Navigation Accuracy and Interference Rejection for an Adaptive GPS - - PowerPoint PPT Presentation

Navigation Accuracy and Interference Rejection for an Adaptive GPS Antenna Array

David S. De Lorenzo, Jason Rife, Per Enge Stanford University GPS Lab Dennis Akos University of Colorado 05 June 2006

The authors gratefully acknowledge the support of the JPALS Program Office, and the Naval Air Warfare Center Aircraft Division through contract N00421-01-C-0022.

6/13/2006 Stanford University JPALS Research 2

Constrained Adaptive Processing

• JPALS has stringent limits on pseudorange & carrier-phase errors

– Required to meet carrier-landing accuracy limits.

• GPS antennas introduce distortion on received signals

– Apparent as deterministic pseudorange and carrier phase biases – Dependent on the incoming signal line-of-sight.

• JPALS will likely require multi-element STAP algorithms to improve

C/No under jamming & RFI conditions.

• STAP algorithms can introduce additional

pseudorange and carrier phase biases.

Goal: Through temporal & spatial constraints on a STAP algorithm, move down & left in the trade space, to a point where deterministic pseudorange & carrier phase corrections based on signal LOS can be applied.

6/13/2006 Stanford University JPALS Research 3

Outline

• Software tools for signal simulation & tracking

– Signal simulator

• C/A or P-code signal generator that includes antenna distortion effects

– Software receiver

• Tracks a wide range of GNSS signals – GPS C/A & P-code, Galileo L1

& E6

• Includes multi-antenna and space-time adaptive signal processing
• Verification of software receiver & multi-signal tracking

performance

• Research methodology:

– Characterize biases vs. RFI rejection – Evaluate different compensation schemes

• Preliminary results

– FRPA vs. CRPA biases and interference rejection

6/13/2006 Stanford University JPALS Research 4

Stanford HW & SW Development

Analog front-end

4-channel GP2015 with 10 MHz common clock

Data collection computer

(2) ICS-650 cards sampling at 5-65 MHz and 12-bit A/D resolution

Software Receiver

all-in view, multi-signal GNSS receiver with STAP array processing

7-element array

rectangular patch antennas manufactured at Stanford University

2m high-gain dish * Possibility of including data from OSU’s multi-element antenna array. HP Vector Signal Analyzer

6/13/2006 Stanford University JPALS Research 5

Software-Based Signal Simulator

Bandlimited WGN & CW interference C/A & “P” code

1.023 & 10.23 Mchip/sec

Front-end

A/D

Front-end

A/D

… …

1480 1500 1520 1540 1560 1580 1600 1620 1640 1660 1680 0.2 0.4 0.6 0.8 1 1.2 Frequency (MHz) Gain Antenna Gain Response for PRN #1 [Az = 0 deg, El = 40 deg] Antenna #1 Antenna #2 Antenna #3 Antenna #4 Antenna #5 Antenna #6 Antenna #7 Front-end BW ~19MHz 1450 1500 1550 1600 1650 1700

• 50

50 100 150 200 250 Frequency (MHz) Phase Antenna Phase Response for PRN #1 [Az = 0 deg, El = 40 deg] Antenna #1 Antenna #2 Antenna #3 Antenna #4 Antenna #5 Antenna #6 Antenna #7 Front-end BW ~19MHz

• Gain/phase data for each look direction (10 S/V

constellation) and antenna (7 rectangular patches)

– Data courtesy Ung-Suok Kim

Gain/phase response for PRN #1

[Azimuth = 0°, Elevation = 40°]

6/13/2006 Stanford University JPALS Research 6

Signal Generation at Intermediate Freq.

