卫星定位理论与方法第13次课伪随机码测距原理
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Use same code at receiver and satellite Synchronize satellites and receivers so they're generating
same code at same time Then we look at the incoming code from the satellite and see
distance GPS needs good clocks and
a fourth SV
4 Once GPS knows distance, it needs to know satellite's position
5 Then correct for ionospheric and trospheric delays.
1 Trilateration from satellites is basis of system.
2 Satellite Ranging
Measuring the distance to a satellite Done by measuring travel time of radio signals
7 secs wrong time
Third measurement (fast clocks)
Won’t go through the other two
5 sec (wrong)
Now third measurement won't go thru the other two.
9 sec (wrong)
4 Knowing where the satellites are
After all, they're 12,600 miles up High orbit
➢Very stable orbits ➢No atmospheric drag ➢Survivability ➢Earth coverage Monitored by Defense Department ➢fly over US possession at least once a day ➢DoD transmits corrections back to satellite Corrections transmitted from satellites to us
1 Trilateration from satellites is basis of system.
1 Trilateration from satellites
By measuring distance from several satellites you can calculate your position
Speed-of-Light Measurement
Measure how long it takes the GPS signal to get to us Multiply that time by 186,000 miles/sec
➢Time (sec) x 186,000 = miles
4 secs
Third measurement would go thru our position if correct
6 secs 8 secs
With fast clock
5 secs wrong time
Bad position because clock is off by one second
a fourth SV
4 Once GPS knows distance, it needs to know satellite's position
5 Then correct for ionospheric and trospheric delays.
1 Trilateration from satellites is basis of system.
To measure the
distance GPS needs good clocks and
a fourth SV
4 Once GPS knows distance, it needs to know satellite's position
5 Then correct for ionospheric and trospheric delays.
4 Ranges to resolve for Latitude, Longitude, Height & Time
Trilateration
In practice 3 measurements are enough We can discard one point One point will be a ridiculous answer
We still need the 4th measurement because there are four dimensions to solve for (X,Y,Z and Time)
How Does GPS Work?
5 Steps to GPS
2 3 GPS measures distance from the satellites using speed of light.
j1 P
(XXj1)2(YYj1)2(ZZj1)2
j2 P
(XXj2)2(YYj2)2(ZZj2)2
j3 P
(XXj3)2(YYj3)2(ZZj3)2
注意：但由于通过测定时间确定距离， j1 必须保持卫星和接收机时间严格同步， 实际上无法精确已知接收机钟差，需 作为待定参数求解，于是必须观测四 课卫星才能三维定位。
The ideal situation (accurate clocks)
In 2 dimensions for sake of drawing
This is where we really are
4 secs
6 secs
Adding a third measurement (accurate clocks)
Code gives us a way to increase signal-tonoise ratio
How Does GPS Work?
5 Steps to GPS
2 3 GPS measures distance from the satellites using speed of light.
how long ago our receiver generated the same code
from satellite from ground receiver
measure time difference between same part of code
Why a code?
Code lets many satellites operate on same frequency
If you've got good clocks, all you need to know is exactly when signal left satellite
How do we know when the signal left the satellite?
One of the Clever Ideas of GPS:
To measure the
distance GPS needs good clocks and
a fourth SV
4 Once GPS knows distance, it needs to know satellite's position
5 Then correct for ionospheric and trospheric delays.
第12次课 伪随机码测距原理 测量与导航工程系 导航与定位教研室 陈明剑
GPS Positioning
Satellite Satellite
Satellite
Satellite
1. Known position of satellites 2. Range measurements from satellites Calculate position&time
Intersection of three spheres is only two points.
Trilateration
Fourth measurement will decide between two points.
Fourth measurement will only go through one of the two points.
5 Atmospheric Corrections
Too bad it's not operating in a vacuum Ionosphere is a band of charged particles Troposphere is our weather
➢ 由于地球本身就是一个球体，可以不需要观测第四颗卫 星，观测三颗卫星就可确定地面点位置（三球定位）
7 sec (wrong)
How Does GPS Work?
5 Steps to GPS
2 3 GPS measures distance from the satellites using speed of light.
To measure the
distance GPS needs good clocks and
➢Status message
How Does GPS Work?
5 Steps to GPS
2 3 GPS measures distance from the satellites using speed of light.
To measure the
distance GPS needs good clocks and
1 Trilateration from satellites is basis of system.
3 Accurate clocks necessary to measure travel time
Making sure both receiver and satellite are synchronized
a fourth SV
4 Once GPS knows distance, it needs to know satellite's position
5 Then correct for ionospheric and trospheric delays.
1 Trilateration from satellites is basis of system.
Second measurement narrows it down to intersection of two spheres
11,000 Miles
Intersection of two spheres is a cirห้องสมุดไป่ตู้le
12,000 Miles
Trilateration
Third measurement narrows to just two points
Whole system depends on very accurate clocks Satellites have atomic clocks
➢Accurate but expensive
Ground receivers just need consistent clocks
➢The secret is in an extra satellite measurement that adjusts the receiver clock
Trilateration
One measurement narrows down our position to the surface of a sphere
11,000 miles
We're somewhere on the surface of this sphere.
Trilateration
你的位置是: 37o 23.323’ N 122o 02.162’ W
How Does GPS Work?
