The spacecraft angular velocity estimation in the orbital stabilization mode by the results of the local vertical sensor measurements

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B0 = CT =  1
0
0
0
 . (14)
In this case the state vector dimension is nx = 4 , of a vector of the observed
variables is my = 1 and the number of decomposition levels additional to
the zero one:
J = ceil
n x
my − 1 = 4 − 1 = 3.
According to the multilevel decomposition introduced above, matrices
Ak , Bk , k = 1, J, have the following appearance
level 1
B ⊥
0 =  0 1 0 0
0 0 1 0
0 0 0 1  ; (15)
B +
0 = 1 0 0 0 ; (16)
A1 = B ⊥
0 A0B ⊥T
0 =  1 0 a42 h
0 1 0
a24 h h 1  ; (17)
B1 = B⊥
0 A0B 0 =  h
a13 h
0  ; (18)
level 2
B ⊥
1 = −a13 1 0
0 0 1
; (19)
B+
1 =
h
a2
13 h2 + h 2
a13 h
a2
13h 2 + h2
0 ; (20)
A 2 = B ⊥
1 A 1B ⊥T
1 =
a2
13 + 1 −a13 a42 h
h − a13a24 h 1
; (21)
B 2 = B⊥
1 A1B 1 =
0
a13h 2 + a24h 2 ; (22)
level 3
B ⊥
2 = 1 0 ; (23)
B+
2 = 0
1
a13 h2 + a24 h2 ; (24)
8 ISSN 0236-3933. HERALD of the BMSTU. Series “Instrument Engineering”. 2014. No. 5