Astronomical Applications Department, U.S. Naval Observatory Linear Least Squares Page 14
4 T
3
2
S
2
2
16 S
0
2
T
4
2
4 S
1
2
T
4
2
+
+
+
2
arctan (
=
,
-
-
+
+
-
-
+
S
2
N 4 S
2
T
0
4 S
2
T
1
4 T
2
S
0
2 T
2
S
1
2 T
3
S
0
T
3
S
1
sqrt 16 T
2
S
2
S
1
T
4
)
16 T
3
S
2
S
0
T
4
8 T
3
S
2
S
1
T
4
32 T
2
S
2
S
0
T
4
16 T
2
S
2
2
T
3
16 S
0
T
4
2
S
1
16 T
2
2
S
2
2
+
-
-
-
-
+
4 T
2
S
1
2
T
3
4 T
3
2
S
0
S
1
16 T
2
S
0
T
3
S
1
8 S
2
T
1
T
3
S
1
8 S
2
T
0
T
3
S
1
-
-
+
+
-
32 S
2
T
1
T
2
S
0
16 S
2
T
1
T
2
S
1
16 S
2
T
1
T
3
S
0
16 T
2
2
S
0
S
1
2 S
2
N T
3
S
1
+
-
-
-
-
32 S
2
T
0
T
2
S
0
16 S
2
T
0
T
2
S
1
16 S
2
T
0
T
3
S
0
4 S
2
N T
2
S
1
4 S
2
N T
3
S
0
-
+
+
+
+
16 T
2
S
0
2
T
3
8 S
2
2
N T
0
8 S
2
2
N T
1
32 S
2
2
T
0
T
1
S
2
2
N2 16 S
2
2
T
0
2
16 S
2
2
T
1
2
-
+
-
-
+
+
+
16 T
2
2
S
0
2
4 T
2
2
S
1
2
4 T
3
2
S
0
2
T
3
2
S
1
2
8 S
2
N T
2
S
0
4 T
3
2
S
2
2
16 S
0
2
T
4
2
+
+
+
+
-
+
+
4 S
1
2
T
4
2
+
2
-
+
+
-
2 T
2
S
2
T
3
S
2
2 S
0
T
4
S
1
T
4
sqrt 16 T
2
S
2
S
1
T
4
16 T
3
S
2
S
0
T
4
+
(
)
,
8 T
3
S
2
S
1
T
4
32 T
2
S
2
S
0
T
4
16 T
2
S
2
2
T
3
16 S
0
T
4
2
S
1
16 T
2
2
S
2
2
4 T
2
S
1
2
T
3
-
-
-
-
+
-
4 T
3
2
S
0
S
1
16 T
2
S
0
T
3
S
1
8 S
2
T
1
T
3
S
1
8 S
2
T
0
T
3
S
1
32 S
2
T
1
T
2
S
0
-
+
+
-
+
16 S
2
T
1
T
2
S
1
16 S
2
T
1
T
3
S
0
16 T
2
2
S
0
S
1
2 S
2
N T
3
S
1
32 S
2
T
0
T
2
S
0
-
-
-
-
-
16 S
2
T
0
T
2
S
1
16 S
2
T
0
T
3
S
0
4 S
2
N T
2
S
1
4 S
2
N T
3
S
0
16 T
2
S
0
2
T
3
8 S
2
2
N T
0
+
+
+
+
-
+
8 S
2
2
N T
1
32 S
2
2
T
0
T
1
S
2
2
N2 16 S
2
2
T
0
2
16 S
2
2
T
1
2
16 T
2
2
S
0
2
4 T
2
2
S
1
2
-
-
+
+
+
+
+
4 T
3
2
S
0
2
T
3
2
S
1
2
8 S
2
N T
2
S
0
4 T
3
2
S
2
2
16 S
0
2
T
4
2
4 S
1
2
T
4
2
+
+
-
+
+
+
2
_Z
+
leastsqrs[18]: Solution 2 substituted into normal eqs
8
( )
cos
2
T
0
8
( )
cos
2
T
1
16
( )
cos
( )
sin
T
2
2
( )
cos
2
N 8
( )
cos
( )
sin
T
3
-
-
+
+
(
[
8
( )
sin
2
T
4
+
) A 4
( )
cos
S
0
2
( )
cos
S
1
4
( )
sin
S
2
-
+
+
0
=
2
( )
cos
( )
sin
N
-
(
,
8
( )
cos
( )
sin
T
0
4
( )
cos
2
T
3
8
( )
cos
2
T
2
8
( )
cos
( )
sin
T
4
8
( )
cos
( )
sin
T
1
-
+
-
+
+
4
( )
sin
2
T
3
8
( )
sin
2
T
2
-
+
) A
2
(
)
-
+
+
2
( )
sin
S
1
4
( )
cos
S
2
4
( )
sin
S
0
A
+
0
=
]
leastsqrs[18]: Throwing out solution 2
leastsqrs[31]: Solution 3 is invalid!
Page 14