Moving Horizon Estimation (MHE)

Definition

The optimization approach that uses a series of measurements that span over time to estimate unknown variables of a dynamical system¹

MHE is non-deterministic → Requires iteration that relies on linear or nonlinear programming solvers. You can’t obtain a definite solution by following a definite and algorithmic path

Advantages

1. MHE outperforms most traditional state-estimation methods (such as EKF) - This is gold in nonlinear dynamical systems because they are rigorously treated with MHE but EKF works reliably only on systems that are almost linear²
2. Additional constraints can be added - This allows us to place bounds on estimated variables

Limitations

1. Increased computational complexity - Systems that have good compute power can benefit immensely from MHE but otherwise, not so much but there are MHE packages that attempt to mitigate this issue

Note

Under certain conditions, MHE reduces to the Kalman filter

J - Optimization function $w_y$ - Weight representing the relative importance of measured variable $y_i$ w_\hat{x} - Weight representing the relative importance of predicted variable ${\hat{x}}_i$ $w_{p_i}$ - Weight penalizing big changes in parameter $p_i$

Footnotes

1. https://en.wikipedia.org/wiki/Moving_horizon_estimation ↩

2. https://www.do-mpc.com/en/latest/theory_mhe.html ↩