A Standalone Approach for Ultra-Tightly Coupled High ...

ITM 2014, Session B5, San Diego, CA, 27-29 January 2014 Page 1/14

A Standalone Approach for Ultra-Tightly

Coupled High Sensitivity GNSS Receiver

Tiantong Ren and Mark G. Petovello

Position, Location And Navigation (PLAN) Group

Department of Geomatics Engineering

Schulich School of Engineering

University of Calgary

Chaminda Basnayake

General Motors

Warren, MI USA

BIOGRAPHIES

Tiantong Ren is a Ph.D. candidate in the Position,

Location And Navigation (PLAN) group in the

Department of Geomatics Engineering at the University

of Calgary. In 2010 he completed a II Level Specializing

Master on Navigation and Related Applications in

Politecnico di Torino, Italy. In 2008 he completed a M.Sc.

on Electronic Engineering in Beihang University, China.

His research interest is GNSS signal processing and high-

sensitivity GNSS receiver design in signal challenged

environments.

Dr. Mark Petovello is a professor in the Position,

Location And Navigation (PLAN) group in the

Department of Geomatics Engineering at the University

of Calgary. He has been actively involved in the

navigation community for over 15 years and has received

several awards for his work. His current research focuses

on software-based GNSS receiver development and

integration of GNSS with a variety of other sensors.

Dr. Chaminda Basnayake is a Senior Research Engineer

at General Motors R&D and Planning where he is leading

the GNSS-based vehicle navigation technology R&D

efforts. His current research focuses on enabling

ubiquitous positioning capability in land vehicles and

using such capabilities in next generation automobile

systems including communications-enabled applications.

ABSTRACT

The tracking threshold in conventional scalar-based

GNSS receivers limits the performance of ML bit

decoding, which is paramount to ML based bit wipe-off.

In this paper, a standalone approach, that is, in the

absence of aiding information, is proposed for the ultra-

tightly coupled high sensitivity GNSS receiver. The

benefits are analyzed and determined of using ultra-

tightly coupled GNSS receiver in the standalone mode to

improve bit decoding and navigation solutions.

The results show the ultra-tight receiver is more robust

than the GNSS-only receivers. In the context of GPS L1

C/A signals, the field test results show ultra-tight receiver

can improve the successful decoding rate (SDR)

compared to scalar-based receiver. Compared to the

vector-based receiver, the ultra-tight receiver is more

immune to the high BER problem in extending coherent

integration time. The position and velocity accuracy of

the standalone ultra-tight receiver has been improved

more than 40% after extending coherent integration time

in the vehicular navigation test in urban canyon. A newly

proposed signal power based update observation selection

strategy has helped to mitigate multipath impacts.

INTRODUCTION

Global Navigation Satellite Systems (GNSS) such as the

Global Positioning System (GPS) can provide users with

accurate navigation and timing services worldwide. They

are vital for applications such as aircraft auto-piloting,

automobile en-route guidance, pedestrian positioning, etc.

Recently, processing weak GNSS signals has been

receiving growing attention because of the increased

demand for navigation in indoors, under dense foliage

canopies and in urban canyons.

High-sensitivity GNSS receivers are capable of providing

satellite measurements for signals attenuated by up to

about 30 dB (Media Tek 2012, Fastrax 2012 and u-blox

2011). For high-sensitivity GNSS receivers, extending

integration time coherently is optimal for obtaining higher

sensitivity, mitigating multipath and cross-correlation

false locks, and avoiding squaring loss. However, longer

coherent integration time is primarily limited by the


navigation message data bit, if present. For coherent

integration beyond the data bit period, navigation data bit

wipe-off is required to avoid energy loss that occurs due

to bit transitions. Furthermore, complete bit wipe-off

requires the knowledge of bit boundaries and bit values.

The process of determining the location of the bit

boundaries and extracting the bit values is herein called

bit synchronization and bit decoding respectively. Bit

synchronization only needs to be achieved once at the

beginning of data processing. However bit wipe-off

requires bit values to be decoded continuously. This paper

focuses on the bit decoding analysis, and bit

synchronization algorithms can be referred to Ren et al

(2012).

By using the navigation data bit aiding and frequency

aiding from an external source, Akos et al (2000) showed

that during acquisition, signals with carrier to noise-

density ratios (C/N0) of 32, 22, 17, and 12 dB-Hz can be

detected if the coherent integration time is at least 8, 200,

400, and 800 ms respectively. Similarly Van Diggelen &

Abraham (2001), Djuknic & Richton (2001) and Di

Esposti (2007) used aiding information from wireless

network broadcasting to improve sensitivity. However, all

of these methods need access to external aiding sources,

and the receiver will correspondingly lose its autonomy

which may not be possible or desirable in all applications.

