A Proof of Strong Consistency of Maximum Likelihood Estimator for Independent Non-Identically Distributed Data

We give a general proof of the strong consistency of the Maximum Likelihood Estimator for the case of independent non-identically distributed (i.n.i.d) data, assuming that the density functions of the random variables follow a particular set of assumptions. Our proof is based on the works of Wald~\cite{wald1949note}, Goel~\cite{goel1974note}, and Ferguson~\cite{ferguson2017course}. We use this result to prove the strong consistency of a Maximum Likelihood Estimator for Orbit Determination.