103
成果轉(zhuǎn)移轉(zhuǎn)化
據(jù)衛(wèi)星信號(hào)所攜帶的信息不同，對(duì)參與定位解算的衛(wèi)
星分配適當(dāng)?shù)膬?yōu)先級(jí)，因此也可以有效減少首次定位
時(shí)間。楊麗新（2017）設(shè)計(jì)了一種快速選星算法，針
對(duì)北斗系統(tǒng)，以衛(wèi)星的不同類型、信噪比大小、衛(wèi)星
仰角質(zhì)量進(jìn)行分級(jí)處理，調(diào)整衛(wèi)星捕獲順序，在減少
首次定位時(shí)間上取得了一定的效果[6]。
Guo Jiuyuan等（2017） 提 出 利 用 多 普 勒 輔 助 測(cè)
距的快速定位方法，該方法對(duì)初始速度誤差較為敏
感，在首次定位時(shí)，要求速度誤差小于54 km/h[7]。Yao
Xiangzhen等（2011）給出了一種基于傳輸時(shí)間維度的
快速搜索方法，該方法需要接收機(jī)時(shí)鐘的輔助，并
且對(duì)接收機(jī)時(shí)鐘有較高的精度要求[8]?！侗倍沸l(wèi)星導(dǎo)
航系統(tǒng)空間信號(hào)接口控制文件——公開服務(wù)信號(hào)B1I
（3.0版）》中所提出的判斷幀ID的方法，在有效減少
硬件資源消耗的同時(shí)，也在一定程度上縮短了首次定
位時(shí)間[9]。
1 非完整時(shí)間條件下A-GPS定位算法分析
通常導(dǎo)航接收機(jī)定位解算過程中所需要的信息包
括信號(hào)發(fā)射時(shí)間、衛(wèi)星位置和速度、偽距測(cè)量值、多
普勒頻率測(cè)量值。當(dāng)接收機(jī)無外部授時(shí)，且信號(hào)層面
僅能獲取毫秒內(nèi)時(shí)間，無法獲得完整信號(hào)時(shí)間時(shí)，使
用傳統(tǒng)的包含4個(gè)狀態(tài)變量的定位算法不能準(zhǔn)確地實(shí)現(xiàn)
定位解算。
大部分接收機(jī)在關(guān)機(jī)時(shí)都會(huì)存儲(chǔ)本機(jī)的位置信
息，在重新上電后，能夠利用最后的位置及其他數(shù)據(jù)
來確定所需參數(shù)初值，幫助捕獲各種GNSS衛(wèi)星的碼相
位和載波相位。這些輔助數(shù)據(jù)不僅能增加接收機(jī)的靈
敏度，還能減少定位所需的時(shí)間。
而A-GPS定位算法中，接收機(jī)所接收的外界加注
的信息通常涵蓋了在信號(hào)捕獲與定位計(jì)算過程中所需
的接收機(jī)位置、時(shí)間、可見衛(wèi)星序列、星歷、多普勒
頻移以及各種誤差校正等數(shù)據(jù)信息。利用這些輔助信
息，接收機(jī)可以在更小的范圍內(nèi)對(duì)待捕獲信號(hào)進(jìn)行搜
索，同時(shí)可以省略從所接收信號(hào)中實(shí)時(shí)對(duì)星歷參數(shù)進(jìn)
行解調(diào)的環(huán)節(jié)。因此A-GPS方法可以加快信號(hào)捕獲，
以獲得較短的首次定位時(shí)間。同時(shí)，當(dāng)信號(hào)搜索范圍
縮小以后，接收機(jī)則有更充裕的時(shí)間來對(duì)較弱的衛(wèi)星
信號(hào)進(jìn)行長時(shí)間的積分。當(dāng)外界提供了豐富的衛(wèi)星導(dǎo)
航電文數(shù)據(jù)時(shí)，這些信息還可以被用來實(shí)現(xiàn)對(duì)長于20
ms的信號(hào)進(jìn)行相干積分，實(shí)現(xiàn)快速數(shù)據(jù)剝離，從而提
高接收機(jī)的信號(hào)捕獲與跟蹤靈敏度。假設(shè)接收機(jī)從輔
助信息中估算出某個(gè)衛(wèi)星信號(hào)的多普勒頻移，從中能
將頻帶搜索數(shù)目減少至沒有輔助時(shí)的十分之一，那么
不考慮其他因素，接收機(jī)信號(hào)捕獲就可以多花10倍的
時(shí)間駐留在每一個(gè)搜索單元上，相應(yīng)的信號(hào)捕獲靈敏
度就可以大約增加10 dB。
2 非完整時(shí)間條件下A-GPS快速定位算法設(shè)計(jì)
針對(duì)接收機(jī)無外部授時(shí)，且信號(hào)層面僅能獲取毫
秒內(nèi)時(shí)間，無法獲得完整信號(hào)時(shí)間的場(chǎng)景下，使用傳
統(tǒng)方式不能完成定位解算的問題，本文提出一種適用
于接收機(jī)時(shí)間誤差達(dá)到秒級(jí)場(chǎng)景下的A-GPS定位算法。
該算法利用外部輔助信息（概略位置、星歷、概略時(shí)間）
和毫秒內(nèi)時(shí)間，即可解算出完整的信號(hào)時(shí)間，以完成
定位解算。
本文所提出A-GPS算法首先需要對(duì)初始條件進(jìn)行
判斷。其需判斷的參數(shù)包括：衛(wèi)星信號(hào)載噪比高于36
dB；單頻接收時(shí)衛(wèi)星數(shù)量不少于5顆，雙頻接收時(shí)不少
于6顆，三頻接收時(shí)不少于7顆；連續(xù)穩(wěn)定接收歷元不
少于10個(gè)。滿足以上條件后，對(duì)算法所需偽距、信號(hào)
時(shí)間進(jìn)行計(jì)算。
在信號(hào)接收條件滿足后，首先計(jì)算所有可見衛(wèi)星
的偽距修正值 。
其中， 表示衛(wèi)星 的測(cè)量偽距，I表示電離層延
遲修正值，T表示對(duì)流層延遲修正值，S表示地球自轉(zhuǎn)
修正值， 表示衛(wèi)星鐘差。
假設(shè)概略時(shí)間為t 0，在星歷最后更新時(shí)間小于30
min的情況下，以60 s為間隔，計(jì)算 時(shí)刻的星
地距離 （其中n=1, 2, … , 30），并求得星
地距離和修正偽距的差值，對(duì)某時(shí)刻的所有衛(wèi)星的此
差值求和。
其中，m表示衛(wèi)星數(shù)量。找到30個(gè)歷元中d(n)最小值
對(duì)應(yīng)的n，得到離當(dāng)前時(shí)間最接近的時(shí)刻 。
計(jì)算 時(shí)刻所有衛(wèi)星的星地距離、修正的偽距，
并求得兩者差值：
然后找到 最小值對(duì)應(yīng)的衛(wèi)星，假設(shè)為衛(wèi)星
1，以其為基準(zhǔn)，修正其他衛(wèi)星：
此后再進(jìn)行A-GPS定位解算。A-GPS定位解算方
程如下：
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now
i
now
i
now
i
now
i
now
i
now
i
now now now ms
i
now ms
mmm
u
u
u
m
u
u
u
u
m
0
0
0
1
0
1 1
1
2
1
2
1
2
1
2
2
2
2
2
g
2
2
2
2
2
2
g
2
2
2
2
2
2
g
2
2
2
2
2
2
g g
2
2
2
2
t t d
t
t
t t t
d
d
d
d
d
d
d
D
D
D
D
D
= - - - +
+
+
