State estimation of nonlinear dynamical systems has long aimed to balance accuracy, computational efficiency, robustness, and reliability. The rapid evolution of various industries has amplified the demand for estimation frameworks that satisfy all these factors. This study introduces a neuromorphic approach for robust filtering of nonlinear dynamical systems: SNN-EMSIF (spiking neural network-extended modified sliding innovation filter). SNN-EMSIF combines the computational efficiency and scalability of SNNs with the robustness of EMSIF, an estimation framework designed for nonlinear systems with zero-mean Gaussian noise. Notably, the weight matrices are designed according to the system model, eliminating the need for a learning process. The framework's efficacy is evaluated through comprehensive Monte Carlo simulations, comparing SNN-EMSIF with EKF and EMSIF. Additionally, it is compared with SNN-EKF in the presence of modeling uncertainties and neuron loss, using RMSEs as a metric. The results demonstrate the superior accuracy and robustness of SNN-EMSIF. Further analysis of runtimes and spiking patterns reveals an impressive reduction of 85% in emitted spikes compared to possible spikes, highlighting the computational efficiency of SNN-EMSIF. This framework offers a promising solution for robust estimation in nonlinear dynamical systems, opening new avenues for efficient and reliable estimation in various industries that can benefit from neuromorphic computing.