The problem of estimating online the unknown parameters of systems and signals is of great interest in classical control theory and appears in different forms in many practical applications. To estimate the unknown parameters of a system, we could use Adaptive Observers and for estimating the unknown parameters of a signal we could model the signal as a system and then apply adaptive observer for parameter estimation of the system and, hence, the signal. Frequency estimation is a fundamental question in systems theory that has many practical applications, for instance in active noise and vibration control in helicopters, disk drives, and magnetic bearings. It is also a challenging theoretical problem since the nonlinear dependence on the unknown frequency stymies the application of standard well-known techniques. In some cases the measured signal may be deformed due to nonlinearities introduced by the sensor, for example when the signal amplitude exceeds the sensor limits or leaves certain operative ranges in which the sensor operates linearly. Note that the latter case could be transformed into the former one, if the signal is appositely cut-off to eliminate the sensor distortions. Common estimation algorithms, such as Adaptive Notch Filter (ANF), do not provide suitable results in response to non-sinusoidal periodic signals like saturated sinusoid. In this research, we consider the problem of frequency estimation of saturated sinusoidal signals. Since a saturated sinusoid has two distinct dynamics over time, we make use of the modeling structure in hybrid dynamical systems. Firstly, we model the saturated sinusoid as the output of a hybrid dynamical system in which the unknown frequency appears as a state and secondly, we design a hybrid observer for estimating the states of the hybrid model and hence the unknown frequency of the saturated sinusoid. In design of this hybrid observer, we first explore the concept of the invariant manifold based reduced-order observer in which a globally convergent, reduced-order observer for general nonlinear systems is addressed. The observer provides asymptotic estimate of the unknown states by rendering attractive an appropriately selected (invariant) manifold in the extended state space. Then we extend the nonlinear observer to estimate the states i impulsive nonlinear systems and a class of hybrid systems with two operating modes. Moreover, we design the hybrid observer for the hybrid model of saturated signal. Compared to the recently proposed method based on the hybrid observer concept, the proposed method in this research has a simpler algorithmic design, simpler structure, lesser number of state variables and better robustness to the variation in the saturation level. The validity of analytical studies are verified by several computer simulations. On the other hand, in this research, the idea of combining hybrid systems and ANF in order to precisely estimate the frequency of a saturated sinusoid has been explored. This results in the introduction of a hybrid model of ANF (HANF) which is designed by taking into account the hybrid behavior of a saturated sinusoid and providing a hybrid model of ANF to cope with this hybrid behavior. Computer simulations demonstrate that the proposed HANF can provide accurate estimation, without any bias and variance, of the frequency of a saturated sinusoid. Keywords frequency estimation, saturated sinusoidal signal, hybrid observer, adaptive notch filter, hybrid systems.