What is a Kalman filter in navigation, and what are its state, process model, and measurement model?

• A. A deterministic estimator that uses only a single measurement to estimate state.
• B. A recursive estimator that combines a process model with noisy measurements to estimate the state; the state includes position, velocity, attitude, and sensor biases; the process model predicts state evolution and the measurement model relates sensors to the state.
• C. A filter that solely removes multipath.
• D. A method to compute TTFF.

Answer: (B)

At its core, a Kalman filter in navigation is a recursive estimator that blends predictions from a process model with noisy measurements to estimate the system’s state. The state typically includes position, velocity, attitude (orientation), and sensor biases (like IMU biases) so the filter can account for drift in sensors over time.

The process model describes how the state evolves from one moment to the next. It propagates position and velocity based on dynamics, updates attitude from known rotation rates, and models how sensor biases may wander. This model provides a predicted state and an associated uncertainty before new measurements arrive.

The measurement model links the actual sensor readings to the current state. It shows how measurements such as GPS position (and sometimes velocity) or other sensors relate to the state variables, again with an uncertainty that captures noise and errors. When a new measurement comes in, the filter combines it with the predicted state using the Kalman gain, refining the estimate and reducing uncertainty.

This combination is what makes the Kalman filter powerful for navigation: it continuously fuses motion dynamics with sensor observations, compensating for noise and biases to produce a more accurate and robust estimate than relying on either model or measurements alone.

The other options don’t fit because one describes a deterministic estimator using a single measurement, which misses the probabilistic fusion and the process model; another describes a function unrelated to state estimation (multipath removal); and the last describes a metric (time to first fix) rather than a state-estimation approach.