Implementation of a Software-defined GPS Receiver

Anthony J. CorbinDr. In Soo Ahn

Thursday, April 20, 2023

Overview Rationale System Description Software Architecture

Coarse Acquisition Fine Acquisition Tracking Positioning

Progress/Results Conclusion/Achievements

Rationale

Reduce Cost Eliminates ASICs or other custom ICs

More Upgradeable GPS Block III Galileo

Cost Cost is driving the mass-adoption of GPS

devices Currently, a GPS chipset in volume costs

around $5 8

The software GPS chipset, which is currently being produced in low volume, costs around $4 2

In high-volume, the cost of a software GPS chipset would likely become negligible

Upgradeable China and the European

Union are developing their own systems7

Russia already has its own system, but is working on making it more compatible with other systems6

The U.S. is beginning work on Block III GPS satellites

For a software-defined receiver, a simple software patch would be, in many cases, sufficient to use these systems

Equipment List

Item Description PC Multi-core PC SiGe GPS Sampler USB Dongle GPS Patch Antenna

Active Patch Antenna

High-Level Block Diagram

Antenna

GPS L1 Signal 1575.42 MHz

PCSampled Signal

4.1304 MHzDisplay

Bandpass Filter - 1575.42 MHz

LNASiGe GPS Sampler

Input: GPS L1 Signal

Outputs: Earth-Centered, Earth-Fixed Coordinates Latitude, Longitude, Altitude

Antenna Stage

USB GPS Dongle USB 2.0 Interface Simple software

interface

Subsystem Requirements

Error Specification(s) Position Error 100 m Sampling Rate 4.1304 MHz Time to First Fix Cold Start : 2 minutes

Warm Start : 12 seconds Display Earth-centered, Earth-fixed Coordinates

Latitude, Longitude, Altitude UTC Time Update

Position Error Estimated position is based on the sampling

rate being 4 times the chipping rate. ¼ of the distance represented by a chip is

therefore the approximate error.

mm

m

s

s

m

f

c

Chip

Chip

31.734

26.293

4Precision

26.2931

10023.1

103

6

8

Time to First Fix [1]

A position fix requires that the ephemeris data is completely received.

This requires a complete frame of data, which takes 30 s to transmit.

However, it is unlikely that the receiver shall begin collecting data at the beginning of a subframe indicating that an extra subframe lasting 6 s must be received.

If the ephemeris data has already been received, the fix time is minimal.

6 Seconds

Subframe 1

Subframe 2

Subframe 3

Subframe 4

Subframe 5

30 Seconds

Functional Software Diagram

Acquire

Track

Satellite

Satellites

.

.

.

.

Timestamp

Size

Sample

Samples

.

.

.

.

010101

Timestamp

Position

Position

Positioning

.

.

.

.

Acquired Satellites

Pseudoranging

Acquisition

Ephemeris Data Collection

Position Vectorization

Satellite Object

+Satellite(in ID : size_t, in ca : CACode*, in Base : Frequencies, in fft : FFTEngine*)+~Satellite()+ID() : size_t+UpdateSamplesPerChip(in CodeF : double)+ComputePosition()+UpdatePosition(in TOW : double)

+Status : SatelliteStatus+fCA : complex<double> *+SampleLength_ : size_t+ClockFactor : double+CA_[1024] : double+SamplesPerChip_[1024] : size_t +NavData_ : EphemerisParameters+SatellitePosition : Position<double>+ID_ : size_t+Base_ : Frequencies+CodeFRem_ : double

Satellite

+Satellites(in Base : Frequencies &)+Satellites(in Base : Frequencies, in Data : string)+~Satellites()+operator [](in index : size_t) : Satellite *+ClearAcq()+DisplayStatus()+Size() : size_t+GetAcquiredSatellites() : AcquiredSatellites *+SaveSatellites(in Filename : string)

-Satellites_ : vector<Satellite*>-Base_ : Frequencies-fft_ : FFTEngine *-ca_ : CACode *

Satellites

+SatelliteStatus(in SNR_ : double, in CodeIndexAcq_ : size_t, in Carrier_ : double)+SatelliteStatus()+operator =(in s : SatelliteStatus)+Acquired() : bool

+SNR : double+CodeIndexAcq : size_t+CodeIndexTOW : double+Carrier : double+CodeF : double+c0_TOW : double+CodeIndex_c0 : double+t_c0 : __int64+Tracked : bool+FrameTime : __int64

«struct»SatelliteStatus

+DataComplete() : bool

+F1 : bool+F2 : bool+F3 : bool+TOW : unsigned int+SV_Code_Phase : unsigned int+SV_Code_Phase_c0 : unsigned int+Week_No : unsigned int+SV_Health_Index : unsigned int+SV_Accuracy_Index : unsigned int+T_GD : double+t_oc : double+a_f2 : double+a_f1 : double+a_f0 : double+DataSetCutover : bool+IODC : unsigned int+IODE2 : unsigned int+IODE3 : unsigned int+C_rs : double+delta_n : double+M_0 : double+C_uc : double+e : double+C_us : double+radA : double+t_oe : double+C_ic : double+Omega_0 : double+C_is : double+i_0 : double+C_rc : double+w : double+Omega_dot : double+IDOT : double+AODO : unsigned int+FIT_Interval_Flag : bool