For extracting the bit values without an external aiding

source, Maximum-Likelihood (ML) algorithms (i.e., ML

bit decoding) introduced in Soloviev et al (2009), have

been shown to outperform other algorithms for weak

GNSS signals. However, the performance of ML bit

decoding relies heavily on the signal tracking

performance (i.e., tracking threshold). Gleason & Gebre-

Egziabher (2009) mentioned that a Costas phase-locked

loop (PLL) had difficulties following the signal at about

35 dB-Hz, below which the process of bit decoding

cannot be performed. In Ren et al (2013), the performance

of ML bit decoding algorithm was shown to be improved

by using a vector-based GNSS receiver. This paper looks

at whether the performance of ML bit decoding and,

subsequently, bit wipe-off, can be further improved in an

ultra-tightly coupled GNSS receiver.

An ultra-tightly coupled GNSS receiver is a system that

integrates GNSS measurements with inertial and/or other

sensor outputs, and uses the integrated estimate of

position and velocity to update the GNSS channel

estimates of the Doppler frequency and code phase.

Generally, compared to a GNSS-only solution, the

advantages of integrating GNSS and inertial sensors

include improved accuracy, smoother trajectories,

availability of an attitude solution, reduced susceptibility

to interference and increased sensitivity (Soloviev et al

2004, Petovello & Lachapelle 2006, and Petovello et al

2008). Specifically, Soloviev et al (2004) demonstrated

the reacquisition and continuous carrier phase tracking of

15 dB-Hz GPS signals in flight test with simulated noise;

Petovello & Lachapelle (2006) showed an ultra-tightly

coupled GPS and inertial navigation system (INS)

architecture is able to track the carrier phase under foliage

up to an attenuation of about 15 dB and still maintains a

velocity solution accurate to a few centimeters per

second. Petovello et al (2008) demonstrated that the ultra-

tight receiver provided about 7 dB of sensitivity

improvement over the standard receivers.

INS has two prevalent dead reckoning (DR) models,

namely the traditional INS mechanizations (e.g., Soloviev

et al 2004, Petovello & Lachapelle 2006, and Petovello et

al 2008), and the vehicle sensor based DR algorithm (e.g., Fouque et al 2008, and Li 2012). The former approach

obtains velocities by integrating accelerometer outputs,

and position increments by integrating the velocities. The

latter DR algorithm – usually used in land vehicle

navigation – directly uses wheel speed sensor information

to obtain the vehicle’s velocity. The main benefit of DR

algorithm over the traditional INS mechanization is the

accuracy of DR algorithm degrades with the travelled

distance rather than with time. All the algorithms

implemented in this paper are based the ultra-tightly

coupled system of GNSS and DR algorithm. Although

different models of vehicles may be equipped with

different vehicle sensor setups, the ultra-tightly coupled

system in this work employs a general configuration,

which contains four wheel speed sensors (two in front and

two in rear), a steering angle sensor, a longitudinal

accelerometer and a vertical gyroscope (i.e., yaw rate

sensor) (WSS/SAS/1A1G). This is a reduced order low-

cost Micro Electro-Mechanical Systems (MEMS)-based

inertial measurement unit (IMU) (1A1G) with WSS and

SAS.

The objective of this paper is to determine the benefits of

using an ultra-tightly coupled GNSS receiver in

standalone mode to improve bit decoding. Furthermore,

the paper uses the estimated data bits to extend coherent

integration using bit wipe-off and then assesses the

accuracy of the resulting navigation solution, and finally

determines the feasibility of the standalone approach.

The contributions of this paper are threefold. First, it

assesses the performance of ML bit decoding in the ultra-

tight system. Second, it assesses the navigation

performance with extended coherent integration time after

bit wipe-off. Third, it gives a strategy for mitigating

multipath impacts in a software-based ultra-tightly

coupled GNSS receiver in signal challenged

environments.

The paper begins by describing the ML bit decoding

algorithm and the vehicle sensor configuration. Next the

ultra-tight system and different architectures of GNSS


receivers used in this paper are introduced. Then a signal

power based strategy is provided for mitigating multipath

impacts. Later the field test performed in this work is

described. Finally the test results are presented and

analyzed.

In the context of this work, the performance of bit

decoding is assessed in terms of the successful decoding

rate (SDR) of bit values. The proposed algorithms are

derived for a generic binary phase shift keying (BPSK)

GNSS signal, but are assessed using GPS L1 C/A signals

only.

SIGNAL AND SYSTEM MODEL

This section gives a brief overview of the ML bit

decoding algorithm used in this paper.

