IntermediateTopic 42 of 101Signals, Control & Comms
Wiener and Kalman filters
Optimal estimators that combine models with noisy measurements.
In depth
The Wiener filter is the optimal linear filter minimising mean-square error given signal and noise statistics. The Kalman filter recursively estimates the state of a linear dynamic system from noisy measurements via predict/update steps, optimal for Gaussian noise. Applications: navigation, tracking, control.
Key points
- Process and measurement noise covariances
- Kalman gain
- Innovations
ExampleGPS/INS navigation fuses accelerometers with GPS fixes using a Kalman filter.
Optimal filters estimate a hidden state from noisy measurements, which underpins navigation, tracking and sensor fusion.
What is Wiener and Kalman filters?
Optimal estimators that combine models with noisy measurements.
Why is it important to understand wiener and Kalman filters?
Optimal filters estimate a hidden state from noisy measurements, which underpins navigation, tracking and sensor fusion.
What does a Kalman filter do?
It combines a model prediction with a measurement at each step, weighting them by their uncertainties to give the best estimate.
What is the Wiener filter?
An optimal linear filter that minimises the mean squared error for a stationary signal, using the spectra of the signal and noise.
How is Wiener and Kalman filters used in practice?
Typical applications include estimating the position of a drone from GPS and inertial sensors, tracking a satellite from noisy radar measurements and filtering a noisy battery state-of-charge estimate.
What should I learn before Wiener and Kalman filters?
Study "Random signals and noise" first (topic 41 of 101 in Signals, Control & Comms). It covers the groundwork this topic builds on.
What are the key points of Wiener and Kalman filters?
Process and measurement noise covariances. Kalman gain. Innovations.
Can you give an example of Wiener and Kalman filters?
GPS/INS navigation fuses accelerometers with GPS fixes using a Kalman filter.
What comes after Wiener and Kalman filters?
The next topic is "Introduction to control systems", which builds directly on this one.
How difficult is Wiener and Kalman filters?
It is classed as Intermediate in Signals, Control & Comms (topic 42 of 101). It is an intermediate topic. Work through the beginner topics in Signals, Control & Comms first.