ORIGINAL ARTICLE

Locata-based precise point positioning for kinematic maritimeapplications

Wei Jiang • Yong Li • Chris Rizos

Received: 22 October 2013 / Accepted: 20 March 2014

� Springer-Verlag Berlin Heidelberg 2014

Abstract The GPS-precise point positioning (PPP) is still

not as popular as network-based real-time kinematic (N-

RTK) for engineering kinematic applications based on

differential positioning principles for several reasons. One

is the fact that the accuracy of kinematic GPS-PPP is lower

than N-RTK solutions. The second reason is that GPS-PPP

requires a comparatively long initialization period. In order

to overcome such shortcomings, a new PPP approach

augmented by a ground-based positioning system such as

‘‘Locata’’ is proposed in this paper. The new approach is

referred to as Locata/GPS-PPP. Locata’s ground-based

technology has rapid geometry change for kinematic

applications; thus, the proposed approach is able to provide

high-accuracy solutions with faster initialization. In the

proposed Locata/GPS-PPP approach, the Locata and GPS

carrier phase measurements are processed simultaneously

in a tightly combined mode and the carrier phase ambi-

guities are resolved as floating-point values on an epoch-

by-epoch basis in order to avoid the need for cycle-slip

repair. In order to evaluate the system performance, a

kinematic field trial was conducted on Sydney Harbor.

A Locata transmitter network was setup on the fringes of

Sydney’s CBD. The experiment demonstrated that the

initial convergence time of the integrated Locata/GPS-PPP

filter is only 10 s, which is significantly faster than the

conventional GPS-PPP method. Comparison of the pro-

posed method with the GPS-PPP and Locata-single point

positioning (SPP) approaches was conducted. The results

confirm that the Locata/GPS-PPP approach can achieve

centimeter-level accuracy for horizontal positioning which

improves 36.4 and 68.8 % over Locata-SPP and GPS-PPP.

The results validate the effectiveness of the proposed

approach for high-accuracy maritime applications.

Keywords Locata � GPS-PPP � Locata/GPS-PPP �Maritime navigation

Introduction

World economic output and international trade have kept

growing over the past decade and will likely further

increase over the next decade. Nowadays, over 90 % of

global trade is carried by sea. As a consequence, ports and

coastal area are busier and more crowded than ever before.

Furthermore, certain applications in port areas or in con-

stricted waterways have very stringent performance

requirements. These are dependent on a precise and robust

positioning system. The global navigation satellite system

(GNSS) can provide good positioning and navigation per-

formance; hence, mariners have access to a more reliable

and more accurate positioning capability than what it

needed in the past. However, GNSS positioning accuracy is

affected by measurement errors. Network-based real-time

kinematic (N-RTK) positioning with fixed ambiguity res-

olution is a widely used technique for RTK carrier phase-

based GNSS positioning (Fotopoulos and Cannon 2001;

Landau et al. 2007). The systematic measurement errors

are mitigated by double-differencing (DD) the raw GNSS

observations made at user ‘‘rover’’ receivers (whose coor-

dinates are to be determined), and a reference station

receiver set up at a point whose coordinate is known.

N-RTK and RTK, in general, can achieve centimeter-level

positioning accuracy in real time and even when the rover

is moving in an erratic and unpredictable way. However,

W. Jiang (&) � Y. Li � C. Rizos

School of Civil and Environmental Engineering, University of

New South Wales, Sydney, Australia

e-mail: w.jiang@student.unsw.edu.au

123

GPS Solut

DOI 10.1007/s10291-014-0373-9

the requirements of such RTK approaches are quite strin-

gent. In the case of single reference station RTK, simul-

taneous GNSS satellite observations by both the rover and

the reference station are needed, and the reference receiver

observations must be transmitted to the user receiver under

certain operational constraints, in order to ensure success-

ful carrier phase DD ambiguity resolution. This is typically

less than 30 km in mid-latitude regions of the world to

support single reference receiver RTK operations, but can

be less than 20 km if ionospheric conditions are too severe.

To satisfy such stringent requirements, a dense network of

reference receivers at 50–70 km spacing is typically nee-

ded to ensure reliable N-RTK service. The substantial

resources for the physical construction and service main-

tenance of N-RTK or RTK mean it is difficult to provide

such centimeter-level accuracy positioning service based

on differential GNSS techniques across large regions (Ge

et al. 2012).

An alternative to the differential positioning techniques is

the precise point positioning (PPP) approach, which is based

on the processing of observations from a single GNSS

receiver only, and employing precise satellite orbit and clock

correction information instead of ephemeris and clock data

encoded within the broadcast navigation message. For PPP,

there is no longer a need to use corrections and/or mea-

surements from one or more GNSS reference stations.