Signal Model

The GNSS signal transmitted through an additive white

Gaussian noise (AWGN) channel and received at the

antenna of a GNSS receiver in the radio frequency (RF)

band is represented by

,

1

( ) ( ) ( )svN

RF RF i RF

i

y t r t n t

(1)

Specifically, it is the sum of svN line-of-sight (LOS)

signals (, ( )RF ir t ) from svN satellites in view, plus a noise

term ( )RFn t . In general, the Signal in Space (SIS) at the

input of a GNSS receiver from the thi satellite has the

following structure

,

, ,

( ) ( ) ( )

cos 2

RF i i i i i i

RF d i RF i

r t Ab t c t

f f t

(2)

where iA is the amplitude of the signal; ( )i ib t is the

navigation message where each binary unit is called a bit;

( )i ic t is the ranging code; i is the time delay

introduced by the transmission channel; RFf is the GNSS

carrier frequency; ,d if is the Doppler frequency shift and

,RF i is the initial carrier phase offset.

After being down-converted in the receiver’s front-end,

signals from different satellites are approximately

orthogonal so that the i subscript can be dropped and

each signal can be written separately as

( ) ( ) ( )

( ) ( )cos 2 ( )IF d

y t r t n t

Ab t c t f f t n t

(3)

where IFf is the nominal intermediate frequency (IF) of

the down-converted signal.

At this stage, the purpose of a GNSS receiver is to

estimate and df , thus allowing for the determination

of the pseudorange and pseudorange range to each

satellite, which is then used to calculate the receiver’s

position, velocity and time (PVT) parameters. To

accomplish this, each and df is estimated from a cross

ambiguity function (CAF), which is the cross-correlation

between the received signal and the locally generated

signal, and is given by

0

0

( , ) ( ) ( )

( ) ( )cos 2

b

b

T

d

t

T

IF d

t

R f y t r t

y t c t f f t

(4)

where ( )r t is the locally generated signal; , df and

are the corresponding locally-generated signal parameters

used to generate ( )r t ; bT is the data bit period, which is

herein assumed to equal the coherent integration time for

cross-correlation. The coherent integration should

accumulate between bit boundaries. Usually bit boundary

locations are detected by a bit synchronization process,

and herein the bit synchronization is assumed to have

been correctly completed. The form of ( , )dR f can be

different if using non-coherent integration though it is not

addressed in this paper. Finally, the ML estimate of

and df is given by

,

ˆˆ, arg max ( , )d

d df

f R f

(5)

Bit sign transition affects the CAF evaluation especially

when the coherent integration time is longer than the bit

period ( bT ). In particular, bit sign transitions modify the

shape of the CAF envelope and may divide the central

peak of CAF in frequency domain into two split side

lobes (Sun & Lo Presti 2010; Jeon et al 2011).

ML Bit Decoding Algorithm

As input, the ML bit decoding algorithm uses several

cross-correlation outputs, each computed using a coherent

integration time equal to the data bit period. After

obtaining the ML estimate of and df , the locally

generated signal and relative parameters can be

represented as ˆ( ) ( )r t r t , ˆ and ˆd df f . If there is

an error in and ˆdf compared to incoming values, i.e.,


and ˆd d df f f , the thk cross-correlation

output of bT is given by

( 1)

, ,

,

ˆˆ ˆ( , ) ( ) ( )

( )sinc( )

exp 2

b

b

kT

k d

t k T

R k C k d b

d b I Q

R f y t r t

A R f T

j f kT n

(6)

which is the cross-correlation output from the signal

period of ( 1) bk T to bkT . Since the right hand side of the

above equation is only a function of and df , we

adopt the following shorthand notation to make this more

explicit

ˆˆ( , ) ( , ) ( , )k d k d kR f R f f R f (7)

,R kA is the amplitude of the cross-correlation output;

, ( )C kR is the normalized ranging code correlation

function with the code phase error of , which results

in a triangle shape attenuation in the cross-correlation

amplitude; df is the Doppler frequency error, which

results in a sinc-shaped attenuation in the cross-correlation amplitude and a rotating carrier phase, and;

is the initial carrier phase error.

Bit decoding is the process of determining data bit values

modulated on carrier. The likelihood function used in the

ML bit decoding algorithm is the inner product between a

cross-correlation output vector starting from a bit

boundary (so as to avoid integrating over a boundary) and

locally generated bit combinations. The cross-correlation

output vector with N bits is given by

1 2

( , )

( , ), ( , ),..., ( , )

d

d d N d

f

R f R f R f

NR (8)

If trying to decode N bits at a time, the number of

possible bit combinations is equal to 12N, and the correct

bit combination is supposed to have the maximum energy.

It is noted that the energy based ML bit decoding method

detects the bit transitions, not the actual bit values (i.e.,

there is a sign ambiguity), but this is sufficient for bit

wipe-off in order to extend coherent integration time.

The bit value combination matrix B ( 12N N ) is defined

as

1 1 ... 1

1 1 ... 1

... ... ... ...

