Hardware & control
Observability
Observability is the property that a system's internal state can be determined from its measured outputs over time, given the known inputs and the assumed model. If different states can generate indistinguishable observations, those differences are unobservable under that sensing setup.
Also known as: state observability, system observability
Updated
A property of the model and measurements
Caltech's output-feedback notes introduce observability as the ability to recover state from measurement history. A state need not be measured directly to be observable: the dynamics can make it inferable from how other measured quantities change.
This is distinct from the quality of a particular state-estimation algorithm. Observability asks whether the information exists under the model. An estimator asks how to use it. A better filter cannot recover information absent from its measurements without adding assumptions, prior information or another source of reference.
For a linear time-invariant model, an observability-matrix rank test gives a precise condition. Nonlinear robotic systems require more care: conclusions can depend on the operating trajectory and on whether the analysis concerns the nonlinear model or a local linearisation. OpenVINS illustrates that distinction using a linearised visual-inertial error-state system.
A smooth trajectory can still have an arbitrary origin
In the visual-inertial setup analysed by OpenVINS, global translation and rotation about gravity are unobservable. A camera and IMU can estimate useful relative motion without independently determining an absolute world origin or global yaw. Those freedoms are not the same as a failed pose estimate; they describe which reference information the sensors do not supply.
Consequently, two valid reconstructions can use different coordinate frames. Before comparing trajectories, specify which frame alignment is allowed and whether external position, heading or map information was available. Do not interpret an arbitrary initial origin as a measured global location.
Overconfidence can conceal missing information
OpenVINS documents how inconsistent linearisation can introduce spurious information along an unobservable direction, producing overconfident uncertainty estimates. A small reported covariance is therefore not sufficient evidence that the underlying state is accurately known.
For humanoid or wearable datasets, document the sensor configuration, reference information, initialisation procedure and motion conditions. Separate absolute measurements from estimates expressed in a locally chosen frame. When an evaluation reports pose accuracy, its alignment convention and treatment of unobservable directions are part of the result, not optional implementation details.
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Related terms
Hardware & control
State estimation
State estimation is the process of inferring variables that are not known exactly—such as a robot’s base pose, velocity, contact state or sensor bias—from noisy measurements, control inputs and a model of how the system evolves. An estimator should provide both an estimate and, where possible, a representation of its uncertainty.
Data & collection
Robot state
Robot state is the set of variables used to describe a robot at a particular time, such as joint positions and velocities, base pose, end-effector pose, gripper state, actuator measurements, or estimated motion. In control theory, a complete state contains enough information to predict future evolution given an action; in robot datasets, “state” often means only the measured or estimated subset that was logged.
Data & collection
Visual-inertial odometry
Visual-inertial odometry estimates a moving sensor rig's motion by combining camera observations with inertial measurements from accelerometers and gyroscopes. Its core output is a relative motion or pose estimate over time, not an independently measured ground-truth trajectory or necessarily a reusable global map.
Data & collection
Sensor calibration
Sensor calibration is the estimation and documentation of parameters that map raw sensor readings into physically meaningful values and known spatial relationships. In robotics it can include scale, bias, distortion, intrinsic camera parameters, sensor-to-sensor or sensor-to-robot transforms, and timing offsets. Calibration does not remove all noise or drift.
Hardware & control
Coordinate frame
A coordinate frame is a defined origin and set of oriented axes used to express positions, orientations, motions, forces, or other spatial quantities. A value has no complete geometric meaning until its frame and convention are known. Transformations relate measurements expressed in frames such as world, robot base, camera, end effector, object, or sensor.