Efficient unscented filtering for nonlinear systems with state constraints

The Unscented Kalman Filter (UKF) is a powerful nonlinear estimation technique and it is used widely in practical applications. But conventional UKF doesn´t incorporate state constraints, therefore it admits of improvement to UKF if the constraints are incorporated with. An easy way to incorporate the state constraints in UKF is using truncation procedure, which truncates a probability density function computed by UKF at the constraint edge. This UKF is called Truncated UKF (TUKF). We propose a new TUKF, which is called Simplex Square Root TUKF (SSR-TUKF). The SSR-TUKF is composed of three algorithms : The square-root PDF truncation method, the spherical simplex unscented transformation, and the Square-Root UKF. And, the SSR-TUKF has better numerical properties and guarantees positive semi-definiteness of the underlying state covariance. Furthermore, the SSR-TUKF can be used in Gaussian sum filter framework. Validity of the proposed methods are illustrated by a numerical example.