• Received signal at master element:
• Mixing signal:
• Signal after LPF:
• Received signal at subsidiary element:
• Signal after mixing & LPF:

( ) ( ) ( ) [ ]

θ π τ τ + + ⋅ − ⋅ − ⋅ t f f t x t D P

D L S 1

2 cos 2

( ) ( ) ( )( ) [ ]

θ π τ τ + Δ + + ⋅ − Δ + ⋅ − Δ + ⋅ t t f f t t x t t D P

D L S 1

2 cos 2

( ) [ ]

t f f

IF L −

⋅

1

2 cos 2 π

( ) ( ) ( ) [ ]

θ π τ τ + + ⋅ − ⋅ − ⋅ t f f t x t D P

D IF S

2 cos

( ) ( ) ( ) ( ) [ ]

t f f t f f t t x t t D P

D L D IF S

Δ + + + + ⋅ − Δ + ⋅ − Δ + ⋅

1

2 2 cos π θ π τ τ

6/13/2006 Stanford University JPALS Research 7

Signal Generation w/ Antenna Distortion

s(t) and gain/phase data are antenna & S/V specific

Gain/phase distortion data available from HFSS simulation

– Verified by comparison to anechoic chamber testing – Data courtesy Ung-Suok Kim

( )

t s

( )

t sout fft

( )

f S

⊗

1 −

fft

• 1.5
• 1
• 0.5

• 1.5
• 1
• 0.5

Autocorrelation of s(t) Autocorrelation of sout(t)

• 50

6/13/2006 Stanford University JPALS Research 8

Standard Satellite Constellation

PRN #1 PRN #2 PRN #3 PRN #4 PRN #5 PRN #6 PRN #7 PRN #8 PRN #9 PRN #10

6/13/2006 Stanford University JPALS Research 9

Wideband Jammer Signal Generation at IF

( )

t j

( )

t jout fft

( )

f J

⊗

1 −

fft

( )

( )

( )

[ ]

∑

Δ + + Δ + ′ + + ⋅

i J L J J IF J

t f f t t f t f f P

i i

1 2

2 2 cos 2 π π

Gain/phase distortion data are currently not available

( ) ( )

t j t j

• ut

≡

• For each jammer – six swept

sinusoids cover frequency band from ~0 Hz to ~fs/2

• Amplitude scaled as needed

to achieve desired J/S ratio

6/13/2006 Stanford University JPALS Research 10

Satellite & RFI Constellation

80 300 10 30 270 9 20 240 8 70 210 7 60 150 6 20 120 5 50 90 4 40 60 3 30 30 2 40 1 Elevation Azimuth PRN 10 270 6 250 5 225 4 120 3 45 2 1 Elevation Azimuth RFI

Bandlimited WGN and/or CW interference

6/13/2006 Stanford University JPALS Research 11

Multi-signal Software GNSS Receiver

• Software Receiver tracks a wide range of GNSS

signals, runs in MATLAB

– GPS C/A and pseudo-P-codes – Galileo L1-B/C and E6-B/C codes

• Includes multi-antenna and space-time adaptive

signal processing

• Supports arbitrary sampling frequency, intermediate

frequency, data format, etc.

– The ideal s/w rcvr is fast, flexible, & uncomplicated You can have 2 out of 3!!

6/13/2006 Stanford University JPALS Research 12

Software Receiver Block Diagram

Weight Control Algorithm

Correlators

integrate & dump

Tracking Loops

Carrier NCO Code NCO

cos

C/No Estimator

Pseudorange & Carrier-phase Bias Estimator

carrier wipeoff code wipeoff

Early Prompt Late

FFT-based Coherent Acquisition

sin

Weight control processing supports FRPA & CRPA antennas and adaptive LMS & Applebaum arrays

6/13/2006 Stanford University JPALS Research 13

Software Receiver Flow Chart

For each tracking channel: 1ms sample buffer aligned w/ start of spreading code Code/carrier phase aligned w/ first sample of 1ms epoch

Discrete operation from stored data sample indexing & alignment

Noncoherent or coherent integration depends on

• nav. data bit alignment

This loop runs on a 1ms schedule

The devil is in the details

6/13/2006 Stanford University JPALS Research 14

Epoch-based Tracking of GNSS Codes

Code start tracked in each ~1ms data epoch

Problems:

