We derive a new adaptive filtering algorithm called the instrumental variable affine projection (IVAP) algorithm and give its fast version (FIVAP algorithm). The IVAP algorithm departs from the AP algorithm and uses an IV. The IV process is generated in a way such that the new algorithm combines between the AP and the fast Newton transversal filter (FNTF) algorithms. Simulations show that the IVAP algorithm is more robust to noise than the AP algorithm. With the IV, the sample covariance matrix loses its Hermitian property and its displacement structure is different from the one of the AP algorithm. Consequently, the derivation of a fast version is done by deriving the IV sliding window covariance fast transversal filter (IV SWC FTF) algorithm. Using this and other ingredients, we derive the FIVAP algorithm whose computational complexity is nearly the same as the FAP algorithm.
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