{"paper":{"title":"Augmented Set-membership Affine Projection Algorithm and Its Performance Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The augmented set-membership affine projection algorithm reduces computational complexity while delivering better performance than the standard augmented affine projection algorithm on colored inputs.","cross_cats":[],"primary_cat":"eess.SP","authors_text":"Chen Wang, Haiquan Zhao, Wenjing Luo, Xiaoqiang Long, Xinnian Guo, Yalin Liu","submitted_at":"2026-05-18T14:05:31Z","abstract_excerpt":"The augmented affine projection algorithm (AAPA) has considerably excellent performance for highly colored input signals. However, the direct matrix inversion operation leads to a high computational complexity, especially with high projection order. Inspired by the excellent characteristics of set-membership filtering (SMF), this paper proposes the augmented set-membership affine projection algorithm (ASM-APA), which not only has low computational complexity but also offers improved performance compared with AAPA. Then, the computational complexity and stability of ASM-APA are analyzed, and th"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The augmented set-membership affine projection algorithm (ASM-APA) not only has low computational complexity but also offers improved performance compared with AAPA, with a provided condition for maintaining stability.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That directly incorporating set-membership filtering into the augmented APA structure preserves or enhances convergence behavior while cutting complexity, without introducing new instability or performance loss under the tested conditions.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The ASM-APA combines set-membership filtering with augmented affine projection to deliver lower computational complexity and improved performance over AAPA for colored signals, supported by complexity and stability analysis.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The augmented set-membership affine projection algorithm reduces computational complexity while delivering better performance than the standard augmented affine projection algorithm on colored inputs.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"86820c262eebc6643d7c1f710195fbc0b02f4e24b0bf80199cc449171ad28a72"},"source":{"id":"2605.18432","kind":"arxiv","version":1},"verdict":{"id":"c8e690ce-39ca-4227-bfa9-be6e98b49cd0","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T23:54:05.601351Z","strongest_claim":"The augmented set-membership affine projection algorithm (ASM-APA) not only has low computational complexity but also 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