– If fs is not an exact multiple of 1000Hz, the extra fractional sample causes a code-phase ramp error – Approaching/receding satellites will cause code wrap (phase skew), leading to dropped sample epochs

PRN1 PRN2 PRN3

Frame-based data epochs Multi-epoch tracking window

Code start tracked in the ~5ms active tracking window Active window Active window

PRN1 PRN2 PRN3

Solutions:

– Sample index for each tracked PRN aligns with 0 code phase – Logic is used to control sample index

• ver-run or under-run

6/13/2006 Stanford University JPALS Research 15

S/W Rcvr Verification: GPS C/A Code Tracking – Real Data

• All-in-view tracking of GPS C/A code signals
• Software

receiver is a combination of in-house code and structures from Kai Borre

• f Aalborg

University

500 1000 1500 2000 2500

• 0.2

0.2 0.4 0.6 0.8 1 Navigation Data Message - PRN 3 Time (ms) Data source: NordNav Rcvr & Dennis Akos 500 1000 1500 2000 2500 1700 1750 1800 Doppler Frequency Time (ms) Doppler frequency (Hz) 500 1000 1500 2000 2500 211 211.5 212 212.5 213 213.5 214 214.5 Position of the C/A Code Start Time (ms) C/A code start (chips) 500 1000 1500 2000 2500 30 35 40 45 50 55 60 Filtered C/No Time (ms) C/No (dB-Hz)

Tracking mode transitions

6/13/2006 Stanford University JPALS Research 16

S/W Rcvr Verification: C/A Code Acquisition – High-Gain Data

• Acquisition of GPS C/A code signal collected with

SRI Dish

– fS = 124.5 MHz – fIF = 43.08 MHz – Data courtesy Grace Gao of the Stanford GPS Lab

Why is the correlation peak rounded?

106.5 107 107.5 108 108.5 109 109.5 0.2 0.4 0.6 0.8 1 C/A Code Correlation - PRN #8 for 1ms Code Phase (chips) Correlation Function (normalized)

6/13/2006 Stanford University JPALS Research 17

106.5 107 107.5 108 108.5 109 109.5 0.2 0.4 0.6 0.8 1 C/A Code Correlation - PRN #8 for 1ms Code Phase (chips) Correlation Function (normalized)

S/W Rcvr Verification: C/A Code Acquisition – High-Gain Data

• Acquisition of GPS C/A code signal collected with

SRI Dish

– fS = 124.5 MHz – fIF = 43.08 MHz – Data courtesy Grace Gao of the Stanford GPS Lab

A band-pass filter was applied to the data before processing.

6/13/2006 Stanford University JPALS Research 18

105.5 106 106.5 107 107.5 108 108.5 109 109.5 0.2 0.4 0.6 0.8 1 C/A Code Correlation - PRN #8 for 1ms Code Phase (chips) Correlation Function (normalized)

S/W Rcvr Verification: C/A Code Acquisition – High-Gain Data

• Acquisition of GPS C/A code signal collected with

SRI Dish

– fS = 124.5 MHz – fIF = 43.08 MHz – Data courtesy Grace Gao of the Stanford GPS Lab

This is the correlation to unfiltered data.

6/13/2006 Stanford University JPALS Research 19

• 400
• 200

200 400 600 800 1000 1200 1400 1600 0.2 0.4 0.6 0.8 1 Code Correlation - Galileo L1/B for 1ms Code Phase (chips) Correlation Function (normalized) Code Correlation Galileo L1/B for 1ms Peak in 1st acq. block Doppler = 2200 Hz Code Ph. = 610.4 chips CPPR = 11.7 CPPM = 332.3

– Galileo L1-B/C and E6-B/C codes determined by Grace Gao of the Stanford GPS Lab

