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.
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
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
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
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
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.