= + -
= +
= -
= + - +
=
=
R
T
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
R
T
S
S
S
S
S
S
S
S
S
S
S
S
S
V
X
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
V
X
W
W
W
W
W
W
W
W
W
W
W
W
W
/
D e m o
( )
( )
( ) ( )
( )
( ) ( ) ( )
( )
( ) ( ( ) ( ) ( )) ( ( ))
( )
( )
(
( )
*
*
*
*
)
I T S t
t n
D t n
d n D t n
d n
t t n
d t t D t
d t
t D t t D t t
x
r
x
r
x
r
y
r
y
r
y
r
z
r
z
r
z
r
T
r
T
r
T
r
x
y
z
t
T
b
t
T
r
60
60
60
60
1
1
1
| |
( ) ( ) ( )
( )
( ) ( )
( ) ( ) ( )
( )
( ) ( ) ( ) ( ) ( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
c
i i s
i
i
c
i
i
m
now
i
now
i
now
i
now
i
now
i
now
i
now now now ms
i
now ms
mmm
u
u
u
m
u
u
u
u
m
0
0
0
1
0
1 1
1
2
1
2
1
2
1
2
2
2
2
2
g
2
2
2
2
2
2
g
2
2
2
2
2
2
g
2
2
2
2
2
2
g g
2
2
2
2
t t d
t
t
t t t
d
d
d
d
d
d
d
D
D
D
D
D
= - - - +
+
+
= + -
= +
= -
= + - +
=
=
R
T
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
R
T
S
S
S
S
S
S
S
S
S
S
S
S
S
V
X
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
V
X
W
W
W
W
W
W
W
W
W
W
W
W
W
/
D e m o
( )
( )
( ) ( )
( )
( ) ( ) ( )
( )
( ) ( ( ) ( ) ( )) ( ( ))
( )
( )
(
( )
*
*
*
*
)
I T S t
t n
D t n
d n D t n
d n
t t n
d t t D t
d t
t D t t D t t
x
r
x
r
x
r
y
r
y
r
y
r
z
r
z
r
z
r
T
r
T
r
T
r
x
y
z
t
T
b
t
T
r
60
60
60
60
1
1
1
| |
( ) ( ) ( )
( )
( ) ( )
( ) ( ) ( )
( )
( ) ( ) ( ) ( ) ( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
c
i i s
i
i
c
i
i
m
now
i
now
i
now
i
now
i
now
i
now
i
now now now ms
i
now ms
mmm
u
u
u
m
u
u
u
u
m
0
0
0
1
0
1 1
1
2
1
2
1
2
1
2
2
2
2
2
g
2
2
2
2
2
2
g
2
2
2
2
2
2
g
2
2
2
2
2
2
g g
2
2
2
2
t t d
t
t
t t t
d
d
d
d
d
d
d
D
D
D
D
D
= - - - +
+
+
= + -
= +
= -
= + - +
=
=
R
T
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
R
T
S
S
S
S
S
S
S
S
S
S
S
S
S
V
X
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
V
X
W
W
W
W
W
W
W
W
W
W
W
W
W
/
D e m o
( )
( )
( ) ( )
( )
( ) ( ) ( )
( )
( ) ( ( ) ( ) ( )) ( ( ))
( )
( )
(
( )
*
*
*
*
)
I T S t
t n
D t n
d n D t n
d n
t t n
d t t D t
d t
t D t t D t t
x
r
x
r
x
r
y
r
y
r
y
r
z
r
z
r
z
r
T
r
T
r
T
r
x
y
z
t
T
b
t
T
r
60
60
60
60
1
1
1
| |
( ) ( ) ( )
( )
( ) ( )
( ) ( ) ( )
( )
( ) ( ) ( ) ( ) ( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
c
i i s
i
i
c
i
i
m
now
i
now
i
now
i
now
i
now
i
now
i
now now now ms
i
now ms
mmm
u
u
u
m
u
u
u
u
m
0
0
0
1
0
1 1
1
2
1
2
1
2
1
2
2
2
2
2
g
2
2
2
2
2
2
g
2
2
2
2
2
2
g
2
2
2
2
2
2
g g
2
2
2
2
t t d
t
t
t t t
d
d
d
d
d
d
d
D
D
D
D
D
= - - - +
+
+
= + -
= +
= -
= + - +
=
=
R
T
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
R
T
S
S
S
S
S
S
S
S
S
S
S
S
S
V
X
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
V
X
W
W
W
W
W
W
W
W
W
W
W
W
W
/
D e m o
( )
( )
( ) ( )
( )
( ) ( ) ( )
( )
( ) ( ( ) ( ) ( )) ( ( ))
( )
( )
(
( )
*
*
*
*
)
I T S t
t n
D t n
d n D t n
d n
t t n
d t t D t
d t
t D t t D t t
x
r
x
r
x
r
y
r
y
r
y
r
z
r
z
r
z
r
T
r
T
r
T
r
x
y
z
t
T
b
t
T
r
60
60
60
60
1
1
1
| |
( ) ( ) ( )
( )
( ) ( )
( ) ( ) ( )
( )
( ) ( ) ( ) ( ) ( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
c
i i s
i
i
c
i
i
m
now
i
now
i
now
i
now
i
now
i
now
i
now now now ms
i
now ms
mmm
u
u
u
m
u
u
u
u
m
0
0
0
1
0
1 1
1
2
1
2
1
2
