In this paper, robust Kalman filtering problem is investigated for a class of two-dimensional (2-D) shift-varying uncertain systems with both additive and multiplicative noises over a finite horizon. The measurement outputs suffer from randomly occurring degradations obeying certain probabilistic distributions, and the norm-bounded parameter uncertainties enter into both the state and the output matrices. The main aim of this paper is to design a robust Kalman filter such that, in the presence of parameter uncertainties and degraded measurements, certain upper bound of the generalized estimation error variance is locally minimized in the trace sense at each shift step. Recursion of the generalized estimation error variances for the addressed 2-D system is first established via the introduction of a 2-D identity quadratic filter, based on which an upper bound of the generalized estimation error variance is obtained. Subsequently, such an upper bound is minimized in the trace sense by properly designing the filter parameters. The design scheme of the robust Kalman filter is presented in terms of two Riccati-like difference equations which can be recursively computed for programmed applications. Finally, a numerical example is provided to demonstrate effectiveness of the proposed filter design method. (C) 2018 Elsevier Ltd. All rights reserved.