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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

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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

1. Introduction

2. Maximum Likelihood DOA Estimation

3. Calibration Algorithm

4. Simulation results

5. Experiment results

1. Introduction

Need for Calibration

Antenna arrays can be used for GPSinterference DOA estimation

DOA estimation accuracy affected by

– Channel Gain & phase errors

– Mutual coupling

– Receiver position errors

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 wewant 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

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.

Maximum Likelihood Hood

Measured Phase & Amplitude of Signal

Modelled Phase & Amplitude from

direct and multipath signal

Amplitude and phase factor of

direct and multipath signal

Steering vectors based on

DOA of direct and multipath signal

Multi-dimensional search over all direct and multipath DOAs amplitude and phase factors

Assume fully correlated direct and multipath signal & M antenna elements

Reducing Dimensionality

Full Cost functionUse N disjoint calibration sourcesInclude Mutual coupling and gain phase errors in model

Amplitude and phase of multipath

Amplitude and phase of direct path

Array orientation error

Steering vector of multi path

Measured phase and amplitude

Unknowns – shown in red

For each Calibration Source: DOA of multipath

Common: Orientation Error, Mutual Coupling Parameters, Gain Phase Errors

Gain Phase errors in each channel

Steering vector of direct signal

Mutual Coupling Model

7 equally spaced circular antennas with an additional antenna in the centre

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

3. Calibration Algorithm

Two Key steps:

Estimate phase and amplitude of N disjoint GPS signals at each antenna

Minimise:

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

Reduce dimensionality by replacing sn by its least squares estimate

Use Alternating Projections: Maximise with respect to one parameter while keeping others fixed.

Multipath DOA Estimation

Array Orientation Estimation

Algorithm Flow ChartInitialisation

Generate R for each satellite using matched filter

Use DOA of each satellite

Orientation error estimation

Multipath signal DoA estimation

Complex number estimation

Mutual coupling estimation

Repeat until

converge

Alternating Projection

Gain/phase estimation

Minimise

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.

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

4 Calibration Simulation

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

1st, 4th, 6th and 10th calibrating sources have 1 multipath signal with SNR of 10dB.

Orientation error: 10 degrees.

2. Gain/phase errors:

3. Mutual coupling matrix coefficients:

C 1 C 2 C 3 C 4

Gain (amplitude) 0.2 0.22 0.15 0.1

Phase (degrees) 174.3⁰ -133⁰ 277.9⁰ 240.7⁰

Ch1 Ch2 Ch3 Ch4 Ch5 Ch6 Ch7 Ch8

Gain 1 1.18 1.22 0.98 0.88 1.04 0.93 1.01

Phase 0⁰ 10.1⁰ 30.2⁰ -31.7⁰ 17.1⁰ -70.3⁰ 10.9⁰ 13.4⁰

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%.

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

5. Experiment Results

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

4. Mutual coupling model only considers coupling from adjacent

antennas.

5. Assume one multipath in each calibrating source (no number

of multipath estimation).

Azimuth Elevation

SV 11 314.3⁰ 48.1⁰

SV 20 226⁰ 44.4⁰

SV 23 279.5⁰ 35⁰

SV 30 52.6⁰ 10.1⁰

SV 32 194⁰ 64.8⁰

Antenna Array Geometry

8 elements monopole antenna array - 7 elements uniformly spaced

circular array with additional 1 element in the centre

Estimated Parameters

After 10 iterations, the calibration converges

Array orientation error

51.71⁰

Mutual coupling coefficients

C 1 C 2 C 3 C 4Gain

(amplitude)0.1085 0.0944 0 0

Phase

(degrees)-165.54 -15.72 0 0

The estimated results are:

The measured value was rotated to 52⁰ which was estimated

by a compass and the magnetic declination in Adelaide

The network analyser measurements of coupling

for C1and C2 are about -20dB

Multipath Estimation Results

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 = 93.5+51.7 = 145.2

SV 11 SV 20 SV 23 SV 30 SV 32

0.3536 0.3143 0.3088 0.2836 0.3043

0.0826 0.1502 0.1001 0.1324 0.1006

-12.6dB -6.4dB -9.8dB -6.6dB -9.6dB

Higher than others

Estimated orientation angle

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 .

2. 18 calibrating sources – longer data collection time

3. Mutual coupling model includes the coupling from all the antennas - smaller aperture.

4. 300 snapshots (originally 143 snapshots) – better GPS Doppler frequency estimation

Experiment Result Comparing with CST Simulation

Simulation

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

Estimation from the experiment

C1

C2

C4C3

C1 = -13 dB

C2 = -12 dB

C3=C4 = -24 dB

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, 2806 - 2814.

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, 152 - 160.

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, 892 - 897.

Friedlander B and Weiss AJ. (1991a) Direction finding in the presence of mutual coupling. IEEE Transactions on Antennas and Propagation 39: 273 -284.

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., 349-414.

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, 1531-1538.

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, 613 - 619.

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 2008.

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, 3220-3228.

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.

Any Questions?