In this chapter, we review various applications of Kalman filtering for coherent optical communication systems. First, we briefly discuss the principles of Kalman filter and its variations including extended Kalman filter (EKF) and adaptive Kalman filter (AKF). Later on, we illustrate the applicability of Kalman filters for joint tracking of several optical transmission impairments, simultaneously, by formulating the state space model (SSM) and detailing the principles. A detailed methodology

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... presented for the joint tracking of linear and nonlinear phase noise along with amplitude noise using EKF. Also, approaches to enhance the performance obtained by EKF by combining with other existing digital signal processing (DSP) techniques are presented. Frequency and phase offset estimation using a two stage linear Kalman filter (LKF)/EKF is also discussed. A cascaded structure of LKF and EKF by splitting the SSM to jointly mitigate the effects of polarization, phase and amplitude noise is also presented. The numerical analysis concludes that the Kalman filter based approaches outperform the conventional methods with better tracking capability and faster convergence besides offering more feasibility for real-time implementations.