Time-varying source separation by joint diagnolization on autocovariances
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2020Copyright
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Sokealla signaalinerottelulla (Blind Source Separation, BSS) pyritään erottelemaan todelliset signaalit havaituista signaaleista, kun ennakkotietoja sekoitusmatriisista ja todellisista signaaleista on vain vähän saatavilla. BSS-ongelmien ratkaisemiseksi on kehitetty erilaisia menetelmiä. Näistä toisen asteen sokea signaalinerottelu (Second-Order Blind Identification, SOBI) tunnistaa lähteet toisen asteen tunnuslukujen avulla (Tong et al., 1994). Tässä opinnäytetyössä tarkastellaan toisen asteen sokean signaalinerottelumallin laajennusta (Yeredor, 2003), jossa sekoitusmatriisi muuttuu ajassa. Työssä esitellään paranneltu versio Yeredorin TV-SOBI (time-varying SOBI) algoritmista sekä sen variaatioita. Algoritmit pyrkivät estimoimaan sekoitusmatriisin ja edelleen latentit signaalit otosautokovarianssimatriisin hajotelman sekä yhteisdiagonalisoinnin avulla. Kehitetyn algoritmin (linearly time-varying SOBI, LTV-SOBI) suorituskysyä arvioidaan simulointien avulla. Suorituskyvyn mittarina käytetään tässä työssä kehitettyä signaali-häiriö suhteen (Signal-to-Inference Ratio, SIR, Yeredor, 2003) laajennusta aikamuuttuvan signaalin tapaukseen. Simulaatiotulokset osoittavat uuden LTV-SOBI-algoritmin paremmuuden verrattuna Yeredorin TV-SOBI-algoritmiin. Tulokset eivät tosin ole vielä optimaalisia. Lisäksi työssä esitellään LTV-SOBI algorithmin R implementointi sekä interaktiivinen R Shiny sovellus, jonka avulla algoritmien suorituskykyä voidaan vertailla.
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Blind Source Separation (BSS) seeks to recover the true signals from the observed ones when only limited information about the mixing matrix and the original sources are available. There are various methodologies established to solvetheBSSproblems, andnotably, Second-OrderBlindIdentification(SOBI) identifiessourcesthroughsecond-orderstatistics(Tongetal., 1994). Thisthesis stretches the Second-Order Source Separation (SOS) model in terms of latent time variation in the mixing mechanism that was initially proposed by Yeredor (2003). An improved algorithm, Linearly Time-Varying SOBI (LTV-SOBI), togetherwithalternativesattemptstoestimatemixingparametersandultimately derives latent independent sources employing sample autocovariance decomposition and joint diagonalization. The performance of LTV-SOBI is analyzed withsimulateddatabyextendingtheperformancemetricSignal-to-interference ratio (SIR, Yeredor, 2003) into the time-varying case. Simulation results suggest the superiority of the new LTV-SOBI algorithm compared with Yeredor’s TV-SOBI algorithm, despite overall results are still non-optimal. In addition to the full implementation of LTV-SOBI algorithm in R, an interactive dashboard is designed to enable further outlook of algorithm performance.
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