1 SVY 207: Lecture 5 The Pseudorange Observable u Aim of this lecture: –To understand how a receiver extracts a pseudorange measurement from a GPS signal

2 The Pseudorange Observable u How is the transmitted signal encoded? –Pseudorandom (PRN) code generation F XOR binary function F Linear feedback registers –C/A code –P code u How is the pseudorange observable formed –Discrete autocorrelation technique

3 PRN Code Generation u XOR (“Exclusive OR”) binary function F Remember this: Is A different to B? If so, the answer is 1. –If A  then XOR  –If  then XOR 

4 PRN Code Generation: 3 stage linear feedback register F The “state” is defined by three numbers ( A, B, C) –Initial state is always filled by 1: ( 1, 1, 1) F New state is calculated using XOR and shift to right –Linear feedback register sequence is (C 1, C 2, C 3,....) –For above example, sequence is ( 1, 1, 1, 0,....)

5 PRN Code Generation u Do the following problem: –Calculate the 3 stage linear feedback register sequence which starts with the state ( 1, 1, 1) –After how many digits does the pattern start to repeat?

6 PRN Code Generation F Pattern repeats after 7 cycles F Note that every possible binary number (A,B,C) appears except for (0,0,0) –In general, sequence length L(N)  N  where  number of bits in shift register L  3  –Sequence generally appears to be random

7 C/A Code –10 stage linear feedback register sequence  Sequence length L(10)  10  –C/A has code repeating sequence of 1023 bits F which appear to be random –C/A bit transitions occur at MHz F Sequence repeats 1000 times per second F Time for each sequence is 1 ms –Chip length (between bits) is 293 metres F Sequence repeats every 300 km F “Ambiguity” in the C/A code –easy to acquire

8 P Code u Generated from a combination of two different registers u P code sequence repeats in days –Each 7 day section is assigned a PRN code F Satellites often identified by their PRN number F PRN 2 refers to week 2 of the sequence F There are 38 possible PRN codes –24 satellites –some PRN codes are unused F PRN sequence is reset at Saturday midnight –start of GPS week

9 What is being measured? F shift bits of replica signal until it matches received signal (TTs)(TTs) Received signal, driven by satellite clock T s Replica signal, driven by receiver clock T Antenna Satellite clock, T s Transmitted signal Receiver clock T

10 Autocorrelation u Replica Signal F Receivers generate same codes as the satellites u Pseudorange Measurement F receiver matches incoming signal with replica signal F The time difference is computed by autocorrelation –Multiply bits from signal and replica signal and sum –The replica signal is shifted one bit at a time until this number is maximized –This is why the codes are designed to look random F The result is multiplied by the speed of light –This measurement is called the pseudorange

11 Autocorrelation Example u Receiver shifts R1 to find max correlation with S1 u Higher precision for codes with more bits  Correlation between PRN codes is small (R1  S2 etc.) u Therefore, interference from other satellites is small u This is how GPS receivers can track many satellites at once