«struct»EphemerisParameters

+Position(in X_ : T, in Y_ : T, in Z_ : T)+Position(in X_ : T, in Y_ : T, in Z_ : T, in Lat_ : T, in Lon_ : T, in Alt_ : T)+Position()+Rotate(in theta : T)+Display()+ToLLA()+DistanceTo(in p2 : Position) : T

+X : T+Y : T+Z : T+Lat : T+Lon : T+Alt : T

Position

T

+Frequencies(in SamplingFrequency : double, in CarrierFrequency : double, in CodeFrequency : double)+Frequencies()+operator =(in f : Frequencies)+SampleLength() : size_t+DataLength() : size_t

+Sampling : double+Code : double+Carrier : double

«struct»Frequencies

Software Architecture

Coarse Acquisition

Fine Acquisition

Tracking

Positioning

Determines the available satellites.

Refines the acquisition.

Fast algorithm to extract satellite orbital data.

Calculates the receiver position.

Coarse/Acquisition Code Generation

A generated C/A code sample is shown to the right.

The signal generated is based on the pseudorandom sequence generation shown on the next slide.

50 100 150 200 250 300

-1

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0

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0.6

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1

C/A Code Generation [1]

1 2 3 4 5 6 7 8 9 10

1 2 3 4 5 6 7 8 9 10

Tap

Tap

GPS L1 Signal

Coarse Acquisition Coarse acquisition searches around the

intermediate frequency in the range +/- 10 KHz with a step of 500 Hz

Frequency Domain Correlation

FFTL1 C/A Code

Generator

+/- 10 KHz500 Hz Step

FFT

conj

IFFT SNR > Threshold?

Acquired Satellite

Yes

No

Frequency Domain Correlation The correlation value

must be checked at every code alignment.

To perform this quickly, the operation is performed in the frequency domain.

As shown in the right, cross-correlation is equivalent to the product of X*() and Y() in the frequency domain.

N

YX

enmyemxN

enmymxN

R

nmymxN

nr

N

n

N

nmjN

m

N

mj

N

n

N

m

N

nj

N

m

)()(

)()(1

)()(1

)(

)()(1

)(

*

1

0

)(1

0

1

0

1

0

1

0

C/A Code Characteristics

Repeats every 1023 chips Cross-correlation between two

satellites’ C/A codes is minimal Correlation value is only large when

the code is perfectly aligned with itself.

Cross-Correlation The first 3D graph

shows the cross-correlation between C/A codes for different satellites for the perfectly aligned case, while the second shows a misaligned case.

The crest in the first graph shows correlation values for the same satellite in the perfectly aligned case.

Correlation Result The graph to the

right shows the results of a correlation between sample data and a known C/A code

The large peak indicates the proper code alignment

Coarse Acquisition – Satellite Search

Coarse Acquisition – IF Search

Fine Acquisition Uses the frequency estimate from Coarse

Acquisition to obtain a more accurate estimate

10 L1 C/A Code Samples 2^(n+1)Length FFT Size

Zero AppendL1 C/A Code Generator

FFT

FFT conj

IFFT MAX Index

Sampling Frequency/FFT Size

Carrier Estimate

Tracking Tracking occurs in

the time domain A Delay-Locked

Loop tracks the Code Frequency

A Phase-Locked Loop tracks the Carrier Frequency

I

Q

Carrier Frequency

Phase Remainder

L1 Code Remainder

Chipping Length Generator

P

E

L

Signal

I_P

I_L

I_E

Q_P

Q_L

Q_E

Code Discriminator

Carrier Discriminator

Delay-Locked Loop [1] The DLL tracks the Code Frequency by generating two

extra C/A code sequences The extra sequences are shifted slightly early and

slightly late with respect to the prompt sequence The differences in the correlation values, as shown

below, indicates the direction in which the prompt sequence must be shifted

C/A Code Tracking The graphs to the

right show the code error output from the delay-locked loop.

The loop parameters have been refined through testing to allow for fast convergence.

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-5

0

5

0 20 40 60 80 100 120 140 160 180 200

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-5

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5

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Carrier Tracking A carrier error signal is

shown on the right. In this example, the

frequency of the carrier appears to be drifting further below the intermediate frequency.

This is due to the Doppler Effect.

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0

10

20

30

0 5000 10000 15000 20000 25000 30000

Navigation Data

-6000

-4000

-2000

0

2000

4000

6000

0 5000 10000 15000 20000 25000 30000

The figures to the right show resolved 50 Hz navigation data after coarse acquisition, fine acquisition, tracking, and post-processing has occurred.

