Discrete vs' Continuous Carrier Tracking Loop Theory, Implementation, and Testing with Large BnT

1
Discrete vs. Continuous Carrier Tracking Loop
Theory, Implementation, and Testing with Large BnT

Giftet
Inc.

• Ilir F. Progri, Member ION, Giftet Inc., Pomona,
  CA
• Clifford W. Kelley, Open Source GPS, CA
• Guojiang Gao, University of Calgary, Canada
• William R. Michalson, Member ION, Worcester
  Polytechnic Institute, Worcester, MA
• Jinling Wang, Member ION, University of New South
  Wales, Australia
• John Lavrakas, President of ION, Advanced
  Research Corp., Newport, OR
• Present at
• ION-GNSS 2007, September 25-28, 2007
• Fort Worth, TX

2
Outline

Giftet
Inc.

• Introduction
• Motivation
• A classic GPS receiver
• Classic GPS L1 receiver tracking strategy
• Features of correlated GPS signals
• Design of classic GPS receiver code delay locked
  loop (DLL)
• Classic carrier tracking theory phase locked
  loop (PLL)

3
Outline Cont.

Giftet
Inc.

• PLL/FLL tracking errors for digital GPS receivers
• GP2021 carrier tracking theory and applications
  (current system under investigation)
• GP2021 channel baseband signal processing
• GP2021 discrete-time carrier and code tracking
  loop theory and applications
• GP2021 discrete-time carrier and code tracking
  loop implementation

4
Outline Cont.

Giftet
Inc.

• Test setup and results
• Test setup
• Ideal signal no noise and no clock errors
• Real GPS signal with noise and clock errors
• Summary and conclusions
• Future work

5
Introduction

Giftet
Inc.

• GPS receivers have been designed and developed
  employing classical control theory which is
  consistent with modern digital communication
  theory.
• Improved receiver performance based on modern
  digital control theory can positively influence
  the contemporary GPS receiver design.
• Nevertheless, the optimal estimator-based method
  still cannot completely meet the requirements for
  urban canyon and indoor navigation.

6
Motivation

Giftet
Inc.

• The majority of textbooks (e.g., Kaplan 1996)
  appear to provide an analog or continuous
  representation on the theory of carrier tracking
  loops. Important design parameters
• noise bandwidth (Bn)
• integration time (T)
• For BnT ltlt 1 the observed input/output
  relationship is good as predicted by the theory
• For BnT 1 the observed input/output relationship
  is bad. No prediction by the theory motivation

7
A Classic L1 GPS Receiver

Giftet
Inc.

• A classic L1 GPS Receiver includes
• Single RF/IF and analog section
• Digital software and receiver hardware section
• Classic GPS L1 receiver tracking strategy
• Display

8
Classic GPS L1 Receiver Tracking Strategy

Giftet
Inc.

• Costas PLL vs. Pull PLL
• FLL-Assisted PLL
• PLL-Assisted DLL
• Current system under investigation
• INS-Assisted DLL/PLL (i.e., INS/GPS ultra-tight
  integration)

9
Features of correlated GPS signals

Giftet
Inc.

• Incoming signal power A
• Navigation data bit D
• Code-delay misalignment
• Doppler error

10
Design of Classic GPS Receiver Code Delay Locked
Loop (DLL)

Giftet
Inc.
DLL tracking errors are investigated, and a set
of proper receiver parameters affecting signal
tracking is chosen in order to provide a high
sensitivity GPS receiver with an effective
tracking performance.
11
Design of Classic GPS Receiver Phase Locked Loop
(PLL)

Giftet
Inc.
Four typical PLL discriminators are given by
Discriminator corrections with respect to carrier
phase error.
In order to avoid the normalization under weak
signal tracking, the two-quadrant arctangent
discriminator D(4) is suggested as the PLL
discriminator of a receiver.
12
PLL/FLL Tracking Errors For Digital GPS Receivers

Giftet
Inc.