1 1 ... 1

B (9)

For an N bit sequence, the inner product between

( , )df NR and the vector mb from the -thm row of B

is given by

1( , ) ( , ) ( 1,2,...2 )N

m d dI f f m N mR b (10)

The ML estimate of bit values can be found by

maximizing the energy of the inner product.

Mathematically, this is given as

2

[ 1,..., 1]

ˆ arg max , ;m dI f

m

mb

b b (11)

Vehicle Sensor Configuration

The DR algorithm uses the vehicle sensors’ output as

measurements to update the system rather than the

mechanization approach used in conventional INS. As

mentioned before, the ultra-tightly coupled system in this

paper employs four wheel speed sensors, a steering angle

sensor, a longitudinal accelerometer and a vertical

gyroscope (WSS/SAS/1A1G). This setup is similar to the

one used in Li (2012) and the system model is given by

0

0

0

n n

b b

y y

b bay y

Ay y

GG G

Ss s

V V

wa a

w

w

w

wb b

wd d

w

W

r r

F

S S

(12)

where nr is the position error vector in navigation frame

(i.e., local level frame or East-North-Up (ENU) frame); b

yV is the longitudinal velocity error in body frame; b

ya

is the longitudinal acceleration error in body frame,

modeled as random walk with the driving noise aw ;

is the pitch error, modeled as first order Gauss-Markov

process with the driving noise w ; is the azimuth

error; is the yaw rate error, modeled as random walk


with the driving noise w ; S is the scale factor error

vector of wheel speed sensors, modeled as first order

Gauss-Markov process with the driving noise wW ; yb is

the longitudinal accelerometer bias, modeled as first order

Gauss-Markov process with the driving noise Aw ; Gd is

the gyroscope drift, modeled as first order Gauss-Markov

process with the driving noise Gw ; and s is the

steering angle error, modeled as first order Gauss-Markov

process with the driving noise Sw . Besides, F is the

dynamics matrix and given by

1 2 3

2

0 0 0 0 0 0 0

0 0 1 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

sin 10 0 0 0 0 0 0 0

coscos

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

W

A

G

S

R R R

F

(13)

where x (e.g., when x represents ) is the

reciprocal of the time constant in each first order Gauss-

Markov process. In addition, 1R , 2R and 3R are the

columns of the fractional dynamics matrix R , and the

fractional system model relevant to nr is given by

3 2

sin cos cos cos sin sin

cos cos sin cos cos sin

sin 0 cos

E

n

N

U

b

y

b

y

b b b

y y y

b b

y y

b

y

r

r

r

V

V

V V V

V V

V

1

r

R

R R R

(14)

GNSS RECEIVERS AND THE STANDALONE

APPROACH

The above algorithms have been assessed in a software-

based GNSS receiver platform called GSNRxTM

, which is

developed in C++ by the PLAN Group at the University

of Calgary. This section describes the different versions

of the software used for processing.

There are three GNSS receiver architectures used in this

work. The first, shown in Figure 1, is the standard (i.e.,

scalar-based) GNSS receiver, which contains independent

local tracking loops/channels dedicated to providing

independent pseudorange and/or pseudorange rate

measurements for PVT calculations.

Figure 1 - Architecture of a standard GNSS receiver

The second architecture is shown in Figure 2 and is a

vector-based high-sensitivity GNSS receiver called

GSNRx-hs™. The difference between a scalar-based

GNSS receiver and a vector-based GNSS receiver is that

the latter sets the numerically controlled oscillators

(NCOs) – inside the local signal generator – from

navigation filter outputs rather than from local channel

filter outputs. A vector-based GNSS receiver requires

knowledge about ephemeris data when updating the

channel parameters. To this end, long term ephemeris

(e.g., Garrison and Eichel 2006) could be used in order to

remain consistent with the motivation of maintaining as

much independence of the receiver as possible from

external data sources. In addition, the GSNRx-hsTM

contains an open-loop tracking structure, which can avoid

the stability problem (Ward et al 2006) caused by long

coherent integration in normal closed-loop tracking. This

is preferred for building the correlator output

measurements with long coherent integration. The

detailed benefits of open-loop tracking can be found in

van Graas et al (2005). This architecture omits the carrier

tracking because it is usually vulnerable in signal

challenged environments.


Figure 2 - Architecture of a conventional GSNRx-hs

TM

receiver with external bit aiding

The third architecture shown in Figure 3 is an ultra-tightly

coupled high sensitivity GNSS receiver, called GSNRx-

hs-dr™. Except for the integrated vehicle sensors and DR

based navigation filter, the GNSS receiver part is similar

to GSNRx-hsTM

. However, the receiver was also modified

for this work to uses ML bit decoding to extend

integration time, as shown in Figure 4. This modified

version can be considered as a standalone ultra-tightly

coupled high-sensitivity GNSS receiver.

