. The challenge is to create a filter that is robust and stable in light of modeling uncertainties and parametric changes due to fault conditions. In this book, a recently developed robust filter, referred to as the Smooth Variable Structure Filter (SVSF), is discussed and its concepts are explored and further investigated. The SVSF's chattering signals are used to establish a monitoring and reconstructing algorithm that can be used to detect and extract changes and added uncertainties in the system. A novel strategy using the Toeplitz and the Observability matrices is proposed to overcome the SVSF’s limitations due to the use of the Luenberger method. This strategy is generalized to high order systems with multiple measurements using new proposed the General System Toeplitz and the General Observability matrices. This strategy is linked to the SVSF and improves its performance in terms of robustness and accuracy.