Gps Signals-soumyadip
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GPS Signal Structure • Sources: – GPS Satellite Surveying, Leick – Kristine Larson Lecture Notes http://www.colorado.edu/engineering/ASEN/asen 4519/asen4519.html
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
Digital Modulation Methods • Amplitude Modulation (AM) also known as amplitudeshift keying. This method requires changing the amplitude of the carrier phase between 0 and 1 to encode the digital signal. • Frequency Modulation (FM) also known as frequencyshift keying. Must alter the frequency of the carrier to correspond to 0 or 1. • Phase Modulation (PM) also known as phase shift keying. At each phase shift, the bit is flipped from 0 to 1 or vice versa. This is the method used in GPS.
Modulation Schematics
Modulo2 recovery of GPS code Modulo2 arithmetic: 0 + 0 = 0; 0 + 1 = 1; 1 + 0 = 1; 1 + 1 = 0 Bit shifts aligned
MUST MOD2 ADD RECEIVERGENERATED CODE TO RECOVER
Superposition of codes details • Superposition of two codes is not unique because the bit transition occurs at the same epoch; remember that both codes and phases are multiples of the fundamental frequency • Need to impose an additional constraint to arrive at a solution quadriphaseshift keying (QPSK), which puts the two codes 90° (π/2)
Phase and Quandrature General General Expression:
y(t) = y1 (t) + y 2 (t) = x1 (t)coswt + x 2 (t)sinwt where
y1 (t) is in phase (I) and y12(t) is in quandrature (Q) All spectral components of y1(t) are 90° out of phase with those of y2(t). This allows this the two signals to be separated in the receiver.
Codes on L1 and L2 S1p (t) = A p P p (t)D P (t)cos(2pf1t) + AcG P (t)D P (t)sin(2pf1 t) where
A p , Ac = amplitudes (power) of P(Y) code and C / A code P P (t) = pseudorandom P(Y) code P
G (t) = C / A code (Gold code) D P (t) = navigation data stream and
S2p (t) = B p P p (t)D P (t)cos(2pf2 t)
Codes on L1 and L2 (con’t.) p
P
P
P
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 (t) = X1 (t)X 2 (t - pT)
0 £ p £ 36 1 = 10.23 Mhz T
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/Acode chip is 1.023 Mhz Pcode chip is 10.23 Mhz
Power = P(t) = y2(t)
Bandwidth º B »
1 T
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.
where T º is chip duration
sin(px) 1 sin c(x) = = px 2p
p
iwx e ò ¶w -p
Digital Signal Processing Techniques • Filtering: Allows one to remove some portion of the frequency spectrum that may contain unwanted signal. – Low Pass Filter: lets all frequencies below a cutoff frequency through. – High Pass Filter: lets all frequencies above a cutoff frequency through. – Band Pass Filter: lets all frequencies within a specified window pass through. The window is called the passband
DSP Techniques, con’t. • Frequency Translation and Multiplication: technique to shift frequency spectrum of some signal to another portion of the frequency domain. – Upconversion: translate signal to higher frequencies. – Downconversion: translate signal to lower frequencies. Commonly done in GPS receivers. Multiply signal by sine function in a “mixer.” Special case is signal squaring and may be used to recover the pure carrier phase from a biphase modulated ranging signal.
DSP Techniques, con’t. • Spread Spectrum: broadly defined as a mechanism by which the bandwidth of the transmitted code is much greater than the baseband information signal (e.g. the navigation message in GPS)
– FDMA: Frequency Division Multiple Access. Requires different carriers. Used by GLONASS. – TDMA: Time Division Multiple Access. Several channels share transmission link. Used by many cellular telephone providers and LORANC. – CDMA: Code Division Multiple Access. Requires pseudorandom codes by transmitted and also generated for correlation within the receiver. Used by GPS.
