This document presents a simulation study and analysis of an improved navigation solution for GPS. It discusses the key parameters used in GPS like ephemeris, clock, and almanac data. It then describes the GPS signal structure and data frames. It proposes using a software-defined receiver approach and implementing tracking loops and position determination using a Kalman filter. It shows how the Kalman filter can optimally track carrier phase and code measurements to estimate position and overcome limitations of traditional tracking loops. Simulation results demonstrate the Kalman filter's ability to accurately estimate position and velocity. The document concludes that the Kalman filter is well-suited for GPS navigation due to its recursive nature and ability to optimally process noisy measurements.

1. Simulation Study, Analysis and
Development of
Improved Navigation Solution for GPS
PPrreesseennttaattiioonn##33
Amit Katti 08D91A0408
Sandeep Patil 08D91A0488
Sainath Reddy 08D91A04A4
A.Katti, S.Patil & S.Reddy

2. Recap
 GPS Overview
 Position and Time from GPS
 C/A and Pseudorange Navigation
And now, the leap…
A.Katti, S.Patil & S.Reddy

3. Simplified GPS Receiver
A.Katti, S.Patil & S.Reddy

4. GPS Data Parameters
A.Katti, S.Patil & S.Reddy
 Ephemeris Parameters:
 Ephemeris data parameters describe Space Vehicle orbits for short sections of
the satellite orbits. Normally, a receiver gathers new ephemeris data each hour,
but can use old data for up to four hours without much error. The ephemeris
parameters are used with an algorithm that computes the SV position for any time
within the period of the orbit described by the ephemeris parameter set.
 Clock Data Parameters:
 Clock data parameters describe the Space Vehicle clock and its relationship to
GPS time.
 Almanac Parameters:
 Almanacs are approximate orbital data parameters for all Space Vehicles.
 UTC & Ionospheric Parameters:
 Each SV sends the amount to which GPS Time is offset from Universal
Coordinated Time. This correction can be used by the receiver to set UTC to
within 100 ns.
 Each complete SV data set includes an ionospheric model that is used in the
receiver to approximates the phase delay through the ionosphere at any location
and time.

5. GPS Satellite Signals –
Block Representation
A.Katti, S.Patil & S.Reddy

6. A.Katti, S.Patil & S.Reddy
Gold Code
 The PRN sequences, Gi (t) and Pi (t), used by the satellites are
called Gold codes. The Gold codes have a very high bandwidth and
are used to spread the spectrum of the data message over a much
wider bandwidth. In the receiver, the spreading effect of the PRN
sequences is removed by using locally generated replicas of the
broadcast Gold codes. Each satellite transmits its own unique Gold
code and the user receives multiple satellite signals at nearly the
same frequency.

7. The Gold Code, Contd…
 The C/A Gold codes are transmitted at a chipping rate of
1.023 Mbps. The individual symbols of the codes are
referred to as chips, as opposed to the bits of the
navigation message. A code g(t) is originally generated
as a binary sequence and is used to modulate the phase
of the carrier signal, as given in the equation below.
A.Katti, S.Patil & S.Reddy

8. GPS Data Frame
A.Katti, S.Patil & S.Reddy

9. GPS Data Format
A.Katti, S.Patil & S.Reddy

10. Pseudorange Navigation
 The position of the receiver is where the pseudo-ranges
from a set of SVs intersect. Position is determined from
multiple pseudo-range measurements at a single
measurement epoch. The pseudo range measurements
are used together with SV position estimates based on
the precise orbital elements (the ephemeris data) sent by
each SV. This orbital data allows the receiver to compute
the SV positions in three dimensions at the instant that
they sent their respective signals.
A.Katti, S.Patil & S.Reddy

11. Pseudorange Navigation
A.Katti, S.Patil & S.Reddy

12. ECEF Coordinate System
A.Katti, S.Patil & S.Reddy

13. Carrier Phase Tracking
A.Katti, S.Patil & S.Reddy

14. GPS Carrier Phase Positioning
A.Katti, S.Patil & S.Reddy

15. Software Approach
 The first task of any receiver is to determine which satellites are in
view. After determining that a given satellite signal is available, the
receiver attempts to track the carrier and PRN components of the
signal.
 A traditional receiver uses a Costas loop to track the carrier and a
Delay-Lock Loop to track the PRN sequence. Using the output of
the tracking loops, the navigation message for each satellite is
decoded.
 The navigation message provides the user with enough information
to calculate the positions of the satellites. The User can thereby,
calculate his position using the pseudo-range measurements from
the tracking loops.
A.Katti, S.Patil & S.Reddy

