State Estimation

Tightly coupled with the study of control is the study of state estimation. The world is a chaotic, messy place, and the field of state estimation provides powerful, efficient algorithms for estimating the state of a dynamical system, such as a robot or aerospace vehicle, given potentially sparse, potentially noisy, potentially inaccurate measurements.

Kalman filter

The Kalman filter is the classical "holy grail" of time-domain state estimation.

Reference: Kalman Filter

Wahba's problem

An interesting, and highly impactful, problem in state estimation is Wahba's problem. First proposed by statistician Grace Wahba in the 1960s, Wahba's problem involves solving the nonconvex program

\[ \min_{R \in \mathrm{SO(3)}} \sum_i w_i \left\Vert y_i - R x_i \right\Vert_2^2 \]

where \( x_i, y_i \) are corresponding unit vectors in \( \mathbb{R}^3 \) and \( w_i \) are positive scalar weights.

Reference: Wahba's Problem

Since the 1960s, a variety of solution methods for Wahba's problem have emerged. Three of the most notable are, in no particular order, the Davenport q-method, singular value decomposition, and convex optimization.

Reference: Davenport q-Method for Wahba's Problem

Reference: Singular Value Decomposition for Wahba's Problem

Reference: Convex Optimization for Wahba's Problem

Factor graphs

TODO

References

More coming soon!