This paper proposes a new sequential state and parameter estimation method for nonlinear state-space mod-els, named Robust PF/SNES, taking account of ensembles not covering true states. PF/SNES is one of the most promising methods for sequential estimation of states and parameters and reportedly showed better performance than the augmented particle filter (Augmented PF) and the augmented Merging PF (Augmented MPF) that are widely used. Augmented PF and Augmented MPF are the extended versions of PF and MPF that handle parameters as states. PF/SNES sequentially estimates states and parameters by updating a probability distribution of parameters (a parameter distribution) using the Separable Natural Evolution Strategies (SNES) and an ensemble using PF at each time step. However, once an ensemble does not cover the true state, the subsequent estimation performance of PF/SNES deteriorates. In order to remedy the problem of PF/SNES, if the accuracy of the ensemble is judged to be low before SNES updates the parameter distribution at each time step, Robust PF/SNES searches for a high-accuracy ensemble by DX-NES-IC, which maximizes a likelihood with respect to an observation at the previous time step, taking account of the incomplete observation and the multimodality of the likelihood space. We compare the estimation performance of Robust PF/SNES with that of PF/SNES, Augmented PF, and Augmented MPF in terms of state MSE (Mean Squared Error) and parameter MSE on some benchmark problems with initial ensembles that do not cover the true states. The benchmark problems are the 2-state, 4-parameter estimation problem of the Van der Pol model, the 40-state, 41-parameter estimation problem of the Lorenz96 model, and the 10-state, 1-parameter estimation problems with an unobservable state or a bi-modal likelihood space. As a result, Robust PF/SNES showed the best performance on all the benchmark problems. Robust PF/SNES improved the accuracy by about 51.34 - 34760.94 times in terms of state MSE and 14.96 - 760.34 times in terms of parameter MSE, compared to PF/SNES.