Location and Timing with CA code in GPS

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Location and Timing with C/A code in GPS

• Wanbin Tang
• Jan 24, 2007

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Outline

• GPS Signal Structure
• Overview
• C/A code
• GPS Time
• GPS receiver
• Acquisition
• Tracking
• Subframe identification
• Pseudorange Calculation
• Satellite position calculation
• User position calculation
• Conclusion

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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

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GPS Signal Characteristics
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Codes on L1 and L2
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Coarse/Acquisition Codes
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PRN Cross-correlation
Correlation of receiver generated PRN code (A)
with incoming data stream consisting of multiple
(e.g. four, A, B, C, and D) codes
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GPS Data Format
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GPS Time

• GPS time is referenced to a universal coordinated
  time (UTC). The GPS zero time is defined as
  midnight on the night of January 5/ morning of
  January 6, 1980. The largest unit used in stating
  GPS time is one week, defined as 604,800 seconds
  (7 24 3600).

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GPS Time

• The GPS timing information transmitted in the air
  interface includes
• 17-bit truncated version of the TOW count covers
  a whole week and the time unit is 6 sec (1.5 sec
  4), which equals one subframe time.
• the 10 most-significant bits (MSBs) as the week
  number

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GPS Time
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Outline

• GPS Signal Structure
• Overview
• C/A code
• GPS Time
• GPS receiver
• Acquisition
• Tracking
• Subframe identification
• Pseudorange Calculation
• Satellite position calculation
• User position calculation
• Conclusion

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A fundamental GPS receiver
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Acquisition

• Requirement
• Search over a frequency range of 10 KHz to cover
  all of the expected Doppler frequency range for
  high-speed aircraft.
• The resolutions of the two important outputs of
  acquisition, the beginning of the C/ A code
  period and the carrier frequency, should reach
  the requirement of the tracking circuits.
• Methods
• Conventional correlation
• Fast Fourier transform (FFT)
• Delay and multiplication

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Acquisition
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FFT (5MSamples/s,1ms Received data)

• Perform the FFT on the 1 ms of input data x(n)
  and convert the input into frequency domain as
  X(k) where nk0 to 4999 for 1 ms of data.
• Take the complex conjugate X(k) and the outputs
  become X(k).
• Generate 21 local codes lsi(n) where i1, 2, . .
  . 21, using equation given in blow. The local
  code consists of the multiplication of the C/A
  code satellite s and a complex RF signal and it
  must be also sampled at 5 MHz. The frequency f i
  of the local codes are separated by 1 KHz.
• lsi Cs exp( j2pif it)
• Perform FFT on lsi(n) to transform them to the
  frequency domain as Lsi(k).
• Multiply X(k) and Lsi(k) point by point and call
  the result Rsi(k).
• Take the inverse FFT of Rsi(k) to transform the
  result into time domain as rsi(n) and find the
  absolute value of the rsi(n). There are a total
  of 105,000 (21 5,000) of rsi(n).
• The maximum of rsi(n) in the nth location and
  ith frequency bin gives the beginning point of
  C/A code in 200 ns resolution in the input data
  and the carrier frequency in 1 KHz resolution.

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Fine frequency estimation

• Strip the C/A code from the 1ms input signal
• At time m, the highest frequency component in 1ms
  of data is Xm(k) ,then the initial phase
• At time n, a short time after m, the phase is
• Fine frequency is

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Tracking
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How to get fine timing resolution

Correlation output within 1chips in ideal
conditions
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Curve Fitting

Correlation output within limited bandwidth
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Basic Simulation Results

• 1 satellite
• Raise cosine filter
• AWGN channel
• 1ms received data processing
• Oversample rate 5
• Delay between the early and ontime tracking
  branch one sample
• Quadratic curving fitting

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Subframe identification

• Convert tracking output to nevigation data
• Using the preamble of pattern(10001011) in the
  first word and parity code (00) to identify
  subframe.

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Psedurange calculation

• In collecting the digitized data there is no
  absolute time reference and the only time
  reference is the sampling frequency. As a result,
  the pseudorange can be measured only in a
  relative way.
• prange (const diff of dat finetime) c
• where c299792458 m/s is speed of light
  const is an arbitrarily chosen constant to make
  all the pseudoranges positive and the fine time
  is obtained from the tracking program.
• the relative transit time (diff of dat) is
  calculated according to
• the beginning points of the C/A code
• the beginning of the first navigation data
• the beginning of subframe 1

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Calculate the satellite position

• Calculate the coarse time of the transmission of
  satellite
• tc TOW - relative transit time
• Using the navigation data and tc, the user can
  determine the satellite position in earth-center
  earth-fixed coordinate system.

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Calculate the satellite position
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Calculate the satellite position

• Calculate the mean motion
• Calculate the mean anomaly MM0 n(tc -toe)
• Calculate the eccentric anomaly E M es sin E
  
• Calculate the overall time correction
• Calculate the true anomaly
• Calculate the angle

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Calculate the satellite position

• Calculate the following correction terms
• Calculate the angle between the accenting node
  and the Greenwich meridian
• Find the position of the satellite and adjust the
  pseudorange

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Calculate user position

• a minimum of four satellites is required to solve
  for the user position
• where bu is the user clock bias error
  expressed in distance.

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Iterative method to update the transmit time

• The time used to calculate the position of a
  satellite and the time used to calculate user
  position are different. The time used to
  calculate the satellite position should be
  adjusted to be the same time for calculating user
  position.
• Update the satellites position with tt and get a
  updated user position. iterative calculae until
  the changes in x, y, z (or xu, yu, zu) are below
  a predetermined value.
• In the end , the absolute position and timing of
  user is determined.

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Outline

• GPS Signal Structure
• Overview
• C/A code
• GPS Time
• GPS receiver
• Acquisition
• Tracking
• Subframe identification
• Pseudorange Calculation
• Satellite position calculation
• User position calculation
• Conclusion

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Conclusion

• The complexity of GPS receiver is mostly
  determined by baseband digital signal processing
• acquisition
• tracking
• multi satellite signal receiving
• The absolute time can be determined after the
  accurate position of user is get.
• The timing resolution and position resolution are
  highly correlated. Roughly to say, if position
  resolution is less than 30m, the timing
  resolution is less than 100ns.

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Thanks !