5 Steps to GPS
2 3 GPS measures distance from the satellites using speed of light.
To measure the
same code at same time Then we look at the incoming code from the satellite and see
distance GPS needs good clocks and
a fourth SV
4 Once GPS knows distance, it needs to know satellite's position
5 Then correct for ionospheric and trospheric delays.
1 Trilateration from satellites is basis of system.
2 Satellite Ranging
Measuring the distance to a satellite Done by measuring travel time of radio signals
7 secs wrong time
Third measurement (fast clocks)
Won’t go through the other two
5 sec (wrong)
Now third measurement won't go thru the other two.
9 sec (wrong)
4 Knowing where the satellites are
After all, they're 12,600 miles up High orbit
➢Very stable orbits ➢No atmospheric drag ➢Survivability ➢Earth coverage Monitored by Defense Department ➢fly over US possession at least once a day ➢DoD transmits corrections back to satellite Corrections transmitted from satellites to us
1 Trilateration from satellites is basis of system.
1 Trilateration from satellites
By measuring distance from several satellites you can calculate your position
Speed-of-Light Measurement
Measure how long it takes the GPS signal to get to us Multiply that time by 186,000 miles/sec
➢Time (sec) x 186,000 = miles
4 secs
Third measurement would go thru our position if correct
6 secs 8 secs
With fast clock
5 secs wrong time
Bad position because clock is off by one second
a fourth SV
4 Once GPS knows distance, it needs to know satellite's position
5 Then correct for ionospheric and trospheric delays.
1 Trilateration from satellites is basis of system.
To measure the
distance GPS needs good clocks and
a fourth SV
4 Once GPS knows distance, it needs to know satellite's position
5 Then correct for ionospheric and trospheric delays.
4 Ranges to resolve for Latitude, Longitude, Height & Time
Trilateration
In practice 3 measurements are enough We can discard one point One point will be a ridiculous answer
We still need the 4th measurement because there are four dimensions to solve for (X,Y,Z and Time)
How Does GPS Work?
5 Steps to GPS
2 3 GPS measures distance from the satellites using speed of light.
j1 P
(XXj1)2(YYj1)2(ZZj1)2
j2 P
(XXj2)2(YYj2)2(ZZj2)2
j3 P
(XXj3)2(YYj3)2(ZZj3)2
注意：但由于通过测定时间确定距离， j1 必须保持卫星和接收机时间严格同步， 实际上无法精确已知接收机钟差，需 作为待定参数求解，于是必须观测四 课卫星才能三维定位。
The ideal situation (accurate clocks)
In 2 dimensions for sake of drawing
This is where we really are
4 secs
6 secs
Adding a third measurement (accurate clocks)
Code gives us a way to increase signal-tonoise ratio
How Does GPS Work?
5 Steps to GPS
2 3 GPS measures distance from the satellites using speed of light.
how long ago our receiver generated the same code
from satellite from ground receiver
measure time difference between same part of code
Why a code?
Code lets many satellites operate on same frequency
If you've got good clocks, all you need to know is exactly when signal left satellite
How do we know when the signal left the satellite?
One of the Clever Ideas of GPS:
To measure the
distance GPS needs good clocks and
a fourth SV
4 Once GPS knows distance, it needs to know satellite's position
5 Then correct for ionospheric and trospheric delays.
第12次课 伪随机码测距原理 测量与导航工程系 导航与定位教研室 陈明剑
GPS Positioning
Satellite Satellite
Satellite
Satellite
1. Known position of satellites 2. Range measurements from satellites Calculate position&time
Intersection of three spheres is only two points.
Trilateration
Fourth measurement will decide between two points.
Fourth measurement will only go through one of the two points.
5 Atmospheric Corrections
Too bad it's not operating in a vacuum Ionosphere is a band of charged particles Troposphere is our weather
➢ 由于地球本身就是一个球体，可以不需要观测第四颗卫 星，观测三颗卫星就可确定地面点位置（三球定位）
7 sec (wrong)
How Does GPS Work?
5 Steps to GPS
2 3 GPS measures distance from the satellites using speed of light.
To measure the
distance GPS needs good clocks and
➢Status message
How Does GPS Work?
5 Steps to GPS
2 3 GPS measures distance from the satellites using speed of light.
To measure the
distance GPS needs good clocks and
1 Trilateration from satellites is basis of system.
3 Accurate clocks necessary to measure travel time
Making sure both receiver and satellite are synchronized
a fourth SV
4 Once GPS knows distance, it needs to know satellite's position
5 Then correct for ionospheric and trospheric delays.
1 Trilateration from satellites is basis of system.
Second measurement narrows it down to intersection of two spheres
11,000 Miles
Intersection of two spheres is a cirห้องสมุดไป่ตู้le
12,000 Miles
Trilateration
Third measurement narrows to just two points
Whole system depends on very accurate clocks Satellites have atomic clocks
➢Accurate but expensive
Ground receivers just need consistent clocks
➢The secret is in an extra satellite measurement that adjusts the receiver clock
Trilateration
One measurement narrows down our position to the surface of a sphere
11,000 miles
We're somewhere on the surface of this sphere.
Trilateration
你的位置是: 37o 23.323’ N 122o 02.162’ W
How Does GPS Work?
5 Steps to GPS
2 3 GPS measures distance from the satellites using speed of light.
To measure the