The top graph shows 32s of data, while the bottom graph shows 3s.

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-2000

0

2000

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6000

0 500 1000 1500 2000 2500 3000

Position Calculation

Ephemeris Data

Pseudoranges

Satellite Positions

.

.

.

.

.

....

....

....

1 111

1

1

1

1

1

1 tc

tc

XZZYYXXSATRCV

SATRCVSATRCVSATRCV

Solve using QR Factorization

Update Receiver Position

Progress MATLAB GPS software [1] has been ported to C++

This includes: Coordinate conversion Tracking loop Acquisition algorithms

DSP design approach was abandoned due to technical issues at a very early stage of the project.

C++ code can accurately find a position from stored sample data.

Developed code has been restructured to run in parallel.

Position Results

51.81 m

Position Results

104.4 m

Position Results

Speed Currently the C++

code requires under a minute (per satellite) to read a full 36 s of satellite data.

Compare this with the Matlab code which takes 6 minutes per satellite.

0

1

2

3

4

5

6

7

C++ Matlab

Tim

e (

Min

ute

s)

Tracking

Intel Threading Building Blocks

Intel’s TBB is a library for creating threaded programs

Platform independent Relatively easy to use

Changes to Project Objectives Finding the satellite positions requires an accurate time…requiring

collection of at least subframes 1-3 of the ephemeris data The equation below shows the number of multiplications per

second required to track one satellite. This does not include C/A code generation, carrier demodulation, or the overhead involved with sampling.

The DSP considered is clocked at 225 MHz which is simply not fast enough.

sMultipliesMillionms

alignmentsarmsSamples/2.98

3*2*16368

Scheduling Telemetry and

Handover words contain a Time-of-Week value that can be used to update the position of the satellites

The TLM/HOW words are sent at the beginning of each subframe which occurs every 6 seconds

6 Seconds

Subframe

1.2 Seconds1.2 Seconds

TLM/HOW Data

Processing Time

6 Seconds

Subframe

6 Seconds

Subframe

Scheduling Scheduling allows a

minimal set of data to be used for position computation

Orbital data is typically valid for several hours

Collect 36s of Data

Extract orbital data

Coarse Acquisition

Fine Acquisition

Tracking

Estimate the Time at which the TLM/HOW word will be

transmitted

Wait until 0.1s before

Collect 1.2s+ of data

Compute position

Conclusions

Results show that implementation is practical on modern PCs

However, application in low cost embedded systems is several years out

Achievements Successful determination of position Real-time satellite availability determination Working C++ based receiver code

Stored data Received data using USB sampler

Wrapped the driver code for the USB device in C++

Multi-threaded object-oriented design Google Earth C++ class wrapper

Recommendations for Future Work

Continue enhancing code for further improvements.

Research neural network approaches.

References [1] Kai Borre, Dennis M. Akos, Nicolaj Bertelsen, Peter Rinder, and Soren

Holdt Jensent, Software-Defined GPS and Galileo Receiver : A Single-Frequency Approach. Birkhauser: Boston, 2007, pp. 29, 83, 105.

[2] SiGe, SE4110L-EK1 Evaluation Board User Guide. [3] SiGe, SE4110L Datasheet. [4] U.S. DoD, Navstar GPS Space Segment/Navigation User Interfaces.

IS-GPS-200 Rev. D. [5] U.S. DoD, World Geodetic System 1984 : Its Definition and

Relationships with Local Geodetic Systems [6] Wikipedia, GLONASS. <http://en.wikipedia.org/wiki/GLONASS> [7] Wikipedia, GALILEO. <http://en.wikipedia.org/wiki/Galileo_gps> [8] EDACafe.com. Atmel Introduces $5 GPS Baseband IC With 3

Meter Accuracy. <http://www10.edacafe.com/nbc/articles/view_article.php?articleid=177910&page_no=2>

Real-time Functionality

Collect 36s of data with a timestamp.

Extract ephemeris data and calculate

initial position.

Collect a small data sample with a

timestamp.

Use the current carrier estimate to perform a

frequency domain correlation with 1 ms of

the small sample

Using the entire small sample estimate the

current carrier frequency and save it.

Estimate pseudoranges.

Estimate new satellite position

given the difference in the

time stamps.

Estimate Position

Updated Schedule

Week Activity 1/23-1/26 GPS Acquisition Software 1/27-2/2 Develop C++ Tracking Algorithm 2/3-2/9 Develop C++ Tracking Algorithm 2/10-2/16 Develop software to calculate position 2/17-2/23 Documentation and software design 2/24-3/1 Redevelop software with updated design using lessons

learned from initial development 3/2-3/8 Continue redevelopment 3/9-3/15 Debug and document redesign 3/16-3/22 Continue debugging and documenting 3/23-3/29 Design display 3/30-4/5 Develop and test display 4/6-4/12 Develop and test display 4/13-4/19 System debugging and documentation 4/20-4/26 System debugging and documentation 4/27-5/3 System debugging and documentation