Moreover, PPP has a lower computational burden in com-

parison with the N-RTK approach (Zumberge et al. 1997).

Unlike the GNSS differential techniques, the measure-

ment error in PPP user side can only be reduced by accurate

bias modeling or parameter estimation, note differential

techniques are used to estimate the biases in PPP server side

solutions. Important modifications include improved satel-

lite orbit and satellite clock error models, atmospheric delay

model/estimation, and application of station effects such as

phase center variation corrections and site displacement due

to earth and ocean loading tides. As with differential tech-

niques, in order to achieve centimeter- to decimeter-level

positioning accuracy, carrier phase measurements must be

used. Hence, there is the challenge of ambiguity resolution.

Due to the existence of uncalibrated phase delays (UPDs),

the ambiguities are no longer integer values. Over the last

five or so years, many researchers have been investigating

the issue of fixing the ambiguities (Ge et al. 2008; Collins

2008; Geng et al. 2010; Chen et al. 2011). However, the

computation process is complex and it is often difficult to

assure a high ambiguity fixing rate. Another more com-

monly used approach estimates the ambiguities as floating-

point values and does not try to fix the ambiguities (Zum-

berge et al. 1998). This approach is easier to implement and

is more reliable; however, such methods typically require

long convergence periods, especially for kinematic posi-

tioning. Furthermore, the resultant accuracy is not as high as

in the case of N-RTK solutions, even after a lengthy initial

convergence period.

Locata is a ground-based positioning system which

transmits CDMA ranging signals at frequencies in the

2.4 GHz industrial, scientific, and medical (ISM) radio

band. Such ranging signals, from transmitters known as

‘‘LocataLites’’, can be tracked by a Locata receiver. Locata

technology is able to operate independently of other navi-

gation systems when a Locata network of four or more

time-synchronized LocataLites (LLs) is operated within a

single network (Barnes et al. 2003; Rizos et al. 2010). A

description of the Locata technology and some results of

earlier testing have been reported in the literature (Barnes

et al. 2003; Choudhury et al. 2009a; Li and Rizos 2010;

Montillet et al. 2009). Such studies have verified that this

technology can be used for a wide range of positioning

applications, including precise indoor positioning (Barnes

et al. 2003; Rizos et al. 2010), slow structural displacement

monitoring (Choudhury et al. 2009a), and kinematic posi-

tioning (Bertsch et al. 2009; Li and Rizos 2010).

Locata technology also has good interoperability with

other GNSS constellations when the transmitted signals are

synchronized with GNSS signals (Locata Corporation

2012). Since Locata is ground-based and GNSS is space-

based, Locata technology can be a good augmentation of

GPS navigation. Thus, it is of interest to investigate an

integrated Locata/GPS-PPP solution strategy. In the pro-

posed Locata/GPS-PPP system, the Locata signals are

synchronized with the GPS time, and the Locata and GPS

carrier phase measurements are processed in a tightly

coupled mode, with the corresponding ambiguities

resolved on an epoch-by-epoch basis.

An overview of the Locata technology and Locata-sin-

gle point positioning (SPP) approach is first given. Then, a

modified GPS-PPP system and the related error models are

described in ‘‘GPS-PPP technology’’ section. In ‘‘Locata/

GPS-PPP system’’ section, the detailed system filter set-

tings are presented. Finally, a field test conducted in Syd-

ney Harbor to evaluate the system performance is

introduced, and the data analysis and results are discussed.

The paper concludes with some final remarks.

Locata technology and Locata-SPP mathematical model

A LocataNet consists of a number of LocataLite trans-

ceivers located within or around a defined service area. The

‘‘user segment’’ includes any number of fixed or moving

Locata user receivers (or ‘‘rovers’’) operating within the

service area, and deriving position and time information

using signals transmitted by the LLs. The Locata firmware

used in this experiment is version 5 which released in 2011

(Locata Corporation 2011). A LocataNet consists of one

GPS Solut

123

master and several slave LLs. Slaves are able to maintain a

constant time frame by synchronizing with the master LL

via direct or cascade procedure. Each LL unit has two

transmitting (Tx1 and Tx2) and one receiving (Rx) anten-

nas, as shown in Fig. 1. The system transmits signals from

the two transmitting antenna to provide spatial diversity.

Each antenna also transmits two signals approximately

60 MHz apart to provide frequency diversity (2.41428 and

2.46543 GHz—referred to as S1 and S6, respectively). The

result is four independent signals from each LL with spatial

and frequency diversity.

