Sensor Fusion

Combining many imperfect sensors into a single estimate that is more accurate and reliable than any one of them alone.

Why combine sensors

Every sensor is imperfect: noisy, biased, limited in range, or occasionally faulty. Sensor fusion combines multiple measurements of related quantities into a single best estimate, exploiting redundancy to reduce noise and detect faults. The fused estimate is typically more accurate and more robust than the best individual sensor, and it can infer quantities no single sensor measures directly.

The core method

The workhorse is recursive Bayesian estimation, of which the Kalman filter is the classic linear case. It maintains an estimate of the system state and its uncertainty, predicts forward using a model, then corrects using each new measurement, weighting model and measurement by their relative confidence. A trusted measurement pulls the estimate strongly; a noisy one barely moves it.

def kalman_update(x, P, z, H, R):
    # x: state estimate, P: covariance, z: measurement
    y = z - H @ x                      # innovation
    S = H @ P @ H.T + R                # innovation covariance
    K = P @ H.T @ inv(S)               # gain: trust measurement vs model
    return x + K @ y, (I - K @ H) @ P

Fault detection through disagreement

Fusion also exposes faults: when one sensor disagrees sharply with the fused estimate from the others, that innovation is a signal the sensor may be failing. This lets a system keep working through a sensor failure and flag the bad sensor, rather than blindly trusting a broken input.

The model dependency

Fusion relies on a model of how the state evolves and how sensors relate to it. A wrong model degrades the estimate, sometimes subtly. So the model is validated, and the filter's own consistency (are the innovations statistically reasonable?) is monitored as a health check.

Kronos framing

Sensor fusion underlies plasma state estimation, subsystem monitoring, and the digital twin's data assimilation for the Hyperion breeder. In the design phase it is developed against simulated sensor data ahead of operation; construction begins in the second quarter of 2027.