Figure 3 - Architecture of a conventional GSNRx-hs-

drTM

receiver with external bit aiding

Figure 4 - Architecture of a new GSNRx-hs-drTM

receiver with ML bit decoding

POWER-BASED OBSERVATION SELECTION

STRATEGY FOR MITIGATING MULTIPATH

In the urban canyon environment, due to massive

reflecting surfaces from buildings and skyscrapers,

multipath can be considered as the most destructive error

source. In order to mitigate multipath impacts, this work

proposes a signal power – as determined by the carrier to

noise-density (C/N0) – based observation selection

strategy for selecting suitable GNSS pseudorange and

Doppler measurements in the navigation filer.

A signal power threshold can be used to mitigate

multipath. From Xie (2013), reflected signal rarely

exceeds 42 dB-Hz in such environments. As such, if a

satellite’s C/N0 is higher than this, all of its measurements

are used. Otherwise, only the Doppler measurement is

used. Although signal power threshold chosen here is 42

dB-Hz, it would ideally be an environment-dependent

value.

The reason for only using Doppler measurement in a LOS

and non-line-of-sight (NLOS) mixed signal channel is

twofold. First, the correct Doppler measurement can be

extracted in the open-loop tracking if the LOS signal and

the NLOS signals can be separated in frequency domain

(Xie & Petovello 2011); the Doppler error caused by

NLOS signal is limited if the LOS signal cannot be

separated from NLOS signals. In other words, the

Doppler bias from NLOS signals should be small -

especially with extended coherent integration time - if

LOS signal and NLOS signals are overlapped in

frequency domain. Second, the vehicle sensors can

correct the system velocity with a higher update rate if the

Doppler update (i.e., velocity update) from GNSS signals

is incorrect. However, in this case, there is no direct

position update from vehicle sensors or DR algorithm,

and any error in position will remain until the next

accurate GNSS update. In other words, the ultra-tight

receiver is more vulnerable to pseudorange errors than

Doppler errors.

This work will assess the performance of this strategy in

the ultra-tight coupled high-sensitivity receiver in urban

canyon test. This method relies on C/N0 estimate

algorithms, and in this work, the C/N0 estimation was

implemented by separately calculating the signal power

and noise power spectral density and then computing their

ratio. The open-loop tracking that can distinguish a LOS

signal and NLOS signals in frequency domain also

mitigates the multipath fading in C/N0 estimation.

A potential problem that needs to be considered is if the

signal power is low, the bit error rate (BER, which equals


to “1 - SDR”) of ML bit decoding will increase when

extending integration time. Specifically, bit wipe-off with

non-zero BER will attenuate the power of correlator

outputs, and a high BER may split the peak in the

frequency domain. Ren et al (2013) has proposed two

methods that select suitable correlator outputs for input

into the ML bit decoding algorithm. The methods have

been shown effective for a GNSS only solution in the

signal challenged dense foliage environment. This work

will assess the necessity of such methods for an ultra-tight

coupled high-sensitivity receiver in the urban canyon test.

TEST DESCRIPTION

First, Monte Carlo simulations based on the signal model

in (6) with 10,000 trials are performed to generate the

ideal results for comparison. The Monte Carlo simulations

assume no tracking errors in the correlator outputs (i.e.,

0, 0df ), and that the bit transition happens with

a probability equals 50%. The Monte Carlo simulation

results are treated as the upper bound of ML bit decoding.

Second, in order to assess the performance of ML bit

decoding in the ultra-tight receiver in real environments, a

vehicular field test was used. In this case, only the GPS

L1 C/A code signal was processed.

The vehicular field test was conducted in a signal

challenged environment, namely in urban canyon in the

downtown of Calgary. An overlooking view of Calgary

downtown is shown in Figure 5 and images captured

along the test trajectory are shown in Figure 6. As can be

seen, there are portions of the test where sky visibility is

highly restricted. The ultra-tightly coupled GSNRx-hs-

drTM

, the vector-based GSNRx-hsTM

and the scalar-based

GSNRxTM

were used for processing the field data. The

C/N0 values estimated by GSNRx-hs-drTM

of all satellites

in view in the urban canyon test are shown in Figure 7.

As shown, the signal power values fluctuate markedly (a

cumulative histogram is also shown in Figure 12). Some

attenuations of C/N0 are higher than 25 dB.

In order to compute SDR values, reference data bits (i.e.,

the true data bits) are obtained from an antenna located on

the roof of the CCIT building at the University of

Calgary, such that the BER of signals is negligible (C/N0

of around 45 dB-Hz).

