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To add to software for #1, look for packages that do forward-mode AD. For Jacobians (many outputs), forward-mode AD is often faster than back-propagation (reverse mode). I use ForwardDiff.jl which usually accepts any function the user might bass in as observation function https://github.com/baggepinnen/LowLevelParticleFilters.jl/blob/master/src/ekf.jl#L45 Here's a nice intro to forward and reverse mode ad https://github.com/MikeInnes/diff-zoo/blob/notebooks/backandforth.ipynb It's the second notebook in a series, might want to read the first as well if you find this topic interesting.