State Observer

A model-based estimator that reconstructs a system's unmeasured internal states in real time from its known inputs and outputs.

Many controllers need the full state — such as joint velocity or body velocity — but sensors typically measure only part of it. A state observer uses the system model together with the measurable inputs and outputs to reconstruct the unmeasured internal states in real time. It maintains an estimate x̂ that evolves alongside the system model and is corrected by the difference between the measured output y and the predicted output Cx̂: dx̂/dt = A x̂ + B u + L (y − C x̂), where A, B, C are the linear model matrices, u is the control input, and L is the observer gain — a larger L corrects faster but also amplifies noise more. This is the Luenberger observer, proposed by David Luenberger, and it requires the system to be observable, meaning the state can in principle be inferred uniquely from the output; by the separation principle, state feedback and the observer can be designed independently. A Kalman filter can be viewed as an observer whose gain L is chosen optimally from the noise statistics, and specialized variants such as the disturbance observer and momentum observer used in robotics estimate external forces rather than the full state.

ExampleA motor has only an encoder measuring position θ. Setting the state to [θ, ω] (with ω the angular velocity) and treating the current-derived torque as the input u, the observer corrects the position estimate while also producing an estimate of ω — one that is less noisy than simply differentiating the measured position to get velocity.

Also called

Luenberger Observer, State Estimator

Related

Kalman Filter · Disturbance Observer · Generalized Momentum Observer · State Estimation · Extended Kalman Filter · Linear Quadratic Gaussian Control

Sources

State observer - Wikipedia