Locata-SPP mathematical model

Locata is able to provide 3D position and time information

if four or more LLs can be tracked. Compared with GNSS

carrier phase processing, Locata carrier phase measure-

ments are affected by fewer errors. Thus, Locata-SPP is

carrier phase-based, which differs from GNSS pseudor-

ange-based SPP. The basic Locata-SPP observation equa-

tion for a measurement between receiver and LL channel i

can be written as:

/iL ¼ qi

L þ ditrop þ c � dT þ Ni

L � kþ ei/ ð1Þ

where /Li is the carrier phase measurement in meters; qL

i is

the geometric range from receiver to the transmitting

antenna i; k is the wavelength of the Locata signal; dtropi is

the tropospheric delay; c is the speed of electromagnetic

radiation (EMR); dT is the receiver clock bias; NLi is the

carrier phase ambiguity, and e/i is the lump-sum of un-

modeled residual errors (including the measurement noise).

Note that there is no transmitter clock error in the obser-

vation equation because of the tight time synchronization

of the LLs, neither is there an ionospheric delay term. The

Locata ambiguities are typically estimated as floating-point

values. The receiver clock error may be estimated, or

eliminated using measurement differencing. The single-

differencing (SD) the carrier phase measurements are

adopted to eliminate the receiver clock error; the SD D/ij

observable is:

D/ijL ¼ /i

L � / jL ¼ Dqij

L þ Ddijtrop þ DN

ijL � kþ v ð2Þ

where j is chosen as the reference signal and i is another

signal of the same frequency. The tropospheric delays in

Ddtropij is calculated by using an appropriate tropospheric

model (Choudhury et al. 2009b), and the ambiguity is

resolved by Locata on-the-fly (OTF) ambiguity resolution

algorithm (Jiang et al. 2013). The unknown parameters in

the Locata-SPP solution are user navigation parameters and

float carrier phase ambiguities, which are estimated for the

rover on an epoch-by-epoch basis using an extended Kal-

man filter (EKF).

GPS-PPP technology

GPS users usually employ the broadcast ephemeris, which

is of comparatively low accuracy of the order of a few

meters. As an alternative, and where the user does not want

to employ the differential positioning mode, more accurate

orbit and satellite clock information can be obtained from

the International GNSS Service (IGS—http://igs.org). The

IGS combined orbit/clock products come in various fla-

vors, from the final, rapid to the ultra-rapid, which became

officially available on November 5, 2000 (Kouba 2009).

Together with utilizing precise satellite orbit and clock

information, satellite antenna offset/variations, site dis-

placement corrections, tropospheric and ionospheric delay

models need to be considered for a high accurate solution.

Satellite signals travelling through the earth’s atmo-

sphere experience both distance delay/advance and bend-

ing effects. Among all the atmosphere layers, the lower

troposphere and upper ionosphere are particularly impor-

tant for GPS-PPP solutions. The ionospheric error is the

dominant source of error in GPS/GNSS positioning, which

depends on the electron density of the ionosphere along the

signal path. Thus, many ionospheric studies focus on ion-

ospheric modeling to improve accuracy in the case of

Fig. 1 LocataLite antenna setup consisting of two transmit antennas

and one receive antenna

GPS Solut

123

single-frequency receivers (Gao et al. 2004). However,

since the ionosphere is dispersive and the ionospheric delay

is frequency dependent, GPS-PPP users of dual-frequency

receivers can employ an ionosphere-free measurement

combination to eliminate the first-order ionospheric signal

delay, which accounts for more than 99 % of that error.

The ionosphere-free model equation can be given as:

/IF ¼f 21

f 21 � f 2

2

/L1 þ�f 2

2

f 21 � f 2

2

/L2 ð3Þ

where f1 and f2 are the frequencies of the L1 and L2 carrier

waves, respectively.

In the case of GPS positioning, the total tropospheric

range delay resulting from propagation of the satellite

signals through the neutral atmosphere is expressed as a

function of the hydrostatic (dry) and wet zenith path delay

with their individual mapping function:

dtrop ¼ dhrdro �Mhydro þ dwet �Mwet ð4Þ

where dhydro and dwet are the hydrostatic and wet zenith

path delay, respectively; and M* denotes the related map-

ping function.

Range delays resulting from the hydrostatic component

of the troposphere, which is the major part of tropospheric

error, can be computed using, say, the Saastamoinen model

(IERS 2010). Surface pressure, height above mean sea

level, and the latitude of the user location are used as the

input to the model.

The troposphere zenith hydrostatic delay can be calcu-

lated with up to 0.2 mm accuracy if precise meteorological

data are used (IERS 2010). However, the real measured

meteorological data are not always available, and one way

to overcome this limitation is by adopting an empirical

global pressure and temperature model (Boehm et al.