DSP Techniques, con’t. • Crosscorrelation: Used by GPS receivers to determine what signal is coming from a specific satellite. Can be generalized to extracting information from any multiplexed digital signal. ì 1 ï 1 Dt C ij (Dt) = ò y i (t)y j (t + Dt)dt = í 1t t0 T ï î »0 t 0 +t
if Dt = 0 if | Dt | £ T if | Dt | > T
where t denotes the integration time and y i (t) and y j (t) are continuous functions (e.g. PRN codes)
PRN Crosscorrelation Correlation of receiver generated PRN code (A) with incoming data stream consisting of multiple (e.g. four, A, B, C, and D) codes
Schematic of C/Acode acquisition
Since C/Acode is 1023 chips long and repeats every 1/1000 s, it is inherently ambiguous by 1 msec or ~300 km. Must modulo2 add the transmitted and received codes after correlation to increase SNR and narrow bandwidth.
Methods to Cope with Antispoofing • Antispoofing: Implemented in 1994 to make P code unavailable to nonmilitary users. Encrypted Pcode is referred to as Ycode. – Squaring: Yields halfwavelength carrier and greatly reduces SNR. Old technology. – Codeaided squaring: Uses mathematical similarity of the Ycode to Pcode. L1 carrier is downconverted and multiplied with a local replica of the Pcode, then squared. Results in less reduction of SNR than simple squaring.
Antispoofing Methods, con’t. • Crosscorrelation: Takes advantage of the fact that both L1 and L2 are modulated with the same P(Y)code, despite lack of knowledge of the actual Pcode. Yields the difference in pseudoranges, P1(Y) P2(Y), and the phase difference of L1 and L2. Again less SNR loss compared with squaring. Can be difficult to track at low elevation angles. Technique employed in Trimble 4000SSi/SSE. • Ztracking: Takes advantage of the fact that Ycode is the modulo2 sum of the Pcode with a lower encryption rate. Yields L1 and L2 Ycode pseudoranges and the full carrier phases of L1 & L2. This method yields the best SNR. Multipath performance is better than other methods. Technique employed in Ashtech Z12 and microZ.
AS Technologies Summary Table Ashtech Z12 & µZ
Trimble 4000SSi
From Ashjaee & Lorenz, 1992
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
Digital Modulation Methods • Amplitude Modulation (AM) also known as amplitudeshift keying. This method requires changing the amplitude of the carrier phase between 0 and 1 to encode the digital signal. • Frequency Modulation (FM) also known as frequencyshift keying. Must alter the frequency of the carrier to correspond to 0 or 1. • Phase Modulation (PM) also known as phase shift keying. At each phase shift, the bit is flipped from 0 to 1 or vice versa. This is the method used in GPS.
Modulation Schematics
Modulo2 recovery of GPS code Modulo2 arithmetic: 0 + 0 = 0; 0 + 1 = 1; 1 + 0 = 1; 1 + 1 = 0 Bit shifts aligned
MUST MOD2 ADD RECEIVERGENERATED CODE TO RECOVER
Superposition of codes details • Superposition of two codes is not unique because the bit transition occurs at the same epoch; remember that both codes and phases are multiples of the fundamental frequency • Need to impose an additional constraint to arrive at a solution quadriphaseshift keying (QPSK), which puts the two codes 90° (π/2)
Phase and Quandrature General General Expression:
y(t) = y1 (t) + y 2 (t) = x1 (t)coswt + x 2 (t)sinwt where
y1 (t) is in phase (I) and y12(t) is in quandrature (Q) All spectral components of y1(t) are 90° out of phase with those of y2(t). This allows this the two signals to be separated in the receiver.