Figure 5 - Calgary downtown area in an overlooking

view (A panoramic shot of downtown Calgary from

the Calgary Tower, Architecture Calgary, Foundation

3D Forums, Web. 1 Mar 2012

<http://www.foundation3d.com/forums/showthread.ph

p?p=222872 >)

Figure 6 – Urban canyon environment in the field test


Figure 7 - C/N0 of all satellites in view in the urban

canyon test estimated by GSNRx-hs-drTM

A reference system consisting of a NovAtel SPAN SE™

unit (which contains a NovAtel OEMV receiver and an

LCI tactical-grade inertial measurement unit (IMU)) was

used to provide the reference trajectory. The estimated 1

accuracy of the reference system (per axis) is 0.2 m for

position and 0.02 m/s for velocity. The land vehicle with a

NovAtel GPS-702-GG antenna and a LCI IMU on top

and a National Instruments PXI-5600 front-end inside is

shown in Figure 8.

Figure 8 - The land vehicle with navigation systems for

field data collection. The upper-left picture shows a

NovAtel GPS-702-GG antenna and a LCI IMU on top

of the vehicle. The upper-right picture shows a

National Instruments PXI-5600 front-end inside the

vehicle. The lower picture shows the land vehicle.

In both tests, the IF data were collected using a National

Instruments PXI-5600 front-end which includes an oven

controlled crystal oscillator (OCXO). The front-end

parameters are shown in Table 1. The front-end has a 16

bit quantization level, although for the data collected

typically only 3-4 bits are necessary (i.e., are non-zero).

The data were processed by and all algorithms were

implemented in the GSNRxTM

software receiver suites as

introduced earlier.

Table 1 - Front-end parameters used for collecting

GNSS data in dense foliage test

Parameter Value (MHz)

Intermediate Frequency 0.42

Sampling Rate (I/Q) 10.0

Bandwidth 5.0

The built-in vehicle sensors – including wheel speed

sensors, inertial sensors and steering angle sensors –

originally equipped in the vehicle to improve the safety

and operational stability, are used in this work to build the

DR system. Wheel speed sensors are used as a low cost

solution to measure vehicle’s speed. A steering angle

sensor is used to measure the wheel turning angle with

respect to the neutral position (Li 2012). With the steering

angle sensor, the front wheel speed sensors can provide

the in-track velocity and yaw rate estimation. The built-in

reduced MEMS IMUs including a longitudinal

accelerometer and a vertical gyroscope (1A1G) are used

to measure acceleration and angular velocity. The in-run

variability of the gyroscope is 113 deg/hr and the angular

random walk is 1044 deg/hr/ Hz .

RESULTS AND ANALYSIS

The analysis proceeds in three steps; first the bit decoding

is assessed; second, receiver performance is evaluated

using known data bits; and, the analysis is repeated using

data bits obtained from the bit decoding process within

the receiver.

Bit Decoding Performance in Ultra-Tight Receiver

First of all, a comparison of estimated C/N0 from the

scalar-based receiver and the ultra-tight receiver is shown

in Figure 9. PRN 25 is selected for comparison purpose

but the results are typical for other satellites. It is noticed

that the signal can be tracked in the ultra-tight receiver

although the signal power is quite low (between about 10

and 30 dB-Hz). In scalar-based receiver, however, during

more than half of time the signal is not tracked (indicated

by a C/N0 value equal to zero).


Figure 9 - C/N0 of PRN 25 in scalar-based receiver and

ultra-tight receiver in the urban canyon test

The SDRs of ML bit decoding as a function of signal

strength in the scalar-based receiver and the ultra-tight

receiver are shown in Figure 10. The number of bits to be

decoded here is two (i.e., N = 2), which is the optimal

number for tolerating Doppler errors (Ren et al 2012). For

every 40 ms of data (approximately from hundreds to ten

thousands samples in all), the bits were decoded and

compared to the known data bits; the SDR is then the

percentage of time the decoding was correct. The

statistics of bit decoding as a function of C/N0 are

calculated using bins with a width of ±2.5 dB.

Compared to the results in the scalar-based receiver, a

marked performance improvement of ML bit decoding in

the ultra-tight receiver is noticed. This shows the benefits

of the ultra-tight receiver for ML bit decoding, which

improves the SDR by 1% – 30% depending on the signal

strength. Compared with the Monte Carlo results, the

difference in SDR between the ultra-tight receiver and

Monte Carlo simulations is due to the non-white noise

factor present in field tests, e.g., due to multipath, as well

as the inherent tracking errors that are present within the

receiver.

Figure 10 - Performance of ML bit decoding as a

function of signal strength in scalar-based receiver

and ultra-tight receiver in the urban canyon test

Figure 11 shows the SDR from each satellite during the

entire field test. Compared to scalar tracking, the

improvement of the SDR resulting from the ultra-tight

receiver ranges from 2% to 30%. Figure 12 shows the

cumulative C/N0 plots of all satellites in the urban canyon

test, and, when cross-referenced against Figure 11 it is

noted that ultra-tight receiver improves the ML bit

decoding of weak signals more significantly.

