Robotics
Observability
Definition
Observability is the property that a system's internal state can be distinguished from other possible states using the available inputs and measurements over time. Unobservable directions can change without producing enough measurement evidence to recover them.
Also known as: System observability
Updated
Measurements must distinguish possible states
A state estimator combines a model with measurements, but it can recover only quantities that affect those measurements. If two different states produce the same measurement history under the same inputs, the estimator has no evidence for choosing between them. Their difference lies in an unobservable direction.
Observability depends on the model, sensor arrangement, input trajectory, and interval being considered. A camera may constrain depth after useful viewpoint motion but not during a motion-degenerate sequence. Song's analysis describes sensing degeneracy as rank deficiency in measurement Jacobians and gives featureless corridors and single-axis rotation during hand-eye calibration as robotics examples.
Humanoid state estimation has known blind directions
Contact and inertial sensing can constrain a legged robot's motion without anchoring every global quantity. Hartley and colleagues show that, for their IMU and contact-sensor model, absolute position and rotation about gravity are unobservable. The filter can estimate locally useful velocity and orientation components while those global directions remain free to drift.
Adding another sensor helps only if its measurements provide independent information about the missing state. More readings from the same degenerate geometry do not necessarily restore observability. Deliberate excitation or viewpoint change can be as important as the number of sensors, which links observability to active system identification and active perception.
Observability is not estimator accuracy
An observable model does not guarantee an accurate estimate. Noise, bias, poor calibration, incorrect data association, and numerical conditioning still matter. Conversely, an unobservable quantity may appear stable because of a prior or regularisation, but that stability is not measurement evidence.
Observability analysis is also tied to assumptions and operating conditions. A local rank test near one trajectory does not prove that every trajectory is informative. Designers should state which states are observable, under which sensors and motions, instead of treating a converged covariance or low residual as proof that the full physical state is known.
Sources
Related terms
State estimation
State estimation infers quantities describing a robot or its environment from measurements and a model. A robot state may include position, orientation, velocity, and other variables that are not all directly measured.
Sensor fusion
Sensor fusion combines information from multiple sensors or estimation sources to produce a shared estimate. The combination must account for coordinate frames, timing, uncertainty, and dependence between inputs.
System identification
System identification estimates a model of a physical system from measured inputs and outputs. In robotics, it can recover parameters such as inertia and friction or learn a more general model of how actions change the system state.
Contact-aided state estimation
Contact-aided state estimation estimates a legged robot's body motion by combining inertial measurements with kinematics and information about which feet or other links are in stationary contact. A trusted contact acts as a temporary reference that constrains drift.