• The total PLL tracking error in a digital PLL can
  be summarized as follows (Gao 2007)
• The total FLL tracking error in a digital FLL can
  be written as follows (Gao 2007)
• To a large extent we have good predictions of the
  continuous tracking loop theory when the product
  BnT 0.1 or 0.2 as indicated in Equation (23)
• However, in general the continuous tracking loop
  theory remains silent for value of BnT 1 or
  some arbitrary values.

13
PLL Phase Tracking Errors with Different
Parameters

Giftet
Inc.
14
GP2021 Carrier Tracking Theory and Applications

Giftet
Inc.

• GP2021 channel baseband signal processing
• Provides the 1st half of the input and output
  relationship
• Provides the input and output test points
• GP2021 discrete-time carrier and code tracking
  loop theory and applications
• Provides the 2nd half of the input and output
  relationship
• We derive an analytical expression of BnT
  stability condition
• GP2021 discrete-time carrier and code tracking
  loop implementation
• We show an implementation example of the BnT
  stability condition for both carrier and code
  tracking loops

15
GP2021 Channel Baseband Processing

Giftet
Inc.
Input Test Points
Output Test Points
Cliff Kelly prepared the block diagram!
16
2nd Order Discrete-time Tracking Loops

Giftet
Inc.
Cliff Kelly prepared the block diagram!
17
BnT Stability Condition

Giftet
Inc.

• The system function H(z) and unit pulse response
  can be computed from
• Stability condition simply says
• For carrier tracking is
  stable
• For code tracking is stable

Z?1
18
Discrete-time Carrier and Code Tracking Loops

Giftet
Inc.
Cliff Kelly prepared the block diagram!
19
Test Setup and Results

Giftet
Inc.

• Test setup
• 42 combinations of BnT products all together
• 39 combinations of BnT 0.3. Carrier tracking is
  stable!
• 2 combinations of BnT 0.5. Carrier tracking is
  marginally stable!
• 1 combination of BnT 1. Carrier tracking is
  unstable!
• Ideal signal no noise and no clock errors
• Real GPS signal with noise and clock errors

20

Giftet
Inc.
Experimental Test Setup
Cliff Kelly prepared the experimental test
setup, conducted the experiments at his home in
CA, and provided the raw data!
21

Giftet
Inc.
GPS Creations Opensource GPS RF Board
22

Giftet
Inc.
GPS Creations Opensource GPS Boards
ISA Interface GPS 1000
PCI Interface GPS 1005
23

Giftet
Inc.
Based on SiGe SE4110L1C Chipset
2 bit A/D 16.3676 MHz Sample rate 4.1304 MHz IF
USB 2.0 Interface
24

Giftet
Inc.
GPS1A Software Receiver
Based on SiGe SE4110L1C Chipset
2 bit A/D 16.3676 MHz Sample rate 4.1304 MHz IF
USB 2.0 Interface
25
(No Transcript)
26
Ideal Signal No Noise And No Clock Errors

Giftet
Inc.
T 1 ms and Bn 1 Hz (No Noise, B 8 MHz, C2
0.0001 lt 1 Stable)
27
Ideal Signal No Noise And No Clock Errors

Giftet
Inc.
T 1 ms and Bn 1 Hz (No Noise, B 8 MHz, C2
0.0001 lt 1 Stable)
28
Ideal Signal No Noise And No Clock Errors

Giftet
Inc.
T 1 ms and Bn 1 Hz (No Noise, B 8 MHz, C2
0.0001 lt 1 Stable)
29
Ideal Signal No Noise And No Clock Errors

Giftet
Inc.
T 1 ms and Bn 1 Hz (No Noise, B 8 MHz, C2
0.0001 lt 1 Stable)
30
Ideal Signal No Noise And No Clock Errors

Giftet
Inc.
T 1 ms and Bn 1 Hz (No Noise, B 8 MHz, C2
0.0001 lt 1 Stable)
31
Ideal Signal No Noise And No Clock Errors

Giftet
Inc.
T 1 ms and Bn 1 Hz (No Noise, B 8 MHz, C2
0.0001 lt 1 Stable)
32
Ideal Signal No Noise And No Clock Errors