1
2
2
2
2
2
g
2
2
2
2
2
2
g
2
2
2
2
2
2
g
2
2
2
2
2
2
g g
2
2
2
2
t t d
t
t
t t t
d
d
d
d
d
d
d
D
D
D
D
D
= - - - +
+
+
= + -
= +
= -
= + - +
=
=
R
T
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
R
T
S
S
S
S
S
S
S
S
S
S
S
S
S
V
X
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
V
X
W
W
W
W
W
W
W
W
W
W
W
W
W
/
D e m o
( )
( )
( ) ( )
( )
( ) ( ) ( )
( )
( ) ( ( ) ( ) ( )) ( ( ))
( )
( )
(
( )
*
*
*
*
)
I T S t
t n
D t n
d n D t n
d n
t t n
d t t D t
d t
t D t t D t t
x
r
x
r
x
r
y
r
y
r
y
r
z
r
z
r
z
r
T
r
T
r
T
r
x
y
z
t
T
b
t
T
r
60
60
60
60
1
1
1
| |
( ) ( ) ( )
( )
( ) ( )
( ) ( ) ( )
( )
( ) ( ) ( ) ( ) ( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
c
i i s
i
i
c
i
i
m
now
i
now
i
now
i
now
i
now
i
now
i
now now now ms
i
now ms
mmm
u
u
u
m
u
u
u
u
m
0
0
0
1
0
1 1
1
2
1
2
1
2
1
2
2
2
2
2
g
2
2
2
2
2
2
g
2
2
2
2
2
2
g
2
2
2
2
2
2
g g
2
2
2
2
t t d
t
t
t t t
d
d
d
d
d
d
d
D
D
D
D
D
= - - - +
+
+
= + -
= +
= -
= + - +
=
=
R
T
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
R
T
S
S
S
S
S
S
S
S
S
S
S
S
S
V
X
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
V
X
W
W
W
W
W
W
W
W
W
W
W
W
W
/
D e m o
( )
( )
( ) ( )
( )
( ) ( ) ( )
( )
( ) ( ( ) ( ) ( )) ( ( ))
( )
( )
(
( )
*
*
*
*
)
I T S t
t n
D t n
d n D t n
d n
t t n
d t t D t
d t
t D t t D t t
x
r
x
r
x
r
y
r
y
r
y
r
z
r
z
r
z
r
T
r
T
r
T
r
x
y
z
t
T
b
t
T
r
60
60
60
60
1
1
1
| |
( ) ( ) ( )
( )
( ) ( )
( ) ( ) ( )
( )
( ) ( ) ( ) ( ) ( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
c
i i s
i
i
c
i
i
m
now
i
now
i
now
i
now
i
now
i
now
i
now now now ms
i
now ms
mmm
u
u
u
m
u
u
u
u
m
0
0
0
1
0
1 1
1
2
1
2
1
2
1
2
2
2
2
2
g
2
2
2
2
2
2
g
2
2
2
2
2
2
g
2
2
2
2
2
2
g g
2
2
2
2
t t d
t
t
t t t
d
d
d
d
d
d
d
D
D
D
D
D
= - - - +
+
+
= + -
= +
= -
= + - +
=
=
R
T
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
R
T
S
S
S
S
S
S
S
S
S
S
S
S
S
V
X
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
V
X
W
W
W
W
W
W
W
W
W
W
W
W
W
/
D e m o
以上
以下
( )
( )
( ) ( )
( )
( ) ( ) ( )
( )
( ) ( ( ) ( ) ( )) ( ( ))
( )
( )
(
( )
*
*
*
*
)
I T S t
t n
D t n
d n D t n
d n
t t n
d t t D t
d t
t D t t D t t
x
r
x
r
x
r
y
r
y
r
y
r
z
r
z
r
z
r
T
r
T
r
T
r
x
y
z
t
T
b
t
T
r
60
60
60
60
1
1
1
| |
( ) ( ) ( )
( )
( ) ( )
( ) ( ) ( )
( )
( ) ( ) ( ) ( ) ( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
c
i i s
i
i
c
i
i
m
now
i
now
i
now
i
now
i
now
i
now
i
now now now ms
i
now ms
mmm
u
u
u
m
u
u
u
u
m
0
0
0
1
0
1 1
1
2
1
2
1
2
1
2
2
2
2
2
g
2
2
2
2
2
2
g
2
2
2
2
2
2
g
2
2
2
2
2
2
g g
2
2
2
2
t t d
t
t
t t t
d
d
d
d
d
d
d
D
D
D
D
D
= - - - +
+
+
= + -
= +
= -
= + - +
=
=
R
T
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
R
T
S
S
S
S
S
S
S
S
S
S
S
S
S
V
X
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
V
X
W
W
W
W
W
W
W
W
W
W
W
W
W
/
D e m o
( ) #
( )
( ) ( )
( )
( ) ( ) ( )
( )
( ) ( ( ) ( ) ( )) ( ( ))
( )
( )
(
( )
*
*
*
*
)
I T S t
t n
D t n
d n D t n
d n
t t n
d t t D t
d t
t D t t D t t
x
r
x
r
x
r
y
r
y
r
y
r
z
r
z
r
z
r
T
r
T
r
T
r
x
y
z
t
T
b
t
T
r
60
60
60
60
1
1
1
| |
( ) ( ) ( )
( )
( ) ( )
( ) ( ) ( )
( )
( ) ( ) ( ) ( ) ( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