S/W Rcvr Verification: Galileo L1/B Code Acquisition – Real Data

608 608.5 609 609.5 610 610.5 611 611.5 612 612.5 613 0.2 0.4 0.6 0.8 1 C/A Code Correlation - PRN #1 for 1ms Code Phase (chips) Correlation Function (normalized)

6/13/2006 Stanford University JPALS Research 20

S/W Rcvr Verification: Galileo L1/C Code Tracking – Real Data

• Tracking of Galileo L1/C BOC(1,1) pilot signal
• No modification

to s/w rcvr except new code generators

• Galileo

L1-B/C and E6-B/C codes determined by Grace Gao of the Stanford GPS Lab

200 400 600 800 1000 1200 1400 1600 1800

• 0.2

0.2 0.4 0.6 0.8 1 Navigation Data Message - Galileo L1/C Time (ms) Data source: Galileo L1 w/ SRI Dish & VSA by Grace Gao 500 1000 1500 2140 2160 2180 2200 2220 2240 2260 Doppler Frequency Time (ms) Doppler frequency (Hz) 500 1000 1500 604 605 606 607 608 609 610 611 Position of the Galileo Code Start Time (ms) Galileo code start (chips)

200ms secondary code

6/13/2006 Stanford University JPALS Research 21

S/W Rcvr Verification: GPS P-Code Tracking – Simulated Data

• GPS pseudo-P-code signals, 10.23 Mchips/sec
• Signals have

sufficient BW to elucidate effects due to differential antenna gain and phase responses

– fS = 80 MHz – fIF = 20 MHz

500 1000 1500 2000

• 0.2

0.2 0.4 0.6 0.8 1 Navigation Data Message - PRN 6 Time (ms) Data source: Multi-Antenna Signal Simulator 500 1000 1500 2000 160 180 200 220 240 260 280 Doppler Frequency Time (ms) Doppler frequency (Hz) 500 1000 1500 2000 5444.35 5444.4 5444.45 5444.5 5444.55 Position of the P-Code Start Time (ms) P-code start (chips) 500 1000 1500 2000 30 35 40 45 50 55 60 Filtered C/No Time (ms) C/No (dB-Hz)

6/13/2006 Stanford University JPALS Research 22

S/W Rcvr Verification: CRPA Processing – Simulated Data

• 7-element CRPA with gradually decreasing C/No
• No special

receiver processing for low C/No

• Loss-of-lock

below C/No

• f ~25 dB-Hz

2000 4000 6000 8000

• 90
• 45

45 90 PLL Discriminator Time (ms) Phase offset (degrees) 2000 4000 6000 8000

• 500

500 DLL Discriminator Time (ms) Code offset (m) 1000 2000 3000 4000 5000 6000 7000 8000 9000 10 20 30 40 50 60 Filtered C/No Time (ms) C/No (dB-Hz)

FRPA CRPA Increasing noise power Loss-of-lock

6/13/2006 Stanford University JPALS Research 23

Navigation Errors due to Multi-Antenna Arrays

Common-mode: errors are shared by all signals on a particular antenna channel Non-common-mode: errors are a function of satellite # az/el-dependent

(also present for single-antenna GPS)

Do errors introduce a pseudorange or carrier-phase bias? What RFI or noise rejection performance is attainable?

Algorithm: errors may be introduced by the weight control algorithm itself

LO

Σ

Tracking Loops

PVT

code replica

IMU

attitude ephemeris

Weight Control Algorithm

tracking reference carrier replica

Front-end A/D I&Q Front-end A/D I&Q Front-end A/D I&Q Front-end A/D I&Q

LO

Σ

Tracking Loops

PVT

code replica

IMU

attitude ephemeris

Weight Control Algorithm

tracking reference

Σ

Tracking Loops

PVT

code replica

IMU

attitude ephemeris

Weight Control Algorithm

tracking reference carrier replica

Front-end A/D I&Q Front-end A/D I&Q Front-end A/D I&Q Front-end A/D I&Q Front-end A/D I&Q Front-end A/D I&Q Front-end A/D I&Q Front-end A/D I&Q

