A considerable number of papers in the literature provide solutions for fixed-gain filters, such as the $\alpha$ -$\beta$ filter, that minimize the mean squared error under various dynamic models. This note demonstrates that those specialized models are unnecessary as the tools to explicitly find optimal fixed gains for arbitrary observable systems are already in the literature. The results produced by this method agree with published results for specialized algorithms. The solution of this letter also obviates the need for special “aeolotropic” filter design. Code implementing the algorithm and simulations is available in Matlab on IEEEXplore.