In many systems the state variables are defined on a compact set of the state space. To estimate the states of such systems, the constrained particle filters have been used with some success. The performance of the standard particle filters can be improved if the measurement information is used during the importance sampling of the filtering phase. It has been shown that the particles obtained in such a way approximate the true state of the system more accurately. The measurement is incorporated into the filtering algorithm through a user-specified detection function, which aims to detect the saturation as it occurs. The algorithm derived from the aforementioned principle is called the Saturated Particle Filter (SPF). In our previous work we have derived a complete SPF framework for the class of systems with one-dimensional constraints. In this paper we derive a novel Convex SPF that extends our method to multidimensional systems with convex constraints. The effectiveness of the new method is demonstrated using an illustrative example. (C) 2014 Elsevier Ltd. All rights reserved.