An interesting phenomenon can also be viewed in Figure

11. Specifically, compared to the vector-based receiver,

the SDR from the ultra-tight receiver only has a slight

improvement. This suggests in the urban canyon test the

SDR cannot be further improved if the signal is blocked

by skyscrapers, even if the navigation solution has been

improved in the ultra-tight receiver. The results of the

navigation solution will be discussed later.

Figure 11 - Performance of ML bit decoding in scalar-

based receiver, vector-based receiver and ultra-tight

receiver in the urban canyon test


Figure 12 - Cumulative C/N0 plots of all satellites in

the urban canyon test

The SDR results in Figure 11 were obtained by setting the

open-loop search space uncertainty as 40 meters (for

pseudorange errors) by 10 Hz (for Doppler errors). This is

an empirical setting, and preferred when processing

GNSS signals in signal challenged environments. Figure

13 shows the SDR resulting from the ultra-tight receiver

with different search space sizes. The result shows that

the SDR has no obvious change with different search

space settings. This confirms the former conclusion that

the SDR cannot be further improved if the signal is

blocked.

Figure 13 - Performance of ML bit decoding with

different search space in ultra-tight receiver in the

urban canyon test

Navigation Results in Ultra-Tight Receiver with

External Bit Aiding

After estimating the data bits, bit wipe-off can be

performed in order to extend the coherent integration

time. However, before evaluating performance of such an

approach, the performance of DR only solution, GNSS

only solution and ultra-tightly coupled system are

assessed first.

The trajectory of DR only and the GNSS-only vector-

based solution are compared to the reference trajectory in

Figure 14. The coherent integration time in the vector-

based receiver is 100 ms using the external bit aiding

method (i.e., perfect bit information). The external bit

aiding method contains no bit errors, so it is expected that

it gives the best results. The trajectory of DR only

solution (green line in Figure 14) looks smooth but has

the accumulated position errors; the GNSS only solution

(red line in Figure 14) has no accumulated bias but is

noisy due to signal blockage and heavy multipath in the

urban canyon.

Figure 14 - Trajectory results of vector-based receiver

and DR only solution in the urban canyon test. The

blue line is the reference trajectory; the red line is the

result from vector-based receiver; and the green line is

the result of DR only solution. The coherent

integration time is 100 ms by external bit aiding.

The red line in Figure 15 shows trajectory result of the

ultra-tight receiver by using all pseudorange and Doppler

measurements. By ultra-tightly integrating the vehicle

sensors with the vector-based GNSS receiver, the

navigation solution has no obvious bias and is less noisy

than the GNSS-only solution. In addition, the “spike” in

the yellow circle in Figure 14 has disappeared. However,

in some area, large position errors are observable due to

multipath. So it is necessary to use the signal power based

observation selection strategy for mitigating multipath

impacts. The green line in Figure 15 shows the trajectory

result of the ultra-tight receiver by using this strategy, and

it is clear that a more accurate and smoother trajectory is

obtained.

Figure 15 - Trajectory results of ultra-tight receiver in

the urban canyon test. The blue line is the reference


trajectory; the red line is the result using all

measurements; and the green line is the result using

all measurements if C/N0 is larger than 42 dB-Hz,

otherwise using Doppler measurements only. The

coherent integration time is 100 ms by external bit

aiding.

Table 2 shows the statistics of the solutions shown above.

It is noted that the ultra-tight receiver with the signal

power based observation selection strategy outperforms

the other systems or settings. As such, the results from the

ultra-tight receiver that follow are based on this approach.

Table 2 – RMS position and velocity errors in DR only

solution, vector-based receiver, ultra-tight receiver

and ultra-tight receiver with new update strategy. The

coherent integration time is 100 ms by external bit

aiding.

RMS Position Error [m]

System North East Up

Vector-Based Receiver 14.3 6.4 64.9

DR Only 96.1 30.7 6.6

Ultra-Tight Receiver 12.3 3 46

Ultra-Tight Receiver with

the Signal Power Based

Observation Selection

Strategy

4 1.3 9.5

RMS Velocity Error [m/s]

System North East Up

Vector-Based Receiver 0.42 0.23 0.36

DR Only 0.59 0.16 0.05

Ultra-Tight Receiver 0.13 0.07 0.11

Ultra-Tight Receiver with

the Signal Power Based

Observation Selection

Strategy

0.11 0.08 0.09

Navigation Results in Ultra-Tight Receiver with ML

Bit Decoding

After assessing the performance of different systems with

external bit aiding, the role of ML based bit wipe-off

method and extended coherent integration time is

evaluated.

