A recursive filtering problem on minimum variance is investigated for a type of two-dimensional systems incorporating noise and a random parameter matrix in the measurement equation, along with random nonlinearity. It methodically describes random variables using statistical characteristics, placing a strong emphasis on the application of random multivariate analysis and computational techniques. A bidirectional time-sequence recursive filter is designed to achieve unbiasedness and reduce error variance effectively. This involves deriving the gain matrix through a completion of squares method and solving a complex difference equation with two independent variances. To facilitate the online implementation of this filter, various formulations and an algorithm are proposed. A numerical study demonstrates the effectiveness of the design in practical applications.