2007), currently recommended as the IGS and International

Earth Rotation and Reference Systems Service (IERS)

standard. Sample code is available at ftp://maia.usno.navy.

mil/conv2010/convupdt/chapter9/GPT2.F (updated June

10, 2013).

Unlike the modeling of troposphere zenith hydrostatic

delay precisely modeling, the troposphere zenith wet delay

is not possible. Instead, the troposphere zenith wet delay is

estimated in PPP solutions as an additional unknown

parameter.

Once the troposphere zenith hydrostatic delay is mod-

eled and the troposphere zenith wet delay is estimated, a

mapping function is required to project the troposphere

zenith delay to the user-satellite slant distance. In this

study, the global mapping function is used (Boehm et al.

2006). It is an empirical function that requires user latitude,

longitude, height, and day of year as input. Sample code is

available at http://maia.usno.navy.mil/conv2010/chapter9/

GMF.F.

Because GPS-PPP does not use measurement differ-

encing, those errors that can be eliminated in the differ-

ential positioning approach have to be taken into account.

Table 1 gives an overview of these effects and the related

mitigation method.

GPS-PPP mathematical model

Errors resulting from relativity and phase windup at the

satellite antenna, the offset–variation of antenna phase center

and site displacement are assumed to have been corrected by

models and are ignored here. The simplified GPS phase

observation equation can be formulated in metric units as:

/i ¼ qi þ dsi � diiono þ di

trop þ c � dT � c � dt þ Ni � kþ ei/

ð5Þ

where the superscript i denotes the satellite, ds is the orbital

error, diono is the ionosphere delay, dt is the satellite clock

error, N is the integer carrier phase ambiguity, and e/ is the

carrier phase measurement noise.

In order to mitigate the ionospheric effect, the iono-

sphere-free model, Eq. (3) is applied, and the observation

equation becomes:

/iIF ¼

f 21

f 21 � f 2

2

/iL1 þ

�f 22

f 21 � f 2

2

/iL2

¼ qi þ dsi þ ditrop þ c � dT � c � dt

þ f 21 � k � Ni

1 � f 22 � k � Ni

2

f 21 � f 2

2

þ ei/IF

ð6Þ

Table 1 GPS-PPP errors and corresponding mitigation methods

Error effects Mitigation method

Satellite-

related

effects

Relativistic effect Official model from GPS

ICD (ICD-GPS-200C

1993)

Satellite antenna

phase center offset

and variation

Absolute phase center

correction model (Kouba

2009) with IGS ANTEX

product

Phase windup Phase windup correction

model (Kouba 2009)

Receiver-

related

effects

Receiver antenna

phase center offset

and variation

Absolute phase center

correction model (Kouba

2009) with IGS ANTEX

product

Sagnac effect Sagnac effect model

(Ashby 2003)

Site

displacement

effects

Solid earth tides Model recommended by

the IERS (2010)Polar tides

Ocean loading

Earth rotation

parameters

GPS Solut

123

The ionosphere-free ambiguity NiIF ¼

f 21�k�Ni

1�f 2

2�k�Ni

2

f 21�f 2

2

is cal-

culated as a lumped term and treated as a non-integer

value. The receiver clock error dT may be either estimated

or eliminated by differencing the ionosphere-free mea-

surements between satellites. When the signal from satel-

lite k is chosen as the reference, the SD ionosphere-free

carrier phase measurement D/IFik can be written as:

D/ikIF ¼ /i

IF � /kIF

¼ DqikG þ Ddsik þ Ddik

trop � c � Ddtik þ DNikIF þ eik

/IF

ð7Þ

The unknown variables are user navigation parameters, the

SD zenith tropospheric wet delay, and the SD ionosphere-

free carrier phase ambiguities. In order to avoid the cycle-

slip problem, the carrier phase ambiguities are resolved on

an epoch-by-epoch basis. The number of estimated states is

greater than the number of measurements; hence, the EKF

is adopted. Similar to Locata-SPP processing, an accurate

dynamic model with first-order GM modeled acceleration

is developed to improve the filter performance, which can

be given as,

_a ¼ � 1=sð Þ � aþ xa ð8Þ

where s is the correlation time constant and xa is zero-

mean white noise.

The carrier phase ambiguities and tropospheric wet

delay are modeled as random walks. The system state

vector is:

xðtÞ ¼ ½ r _r €r Ddwet DN1kIF DN2k

IF � � � DNmkIF �

T

ð9Þ

where Ddwet is the SD zenith tropospheric wet delay and

m is the number of ionosphere-free carrier phase

measurements.

