Patent ID: 8248304

Claim:
A method for determining the angles of arrivals of coherent sources in a system comprising several nonuniform sensors, the signals being propagated along coherent or substantially coherent paths between a source and said receiving sensors of the network, wherein use is made of at least one modal interpolation function z(θ) k that is omnidirectional in azimuth where z(θ)=exp (jθ) with θ corresponding to an angle sector on which the interpolation of the steering vectors a (θ) of the sensor network is carried out in order to process the signals transmitted by the sources and received on the sensor network and a spatial smoothing technique is applied in order to decorrelate the coherent sources, the interpolation function W e(θ) is expressed in the following manner: a ⁡ ( θ ) ≈ W ⁢ ⁢ e ⁡ ( θ ) ⁢ ⁢ with ⁢ ⁢ e ⁡ ( θ ) = [ z ⁡ ( θ ) - L ⋮ z ⁡ ( θ ) L ] = [ exp ⁡ ( - j ⁢ ⁢ L ⁢ ⁢ θ ) ⋮ exp ⁡ ( j ⁢ ⁢ L ⁢ ⁢ θ ) ] ⁢ ⁢ for ⁢ ⁢ 0 ≤ θ < 360 ⁢ ° the matrix W of dimension N×(2L+1) is obtained by minimizing in the sense of the mean squares the deviation ∥a(θ)−We(θ)∥ 2 for azimuths verifying 0≦θ<360°, the length of the interpolation 2L+1 depends on the aperture of the network, and in that the interpolation function comprises several interpolation matrices W i1 . . . iP with P corresponding to the number of disjointed sectors on which the joint interpolation of the received signals is carried out, the determination of the matrix and the width of interpolation δθ of each sector comprising at least the following steps: Step No. A.1: δθ=180°/P and θ i P =2δθ(p−1) for 1≦p≦P Step No. A.2: Calculate the interpolation matrix W i1 . . . iP by minimizing in the sense of the mean squares ∥a(θ)−W i 1 . . . i P e(θ)∥ 2 for |θ−θ i P |<δθ and 1≦p≦P Step No. A.3: Calculate the criterion A_dB(ê 1 (θ),ê 2 (θ)) A_dB ⁢ ( e ^ 1 ⁡ ( θ ) , e ^ 2 ⁡ ( θ ) ) = max  θ - θ i P  < δθ ⁢ ⁢ for ⁢ ⁢ 1 ≤ p ≤ P , n ⁢ { 20 ⁢ ⁢ log 10 ⁡ (  e ^ n ⁡ ( θ ) e ^ n + 1 ⁡ ( θ )  ) } , ⁢ with ⁢ ⁢ W i 1 ⁢ ⁢ … ⁢ ⁢ i P - 1 ⁢ a ⁡ ( θ ) = [ e ^ 1 ⁡ ( θ ) ⋮ e ^ N ⁡ ( θ ) ] where δθ is the minimal value for which the amplitude error A_dB is less than a given value A_dB_ref, Step No. A.4: If A_dB(ê 1 (θ),ê 2 (θ))>A_dB_ref, then do δθ=δθ/2 and return to step A.2 Step No. A.5: Calculation of K=180 /(Pδθ) Step No. A.6: For all P-uplets (i 1 . . . i P ) verifying 0≦i 1 ≦ . . . ≦i P <K with K being the number of sectors on which the interpolation is carried out: Step No. A.6.1: Calculation of θ i P =2δθ×i P for 1≦p≦P Step No. A.6.2: Calculation of the interpolation matrix W i 1 . . . i P by minimizing in the sense of the mean squares ∥a(θ)−W i 1 . . . i P e(θ)∥ 2 for |θ−θ i P |<δθ and 1≦p≦P Step No. A.6.3: Return to step A.6.1 if all the P-uplets (i 1 . . . i P ) verifying 1≦i 1 ≦ . . . ≦i P ≦K are not explored.