ERROR MODEL FOR SPATIAL SPECTRUM ESTIMATION OF M ILL IM ETER2WAVE THERMAL RAD IATION ARRAY

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1 J. Infrared M illim. W aves Vol. 29, No. 2 Ap ril, 2010 : ( , 3,,, (, :,.,,,.,,. : ; ; ; ; : TN911. 7: A ERROR MODEL FOR SPATIAL SPECTRUM ESTIMATION OF M ILL IM ETER2WAVE THERMAL RAD IATION ARRAY WU Lu2Lu, HU Fei 3, ZHU Yao2Ting, L IQ ing2xia, J IN Rong (Department of Electronics & Information Engineering, Huazhong University of Science and Technology,W uhan430074, China Abstract: In order to app ly spatial spectrum estimation to m illimeter2wave thermal radiation array receiving system for de2 tecting targets with superior resolution, it is needed to solve two key p roblem s which are weaknesses of thermal signalsen2 ergy em itted from targets and the decline of performance caused by array errors. To solve these p roblem s, an array error model with low signal2noise ratio ( SNR was p resented. In this model, the influences of amp litude and phase errors on sig2 nal source and channel noise were considered, and the perturbation range of the eigenvalues and the error distance of the signal eigenvector space of the autocorrelation matrix received by arrays were derived. Then the calibration algorithm for amp litude and phase errors based on the model was p roposed, which could make the spatial spectrum estimation with high resolution be used in m illimeter2wave radiation array system effectively. The effectiveness and correctness of the model are verified by the experiments. Key words: m illimeter2wave thermal radiation; low signal noise ratio ( SNR ; array errors; calibration; spatial spectrum estimation,,, [ 1 ].,,..,,,,,.,, : , : Rece ived da te: , rev ised da te: : ( ,863 (2006AA09Z143 :(19802,,,,. 3 : hufei@hust. edu. cn

2 124 29,, [ 24 ],. (, [ 5 ] 15dB [ 59 ]., ( - 20dB,.,,,.,, [ 1 ] : X ( t old =a ( s S ( t + N ( t, (1 X ( t old N 1, N N, s, a ( s, S ( tm 1, N ( tn 1, R old : R old = o 2 sa ( s a H ( s H + 2 I, (2, 2 s, 2, N N : = d iag [ 1 2 N ], diag, (3 i i1: i = i e j 1 i = 2, 3,, N, (4, i i i. ( 1 (2,, S ( t, N ( t.,,,,n ( t. : X ( t new =a ( s S ( t +N ( t, (5 R new : R new = o 2 sa ( s a H ( s H + 2 H. (6 (6,,. 2 H, a ( s [ 1, 5 ] R org ( : R org X =a ( s = o 2 sa ( s a H ( s H. (7 = [ 1 a 1 ( s 2 a 2 ( s N a N ( s ] T, (8 R org = o 2 s XX H, (9 R org X = o 2 s XX H X = ( o 2 s X H X X = 1 X, (10 1 = 2 s XX H = 2 s a ( s R org, X = a ( s. R org R org : = U d iag [ 1 2 N ] U H = U d iagg o 2 s a ( s 00U H, (11 U, diag [ 1 2 N ], 1 = 2 s a ( s, 2 = 3 = = N = 0. R old = R org + 2 I, (12 i I - R org = i I - (R old - 2 I = ( i + 2 I - R old = i I - R old = 0. (13, R old : R old = U d iag [ 1 2 N ]U H = U d iag [ ]U H = U d iag [ o 2 s a ( s ]U H, (14 U, diag [ 1 2 N ], 1 = 2 s a ( s + 2, 2 = 3 = = N = 2. (1 ( 2 (13 (14, (1X ( t old,, 2 ; ( 2 2 R old i,.

3 2 : 125,. ( (5 ( 6 R new : R new = R org + 2 H, (15 2 H = d iag [ N ] = d iagg N. (16 1 [ 10 ], R new i : i + 2 m in ( i i + 2 max(. (17, (17: i - 2 (max ( - m in ( i i. (18 i ( 18, R new i : o 2 s a ( s - 2 (max( - m in ( i o 2 s a ( s 2 s N - 2 (max( 2 - m in i (2 i i 2 s N a, (19 2 (m in ( - max ( 0. (20 (19 (20, ( 1 R new 2 i ; (2 2, i, R new ; ( 3 s2 µ 2,, i i, R new R old,. 2 [ 10 ], E = 2 ( H - I, (21 R new = R old + E, (22 D = R new X - X 1 = (R new - 1 I X. (23 9 == 1 = 1 + 2, (24 = max (, (25 R new R old : sin ( (X Rold, X R new D /. (26 (26,, R new R old,. 1 (25,max( > 1, = 2 s a ( s m ax ( a i N = 2 s max ( = 2 s s imax( 1 max ( m ax (, (27 (27, 2,, R new R old, 2. 2 S ( t, S ( t N ( t, X ( t, R new, R new,. 1 s, a ( s. 1 I. R n new : 2 n R new R n new = inv ( n R new inv ( ( n H = 2 s inv ( n a ( s a H ( s H inv ( ( n H + nv ( n H inv ( ( n H, (28, inv., n R n new, n, inv ( n H inv ( ( n H I, R n new. R n new, : R n new = U n n U nh, (29, n : n = d iagg n 1 n 2 n N, > n 2 n 3. (30 n 1 U n : U n = gu n 1 u n 2 u n N. (31 n + 1 n N = kd iag ( u n 1 3 inv ( d iag ( a ( s, (32 = / 1, (33

126 29 n + 1 : = n 3. (34 3 (,, n - <. (35, n + 1.

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(2009) Journal of Rem ote Sensing (, 2006) 2. 1 (, 1999), : ( : 2007CB714402) ;

(2009) Journal of Rem ote Sensing (, 2006) 2. 1 (, 1999), : ( : 2007CB714402) ; 100724619 (2009) 0220183207 Journal of Rem ote Sensing 1, 2, 3, 3, 3, 1 1., 100101; 2., 100049; 3., 100080 :,,, 3, ( ),1%,, :,,, : TP79 : A 1 20,,,,;, (, 1999),,,,, (, 2006),,,,, 2 2. 1 : 2007209217; :