The kernel mapping is a popular method for designing nonlinear process monitoring techniques. In most cases, kernel mapping is achieved by using the radial basis kernel function which, in theory, is able to provide an infinite order nonlinear mapping. However, such an infinite order mapping might be redundant and inefficient as the order of nonlinear relationship between process variables of industrial process system is often limited by many physical constraints. To address this issue, an efficient nonlinear mapping method called the constructive polynomial mapping (CPM) is utilized in lieu of the radial basis kernel function to avoid the excessive modeling redundancy. In addition, the CPM is integrated with the dynamic principal component analysis and the linear Gaussian state space model to build improved latent variable models for nonlinear and dynamic process monitoring. The promising performance of the proposed models has been demonstrated through two case studies. (C) 2017 Elsevier Ltd. All rights reserved.