c
i i s
i
i
c
i
i
m
now
i
now
i
now
i
now
i
now
i
now
i
now now now ms
i
now ms
mmm
u
u
u
m
u
u
u
u
m
0
0
0
1
0
1 1
1
2
1
2
1
2
1
2
2
2
2
2
g
2
2
2
2
2
2
g
2
2
2
2
2
2
g
2
2
2
2
2
2
g g
2
2
2
2
t t d
t
t
t t t
d
d
d
d
d
d
d
D
D
D
D
D
= - - - +
+
+
= + -
= +
= -
= + - +
=
=
R
T
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
R
T
S
S
S
S
S
S
S
S
S
S
S
S
S
V
X
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
V
X
W
W
W
W
W
W
W
W
W
W
W
W
W
/
D e m o
#
( )
( )
( ) ( )
( )
( ) ( ) ( )
( )
( ) ( ( ) ( ) ( )) ( ( ))
( )
( )
(
( )
*
*
*
*
)
I T S t
t n
D t n
d n D t n
d n
t t n
d t t D t
d t
t D t t D t t
x
r
x
r
x
r
y
r
y
r
y
r
z
r
z
r
z
r
T
r
T
r
T
r
x
y
z
t
T
b
t
T
r
60
60
60
60
1
1
1
| |
( ) ( ) ( )
( )
( ) ( )
( ) ( ) ( )
( )
( ) ( ) ( ) ( ) ( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
c
i i s
i
i
c
i
i
m
now
i
now
i
now
i
now
i
now
i
now
i
now now now ms
i
now ms
mmm
u
u
u
m
u
u
u
u
m
0
0
0
1
0
1 1
1
2
1
2
1
2
1
2
2
2
2
2
g
2
2
2
2
2
2
g
2
2
2
2
2
2
g
2
2
2
2
2
2
g g
2
2
2
2
t t d
t
t
t t t
d
d
d
d
d
d
d
D
D
D
D
D
= - - - +
+
+
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= + - +
=
=
R
T
S
S
S
S
S
S
S
S
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S
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W
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W
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W
W
V
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W
W
W
W
W
W
W
W
W
W
W
W
W
/
D e m o
( ) #
( )
( ) ( )
( )
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( )
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( )
( )
(
( )
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I T S t
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x
r
x
r
x
r
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r
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r
y
r
z
r
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r
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r
T
r
T
r
T
r
x
y
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t
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b
t
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r
60
60
60
60
1
1
1
| |
( ) ( ) ( )
( )
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( )
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i
now ms
mmm
u
u
u
m
u
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u
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m
0
0
0
1
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1
2
1
2
1
2
1
2
2
2
2
2
g
2
2
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2
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2
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2
g
2
2
2
2
2
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2
2
2
2
t t d
t
t
t t t
d
d
d
d
d
d
d
D
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= - - - +
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R
T
S
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S
S
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/
D e m o
( )
( )
( ) ( )
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x
