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Unscented Kalman Filter (UKF) (Julier & Uhlmann, 1997) was developed as an improvement of Extended Kalman Filter (EKF) (Grewal & Andrews, 2001) for discrete-time filtering of the nonlinear dynamic systems. Comparison between different statistical approaches on the state and parameter estimation of the dynamic systems revealed that the performance of UKF is superior to EKF in many Kalman Filter (KF) applications (Chow et al., 2007); (Xiong et al., 2006); (Wan & Merwe, 2001); (Kandepu et al., 2008). Nonlinear dynamic systems with uncertain observations were often appeared in, for instance, communication systems (Wan & Merwe, 2001), medical systems (Polak & Mroczka, 2006) and machine learning (Chen, 2003). Medical systems, described by stochastic difference equations with measurement models including nonlinear and non-Gaussian components, are good candidates for the UKF analysis. Although there are many medical signal applications of Kalman Filters (KF); (Vauhkonen et al., 1998) and EKF (Avendano et al., 2006), some medical diagnostic and therapeutic measures are processed by UKF from indirect sensor measurements including statistical brain signal analysis to study cognitive brain functions by Electroencephalography (EEG) and functional Magnetic Resonance Imaging (fMRI) (Brochwell et al., 2007), ECG model-based denoising (Sameni et al., 2007), medical image processing (Ijaz et al., 2008), and evoke potential analysis in the neuroscience. These works demonstrated that UKF can be considered as an effective framework for medical signal analysing, modelling and filtering. Also, it was shown that UKF is a promising alternative in a variety of applications’ domains including state and parameter estimation simultaneously which is dual estimation. Respiratory mechanics is the dynamic relationship between appropriate pressures and flows in the respiratory system and assessment of it is an important problem in the diagnosis and monitoring of respiratory disorders, especially of Chronic Obstructive Pulmonary Disease (COPD). The primarily goal on the determination of the respiratory mechanics is the computation, or estimation, of the respiratory parameters non-invasively, continuously, effectively and without any patient cooperation. Direct approach to this problem is the measurement of the mechanics by the lung catheter or the alveolar capsule (Bates & Lutchen, 2005). However, these direct measurement methods are invasive and not suitable for continuous monitoring. On the other hand, the studies revealed that analysis of pressure O pe n A cc es s D at ab as e w w w .in te ch w eb .o rg

Electroencephalography (EEG) signals are frequently used for the detection of epileptic seizures. In this chapter, advanced signal analysis methods such as Empirical Mode Decomposition (EMD), Ensembe (EMD), Dynamic mode decomposition (DMD), and Synchrosqueezing Transform (SST) are utilized to classify epileptic EEG signals. EMD and its derivative, EEMD are recently developed methods used to decompose nonstationary and nonlinear signals such as EEG into a finite number of oscillations called intrinsic mode functions (IMFs). In this study multichannel EEG signals collected from epilepsy patients are decomposed into IMFs, and then essential IMFs are selected. Finally, time- and spectral-domain, and nonlinear features are extracted from selected IMFs and classified. DMD is a new matrix decomposition method proposed as an iterative solution to problems in fluid flow analysis. We present single-channel, and multi-channel EEG based DMD approaches for the analysis of epileptic EEG signals. As a third method, we use the SST representations of seizure and pre-seizure EEG data. Various features are calculated and classified by Support Vector Machine (SVM), k-Nearest Neighbor (kNN), Naive Bayes (NB), Logistic Regression (LR), Boosted Trees (BT), and Subspace kNN (S-kNN) to detect pre-seizure and seizure signals. Simulation results demonstrate that the proposed approaches achieve outstanding validation accuracy rates.