Undergrad Senior Design Thesis

A.Katti, S.Patil & S.Reddy

Simulation Study, Analysis and Development of

Improved Navigation Solution for GPS

Amit Katti 08D91A0408

Sandeep Patil 08D91A0488

Sainath Reddy 08D91A04A4

Presentation#3Presentation#3


Recap GPS Overview Position and Time from GPS C/A and Pseudorange Navigation

And now, the leap…


Simplified GPS Receiver


GPS Data Parameters 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.


GPS Satellite Signals – Block Representation


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.


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.


GPS Data Frame


GPS Data Format


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.


Pseudorange Navigation


ECEF Coordinate System


Carrier Phase Tracking


GPS Carrier Phase Positioning


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.


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.


Front-End GPS Receiver


Code Acquisition


Tracking Loops

Phase Locked Loop Costas Loop Delay Locked Loop


Position Determination

Least Squares Estimation Kalman Filtering

Linear KF Extended KF


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.


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.


KF Working - Algorithm


State Transition Matrix

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


Extended KF Transition Matrix


States of a Kalman Filter

Position Error Velocity Error GPS Receiver Clock Bias Clock Drift


States of a Kalman Filter

Apriori State or Pre-Prior State Kalman Gain Covariance Error Matrix Noise Elimination


MATLAB® Results for the Kalman Filter

Vehicle Position Position Measurement and Estimation Error True & Estimated Velocity Velocity Estimation Error


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.


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


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.

Engineering

Undergrad Senior Design Thesis