Hatke, 1998 Fante & Vaccaro, 2000 Gupta & Moore, 2001 Moore, 2002 Fante, et.al., 2004 McGraw, et.al., 2004 Hatke & Phuong, 2004 Kim, et.al., 2004 Kim, 2005

Pseudorange/Carrier-phase errors

6/13/2006 Stanford University JPALS Research 24

Methodology – Biases vs. RFI Rejection

• Develop adaptive algorithms that balance noise/RFI

rejection against pseudorange & carrier-phase errors – through constraints on weight adjustment

– End-to-end: from signal reception through the receiver tracking loops to the pseudorange and carrier phase estimates Goal: Through temporal & spatial constraints on a STAP algorithm, move down & left in the trade space, to a point where deterministic pseudorange & carrier phase corrections based on signal LOS can be applied.

6/13/2006 Stanford University JPALS Research 25

• 1.5
• 1
• 0.5

0.5 1 1.5 1 2 3 4 5 6 7 x 10

4

Code Offset (chips) Correlation Output PRN #1 PRN #2 PRN #3 PRN #4 PRN #5 PRN #6 PRN #7 PRN #8 PRN #9 PRN #10

200 400 600 800 1000

• 6
• 4
• 2

2 4 6 Time (ms) Carrier Phase Error (cm) Carrier Phase Estimates vs. Truth Values PRN 1 PRN 2 PRN 3 PRN 4 PRN 5 PRN 6 PRN 7 PRN 8 PRN 9 PRN 10 PRN 11

Preliminary Results: GPS P-Code w/ Antenna Distortion

• Simulated data and complete visibility of tracking output

allow comparison between predicted and true pseudorange and carrier phase values

Carrier phase biases Pseudorange bias – distortion

• f P-code correlation peak

Test satellite – zero bias

6/13/2006 Stanford University JPALS Research 26

35 40 45 50 55 60

• 6
• 4
• 2

2 4 6 C/No (dB-Hz) Carrier Phase Error (cm)

Carrier-phase Errors (cm)

35 40 45 50 55 60

• 5
• 4
• 3
• 2
• 1

1 C/No (dB-Hz) Code Phase Error (m)

Pseudorange Errors (m)

Preliminary Results: FRPA vs. CRPA Processing – no RFI

• Code/carrier errors are not

affected by deterministic array processing

• C/No enjoys healthy boost

under these conditions

200 400 600 800 1000 1200 1400 1600 1800 2000 35 40 45 50 55 60 Time (ms) C/No (dB-Hz) Filtered C/No PRN 1 PRN 2 PRN 3 PRN 4 PRN 5 PRN 6 PRN 7 PRN 8

FRPA CRPA

6/13/2006 Stanford University JPALS Research 27

Future Work – Exploring the Trade Space

1. Simulate signals with desired characteristics (C/No, J/S ratio, antenna distortion, etc.) 2. Track with Software Receiver (FRPA, CRPA, LMS, Applebaum processing) 3. Characterize C/No vs. pseudorange and carrier phase biases for various scenarios 4. Apply compensation schemes

Spatial Constraints Temporal Constraints Distortion C/No J/S level Applebaum LMS CRPA FRPA

6/13/2006 Stanford University JPALS Research 28

Conclusions

• Signal simulator captures parameters of interest

– Broadband RFI, antenna gain/phase variation based on detailed characterization models

• Software receiver supports adaptive

algorithms and estimation of pseudorange & carrier phase errors

• Methodology is yielding data about

tradeoffs between RFI rejection and code/carrier estimation errors

• Tools will support implementation

and testing of antenna compensation schemes

Backup

6/13/2006 Stanford University JPALS Research 30

5 10 15 20 25 30 35 40 Frequency (MHz) Power/frequency (dB/Hz) Power Spectral Density Estimate via Welch

