What does observability mean in a GNSS/INS Kalman filter, and why is it important?

• A. The ability to observe the sky for satellite visibility.
• B. The ability to infer all state variables from measurements over time; lack of observability leaves some states poorly estimated.
• C. The measure of how often you can observe the system state in real time.
• D. Observability is irrelevant in Kalman filters.

Answer: (B)

Observability in a GNSS/INS Kalman filter is about whether the measurements collected over time provide enough information to reconstruct the full state of the system. In this context, the state might include position, velocity, attitude, accelerometer bias, gyroscope bias, and receiver clock bias. If the system is fully observable, these states can be determined uniquely (at least in a statistical sense) from the measurement history as the filter processes data. If some states are not observable, the filter can only constrain them weakly, leading to large uncertainties, drift, or incorrect estimates even with long data sequences.

This matters a lot in practice because GNSS measurements and inertial data interact: GNSS helps pin down absolute position and clock biases, while inertial sensors provide high-rate motion information. Depending on motion, satellite geometry, and sensor quality, certain states may be readily inferred (e.g., position and some biases) while others (like gyro bias) may remain poorly determined unless the geometry or dynamics provide enough excitation, or additional sensors are added. When observability is lacking, you might see drifting estimates for those states or inflated uncertainty, undermining navigation accuracy.

So the statement that describes observability as the ability to infer all state variables from measurements over time, with poorly observed states remaining poorly estimated, captures the essential idea. The other options describe satellite visibility, the frequency of state observations, or claim irrelevance, none of which define the concept correctly.