This paper is concerned with the recursive filtering problem for a class of discrete-time nonlinear stochastic systems with random parameter matrices, multiple fading measurements and correlated noises. The phenomenon of measurement fading occurs in a random way and the fading probability for each sensor is governed by an individual random variable obeying a certain probability distribution over the known interval [beta(k), gamma(k)]. Such a probability distribution could be any commonly used discrete distribution over the interval [beta(k), gamma(k)] that covers the Bernoulli distribution as a special case. The process noise and the measurement noise are one-step autocorrelated, respectively. The process noise and the measurement noise are two-step cross-correlated. The purpose of the addressed filtering problem is to design an unbiased and recursive filter for the random parameter matrices, stochastic nonlinearity, and multiple fading measurements as well as correlated noises. Intensive stochastic analysis is carried out to obtain the filter gain characterized by the solution to a recursive matrix equation. The proposed scheme is of a form suitable for recursive computation in online applications. A simulation example is given to illustrate the effectiveness of the proposed filter design scheme. (C) 2013 Elsevier Ltd. All rights reserved.