Patent Document ID: 9264809
Application ID: 14285400
Patent Flag: 1

Claim One:
1. A method comprising the steps of: determining a grid of G tentative locations r g of one or more K acoustic sources; using an acoustic model to predict replicas caused by simulated acoustic sources at locations in , wherein the replicas are Fourier coefficient vectors at F frequencies {ω f } f=1 F corresponding to the acoustic pressure field as sampled by an acoustic sensor array having N sensors; collecting, using the acoustic sensor array, time series data of actual acoustic measurements at each sensor of the acoustic sensor array due to the acoustic sources; using a discrete-time Fourier transform (DFT) on the collected time series data partitioned to m blocks to compute Fourier coefficients at frequencies {ω f } f=1 F for all sensors; constructing DFT coefficient vectors y m,f ∈ N , ∀m,f using the Fourier coefficients previously obtained via the DFT; modeling DFT coefficient vectors at ω f for the m-th measurement block of the collected time series data as y m,f =Σ g=1 G s g,f (p g,f +v g,f )+ε m,f , ∀m, f, where s g,f denotes the acoustic gain at ω f for a source located at r g , p g,f ∈ N is the replica for ω f corresponding to a source located at r g normalized so that ∥p g,f∥ 2 =1, v g,f ∈ N is an unknown perturbation vector effecting p g,f , and ε m,f denotes the Fourier coefficients at ω f corresponding to the noise in the m-th block; discarding locations within from a set of tentative source locations via a regression-coefficient screening procedure that depends on the available measurements, desired sparsity level, and specific form of an estimator for a complex-valued matrix S comprising all regression coefficients {s g,f }; estimating S as S ^ := arg ⁢ ⁢ min S ∈ G × F ⁢ 1 2 ⁢ M ⁢ ∑ f = 1 F ⁢ ⁢  Y f - ( P f + V f ) ⁢ s f ⁢ 1 M ′  F 2 + μ ⁢ ∑ g = 1 G ⁢  ϛ g  q , where, for a given ω f , Y f :=[y 1,f ,. .. y M,f ] comprises all MDFT Fourier coefficient vectors, P f :=[p 1,f ,. .. , p G,f ]∈ N×G comprises all normalized replicas corresponding to locations in where ∥p g,f∥ 2 =1, ∀g, f, V f :=[v 1,f ,. .. , v G,f ]∈ N×G is a complex-valued matrix comprising all perturbation vectors for ω f , μ is a tuning parameter controlling sparsity of the groups formed by the rows of S, ç g :=[s g,1 ,. .. , s g,F ]′∈ F comprises the vector corresponding to the g-th row of S, s f :=[s 1,f ,. .. , s G,f ]′∈ F comprises the vector corresponding to the f-th column of S, 1 M ′ an M×1 vector of ones, and q∈(1, ∞]; and constructing one or more SLMs over per frequency ω f using Ŝ, wherein each location on a particular SLM is associated with its corresponding acoustic gain estimate ŝ g,f , wherein estimates of the actual locations of the K acoustic sources correspond to the locations of the K-largest in magnitude coefficients ŝ g,f depicted in the SLM.