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Doppler frequency measurement errors oan 
be taken to be normally distributed, 
meaning that actual Doppler signals are 
described by narrow-band normal random 
processes (Papurt,1981), characterized by 
an asymptotically normal instantaneous- 
frequency distribution at a high 
signal/noise ratio  (Jemw,1974). Then, 
considering a set of the pixels  F, 
corresponding to Q, a5 a vector and with 
an expectation G,, the conventional joint 
density of the probability of Doppler 
frequencies of the area Q, pixels can be 
written as 
1 
Pf —{F, GJM, c, 6 » 
(2%) 4 |M, | 
(13) 
where M, is the correlation matrix of 
measurement errors, |M,| is the matrix M, 
determinant, n, is the vector P, number 
of dimensions, equal to the number of 
region Q, elements. 
Since frequency measurement errors of 
different pixels do not correlate 
(Sullivan, 1980; Wang, 1984), the 
correlation matrix M is diagonal 
M,= uds (14) 
where O g is the Doppler frequenoy 
1 
variance for the 1-th pixel of the Q, 
region. 
For definiteness sake let elements of 
two regions, Q Kcd a, "im will be 
designated by a = Q n TW and a, -Qf W, 
will be in the E prem position. in the 
slidi window W. It is necessary to 
determine the state 8, of the central 
pixel (I,y), i.e. to seleot one. of ihe 
following hypotheses: H (T,y)€ Q and 
Su K or H,- (T,y) € Q, and Sy = M- 
SE in (11), (13) dn. (12) and 
taking the logarithm of it, we obtain 
(f,-g,)* (f B8] 
X Inu i |» a+ ure ] 
i 
  
  
2 299 
teatÜre.u) “Ti aeg? 2) 
"ay (f,- g,)? 
E cos id Is Baur Ep J+ 
82k teQ, i 
(E^ (15) 
* M. in 9t seri iin a = 7 
9: aZ (r,y)€Q 
wg.) = 9 x 
887 
where E is the exponential funetion index 
in (141). 
Expression (15) includes the unknown 
parame ters g,- To use the proposed 
algorithm, ,&, Shall be substituted by the 
estimates £Z g,- In Doppler images, moving 
object patterns are planes. In this case 
T of an objeot element is defined by 
the expression 
m7 [Et 8,5 + 9 ]a (16) 
where g, is a projection of an object 
translatory motion on to the line of 
sight; €,,0, are angular rates of an 
object rotation relative to the orthogon- 
al axes lying in the plane perpendicular 
to the line of sight; q is a proportion- 
2117 factor; I,y are the pixel coordina- 
es 
Then the veotor F, can be represented as 
F,- T,G,q + 8, (17) 
where T zt 1, , X, Y ) is the transforma- 
tion AU uU dimenp ien n, x. 
Gu ES Ep ©, )* 1s inf ith region 
velocity vector: ‘9 is the measurement 
1 
errore vector; n, is the number of pixels 
in ith region. 
i 
The  veotor G, can be found by the 
least-squares technique for  varying- 
accuracy measurements. It is easy to 
demonstrate that it is accomplished by 
solving the following linear-equation set 
( (18) 
  
Tl 
r 2 J 
4 TIO. T zi f rdüd 
|i) ; 12%, T2, jy] > jT, 
J=1 J=1 
J nig ni 
&, yt TU m yu ‚ya, as fy, 
y J=1 i=? 
v 
=1 di 
  
Here summation is taken aver all the 
pixels of the region Q; or Q . Sings the 
found value of the sine d estimate G? has 
its own correlation matris of TOT. the 
refined variances A and 9,“ shall be 
substituted for 0,“ and 0” in (15). When 
the central pixel state varies, its value 
has an effect on unknown parameter 
estimates being computed. n i To in 
that in (15), values of a, € E. 8,