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Three Segments of the GPS
Space Segment

User Segment Control Segment Ground Antennas Master Station Monitor Stations

Space Segment
• 24+ satellites
– 6 planes with 55° inclination – Each plane has 4-5 satellites – Broadcasting position and time info on 2 frequencies – Constellation has spares

Space Segment
• Very high orbit
– 20,200 km – 1 revolution in approximately 12 hrs – Travel approx. 7,000mph

• Considerations
– Accuracy – Survivability – Coverage

User Segment
Military. Search and rescue. Disaster relief. Surveying. Marine, aeronautical and terrestrial navigation. Remote controlled vehicle and robot guidance. Satellite positioning and tracking. Shipping. Geographic Information Systems (GIS). Recreation.

GPS Signal Requirements
• Method (code) to identify each satellite • The location of the satellite or some information on how to determine it • Information regarding the amount of time elapsed since the signal left the satellite • Details on the satellite clock status

Important Issues to Consider
• • • • • Methods to encode information Signal power Frequency allocation Security Number and type of codes necessary to satisfy system requirements

Overview of Satellite Transmissions
• All transmissions derive from a fundamental frequency of 10.23 Mhz
– L1 = 154 • 10.23 = 1575.42 Mhz – L2 = 120 • 10.23 = 1227.60 Mhz

• All codes initialized once per GPS week at midnight from Saturday to Sunday
– Chipping rate for C/A is 1.023 Mhz – Chipping rate for P(Y) is 10.23 Mhz

Schematic of GPS codes and carrier phase

GPS Signal Characteristics

Codes on L1 and L2
S1p (t) = A p P p (t)D P (t)cos(2πf1t) + AcG P (t)D P (t)sin(2πf1 t)
where A p , Ac = amplitudes (power) of P(Y) - code and C / A - code P P (t) = pseudorandom P(Y) - code G (t) = C / A - code (Gold code)

DP (t) = navigation data stream and

S2p (t) = B p P p (t)D P (t)cos(2πf2 t)

Codes on L1 and L2 (con’t.)
P (t)D (t) and G (t)D (t) imply modulo - 2 addition and the P(Y) - code is also a modulo - 2 sum of two pseudorandom data streams:
p P P P

P p (t) = X 1 (t)X 2 (t − pT)
0 ≤ p ≤ 36 1 = 10.23 Mhz T
The GPS system defines 36 specific phase shifts to be used, resulting in 36 unique codes (called Gold Codes) that could be transmitted by satellites. Since the satellite number is represented in the navigation message by only 5 data bits, only 32 of these 36 codes are actually used. The others are reserved for other uses, such as ground transmitters.

GPS signal strength - frequency domain
Note that C/A code is below noise level; signal is multiplied in the Receiver by the internally calculated code to allow tracking. C/A-code chip is 1.023 Mhz P-code chip is 10.23 Mhz
1 T

Power = P(t) = y2(t)

Bandwidth ≡ B ≈

where T ≡ is chip duration

The calculated power spectrum derives from the Fourier transform of a square wave of width 2π and unit amplitude. Common function in DSP called the “sinc” function.

sin(π x) 1 sin c(x) = = πx 2π



e iωx∂ω

Schematic of C/A-code acquisition

Since C/A-code is 1023 chips long and repeats every 1/1000 s, it is inherently ambiguous by 1 msec or ~300 km. Must modulo-2 add the transmitted and received codes after correlation to increase SNR and narrow bandwidth.

Terminology of GPS
• SPS(Standard Positioning Service)
– GPS positioning service based on the single frequency C/A code

• PPS(Precise Positioning Service)
– GPS positioning service based on the dual frequency P code

• Pseudorange
– The time shift required to align a replica of the GPS code generated in the receiver with the received GPS code, scaled into distance by the speed of light

Determining Range
• Receiver and satellite use same code • Synchronized code generation • Compare incoming code with receiver generated code
Measure time difference between the same part of code
Series of ones and zeroes repeating every 1023 bits. So Complicated alternation of bits that pattern looks random thus called “pseudorandom code”.

From satellite From receiver

lite tel Sa

Sa tell

e llit te Sa

Sa te llit e

1. Known position of satellites 2. Range measurements from satellites Calculate position&time

GPS Time Measurement
• • • Time event -- coded pulse
N Code Identifies TT t Receive N TT N TR t

Range -- Time difference between two matching events Pseudo range -- Time difference between event and inaccurate reference Actual receive time TR Observed receive time TR = TR '+δT Carrier phase φ Doppler

TT Transmit

ΔT = TR − TT

sinφ (t )




dφ φ (t + Δt ) − φ (t ) = lim t0 dt Δt →0 Δt Accumulated delta range ADR = φ0 (T ) − φ0 (T0 ) ; No cycle ambiguity


φ0 (t ) = Oberved Phase = φ (t ) ± 2πn

Relationship Between Pseudorange and True Range
• Pseudorange
~ Ri = C ⋅ (Tuser − Tsat )

= C ⋅ (TT + TRi + TAi + ΔTu ) − (TT + ΔTSi )



• where,


= system time of transmission = free space propagation time = R/C = delay due to ionosphere, troposphere = user clock bias = satellite clock bias

Differential Correction
• • • • Technique used to correct some of these errors Referred to as “differential GPS” or DGPS In DGPS, two GPS receivers are used One receiver is located at an accurately surveyed point referred to as the “base station” • A correction is calculated by comparing the known location to the location determined by the GPS satellites • The correction is then applied to the other receiver’s (known as the “rover”) calculated position

DGPS Methods
• Post-processing
– Corrections performed after the data is collected – Special software required

• Real-time
– Corrections are performed while the data is being collected – Need special equipment to receive the DGPS signal

Wide Area Augmentation System - WAAS
• • • • New “real-time” DGPS Satellite based FAA initiative….now fully operational Series of ~25 ground reference stations relay info to master control station • Master control station sends correction info to WAAS satellite

WAAS Satellites
• • • WAAS satellites are geo-stationary On east coast, WAAS satellite sits off coast of Brazil over equator at 53.96° West (#35 on Garmin) On west coast, WAAS satellite sits over Pacific ocean at 178.0° East (#47 on Garmin) Ability to get signal deteriorates in northern latitudes (satellite is lower on the horizon) If you can get WAAS satellite signal……..~3 meter accuracy However, cannot always get signal due to obstructions More WAAS satellites becoming available in future – Europeans (EGNOS) – Japanese (MSAS)

• • • •

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