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The Kalman filter is often used for tracking and estimation of effects such as LPN and NLPN in long haul coherent optical communication systems. However, real-time symbol-by-symbol estimation of these parameters is computationally challenging. We use a multi-rate Kalman filtering scheme that allows for different sampling and state update rates in the system. This scheme achieves high Q-factor by making use of maximum available samples while reducing computational load. Simulations are performed for 200 Gbps PDM-16-QAM system by transmitting 20000 symbols over 800 km optical channel. The filter has Q-factor of 17.25 dB with state estimates being updated after every 20 samples. The filter shows more than 1 dB improvement in Q-factor when compared to a KF where the intermediate samples are not utilised for phase estimation.