Our study aimed to improve the poor performance of existing filters, such as EKF, UKF and CKF, that results from their weak approximation ability to nonlinear systems. This paper proposes a new extended Kalman filter bank focusing on a class of product-type strong nonlinear systems composed by system state variables, time-varying parameters and non-linear basic functions. Firstly, the non-linear basic functions are defined as hidden variables corresponding to system state variables, and then the strong nonlinear systems are described simplistically. Secondly, we discuss building two dynamic models between their future values of parameters, as well as hidden variables and their current values based on the given prior information. Thirdly, we recount how an extended Kalman filter bank was designed by gradually linearizing the strong nonlinear systems about system state variables, time-varying parameters and hidden variables, respectively. The first extended Kalman filter about future hidden variables was designed by using these estimates of the state variables and parameters, as well as hidden variables at current. The second extended Kalman filter about future parameters variables was designed by using these estimates of the current state variables and parameters, as well as future hidden variables. The third extended Kalman filter about future state variables was designed by using these estimates of the current state variables, as well as future parameters and hidden variables. Fourthly, we used digital simulation experiments to verify the effectiveness of this method.