Mutual Coupling Estimation for GPS Antenna Arrays in the Presence of Multipath

Transcription

1 Mutual Coupling Estimation for GPS Antenna Arrays in the Presence of Multipath Zili Xu, Matthew Trinkle School of Electrical and Electronic Engineering University of Adelaide PACal 2012 Adelaide 27/09/2012

2 1. Introduction 2. Maximum Likelihood DOA Estimation 3. Calibration Algorithm 4. Simulation results 5. Experiment results

3 1. Introduction

4 Need for Calibration Antenna arrays can be used for GPS interference DOA estimation DOA estimation accuracy affected by Channel Gain & phase errors Mutual coupling Receiver position errors

5 Errors To Be Calibrated Calibrating source: GPS signals (supply DOA information, used as disjoint calibrating sources) GPS signals are 15 db below the noise Apply matched filter to the particular GPS signal we want to use for calibration => processing gain > 30 db Errors to be estimated: 1. Array orientation error 2. Gain/phase errors in each channel 3. Mutual coupling between antennas

6 Multipath Effect of Calibrating Source Multipath may be present on calibration sources. Causes errors in DOA and calibration parameters Likely to be correlated with direct path (only 2 MHz BW) DOA difficult to estimate Requires Spatial smoothing => would still allow MUSIC to work Maximum Likelihood Techniques => multi-dimensional search requiring high computational load.

7 Maximum Likelihood Hood Assume fully correlated direct and multipath signal & M antenna elements Modelled Phase & Amplitude from direct and multipath signal Steering vectors based on DOA of direct and multipath signal Measured Phase & Amplitude of Signal Amplitude and phase factor of direct and multipath signal Multi-dimensional search over all direct and multipath DOAs amplitude and phase factors

8 Reducing Dimensionality

9 Full Cost function Use N disjoint calibration sources Include Mutual coupling and gain phase errors in model Steering vector of direct signal Array orientation error Amplitude and phase of direct path Measured phase and amplitude Gain Phase errors in each channel Steering vector of multi path Amplitude and phase of multipath Unknowns shown in red For each Calibration Source: DOA of multipath Common: Orientation Error, Mutual Coupling Parameters, Gain Phase Errors

10 Mutual Coupling Model 7 equally spaced circular antennas with an additional antenna in the centre

11 Solution Existence Condition Consider current array configuration with N disjoint calibrating sources (assume there is 1 multipath signal in each source & 8 antennas) Array uncertainties: Multipath DOA: 2N Relative Gain/phase error: 2*7 Mutual Coupling parameters: 2(8/2) Orientation error: 1 Least squares equations given by N disjoint sources: 2N(8-1) 2N+14+2(8/2)+1 2N(8-1) So N 3

12 3. Calibration Algorithm Two Key steps: Estimate phase and amplitude of N disjoint GPS signals at each antenna Minimise:

13 Estimate gain & phase of the n th GPS signal at each antenna Column vector with Gain and phase of GPS signal, also includes highly correlated Multipath signals

14 Reduce dimensionality by replacing s n by its least squares estimate Use Alternating Projections: Maximise with respect to one parameter while keeping others fixed. Array Orientation Estimation Multipath DOA Estimation

15 Algorithm Flow Chart Initialisation Generate R for each satellite using matched filter Use DOA of each satellite Orientation error estimation Alternating Projection Minimise Multipath signal DoA estimation Complex number estimation Repeat until converge Gain/phase estimation Mutual coupling estimation

16 Convergence Check If the difference in the previous and current cost function is larger than a preset threshold ε, Then another iteration of the algorithm is performed, otherwise the calibration algorithm will stop and the current array orientation error, mutual coupling matrix are taken to be the estimated results.

17 The Number of Multipath Estimation (possible solution) Least squares based Wiener filter is applied to estimate the multipath signals in the time domain 70 C/A code periods are used in the Wiener filter and the filter has 60 taps Multipath is one sample delayed SNR of direct path signal: -24dB SNR of multipath signal: -32dB

18 4 Calibration Simulation

19 Simulation Scenario 7 elements circular array with 1 additional antenna in the centre (Radius = 1.25λ). 12 calibrating sources with the SNR of 20dB 250 snapshots 1 st, 4 th, 6 th and 10 th calibrating sources have 1 multipath signal with SNR of 10dB. Orientation error: 10 degrees. 2. Gain/phase errors: Ch1 Ch2 Ch3 Ch4 Ch5 Ch6 Ch7 Ch8 Gain Phase 0⁰ 10.1⁰ 30.2⁰ -31.7⁰ 17.1⁰ -70.3⁰ 10.9⁰ 13.4⁰ 3. Mutual coupling matrix coefficients: C 1 C 2 C 3 C 4 Gain (amplitude) Phase (degrees) 174.3⁰ -133⁰ 277.9⁰ 240.7⁰

20 Simulation Estimated Errors The calibration algorithm converges after 25 iterations. After the calibration, both of the gain/phase error and mutual coupling estimation are quite accurate with the estimation errors below 1%.

