Super-resolution direction-finding error estimation method for wideband signal based on spatial sparsity optimization
A wideband signal, sparse optimization technology, applied in direction finders using radio waves, orientators for measuring directions, radio wave direction/deviation determination systems, etc., can solve problems such as inapplicable broadband signals
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specific Embodiment approach 1
[0067] A wideband signal super-resolution direction finding error estimation method based on spatial sparse optimization, including the following steps:
[0068] Step 1: Establish an array signal model that includes mutual coupling errors between array elements, array channel amplitude-phase inconsistency errors, and array element position errors:
[0069] When there are mutual coupling errors between array elements, array channel amplitude and phase inconsistency errors, and array element position errors in the array, the array output can be expressed as
[0070] X"'(f i )=A"'(f i ,α)S(f i )+N(f i )
[0071] =W (1) (f i )W (2) (f i )W (3) (f i ,α)·A(f i ,α)S(f i )+N(f i )
[0072] =W (1) (f i )W (2) (f i )A(f i ,α)S(f i )+Λ (3) (f i )w (3) (f i )+N(f i ), i=1,2,...,J (12)
[0073] =W (1) (f i )W (3) (f i ,α)·A(f i ,α)S(f i )+Λ (2) (f i )w (2) (f i )+N(f i )
[0074] =W (2) (f i )W (3) (fi ,α)·A(f i ,α)S(f i )+Λ (1) (f i )w (1) (f ...
specific Embodiment approach 2
[0121] The specific steps for establishing an array signal model that simultaneously includes mutual coupling errors between array elements, array channel amplitude-phase inconsistency errors, and array element position errors described in step 1 of this embodiment are as follows:
[0122] Step 1.1: Build an ideal array signal model:
[0123] Such as figure 1 As shown, there are K far-field broadband signals s k (t), k=1,2,...,K, incident on the broadband uniform linear array composed of M omnidirectional array elements, the arrival direction is α=[α 1 ,…,α k ,…,α K ], the array element spacing is d; the far-field broadband signal s k (t), referred to as broadband signal s k (t);
[0124] Taking the first array element as the phase reference point, ideally, the output of the mth array element is expressed as
[0125]
[0126] in, Indicates the kth broadband signal s k (t) The delay of reaching the mth array element relative to its arrival at the phase reference po...
specific Embodiment approach 3
[0182] The expectation maximization method described in step 2 of this embodiment is used to determine w (1) (f i ), w (2) (f i ), w (3) (f i ), μ 2 (f i ) and δ l (f i ) The specific steps for iterative estimation are as follows:
[0183] In the E-step step in the expectation maximization method, the first Calculate the distribution function of
[0184]
[0185] The operator represents the expectation of the solution condition;
[0186] In the M-step step in the expectation maximization method, the distribution functions are obtained respectively Derivatives for each unknown parameter, that is, for Take extreme values to solve for each unknown parameter;
[0187]
[0188]
[0189]
[0190]
[0191]
[0192] Let the above derivatives be 0 respectively, then the estimated value of each unknown parameter at the pth iteration can be obtained
[0193]
[0194]
[0195]
[0196]
[0197]
[0198] Where (p) represents the number of ...
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