g-h Filter

Also called the $\alpha$-$\beta$ filter, this is a class of filter algorithms used to make accurate estimates of something with noisy data g - Scaling factor for the measurements h - Scaling factor for the rate of change of measurements There are two steps in the algorithm — the prediction and update step

• Prediction / System Propagation prediction = previous estimate + (gain rate $\times$ time step)
• Update / Measurement Update gain rate = gain rate + (h $\times$ residual) new estimate = prediction + (g $\times$ residual)

Note

The residual is the difference between measurement and prediction. A smaller residual implies better performance

Many filters such as the Kalman Filter and Benedict-Bordner filter are based on the g-h filter

The filter is only as good as the mathematical model used to define the system

Changing g Increasing g will make the estimates more closely follow the measurement rather than the prediction. We will consider noise too Lowering g means we reject noise but legitimate signal changes may be lost too

If the measurements aren’t too reliable, set a smaller g

Changing h Increasing h allows the filter to more quickly react to rapid changes in the system state

If the data’s fluctuating slowly, set a smaller h