The proposed Hessian-Sum-Mixture approach can be extended to handle non-Gaussian posterior distributions by incorporating techniques from Bayesian inference. In multi-modal state estimation problems, where the posterior distribution is non-Gaussian due to the presence of multiple modes, methods like Markov Chain Monte Carlo (MCMC) sampling or Sequential Monte Carlo (SMC) methods can be employed. These techniques allow for sampling from complex, non-Gaussian distributions and can be integrated with the Hessian-Sum-Mixture approach to handle the uncertainty inherent in multi-modal distributions. By combining the Hessian-Sum-Mixture method with Bayesian inference techniques, the estimation process can better capture the true underlying distribution of the states, even in the presence of multiple modes.