1480 1500 1520 1540 1560 1580 1600 1620 1640 1660 1680 0.2 0.4 0.6 0.8 1 1.2 Frequency (MHz) Gain Antenna Gain Response for PRN #1 [Az = 0 deg, El = 40 deg] Antenna #1 Antenna #2 Antenna #3 Antenna #4 Antenna #5 Antenna #6 Antenna #7 Front-end BW ~40MHz 1450 1500 1550 1600 1650 1700

• 50

50 100 150 200 250 Frequency (MHz) Phase Antenna Phase Response for PRN #1 [Az = 0 deg, El = 40 deg] Antenna #1 Antenna #2 Antenna #3 Antenna #4 Antenna #5 Antenna #6 Antenna #7 Front-end BW ~40MHz 1480 1500 1520 1540 1560 1580 1600 1620 1640 1660 1680 0.2 0.4 0.6 0.8 1 1.2 Frequency (MHz) Gain Antenna Gain Response for PRN #8 [Az = 240 deg, El = 20 deg] Antenna #1 Antenna #2 Antenna #3 Antenna #4 Antenna #5 Antenna #6 Antenna #7 Front-end BW ~40MHz 1450 1500 1550 1600 1650 1700 80 100 120 140 160 180 200 220 240 260 280 Frequency (MHz) Phase Antenna Phase Response for PRN #8 [Az = 240 deg, El = 20 deg] Antenna #1 Antenna #2 Antenna #3 Antenna #4 Antenna #5 Antenna #6 Antenna #7 Front-end BW ~40MHz 1480 1500 1520 1540 1560 1580 1600 1620 1640 1660 1680 0.2 0.4 0.6 0.8 1 1.2 Frequency (MHz) Gain Antenna Gain Response for PRN #10 [Az = 300 deg, El = 80 deg] Antenna #1 Antenna #2 Antenna #3 Antenna #4 Antenna #5 Antenna #6 Antenna #7 Front-end BW ~40MHz 1450 1500 1550 1600 1650 1700

• 60
• 40
• 20

20 40 60 80 100 120 140 Frequency (MHz) Phase Antenna Phase Response for PRN #10 [Az = 300 deg, El = 80 deg] Antenna #1 Antenna #2 Antenna #3 Antenna #4 Antenna #5 Antenna #6 Antenna #7 Front-end BW ~40MHz

PRN #1 PRN #8 PRN #10

Antenna Distortion Effects (2)

• Fourier transform of complex

signal multiplied by antenna response characteristics

– Gain/phase data re-centered at IF

• Inverse Fourier transform

back to time domain

• Real-valued samples stored

to disk

• Gain/phase distortion data

available from HFSS simulation

– Verified by comparison to anechoic chamber testing – Data courtesy Ung-Suok Kim

6/13/2006 Stanford University JPALS Research 31

Wideband Jammer Signal Generation at IF

• For each jammer – six swept sinusoids cover

frequency band from ~0 Hz to ~fs/2

– Pseudo-random center frequencies – For fs = 80 MHz and fIF = 20 MHz, each wave covers 10 MHz

• Amplitude scaled as

needed to achieve desired J/S ratio

( )

( )

( )

[ ]

∑

Δ + + Δ + ′ + + ⋅

i J L J J IF J

t f f t t f t f f P

i i

1 2

2 2 cos 2 π π

5 10 15 20 25 30 35 40 Frequency (MHz) Power/frequency (dB/Hz) Power Spectral Density Estimate via Welch

6/13/2006 Stanford University JPALS Research 32

Spatial & Temporal D.O.F

• Spatial: geometry of gain pattern,

width (selectivity) of beams/nulls

• Temporal: spectral response of array,

nulling of wideband signals LMS Weight Adjust Circuit

Δ

w11

Δ

w21

s(t) r(t) - LMS reference

Σ

+ –

Σ

w12 w22

Σ

Tracking Loops

replica

ε Spatial Temporal

from Widrow & Stearns, Adaptive Signal Processing (1985)