The system dynamic model of EKF describes how the

true state of the system evolves over time. The dynamic

model, the transition matrix, and the process noise vector

can be written as:

_x tð Þ ¼ F tð Þ � x tð Þ þ x tð Þ ð10Þ

F tð Þ ¼

03�3 I3�3 03�3 03� mþ1ð Þ03�3 03�3 I3�3 03� mþ1ð Þ

03�3 03�3 � 1

s� I3�3 03� mþ1ð Þ

0 mþ1ð Þ�3 0 mþ1ð Þ�3 0 mþ1ð Þ�3 0 mþ1ð Þ� mþ1ð Þ

26664

37775

ð11Þx tð Þ ¼

01�3 01�3 xa xa xa xDdwetxDN1k

IFxDN2k

IF. . . xDNmk

IF

� �T

ð12Þ

where xDdwetis the process noise of the tropospheric wet

delay. The symbol xDN�kIF

denotes the process noise of SD

GPS ionosphere-free ambiguity.

The measurement model (7) is nonlinear; thus, the EKF

linearize the function around the current predicted esti-

mates. The measurement model is:

z tð Þ ¼ H tð Þ � x tð Þ þ t tð Þ ð13Þ

The measurement vector z(t), which is formed from the set

of error-corrected SD GPS carrier phase, and the design

matrix H can be written as,

zðtÞ ¼ D/1kIF D/2k

IF � � � D/mkIF

� �T ð14Þ

ð15Þ

where e� is the line-of-sight vector between receiver and

satellite. The measurement noise vector is t tð Þ�N 0;Rð Þ,and the measurement noise covariance matrix R is defined

by the variance of the measurements.

Locata/GPS-PPP system

In the proposed configuration, Locata and GPS carrier

phase measurements are jointly processed at the tightly

coupled mode. The tightly couple mode means that the raw

observations of all sensor systems are input to a common

navigation filter (Rizos et al. 2008). For the proposed Lo-

cata/GPS-PPP system, a common system estimator is

designed to process the measurements of both Locata and

GPS carrier phase simultaneously and achieve the optimal

navigation solution of position, velocity, and acceleration.

Referring to the foundation of the Locata-SPP and GPS-

PPP mathematical models described above, the measure-

ment functions of Locata and GPS keep independently and

will not affect each other, the respective carrier phase float

ambiguities of Locata and GPS will estimated via the

common EKF estimation along with the navigation

solutions.

Since Locata and GPS systems use different antennas,

the lever arm correction needs to be applied. Here, the

Locata antenna position is referred to the GPS antenna

center with the lever arm estimated as unknown parameters

at each epoch. The length of the lever arm is known

beforehand and treated as an additional measurement. The

system state vector is:

GPS Solut

123

where dg* represent the unknown lever arm components.

The acceleration is modeled as a first-order GM process,

while other items such as tropospheric wet delay, lever arm,

and carrier phase ambiguities are modeled as random biases.

According to the EKF dynamic model, shown in (10),

the transition matrix F and process noise vector x tð Þ in the

dynamic model can be written as:

F tð Þ ¼

03�3 I3�3 03�3 03� nþmþ4ð Þ03�3 03�3 I3�3 03� nþmþ4ð Þ

03�3 03�3 � 1

s� I3�3 03� nþmþ4ð Þ

0 nþmþ4ð Þ�3 0 nþmþ4ð Þ�3 0 nþmþ4ð Þ�3 0 nþmþ4ð Þ� nþmþ4ð Þ

26664

37775

ð17Þ

where xdg is the process noise of the lever arm.

Since the lever arm considered, and the GPS antenna

center are computed as the user location, the premeasured

lever arm distance and the Locata geometric range in (1)

from Locata antenna center to the LL could be written as:

lLA ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffidg2

x þ dg2y þ dg2

z

qð19Þ

qiL ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffixþ dgx � xið Þ2þ yþ dgy � yi

� �2þ zþ dgz � zi� �2

q

ð20Þ

where x, y, and z represent the user coordinates in earth-

centered earth-fixed frame.

The measurements used for Locata/GPS-PPP solutions

are the combination of Locata carrier phase and GPS car-

rier phase, where the error effects on GPS carrier phase can

be mitigated by the model described in ‘‘GPS-PPP tech-

nology’’ section. Therefore, the measurement vector and

the design matrix in (13) can be written as:

z tð Þ ¼D/1j

L D/2jL � � � D/nj

L D/1kIF D/2k

IF � � � D/nkIF htide lLA

� �

ð21Þ

H ¼H11 H12 In�n 0m�m

H21 0 mþ1ð Þ�3 0n�n Im�m

H31 H32 02�n 02�m

24

35; ð22Þ

where

,

H12 ¼

oq1L

odgx

� oq jL

odgx

oq1L

odgy

� oq jL

odgy

oq1L

odgz

� oq jL

odgz

oq2L

odgx

� oq jL

odgx

oq2L

odgy

� oq jL

odgy

oq2L

odgz

� oq jL

odgz

..

