The Prediction Model
The most common representation is
where is the predicted signal value, the previous observed values, and the predictor coefficients. The error generated by this estimate is
where is the true signal value.
These equations are valid for all types of (one-dimensional) linear prediction. The differences are found in the way the parameters are chosen.
For multi-dimensional signals the error metric is often defined as
where is a suitable chosen vector norm. Predictions such as are routinely used within Kalman filters and smoothers to estimate current and past signal values, respectively.
Read more about this topic: Linear Prediction
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