We consider a Hidden Markov model in which for each discrete hidden state \(s\in\left\{0,\ldots,N\right\}\) there exists a continuous multivariate emission probability distribution \(p_s(\vec{x})\) for the M-dimensional observation vectors \(\$\vec{x}\$\)\(\vec{\left\{x_{t^{\left\{\left(s\right)\right\}}}\right\}}\). Similar to a Kernel Density Approximation, we describe the $p_s(\vec{x})$ as sums of Gaussian functions that are automatically derived from a series of observations $\left\{\vec{x}_t^{(s)}\right\}$ recorded in each hidden state $s$. This model, here called HMGM model, is numerically implemented (available as an open source C++ package) and validated using surrogate data for which the underlying hidden states are known.