Linear Prediction

x = prediction coefficients a_k

_{H = last p samples}

predicted z_n+1 = Sum_of (a_kz_n-k) k=1,..,p

error_n+1 = z_n+1 - Sum_of (a_kz_n-k)

Coefficients represent vocal tract filter

Errors represent laryngal and noise source

But can't we already do linear prediction?

Yes, but...

1. A "frame" ("window") at a time. Coefficients assumed constant over frame

2. Frames treated as independent. No way of enforcing continuity

3. Best fit tries to fit larynx pulses along with the rest.

Kalman filter can ignore points (not do an update) when the error is above a threshold.

4. Kalman confidence measure can be useful when making decisions based on pole estimates. E.g., formant tracking.