To begin, the navigation results from the vector-based

receiver are included in Figure 16 when bit decoding is

used to extend the coherent integration; this will later be

compared to the results using ultra-tight integration. Note

that the signal power based observation selection strategy

was not used in the vector-based receiver because the

reduction in the number of observations caused by the

strategy results in poor navigation performance. Results

show that the position solution with 100 ms of integration

no obvious improvement compared to the 20 ms (i.e., no

bit wipe-off needed) result in horizontal direction, and is

actually worse in vertical direction. This phenomenon is

due to errors in bit decoding and thus bit wipe-off, as

mentioned before.

It is noted that although methods of selecting suitable

correlator outputs for input into the ML bit decoding

algorithm (e.g., Ren et al, 2013) can mitigate the high

BER problem in the vector-based receiver, such

approaches were not used here. The reason is because the

results with external bit aiding shown in Table 2 represent

the best case scenario and these results are already far

worse than those of the ultra-tight receiver.

Figure 16 - RMS position and velocity errors in

different directions by using ML bit decoding based

bit wipe-off from vector-based receiver in the urban

canyon test

In the ultra-tight receiver, Figure 17 shows the

comparison of navigation results (position and velocity)

using coherent integration times of 20 ms, 100 ms using

external bit aiding (i.e., known bits) and 100 ms using bit

wipe-off from ML bit decoding. The position and velocity

accuracy has been markedly improved (more than 40%)

after extending coherent integration time from 20 ms to

100 ms in this case. Furthermore, as shown in Figure 17,

in the ultra-tight receiver, without any method of dealing

with the high BER problem, the navigation results with

100 ms from ML bit decoding are markedly better than

the 20 ms results, and very close to the 100 ms results

using external bit aiding. This implies that ultra-tight

receivers are more immune to the high BER problem, and

are thus better able to extend coherent integration time

compared to the vector-based receiver. In the ultra-tight

receiver with 100 ms from ML bit decoding, the RMS

position error in horizontal and vertical is less than 5 m


and 10 m respectively, and the RMS velocity error in

horizontal and vertical is both less than 0.2 m/s.

Figure 17 - RMS position and velocity errors in

different directions by using ML bit decoding based

bit wipe-off from ultra-tight receiver in the urban

canyon test

Finally, the trajectory results from the standalone ultra-

tight GSNRx-hs-drTM

software receiver are shown in

Figure 18. With the coherent integration time of 100 ms

from ML bit decoding, the navigation solution is very

close to the reference trajectory in the urban canyon test.

Figure 18 – Trajectory results of standalone ultra-

tight receiver using the coherent integration time of

100 ms from ML bit decoding in the urban canyon

test. The blue line is the reference trajectory; the red

line is the result from standalone ultra-tight receiver.

CONCLUSIONS AND FUTURE WORK

This paper assesses the performance of ML bit decoding

in an ultra-tightly coupled GNSS receiver, presents an

analysis of the navigation performance with extended

coherent integration time after bit wipe-off, and gives an

update strategy for selecting the pseudorange and/or

Doppler measurements in a standalone software-based

ultra-tight GNSS receiver in weak signal environments.

The SDR of ML bit decoding in an ultra-tight receiver is

assessed as a function of received signal power. In the

context of GPS L1 C/A signals, the field test results show

that an ultra-tight receiver can improve the SDR by 1% –

30% over scalar-based receiver depending on the signal

strength. The ultra-tight receiver is also shown to be more

robust than the vector-based receiver, that it is more

immune to the high BER problem and does not require

any correlator outputs selection method in extending

coherent integration time. The navigation results show

that extended coherent integration with ML based bit

wipe-off method can help to improve the navigation

performance in signal challenged environments. The

position and velocity accuracy has been improved more

than 40% after extending coherent integration time from

20 ms to 100 ms in the vehicular navigation test. The

navigation results with extended coherent integration time

from ML bit decoding are close to those from external bit

aiding, and the latter are considered as containing no bit

errors and expected giving the best results.

A newly proposed signal power based observation

selection strategy has helped to overcome the inaccurate

GNSS measurements problem existing in heavy multipath

(fading) areas. It is shown that after implementing the

strategy in the standalone ultra-tight receiver with 100 ms

from ML bit decoding, the RMS position error in

horizontal and vertical is less than 5 m and 10 m

respectively, and the RMS velocity errors in horizontal

and vertical both are less than 0.2 m/s. This confirms the

feasibility of the standalone approach.

Future work will use more field tests under different

environments to test the robustness of this standalone

system.

ACKNOWLEDGMENTS

The research presented in this paper was conducted as

part of a collaborative research and development grant

between the University of Calgary, General Motors of

Canada, and Natural Sciences and Engineering Research

Council of Canada.

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