21 Beampattern Ideal beampattern (blue) and beampattern without calibration (red), main beam steering direction: 180⁰, elevation angle = 0⁰ Ideal beampattern (blue) and beampattern with calibration (green), main beam steering direction: 180⁰, elevation angle = 0⁰

22 5. Experiment Results

23 Experiment 1 1. Matched Filter Integration Time: 143ms 2. 5 satellites SV 11, 20, 23 30, 32 were obtained. 3. SNR of about 18dB after integration. 4. Azimuth and Elevation angles of GPS signals Azimuth Elevation SV ⁰ 48.1⁰ SV ⁰ 44.4⁰ SV ⁰ 35⁰ SV ⁰ 10.1⁰ SV ⁰ 64.8⁰ 4. Mutual coupling model only considers coupling from adjacent antennas. 5. Assume one multipath in each calibrating source (no number of multipath estimation).

24 Antenna Array Geometry 8 elements monopole antenna array - 7 elements uniformly spaced circular array with additional 1 element in the centre

25 Estimated Parameters After 10 iterations, the calibration converges The estimated results are: Array orientation error The measured value was rotated to 52⁰ which was estimated by a compass and the magnetic declination in Adelaide Gain (amplitude) Phase (degrees) 51.71⁰ Mutual coupling coefficients C 1 C 2 C 3 C The network analyser measurements of coupling for C1and C2 are about -20dB

26 Multipath Estimation Results SV 11 SV 20 SV 23 SV 30 SV dB -6.4dB -9.8dB -6.6dB -9.6dB SV 30: The elevation angle of SV 30 is only 10.1⁰, so the multipath could be caused by the ground reflection. SV 20: Elevation = 44.4 Azimuth = 226 Algorithm estimated multipath: Azimuth = 93.5 Elevation = 48.5 Set north as x axis: Azimuth = = Higher than others Estimated orientation angle

27 Experiment 2 Smaller Aperture Array Differences from the Experiment 1 1. The aperture of the antenna is reduced to 10cm (originally 25cm). Expect more obvious and higher mutual coupling calibrating sources longer data collection time 3. Mutual coupling model includes the coupling from all the antennas - smaller aperture snapshots (originally 143 snapshots) better GPS Doppler frequency estimation

28 Experiment Result Comparing with CST Simulation Simulation C2 C2 = -12 db C1 C1 = -13 db C3 C4 C3=C4 = -24 db Estimation from the experiment Estimated mutual coupling coefficients C 1 (S2,1) C 2 (S3,2) C 3 (S4,2) C 4 (S5,2) Coupling Gain (db) -14dB -13.8dB -20dB -22.1dB

29 References Backen S, Akos DM and Nordenvaad ML. (2008) Post-processing dynamic GNSS antenna array calibration and deterministic beamforming. Proceedings of the 21st International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS 2008). Savannah, GA, Brenneman M and Morton Y. (2010) An Efficient Algorithm for Short Delay Time Multipath Estimation and Mitigation. Proceedings of the 23rd International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS 2010). Portland, OR, Chang C-L and Juang J-C. (2008) A new pre-processing approach against array uncertainty for GNSS position. IEEE/ION Position Location and Navigation Symposium. Monterey, CA, Friedlander B and Weiss AJ. (1991a) Direction finding in the presence of mutual coupling. IEEE Transactions on Antennas and Propagation 39: Friedlander B and Weiss AJ. (1991b) Self-calibration for high resolution array processing. In: Haykin S (ed) Advances in Spectrum Analysis and Array Processing. Englewood Cliffs, New Jersey: Prentice-Hall, Inc., Kim US, De Lorenzo DS, Akos D, et al. (2004a) Precise phase calibration of a controlled reception pattern GPS antenna for JPALS. IEEE/ION Position Location and Navigation Symposium. Monterey, CA. Kim US, De Lorenzo DS, Gautier J, et al. (2004b) Phase effects analysis of patch antenna CRPAs for JPALS. Proceedings of the 17th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS 2004). Long Beach, CA, Solomon ISD. (1998) Over-the-Horizon radar array calibration. Department of Electrical and Electronic Engineering. Adelaide, Australia: University of Adelaide. Trinkle M and Gray DA. (2002) Interference localisation trials using adaptive antenna arrays. Proceedings of the 15th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 2002). Portland, OR, Wang J and Amin MG. (2008) Multiple interference cancellation performance for GPS receivers with dual-polarized antenna arrays. EURASIP Journal on Advances in Signal Processing XU Z, Trinkle M and Gray DA. (2010) A modelled eigenstructure based antenna array calibration algorithm for GPS. Proceedings of the 23rd International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS 2010). Portland, OR, XU Z, Trinkle M and Gray DA. (2011) A Maximum-likelihood approach based mutual coupling calibration algorithm in the presence of multipath for GPS antenna array. Proceedings of the 24th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS 2011). Portland, OR. Zheng Y. (2008) Adaptive antenna array processing for GPS receivers. School of Electrical and Electronic Engineering. Adelaide, Australia: University of Adelaide.

30 Any Questions?