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Table 1 PARALIND decomposition algorithm

From: PARALIND-based blind joint angle and delay estimation for multipath signals with uniform linear array

Step 1: Initialization
  Initialize matrices J ( 0 ) , A θ ( 0 ) , F ϕ ( 0 ) and S ( 0 ) , k = 0
Step 2: k = k + 1
Step 3: Update J based on (21), given S ( k ) , F ϕ ( k ) and A θ ( k ) :
j ( k + 1 ) = ( S ( k ) F ϕ ( k ) A θ ( k ) ) x ¯ J ( k + 1 ) = unvec ( j ( k + 1 ) )
Step 4: Update S based on (22), given F ϕ ( k ) , A θ ( k ) and J ( k + 1 ) :
S ( k + 1 ) = ( F ϕ ( k ) A θ ( k ) ) ( J ( k + 1 ) ) T X ¯
Step 5: Update F ϕ based on (23), given A θ ( k ) , S ( k + 1 ) and J ( k + 1 ) :
F ϕ ( k + 1 ) = A θ ( k ) ( S ( k + 1 ) J ( k + 1 ) ) Z ¯
Step 6: Update A θ based on (24), given S ( k + 1 ) , J ( k + 1 ) and F ϕ ( k + 1 ) :
A θ ( k + 1 ) = ( S ( k + 1 ) J ( k + 1 ) ) F ϕ ( k + 1 ) Y ¯
Step 7: Calculate the fitting residual value:
  ɛ ( k + 1 ) = | | ( F ϕ ( k + 1 ) A θ ( k + 1 ) ) ( S ( k + 1 ) J ( k + 1 ) ) T ( F ϕ ( k ) A θ ( k ) ) ( S ( k ) J ( k ) ) T | | F
  repeat step 2-7 until | ɛ ( k + 1 ) ɛ ( k ) | < 1 e 8 .
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