Stationary, Cyclostationary and Nonstationary Analysis of GNSS Signal Propagation Channel Shashank Satyanarayana

Transcription

1 Stationary, Cyclostationary and Nonstationary Analysis of GNSS Signal Propagation Channel Shashank Satyanarayana Position, Location And Navigation (PLAN) Group Department of Geomatics Engineering, University of Calgary ION Alberta Lunch Meeting Oct

2 Objectives Empirical characterization of GPS signal amplitude under various scenarios such as urban, semi urban, foliage and indoors Probability x s 5-5 s 5-75 s 75- s - s Empirical validation of statistical models for signal amplitude such as single and multiple state models Amplitude Values, sqrt(i +Q ) x 4 Stationary, cyclostationary and nonstationary analysis of GPS signal amplitude under harsh environments Correlation Values x I Value Q Value Time (s) /4

3 Background Classes of Stochastic Processes (Gardner, 994). Nonstationary Polycyclostationary Cyclostationary Stationary Stationarity in wide-sense m = m ( t ) = m ( t ) x x x R ( τ ) = R ( t, t ) = R ( t t ) xx xx xx Cyclostationarity in a widesense mx() t = mx( t+ nt ) R (, t τ ) = R ( t+ nt, τ ) xx xx Cyclic Autocorrelation Function (CAF) Spectral Correlation Density function (SCD) Non-stationary signals Short-Time Fourier Transform Wigner-Ville Distribution /4

4 Methodology Data aiding from a reference receiver. Synchronous data were collected from two receivers with one antenna in a relatively open sky condition and another being in harsh environment. Reference Receiver Data bits, Doppler and code phase, Carrier phase Rover Receiver Signal analysis at the correlator output level Incoming signal N () I, Q Values Amplitude of the signal is computed as Complex Carrier Generator C/A Code Generator Impact of correlation on the fading phenomenon 4/4

5 Test Setup Roof Top Antenna Amplifier Indoor Antenna Amplifier Indoor Antenna Amplifier NI-PXI 566 Channel Channel Channel 5/4

6 Open Sky Scenario Probability 6 x PRN 6, Rooftop Rician Rice Amplitude Values, sqrt(i +Q ) Probability x PRN8 s Data 5 Probability x s 5-5 s 5-75 s 75- s - s Amplitude Values, sqrt(i +Q ) x Amplitude Values, sqrt(i +Q ) x 4 6/4

7 Open Sky with Single Reflector (/) Feb 9, 7: pm ( hour) West Gate, CCIT /4

8 Open Sky with Single Reflector (/).5 x 4 I Value Q Value x -4 PRN, minutes Data Correlation Values.5 Probability Time (s) Amplitude Values, sqrt(i +Q ) x 4 8/4

9 Open Sky with Single Reflector (/) 9/4

10 Open Sky with Multiple Reflector (/) Signal Level (db) Signal Level (db) Static Antenna, PRN:8, Coherent Integration = ms Moving Antenna, PRN:8, Coherent Integration = ms Time (s) 6 x -6 5 PRN:8, Moving Antenna, Coherent Integration = ms Non Paramteric Rice x -7 PRN:8, Static Antenna, Coherent Integration ms Non Paramteric Rice Density 4 Density Amplitude Values, sqrt(i +Q ) x Amplitude Values, sqrt(i +Q ) x 7 /4

11 Open Sky with Multiple Reflector (/) (Fontan, 8) Signal Level (db) Signal Level (db) Static Antenna, PRN:, Coherent Integration =4 ms Moving Antenna, PRN:, Coherent Integration =4 ms Time (s) /4

12 Foliage: Static/Dynamic PRN (Static) PRN 9 (Static) PRN (Dynamic) PRN (Dynamic) 8 5 /4

13 Indoor Data(Lab): Static/Dynamic /4

14 Conclusions Various single and multistate parametric models for signal amplitude variations were validated Possibility of applying cyclostationary and nonstationary analysis for the characterization of GNSS signals harsh scenarios were explored Under static scenarios, first order periodicities were observed in the presence of a strong reflector Channel coherence time of up to 4-5 minutes were observed in static scenarios. Signal variations become more random when the receiver is in dynamic condition and the amplitude can be more easily described using parametric models 4/4