https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python
Data is noisy, sensors may be inaccurate Combine knowledge of the past and that of the system to reliably make data estimates Never throw away inaccurate data
Real sensors are more likely to provide measurements that are closer to the true value
Blend of prediction and measurement
Measurement - Prediction = Residual
g-h filter or filter
g - scaling for the measurement
- Smaller g — closer to predictions
- Larger g — closer to measurements
- g greater than 1 — overshoot from measurement
h - scaling for the rate h is the factor that decides the reactivity of the filter to changes in the data. If h is small, the filter will react more slowly to changes in data, while a high h would imply faster responses. High h may also cause a increase in frequency of the ringing before reaching the steady state
- Make prediction based on what we know
prediction = previous_estimate + rate * time_step - Update estimate and rate
updated_estimate = prediction + g * (measurement - prediction)updated_rate = rate + h * (measurement - prediction)/time_step - Repeat
Terminology
- System - What we want to estimate
- State - The actual configuration of the system or the actual value
- Estimate - The filter’s estimate of the state
- Measurement - A measured value of the state
- Process model - How we think the state will change
- System propagation - The prediction step
- Measurement update - The update step
Kalman filters dynamically vary g and h Problem of g-h filter - Systemic error (only as good as mathematical model. For example, if we introduction an acceleration factor while creating the data, the prediction falls behind the measurements and h is not enough to compensate for it here - a fundamental shortcoming of g-h filters)