Independent lines of seismic evidence have suggested that pore fluid pressure at the depth range of episodic slow slip events (SSEs) may undergo periodic fluctuations synced with the SSE slip cycles. Here we develop a numerical simulation framework that integrates the SSE model governed by the rate- and state-dependent friction with Bayesian data assimilation to optimize time-variable fault friction parameters, with constraints from the northern Cascadia GPS time series. In our synthetic experiments with rate-state friction model generated surface displacement time series and added Gaussian noise, both model parameters, effective normal stress σ ̅ (normal stress σ minus pore pressure p) and characteristic slip distance L, converge to their true values in 5-10 iterations from initial guesses 10-20% off from the true values, demonstrating the feasibility of the data assimilation framework. We then apply the framework to 1000-day (2009-2011) GPS time series that encompasses two SSE cycles at 30 stations in northern Cascadia. A sliding time window of 9 months is chosen for each optimization epoch, which is a trade-off that includes sufficient information for next-step prediction and on the other hand allows temporal distinction between the inter- versus intra-SSE time periods. Our preliminary results, tested with the 2009-2011 dataset, show clear cyclic fluctuations in the optimized σ ̅ values during SSE cycles. Specifically, σ ̅ increases (p drops) during intra-SSE period; σ ̅ decreases (p increases) during inter-SSE period, which is consistent with the proposed pore pressure build-up and release processes, i.e., fault-valve model, at the SSE depth ranges.