Spatial time-frequency DOA (Direction of Arrival) estimation method based on Jacobi rotation joint diagonalization
A joint diagonalization and azimuth estimation technology, which is applied to a system that determines direction or offset, and a direction finder using ultrasonic/sonic/infrasonic waves, etc., can solve the problem of using only a single one in the azimuth estimation of space-time-frequency distribution matrix
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specific Embodiment approach 1
[0048] 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:
[0049] 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);
[0050] 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
[0051] D X X ( ...
specific Embodiment approach 2
[0087] 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:
[0088] 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:
[0089] a ( θ m ) = [ 1 , e j 2 πf m ...
specific Embodiment approach 3
[0102] 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:
[0103] 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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