. ... ..

.

oqnL

odgx

� oq jL

odgx

oqnL

odgy

� oq jL

odgy

oqnL

odgz

� oq jL

odgz

266666666664

377777777775

;

,

, H32 ¼01�3olLA

og

24

35

where L and k are geodetic latitude and longitude, respec-

tively, htide denotes the tide height measurements which is

provided from the tide-gauge records as the additional vertical

measurements, and the standard deviation is 0.01 m.

The measurement covariance matrix R is diag (RDuL;

RDuIF; r2

htide; r2

lLA). Since both Locata and GPS measure-

ments are processed in the SD mode, the SD carrier phase

x tð Þ ¼ r _r €r Ddwet dgx dgy dgz DN1jL DN

2jL � � � DN

njL DN1k

IF DN2kIF � � � DNmk

IF

h iT

ð16Þ

x tð Þ ¼ 01�3 01�3 xa xa xa xDdwetxdg xdg xdg xDN

1jL� � � xDN

njL

xDN1kIF� � � xDNmk

IF

h iT

ð18Þ

GPS Solut

123

measurements are correlated with each other, the covari-

ance is therefore assumed to be half of the variance, which

can be written as,

RDu� ¼r2

D/�2

2 1 � � � 1

1 2 � � � 1

..

. ... . .

.1

1 1 1 2

2664

3775 ð23Þ

where r2D/�, r2

htideand r2

lLAare the noise variance of SD

carrier phase measurements, tide height and lever arm

distance, respectively.

Experiment and result analysis

The experiment was conducted in October 2012 on Sydney

Harbor, on the fringes of Sydney’s CBD where the multi-

path effect is quite severe. A Locata user unit and a Leica

GNSS dual-frequency receiver were installed on a survey

vessel provided by the Sydney Ports Authority, with

antenna locations as shown in Fig. 2. The distance between

Locata and GNSS antenna center was measured beforehand

as 0.24 m. The GPS antenna center was considered to be

the required user location, and the Locata antenna center

was lever arm corrected so that its coordinate referred to

the GPS antenna center.

In this test, the LocataNet comprised eight LocataLites,

six of them installed along the shore, and the remaining

two located further away, with one on the Sydney Harbor

Bridge (LL7) and the other at Kirribilli (LL8). They were

time-synchronized in a cascaded mode with the master LL

(LL3) configured for synchronization with respect to GPS

time. The configuration of the LocataNet is shown in

Fig. 3.

In order to establish a reference trajectory for accuracy

assessment, the GNSS integer ambiguity-fixed solution

Fig. 2 Test vessel and installed Locata and GPS antennas

Fig. 3 Sydney Harbor experiment configuration and vessel trajectories

GPS Solut

123

computed by the Leica Geo Office (LGO) software served

as the ground-truth. A precisely surveyed point was set up

as the base station where a dual-frequency GPS receiver

was installed. The distance between the GNSS base station

and the rover trajectory was less than 10 km. The whole

trajectory and the base station are shown in Fig. 3, where

the red line denotes the trajectory and the green dot is the

base station. The raw data from the Locata rover and GNSS

receiver were collected and post-processed. Both Locata

and GPS data output rates were set to 10 Hz. Tide height

data were recorded by the Fort Denison Tide Gauge,

updated every 6 min.

The trajectory solution using the GPS-PPP approach was

first conducted. Figure 4 shows the GPS geometry during

the experimental period, which lasts for 2 h and 45 min.

The horizontal dilution of precision (HDOP), vertical

dilution of precision (VDOP), and the number of visible

satellites are plotted. There were 6–9 available satellites

during this period, and by applying the SD PPP approach,

5–8 SD observables could be obtained.

Figure 5 is a plot of the difference between the GPS-

PPP solutions and the ground-truth solutions. The differ-

ence is analyzed in the local navigation frame (north-east-

down). It can be seen from the plot that the convergence

period lasts for approximately 500 s, after that the accuracy

of the three position components are less than half meter.

Table 2 summaries the accuracy of the GPS-PPP solutions,

with the exclusion of the initial 500 s convergence period.