Codes on L1 and L2 S1p (t) = A p P p (t)D P (t)cos(2pf1t) + AcG P (t)D P (t)sin(2pf1 t) where
A p , Ac = amplitudes (power) of P(Y) code and C / A code P P (t) = pseudorandom P(Y) code P
G (t) = C / A code (Gold code) D P (t) = navigation data stream and
S2p (t) = B p P p (t)D P (t)cos(2pf2 t)
Codes on L1 and L2 (con’t.) p
P
P
P
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 (t) = X1 (t)X 2 (t - pT)
0 £ p £ 36 1 = 10.23 Mhz T
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/Acode chip is 1.023 Mhz Pcode chip is 10.23 Mhz
Power = P(t) = y2(t)
Bandwidth º B »
1 T
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.
where T º is chip duration
sin(px) 1 sin c(x) = = px 2p
p
iwx e ò ¶w -p
Digital Signal Processing Techniques • Filtering: Allows one to remove some portion of the frequency spectrum that may contain unwanted signal. – Low Pass Filter: lets all frequencies below a cutoff frequency through. – High Pass Filter: lets all frequencies above a cutoff frequency through. – Band Pass Filter: lets all frequencies within a specified window pass through. The window is called the passband
DSP Techniques, con’t. • Frequency Translation and Multiplication: technique to shift frequency spectrum of some signal to another portion of the frequency domain. – Upconversion: translate signal to higher frequencies. – Downconversion: translate signal to lower frequencies. Commonly done in GPS receivers. Multiply signal by sine function in a “mixer.” Special case is signal squaring and may be used to recover the pure carrier phase from a biphase modulated ranging signal.
DSP Techniques, con’t. • Spread Spectrum: broadly defined as a mechanism by which the bandwidth of the transmitted code is much greater than the baseband information signal (e.g. the navigation message in GPS)
– FDMA: Frequency Division Multiple Access. Requires different carriers. Used by GLONASS. – TDMA: Time Division Multiple Access. Several channels share transmission link. Used by many cellular telephone providers and LORANC. – CDMA: Code Division Multiple Access. Requires pseudorandom codes by transmitted and also generated for correlation within the receiver. Used by GPS.
DSP Techniques, con’t. • Crosscorrelation: Used by GPS receivers to determine what signal is coming from a specific satellite. Can be generalized to extracting information from any multiplexed digital signal. ì 1 ï 1 Dt C ij (Dt) = ò y i (t)y j (t + Dt)dt = í 1t t0 T ï î »0 t 0 +t
if Dt = 0 if | Dt | £ T if | Dt | > T
where t denotes the integration time and y i (t) and y j (t) are continuous functions (e.g. PRN codes)
PRN Crosscorrelation Correlation of receiver generated PRN code (A) with incoming data stream consisting of multiple (e.g. four, A, B, C, and D) codes
Schematic of C/Acode acquisition
Since C/Acode is 1023 chips long and repeats every 1/1000 s, it is inherently ambiguous by 1 msec or ~300 km. Must modulo2 add the transmitted and received codes after correlation to increase SNR and narrow bandwidth.
Methods to Cope with Antispoofing • Antispoofing: Implemented in 1994 to make P code unavailable to nonmilitary users. Encrypted Pcode is referred to as Ycode. – Squaring: Yields halfwavelength carrier and greatly reduces SNR. Old technology. – Codeaided squaring: Uses mathematical similarity of the Ycode to Pcode. L1 carrier is downconverted and multiplied with a local replica of the Pcode, then squared. Results in less reduction of SNR than simple squaring.
Antispoofing Methods, con’t. • Crosscorrelation: Takes advantage of the fact that both L1 and L2 are modulated with the same P(Y)code, despite lack of knowledge of the actual Pcode. Yields the difference in pseudoranges, P1(Y) P2(Y), and the phase difference of L1 and L2. Again less SNR loss compared with squaring. Can be difficult to track at low elevation angles. Technique employed in Trimble 4000SSi/SSE. • Ztracking: Takes advantage of the fact that Ycode is the modulo2 sum of the Pcode with a lower encryption rate. Yields L1 and L2 Ycode pseudoranges and the full carrier phases of L1 & L2. This method yields the best SNR. Multipath performance is better than other methods. Technique employed in Ashtech Z12 and microZ.
AS Technologies Summary Table Ashtech Z12 & µZ
Trimble 4000SSi
From Ashjaee & Lorenz, 1992