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r
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r
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r
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r
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r
T
r
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r
T
r
x
y
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t
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t
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r
60
60
60
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1
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| |
( ) ( ) ( )
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i
now ms
mmm
u
u
u
m
u
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u
u
m
0
0
0
1
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1 1
1
2
1
2
1
2
1
2
2
2
2
2
g
2
2
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2
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2
2
2
2
2
2
g
2
2
2
2
2
2
g g
2
2
2
2
t t d
t
t
t t t
d
d
d
d
d
d
d
D
D
D
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= - - - +
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R
T
S
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S
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W
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W
W
W
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W
/
D e m o
( )
( )
( ) ( )
( )
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( )
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(
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I T S t
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x
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r
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r
y
r
z
r
z
r
z
r
T
r
T
r
T
r
x
y
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t
T
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t
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r
60
60
60
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1
1
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| |
( ) ( ) ( )
( )
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now now now ms
i
now ms
mmm
u
u
u
m
u
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u
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0
0
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1
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1
2
1
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2
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2
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2
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2
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2
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2
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2
2
2
2
g
2
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2
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2
2
2
2
t t d
t
t
t t t
d
d
d
d
d
d
d
D
D
D
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= - - - +
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R
T
S
S
S
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S
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W
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W
W
W
V
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W
W
W
W
W
W
W
W
W
W
W
W
W
/
D e m o
( ) #
( )
( ) ( )
( )
( ) ( ) ( )
( )
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( )
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(
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*
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I T S t
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x
r
x
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x
r
y
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y
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y
r
z
r
z
r
z
r
T
r
T
r
T
r
x
y
z
t
T
b
t
T
r
60
60
60
60
1
1
1
| |
( ) ( ) ( )
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now now now ms
i
now ms
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u
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u
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u
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u
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0
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2
1
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2
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2
2
2
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2
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2
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2
2
2
2
2
2
g
2
2
2
2
2
2
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2
2
2
2
t t d
t
t
t t t
d
d
d
d
d
d
d
D
D
D
D
D
= - - - +
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R
T
S
S
S
S
S
S
S
S
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S
S
S
S
S
S
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T
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S
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V
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W
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W
W
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W
W
W
W
W
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W
W
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W
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/
D e m o
( )
( )
( ) ( )
( )
( ) ( ) ( )
( )
( ) ( ( ) ( ) ( )) ( ( ))
( )
( )
(
( )
*
*
*
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)
I T S t
t n
D t n
d n D t n
d n
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t D t t D t t
x
r
x
r
x
r
y
r
y
r
y
r
z
r
z
r
z
r
T
r
T
r
T
r
x
y
z
t
T
b
t
T
r
60
60
60
60
1
1
1
| |
( ) ( ) ( )
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c
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m
now
i
now
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now
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now
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now
i
now
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now now now ms
i
now ms
mmm
u
u
u
m
u
u
u
u
m
0
0
0
1
0
1 1
1
2
1
2
1
2
1
2
2
2
2
2
g
2
2
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2
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2