The standard deviation (STD), the root mean square (RMS)

value, distance root mean square (DRMS) for 2D (hori-

zontal components), and mean radial spherical error

(MRSE) for 3D are listed. The DRMS and MRSE are 0.14

and 0.23 m, respectively. The STDs are 0.07 and 0.08 m

for the north and east components, and 0.17 m for the

vertical. The RMS values for the horizontal components

are 0.08 m (north) and 0.11 m (east), and for the vertical

direction, it is 0.18 m. The statistics values indicate that the

vertical accuracy is typically two times of the horizontal

component accuracy.

The yellow line in Fig. 3 denotes the trajectory for the

Locata/GPS-PPP approach. In this session, both Locata and

GPS signals were tracked and the vessel travelled in a

continuous circular motion for approximately 15 min.

Figure 6 is a plot of the geometric conditions. During this

period, 7–8 GPS satellites and 4–8 LLs with 11–32 Locata

signals could be tracked, where each LL transmits a cluster

of four signals. Excluding one satellite and two Locata

signals as the reference in the Locata/GPS-PPP system, a

total 15–37 SD observables were obtained. In order to

make a further geometry analysis, the average HDOP and

VDOP of the GPS system, Locata/GPS system, and Locata

standalone are compared in Table 3. Since LocataNet was

configured in an almost planar configuration, the vertical

geometry of Locata standalone is poor. Therefore, only

HDOP of Locata standalone is compared in Table 3. The

HDOP of the Locata standalone is also depicted in Fig. 6 in

green line. Compared with GPS system, Locata/GPS gives

an improvement of 65.8 and 72.2 % on HDOP and VDOP,

respectively; while compared with Locata standalone, the

proposed Locata/GPS system improves 30 % on HDOP. It

Fig. 4 Geometric conditions for GPS positioningFig. 5 GPS-PPP solution accuracy with respect to the ground-truth

solution

Table 2 Error analysis of GPS-PPP solutions

STD (m) RMS (m) Horizontal DRMS (m) MRSE (m)

North 0.070 0.081 0.137 0.230

East 0.077 0.110

Vertical 0.168 0.185 –

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can be seen on both horizontal and vertical directions,

Locata/GPS could give the most optimal geometry.

Since more than four LLs were used during the exper-

iment, the Locata-SPP solution can be computed using the

method described in ‘‘Locata technology and Locata-SPP

mathematical model’’ section. Difference between Locata-

SPP solution and the ground-truth is depicted in Fig. 7, and

Fig. 6 Geometric conditions

for integrated Locata/GPS

system and horizontal geometry

condition of Locata standalone

system

Fig. 7 Locata-SPP accuracy with respect to the ground-truth solution Fig. 8 Locata/GPS-PPP accuracy with respect to the ground-truth

solution

Table 3 DOP comparison of

GPS, Locata standalone, and

Locata/GPS

Ave.

HDOP

Ave.

VDOP

GPS 1.213 2.252

Locata 0.594 –

Locata/

GPS

0.415 0.626

Table 4 Error analysis of Locata-SPP solutions

STD (m) RMS (m) Horizontal DRMS (m) MRSE (m)

North 0.036 0.041 0.055 0.077

East 0.029 0.037

Vertical 0.053 0.053 –

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123

the solution statistics analysis of the period without initial

convergence is shown in Table 4. The horizontal DRMS

and MRSE of Locata-SPP solution are 0.055 m and

0.077 m, respectively, which indicates that the Locata-SPP

can provide the positioning solution of better than 1

decimeter.

Figure 8 shows the difference between the position

solutions computed using the integrated Locata/GPS-PPP

approach and the ground-truth solutions. With the same

initial state value, the convergence time using the Locata/

GPS-PPP approach is very short, at most the first 100

epochs (10 s), which is a significant reduction in compar-

ison with the GPS-PPP approach which has a convergence

period of about 500 s. The error analysis is summarized in

Table 5, with the exclusion of the first 10 s convergence

period. Similar to Table 3, STD, RMS, horizontal DRMS

and MRSE are listed. The RMS values are 0.03, 0.01, and

0.05 m for the north, east, and vertical directions, respec-

tively. The horizontal DRMS is 0.035 m and the MRSE is

0.065 m. Compared with the GPS-PPP solutions, all the

statistics evaluations indicate a great improvement.

A comparison of the three systems is conducted in Fig. 9

and Table 6. Since the rover is installed on a maritime

vessel, the horizontal positioning performance is more

important than for the vertical. Figure 9 and Table 6 thus

focus on the north and east components. The green line and

the blue line are the Locata-SPP and Locata/GPS-PPP

solution differences with respect the ground-truth. The red

line represents the GPS-PPP solution difference, which is

extracted from the solutions for the whole trajectory in

Fig. 5. Therefore, this trajectory is used for comparison

purposes, after neglecting the initial convergence period.

