Kalman Filtresi

Giriş
Kontrol teorisini bilmeden Kalman Filtresini anlamak kolay değil.

Kalman filtresi periyodik ölçüm ile çalışır. Açıklaması şöyle.

1. Kalman Filters are discrete. That is, they rely on measurement samples taken between repeated but constant periods of time. Although you can approximate it fairly well, you don't know what happens between the samples.
2. Kalman Filters are recursive. This means its prediction of the future relies on the state of the present (position, velocity, acceleration, etc) as well as a guess about what any controllable parts tried to do to affect the situation (such as a rudder or steering differential).
3. Kalman Filters work by making a prediction of the future, getting a measurement from reality, comparing the two, moderating this difference, and adjusting its estimate with this moderated value.
4. The more you understand the mathematical model of your situation, the more accurate the Kalman filter's results will be.
5. If your model is completely consistent with what's actually happening, the Kalman filter's estimate will eventually converge with what's actually happening.

Bazı kavramların açıklaması şöyle.

State Prediction (Predict where we're gonna be)
Covariance Prediction (Predict how much error)
Innovation (Compare reality against prediction)
Innovation Covariance (Compare real error against prediction)
Kalman Gain (Moderate the prediction)
State Update (New estimate of where we are)
Covariance Update (New estimate of error)

Covariance bir şeyin ne kadar güvenilir olduğunu gösterir. Yan genel anlamda covariance'ın düşük olması iyidir.