## Abstract

Basically, the term “Filtering” is referred to a technique to extract information (signal in this context) from noise contaminated observations (measurements). If the signal and noise spectra are essentially non-overlapping, the design of a frequency domain filter that allows the desired signal to pass while attenuating the unwanted noise would be a possibility. A classical filter could be either low pass, band pass/stop or high pass. However, when the noise and information signals are overlapped in spectrum, then the design of a filter to completely separate the two signals would not be possible. In such a situation the information has to be retrieved through estimation, smoothing or prediction. Figure 2.1 shows a general diagram of an open-loop system (plant) subject to noise contamination at the output end.

## References

- Allison PD (2002) Missing data: quantitative applications in the social sciences. Br J Math Stat Psychol 55(1):193–196CrossRefGoogle Scholar
- Blind R, Uhlich S, Yang B, Allgower F (2009) Robustification and optimization of a kalman filter with measurement loss using linear precoding. In: 2009 American Control Conference, ACC’09, IEEE, pp 2222–2227Google Scholar
- Chatfield C (2016) The analysis of time series: an introduction. CRC Press, Boca RatonzbMATHGoogle Scholar
- Chung KL (2001) A course in probability theory. Academic, CambridgeGoogle Scholar
- Grewal M, Andrews A (2001) Kalman filtering: theory and practice using matlabGoogle Scholar
- Khan N (2012) Linear prediction approaches to compensation of missing measurements in kalman filtering. PhD thesis, University of LeicesterGoogle Scholar
- Khan N, Fekri S, Gu D (2010) Improvement on state estimation for discrete-time LTI systems with measurement loss. Measurement 43(10):1609–1622CrossRefGoogle Scholar
- Khan N, Gu D-W (2009) Properties of a robust kalman filter. IFAC Proc 42(19):465–470CrossRefGoogle Scholar
- Loeve M (1963) Probability theory, 3rd edn. New YorkGoogle Scholar
- Mehta S, Chiasson J (1998) Nonlinear control of a series DC motor: theory and experiment. IEEE Trans Ind Electron 45(1):134–141CrossRefGoogle Scholar
- Papoulis A, Pillai SU (2002) Probability, random variables, and stochastic processes. Tata McGraw-Hill Education, New YorkGoogle Scholar
- Phillips CL, Parr JM, Riskin EA (1995) Signals, systems, and transforms. Prentice Hall, Upper Saddle RiverzbMATHGoogle Scholar
- Vaseghi SV (2008) Advanced digital signal processing and noise reduction. Wiley, New JerseyCrossRefGoogle Scholar
- Vaidyanathan P (2007) The theory of linear prediction. Synth Lect Signal Process 2 (1):1–184CrossRefGoogle Scholar
- Wiener N (1949) Extrapolation, interpolation, and smoothing of stationary time series, vol 7. MIT press, CambridgezbMATHGoogle Scholar