Square-root cubature Kalman filter (SCKF) is more effective for nonlinear state estimation than an unscented Kalman filter. In this paper

we study the design of nonlinear filters based on SCKF for the system with one step noise correlation and abrupt state change. First

we give the SCKF that deals with the one step correlation between process and measurement noises

SCKF-CN in short. Second

we introduce the idea of a strong tracking filter to construct the adaptive square-root factor of the prediction error covariance with a fading factor

which makes SCKF-CN obtain outstanding tracking performance to the system with target maneuver or abrupt state change. Accordingly

the tracking performance of SCKF is greatly improved. A universal nonlinear estimator is proposed

which can not only deal with the conventional nonlinear filter problem with high dimensionality and correlated noises

but also achieve an excellent strong tracking performance towards the abrupt change of target state. Three simulation examples with a bearings-only tracking system are illustrated to verify the efficiency of the proposed algorithms.