Space-Time-Frequency Orientation Estimation Method Based on Joint Diagonalization of Jacobian Rotation
A technology of joint diagonalization and azimuth estimation, applied in systems for determining direction or offset, direction finders using ultrasonic/sonic/infrasonic waves, etc., which can solve the problem of space-time-frequency distribution matrix azimuth estimation only using a single one.
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specific Embodiment approach 1
[0046] Specific implementation mode 1: The space-time-frequency orientation estimation method based on Jacobian rotation joint diagonalization in this implementation mode is specifically prepared according to the following steps:
[0047] Step 1. According to the array received signal X(t), construct the space-time-frequency distribution matrix D of the array received signal XX (t,f);
[0048] Among them, t represents the time variable, f represents the frequency variable, and the subscript X represents the array receiving signal, and the expression form using two subscripts X is the space-time-frequency distribution matrix D XX The expression (2) of (t, f) is related, and the conjugate X of the signal X and X is used in the expression (2). * Two sets of data, where X * can also be obtained from X, so use D XX (t, f) represents the space-time-frequency distribution matrix
[0049]
[0050] x * ( ) represents the complex conjugate matrix of X( ); l is an intermediate va...
specific Embodiment approach 2
[0083] Specific embodiment 2: The difference between this embodiment and specific embodiment 1 is that in step 1, according to the array received signal X(t), the space-time-frequency distribution matrix D of the array received signal is constructed XX (t, f) is specifically:
[0084] Step one, such as figure 1 As shown in , it is assumed that there is a uniform linear array in space, the number of array elements is N, and the distance between array elements is d; there are M narrowband source signals in the far field of the uniform linear array, and the incident angle of the mth narrowband signal source is θ m , then the steering vector a(θ m )for:
[0085]
[0086] Among them, f m Indicates the frequency of the mth narrowband signal, c indicates the spatial signal propagation velocity, [ ] T Represents the matrix transpose, j represents the imaginary unit; m=1,...,M; e is a natural constant; M is the total number of narrowband source signals;
[0087] Thus, the a...
specific Embodiment approach 3
[0098] Embodiment 3: The difference between this embodiment and Embodiment 1 or 2 is that the coordinates corresponding to the coordinate index numbers extracted in step 3 are (p, p), (p, q), (q, p) and (q,q); elements according to coordinates (p,p) elements of coordinates (p,q) elements of coordinates (q,p) and elements with coordinates (q,q) Specifically:
[0099] Formula (7) is the kth space-time-frequency distribution matrix D XX (t k ,f k ), let the matrix D XX (t k ,f k ) elements with the symbol a k to represent, then the element in row p and column p in the matrix is (that is, the elements of coordinates (p,p) are ), the elements in row p and column q are expressed as (that is, the elements of the coordinates (p,q) are ), the elements in the qth row and the pth column are expressed as (that is, the elements of the coordinates (q,p) are ), the elements in the qth row and the qth column are expressed as (that is, the elements of the coordinates...
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