Novel cubature Kalman filtering for systems involving nonlinear states and linear measurements

This paper extends the cubature Kalman filter (CKF) to deal with systems involving nonlinear states and linear measurements (herein called the nonlinear–linear combined systems) with additive noise. The method is referred to as the nonlinear–linear square-root cubature Kalman filtering (NL-SCKF). In NL-SCKF, the cubature rule, combined with a QR decomposition, singular value decomposition and a linear update without requirement of cubature points, is designed to update nonlinear states and linear measurements. In addition, the convergence analysis of NL-SCKF is performed. Simulation results in two selected problems, namely filtering chaotic signals and chaos-based communications, indicate that the proposed NL-SCKF with lower computation complexity achieves the same accuracy as the standard SCKF, and outperforms CKF significantly.