Full-duplex two-way relay (FD-TWR) system has potential to increase the spectral efficiency in the future 5G wireless system. Full-duplex transceiver suffers from inevitable self-interference (SI) which can be alleviated by active self-interference cancellation (SIC) method. However, the mitigation capability of SIC mechanism is limited specifically due to inherent non-linearities of transmitter and receiver front end. As a consequence, residual self-interference (RSI) will degrade the systems signal-to-noise ratio (SNR) and throughput. Non-linearity in RF power amplifier in collusion with time-variant channel results is a great challenge in efficient signal detection and successful SI suppression. In contrast to classical schemes, which consider non-linear distortion at the transmitter, we present a semi-blind data detection and non-linear channel estimation in the presence of RSI at the receiver. Attributed to non-linearity, the target posterior probability density function is mathematically intractable. In this paper, a sequential importance sampling based particle filtering is used for joint data detection and estimation. Intractable distribution is approximated by using weighted random measures. A Taylors series expansion is used to locally linearize the non-analytic form of distribution. Numerical results validate the joint detection and channel estimation scheme. The robustness of the scheme is verified in presence of RSI under high mobility.