Sinusoidal Signal Detection using the Minimum Description Length and the Predictive Stochastic Complexity

Sirlusoidal sigrial detcctkm is discussed in various fields rangir~g frorri telec:orr~rr~ur~ic~~t,io~~s to array processirlg and spectrurri estirriation. Various tecl~rliques have bee11 proposed in the literat,ure for si~iusoidal sigrlal detection arid enurrieratior~; see [I]. Here, we propose two er~urr~eratior~ teclmiques b e d or1 the rr~inirriurr~ tlcscriptivr~ ler~glit (MDL) [2] and the predictive st,ochi~stic corriplexity (PSC) [3] principles. MDL a d PSC estimate t , l ~ model order by rr~i~~irriixir~g the Kul1t)xli-Leibler tlistauce between the true rr~odel a r~d the c-:st,irriated orri:. Duc to terr~poral co1iercm:y of sirlusoids, direct c 2 p plicatior~ of MDL and PSC generates erroneous results t,l~e rlurriber of signals is always detecled as 1. Here, we iritroduce arl allerr~ative approach, sirrlilar to the orlev presented in [4] arid [5]. The proposed technique is based on decorr~posirig I,he observatior~ vectors ir~to tlieir orthogorlal corripor~erits iri the sig11a1 and noisc subspaces. Usir~g tllc: MDL or PSC pririciple, the noise corr~por~erits are encoded. This procedure is performed Sur all possible rnodels aud the rr~ir~irr~urr~ codrlerlgtl~ is selected i,o estimat,e the r~urril~er or sir~usoicls. The sirnulat,ior~ study shows (,hat tlie PSC has a bet,tcr perfor~rlnr~r:ce iri rlonstai.io11ar.y er~viror~rrier~ts. 2 Problem formula ti or^