add tutorial on disturbance modeling for state estimation

[baggepinnen]

No description provided.

[ChrisRackauckas]

It would probably be good to show an example of using sampled disturbances, using an interpolation block? That's a FAQ.

[baggepinnen]

I added a link and mention of the MTKstdlib blocks module and their tutorial on using the interpolation block for sampled input signals

[ChrisRackauckas]

ERROR: LoadError: AssertionError: latexify does not support objects of type AnalysisPoint.

[cstjean]

Suggested change

To make use of the model defined above for state estimation, we may want to generate a Julia functions for the dynamics ``f`` and the output equations ``g`` that we can plug into, e.g., a nonlinear version of a Kalman filter or a particle filter, etc. MTK contains utilities to do this, namely, [`generate_control_function`](@ref) and [`build_explicit_observed_function`](@ref) (described in more details in ["Input output"](@ref inputoutput)). These functions take keyword arguments `disturbance_inputs` and `disturbance_argument`, that indicate which variables in the model are considered part of ``w``, and whether or not these variables are to be added as function arguments to ``f``, i.e., whether we have ``f(x, u, p, t)`` or ``f(x, u, p, t, w)``. If we do not include the disturbance inputs as function arguments, MTK will assume that the ``w`` variables are all zero, but any dynamics associated with these variables, such as disturbance models, will be included in the generated function. This allows a state estimator to estimate the state of the disturbance model, provided that this state is [observable](https://en.wikipedia.org/wiki/Observability) from the measured outputs of the system.

To make use of the model defined above for state estimation, we may want to generate a Julia function for the dynamics ``f`` and the output equations ``g`` that we can plug into, e.g., a nonlinear version of a Kalman filter or a particle filter, etc. MTK contains utilities to do this, namely, [`generate_control_function`](@ref) and [`build_explicit_observed_function`](@ref) (described in more details in ["Input output"](@ref inputoutput)). These functions take keyword arguments `disturbance_inputs` and `disturbance_argument`, that indicate which variables in the model are considered part of ``w``, and whether or not these variables are to be added as function arguments to ``f``, i.e., whether we have ``f(x, u, p, t)`` or ``f(x, u, p, t, w)``. If we do not include the disturbance inputs as function arguments, MTK will assume that the ``w`` variables are all zero, but any dynamics associated with these variables, such as disturbance models, will be included in the generated function. This allows a state estimator to estimate the state of the disturbance model, provided that this state is [observable](https://en.wikipedia.org/wiki/Observability) from the measured outputs of the system.