For real time mechanical and electrical applications, the MHE is generally not competitive (at present) However, there many types of dynamic systems that are much slower like chemical plants (minute to hour level control) that can accommodate MHE’s execution time scales.
If you need to simultaneously handle nonlinearities and constraints, it may be a superior choice.
Also there are potential ways to make MHE run faster. For certain forms of the optimization problem (like a linear or quadratic program), it’s possible to convert it to a lookup table (search for “explicit MPC”) which can then be implemented in an embedded system for fast lookups.
That said, I agree with you in practice. An nonlinear optimization problem tends to be a numerical black box and can be hard to diagnose when things go wrong. The Kalman family of algorithms is much more straightforward (only involves function evaluations), faster and have failure modes that are much more easily understood. They just don’t do so well with constraints.
If you need to simultaneously handle nonlinearities and constraints, it may be a superior choice.
Also there are potential ways to make MHE run faster. For certain forms of the optimization problem (like a linear or quadratic program), it’s possible to convert it to a lookup table (search for “explicit MPC”) which can then be implemented in an embedded system for fast lookups.
That said, I agree with you in practice. An nonlinear optimization problem tends to be a numerical black box and can be hard to diagnose when things go wrong. The Kalman family of algorithms is much more straightforward (only involves function evaluations), faster and have failure modes that are much more easily understood. They just don’t do so well with constraints.