Giftet
Inc.
T 20 ms and Bn 50 Hz (No Noise, B 8 MHz,
C2 4.1814 gtgt 1 Unstable)
33
Ideal Signal No Noise And No Clock Errors

Giftet
Inc.
T 20 ms and Bn 50 Hz (No Noise, B 8 MHz,
C2 4.1814 gtgt 1 Unstable)
34
Ideal Signal No Noise And No Clock Errors

Giftet
Inc.
T 20 ms and Bn 50 Hz (No Noise, B 8 MHz,
C2 4.1814 gtgt 1 Unstable)
35
Ideal Signal No Noise And No Clock Errors

Giftet
Inc.
T 20 ms and Bn 50 Hz (No Noise, B 8 MHz,
C2 4.1814 gt 1 Unstable)
36
Real GPS Signal With Noise And Clock Errors

Giftet
Inc.
T 1 ms and Bn 1 Hz (With Noise, B 16 MHz,
C2 0.0001 lt 1 Stable)
37
Real GPS Signal With Noise And Clock Errors

Giftet
Inc.
T 1 ms and Bn 1 Hz (With Noise, B 16 MHz,
C2 0.0001 lt 1 Stable)
38
Real GPS Signal With Noise And Clock Errors

Giftet
Inc.
T 1 ms and Bn 1 Hz (With Noise, B 16 MHz,
C2 0.0001 lt 1 Stable)
39
Real GPS Signal With Noise And Clock Errors

Giftet
Inc.
T 1 ms and Bn 1 Hz (With Noise, B 16 MHz,
C2 0.0001 lt 1 Stable)
40
Real GPS Signal With Noise And Clock Errors

Giftet
Inc.
T 1 ms and Bn 1 Hz (With Noise, B 16 MHz,
C2 0.0001 lt 1 Stable)
41
Real GPS Signal With Noise And Clock Errors

Giftet
Inc.
T 1 ms and Bn 1 Hz (With Noise, B 16 MHz,
C2 0.0001 lt 1 Stable)
42
Real GPS Signal With Noise And Clock Errors

Giftet
Inc.
(T 10 ms, Bn 50 Hz) or (T 20 ms, Bn 25
Hz) (With Noise, B 16 MHz, C2 1.7 Marginally
Stable)
43
Real GPS Signal With Noise And Clock Errors

Giftet
Inc.
T 20 ms and Bn 50 Hz (With Noise, B 16 MHz,
C2 4.1814 gtgt 1 Unstable)
44
Summary and Conclusions

Giftet
Inc.

• When BnT is close to one, signal tracking loops
  in a digital receiver will become unstable (as
  proved by Ilir).
• Furthermore, even when BnT is much smaller than
  1, if the integration time T is very long, it is
  still possible that a digital receiver will crash
  in run
• the accumulated phase tracking errors induced by
  receiver dynamics and oscillator instability in
  one integration time interval may reach the
  tracking threshold (as proved by Gao 2007)

45
Summary and Conclusions Cont.

Giftet
Inc.

• In conclusion, for a digital GPS receiver, the
  expression for PLL/FLL tracking errors has to be
  modified.
• Our paper has shown two new expressions (i.e.
  Equations (28) and (29)) to calculate the total
  carrier/carrier phase tracking error in a digital
  GPS receiver. (Gao 2007)
• Furthermore, because signal tracking loops will
  be unstable, when BnT is above 0.34 (for PLL) or
  0.16 (for DLL), therefore, there is a condition
  which must be added on Equations (28) and (29)
  and this condition is
• 0 lt BnT lt 0.34 (for PLL, Progri Equation (49))
• 0 lt BnT lt 0.16 (for DLL, Progri Equation (49)).

46
Future work

Giftet
Inc.

• However, equation (49) provides an infinite
  number of combinations of the product BnT.
• Further more results with real data appear to
  indicate that for very small values of T there is
  a large variance associated with the phase noise.
• Come up with a closed form analytical expression
  that will provide the minimum accumulated carrier
  phase variance as a function of the BnT.