6/13/2006 Stanford University JPALS Research 33

slave master

Sampling Clock

Synchronization Cables

PCI Bus IDE HD NovAtel SuperStar

Analog line

Host PC

Serial cable

NovAtel SuperStar

power/ground wires and buffer circuits left off for clarity

Interference Generator

4 Antennas 4 SuperStars 2 ICS-650 cards Common Clock

NovAtel SuperStar

GPS Display ICS-650 ICS-650

NovAtel SuperStar 10 MHz Clock

Analog line Analog line Analog line

ICS-650 12-bit A/D 5-65 MHz 2-channel SuperStar II Zarlink GP2015 4.309 MHz IF

4-Channel Test Hardware – Schematic

6/13/2006 Stanford University JPALS Research 34

Proposed 1st-gen Hardware Implementation

LO

Σ

Tracking Loops

PVT

code replica

Adaptive Weight Algorithm

LMS reference carrier replica

Front-end A/D I&Q Front-end A/D I&Q Front-end A/D I&Q Front-end A/D I&Q S/V-specific signal processing

LMS-based Adaptive Blind Beamforming

Multi-Element GPS ASIC

6/13/2006 Stanford University JPALS Research 35

Software Receiver Block Diagram

Weight Control Algorithm

Correlators

integrate & dump

Tracking Loops

Carrier NCO Code NCO

cos

C/No Estimator

Pseudorange & Carrier-phase Bias Estimator

carrier wipeoff code wipeoff

Early Prompt Late

FFT-based Coherent Acquisition

sin

Let’s focus on this block for a moment.

6/13/2006 Stanford University JPALS Research 36

Generic Adaptive Antenna Array

from Compton, Adaptive Antennas (1988)

Σ

Feedback Control Performance Index Array Output

Gain and Phase Adjustment

Maximize SINR at the array output (e.g., Applebaum, 1976; Frost, 1972) Minimize MSE between the actual array output and the ideal array output (e.g., Widrow, et. al., 1967) Optimization Criteria

• Using feedback

to optimize some performance index

6/13/2006 Stanford University JPALS Research 37

Σ

Tracking Loops

PVT

code replica

IMU

attitude ephemeris

Weight Control Algorithm

replicated signal carrier replica

Front-end A/D I&Q Front-end A/D I&Q Front-end A/D I&Q Front-end A/D I&Q

Adaptive Array Processing for GPS

covariance estimate

6/13/2006 Stanford University JPALS Research 38

Σ

Tracking Loops

PVT

code replica

IMU

attitude ephemeris

Weight Control Algorithm

replicated signal carrier replica

Front-end A/D I&Q Front-end A/D I&Q Front-end A/D I&Q Front-end A/D I&Q

Adaptive Array Processing for GPS

Deterministic CRPA: signal arrival and platform/array orientation Adaptive w/ maximum SINR, e.g. Applebaum: signal arrival, platform/array orientation, and SINR metric Adaptive w/ minimum MSE, e.g. Widrow LMS: ideal array output reference signal and SINR metric

covariance estimate

e.g., Hatke, 1998; Nicholson, et al., 1998; Fante & Vaccaro, 2000; Gupta & Moore, 2001;Hatke & Phuong, 2004; Fante, et al., 2004 e.g., Gecan & Zoltowski, 1995

6/13/2006 Stanford University JPALS Research 39

Σ

Tracking Loops

PVT

code replica

IMU

attitude ephemeris

Weight Control Algorithm

replicated signal carrier replica

Front-end A/D I&Q Front-end A/D I&Q Front-end A/D I&Q Front-end A/D I&Q

Adaptive Array Processing for GPS

But what happens when there are errors introduced by the hardware that are not completely mitigated by software or calibration?

Antenna phase-center and group delay effects Front-end filter and timing effects