16. Why Software Approach?
 Minimum Hardware Use.
 Flexible
 Single program can be used to digitalize more than 1
frequency.
 New algorithms can easily be developed without
changing the design of hardware.
A.Katti, S.Patil & S.Reddy

17. Front-End GPS Receiver
A.Katti, S.Patil & S.Reddy

18. Code Acquisition
A.Katti, S.Patil & S.Reddy

19. Tracking Loops
 Phase Locked Loop
 Costas Loop
 Delay Locked Loop
A.Katti, S.Patil & S.Reddy

20. Position Determination
 Least Squares Estimation
 Kalman Filtering
A.Katti, S.Patil & S.Reddy
 Linear KF
 Extended KF

21. The Linear Kalman Filter
The Kalman filter has the capacity to overcome the drawbacks of
the traditional tracking loop. The Kalman filter is, in essence, a filter
with time varying gains. The gains vary with changing measurement
noise statistics and process noise statistics. The measurement
noise statistics change with C/No levels and jamming.
The process noise statistics change with user dynamics. Provided
with the process and measurement noise covariance matrices, the
Kalman filter can optimally separate signal from noise. The tasks of
tracking the carrier and code can be combined in one Kalman filter,
which replaces the two tracking loops in each channel with a single
Kalman filter per satellite.
A.Katti, S.Patil & S.Reddy

22. How does the KF Work?
 The Kalman filter used to track the carrier and code is similar to
the filter used to track the user’s position.
 The measurements provided to the filter are not measurements
of the states directly, but rather the errors between certain states
and those of the received signal.
 The measurements are therefore residuals. The filter has access
to three residuals, which are measurements of the error in the
phase and frequency of the carrier, and the error in the phase of
the local Gold code.
A.Katti, S.Patil & S.Reddy

23. KF Working - Algorithm
A.Katti, S.Patil & S.Reddy

24. State Transition Matrix
A.Katti, S.Patil & S.Reddy
θc,k+1 = IF Carrier
Phase
fc,k+1 = Second State
Derivative of IF
Carrier Phase
f’c,k+1 = Varying Bias –
Third State
θG,k+1= Local Gold
Code Phase

25. Extended KF Transition Matrix
A.Katti, S.Patil & S.Reddy

26. States of a Kalman Filter
 Position Error
 Velocity Error
 GPS Receiver Clock Bias
 Clock Drift
A.Katti, S.Patil & S.Reddy

27. States of a Kalman Filter
 Apriori State or Pre-Prior State
 Kalman Gain
 Covariance Error Matrix
 Noise Elimination
A.Katti, S.Patil & S.Reddy

28. MATLAB® Results for the
Kalman Filter
 Vehicle Position
 Position Measurement and Estimation Error
 True & Estimated Velocity
 Velocity Estimation Error
A.Katti, S.Patil & S.Reddy

29. Why is KF Better than other
methods?
 The main advantage of the information filter is that N measurements
can be filtered at each time-step simply by summing their
information matrices and vectors.
 The Kalman filter operates recursively on streams of noisy input
data to produce a statistically optimal estimate of the underlying
system state.
 Because of the algorithm's recursive nature, it can run in real time
using only the present input measurements and the previously
calculated state; no additional past information is required.
A.Katti, S.Patil & S.Reddy

30. Applications of KF
 Satellite Navigation Systems
 Auto-Pilot
 Brain-Computer Interface
 3D Modeling
 Radar Tracker
 Tracking of objects in Computer Vision
 Altitude and Heading Reference Systems
A.Katti, S.Patil & S.Reddy

31. A.Katti, S.Patil & S.Reddy
Conclusion
 We took up this project as a part of the thesis because of
our immense interest towards Satellite Communication
Systems.
 We thank Mr. G Srinivasa Rao, the internal guide for his
excellent guidance and presentation strategy.
 We also thank all other faculty members and the project
coordinators to have helped us throughout.