This paper addresses robust stability analysis for moving horizon estimation (MHE) in nonlinear systems and proposes new conditions for tuning the MHE cost function parameters. These conditions are directly linked to the MHE window size and the incremental exponential input/output-to-state stability (i-EIOSS) coefficients of the system. Our approach begins by introducing a general constraint equation within the MHE optimization program, combined with a filtering prior prediction technique. This