Multidimensional projection filters via automatic differentiation and sparse-grid integration

• We use automatic differentiation and sparse-grid integration to automate the construction of projection filter. present methods for constructing filters multidimensional filtering problems using a non-Gaussian parametric density. show that practical performance filter is comparable particle finite difference based solutions Kushner–Stratonovich equation. An open-source implementation method available. The technique approximating optimal problems. In filters, stochastic partial differential equation governs propagation density projected manifold densities, resulting in finite-dimensional Despite fact are capable representing complicated probability their current implementations limited Gaussian family or unidimensional applications. This work considers combination numerical construct algorithms more generic Specifically, we provide detailed exposition this exponential family, how apply cases. demonstrate numerically on comparison finite-difference solution bootstrap with systematic resampling, proposed algorithm retains an accurate approximation while requiring comparatively low number quadrature points. Due used calculate expected values natural statistics Fisher metric, highly scalable. They therefore suitable many applications which dimensions exceeds limit but where Gaussian-approximations deemed unsatisfactory.