g
2
2
2
2
2
2
g
2
2
2
2
2
2
g g
2
2
2
2
t t d
t
t
t t t
d
d
d
d
d
d
d
D
D
D
D
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= - - - +
+
+
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R
T
S
S
S
S
S
S
S
S
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S
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V
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W
W
W
V
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W
W
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W
W
W
W
W
W
W
W
/
D e m o
( )
( )
( ) ( )
( )
( ) ( ) ( )
( )
( ) ( ( ) ( ) ( )) ( ( ))
( )
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(
( )
*
*
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)
I T S t
t n
D t n
d n D t n
d n
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t D t t D t t
x
r
x
r
x
r
y
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y
r
y
r
z
r
z
r
z
r
T
r
T
r
T
r
x
y
z
t
T
b
t
T
r
60
60
60
60
1
1
1
| |
( ) ( ) ( )
( )
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m
now
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now
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now
i
now
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now now now ms
i
now ms
mmm
u
u
u
m
u
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u
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m
0
0
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2
1
2
1
2
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2
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2
2
2
2
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2
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2
2
2
2
2
2
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2
2
2
2
2
2
g g
2
2
2
2
t t d
t
t
t t t
d
d
d
d
d
d
d
D
D
D
D
D
= - - - +
+
+
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= + - +
=
=
R
T
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
R
T
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S
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S
S
S
S
S
S
S
S
S
S
V
X
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
V
X
W
W
W
W
W
W
W
W
W
W
W
W
W
/
D e m o
( ) #
( )
( ) ( )
( )
( ) ( ) ( )
( )
( ) ( ( ) ( ) ( )) ( ( ))
( )
( )
(
( )
*
*
*
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)
I T S t
t n
D t n
d n D t n
d n
t t n
d t t D t
d t
t D t t D t t
x
r
x
r
x
r
y
r
y
r
y
r
z
r
z
r
z
r
T
r
T
r
T
r
x
y
z
t
T
b
t
T
r
60
60
60
60
1
1
1
| |
( ) ( ) ( )
( )
( ) ( )
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( )
( ) ( ) ( ) ( ) ( )
( )
( )
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( )
( )
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c
i i s
i
i
c
i
i
m
now
i
now
i
now
i
now
i
now
i
now
i
now now now ms
i
now ms
mmm
u
u
u
m
u
u
u
u
m
0
0
0
1
0
1 1
1
2
1
2
1
2
1
2
2
2
2
2
g
2
2
2
2
2
2
g
2
2
2
2
2
2
g
2
2
2
2
2
2
g g
2
2
2
2
t t d
t
t
t t t
d
d
d
d
d
d
d
D
D
D
D
D
= - - - +
+
+
= + -
= +
= -
= + - +
=
=
R
T
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
R
T
S
S
S
S
S
S
S
S
S
S
S
S
S
V
X
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
W
V
X
W
W
W
W
W
W
W
W
W
W
W
W
W
/
D e m o