The zoom-in plots in Fig. 9 compare the initial conver-

gence period of the Locata-SPP and Locata/GPS-PPP

Fig. 9 Horizontal accuracy and

convergence speed comparison

of GPS-PPP, Locata-SPP, and

Locata/GPS-PPP, the zoom-in

plots are the position in the first

30 s

Table 5 Error analysis of Locata/GPS-PPP solutions

STD (m) RMS (m) Horizontal DRMS (m) MRSE (m)

North 0.028 0.033 0.035 0.065

East 0.011 0.013

Vertical 0.054 0.054 –

Table 6 Error analysis of GPS-

PPP, Locata-SPP, and Locata/

GPS-PPP

STD (m) RMS (m) Horizontal DRMS (m) Convergence time (s)

North East North East

GPS-PPP 0.043 0.034 0.107 0.034 0.112 500

Locata-SPP 0.036 0.029 0.041 0.037 0.055 20

Locata/GPS-PPP 0.028 0.011 0.033 0.013 0.035 10

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solutions, from which one can see that the convergence

time of the Locata-SPP system is approximately 200

epochs, that is, 20 s. While the convergence time of the

Locata/GPS-SPP system is about 10 s, which is shorter

than that of the Locata-SPP system. The Locata/GPS-PPP

system therefore converges about two times faster than the

Locata-SPP approach. Both of these two systems, however,

have shorter convergence period than the GPS-PPP

approach, which is 500 s as shown in Fig. 5.

Excluding the initial filter convergence period and

considering only the after-convergence system perfor-

mance, the solution of the integrated Locata/GPS-PPP

system is more stable than the other two approaches. The

statistics comparison of the three approaches during the

experiment is shown in Table 6. One can see that all the

three indicators show that the Locata/GPS-PPP approach

gives the most accurate solution. With respect to the hor-

izontal DRMS, the Locata/GPS-PPP approach shows an

improvement of 36.4 % against the Locata-SPP solution;

Comparing with the GPS-PPP approach, the improvement

is more obvious, such as 68.8 %. All the indicators illus-

trate that the Locata/GPS-PPP approach has the best per-

formance, not only providing the most stable and accurate

solution, but also having the fastest filter convergence

speed.

Concluding remarks

In this study, the potential of using the Locata/GPS-PPP

approach for kinematic maritime applications was inves-

tigated. This proposed method integrates the GPS-PPP and

the Locata-SPP positioning approaches in order to provide

high-accuracy point positioning solutions without require-

ment for a GNSS reference station. The Locata and GPS

carrier phase are processed simultaneously in a tightly

combined mode with the ambiguities estimated on an

epoch-by-epoch as floating-point values. The unknown

lever arm between the Locata antenna and the GPS antenna

is estimated by the system filter.

A field test was conducted on Sydney Harbor to evaluate

the system performance. An analysis of the GPS-PPP,

Locata-SPP, and Locata/GPS-PPP approaches was con-

ducted. It was demonstrated that the Locata/GPS-PPP

system can achieve positioning accuracy at the centimeter

level, which is better than either the GPS-PPP or the Lo-

cata-SPP approach. Moreover, the initial filter convergence

time of the proposed method is significantly shorter com-

pared with the GPS-PPP approach. These advantages dis-

tinguish the Locata/GPS-PPP approach from the

conventional GPS-PPP approach and as an effective navi-

gation approach to provide high accurate positioning

solution for kinematic maritime application.

Acknowledgments The first author wishes to thank the Chinese

Scholarship Council (CSC) for supporting her studies at the Univer-

sity of New South Wales. The authors acknowledge the valuable

assistance provided by Locata Corporation and Land and Property

Information NSW.

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Wei Jiang is a Ph.D. candidate

in the School of Civil and

Environmental Engineering at

the University of New South

Wales, Australia. She received

her bachelor degree at the

School of Automation, North-

western Polytechnical Univer-

sity, China. Her current research

interests include Locata/GNSS/

INS multi-sensor integration

and in particular the implemen-

tation of new navigation and

data fusion algorithms.

Yong Li is a Senior Research

Fellow at the Satellite Naviga-

tion and Positioning Lab, within

the School of Civil and Envi-

ronmental Engineering, the

University of New South Wales

(UNSW), Sydney, Australia. He

was involved in the develop-

ment of spaceborne GPS

receivers for altitude determi-

nation and formation flying

missions, and MEMS-/GNSS-

based multisensor system for

pedestrian and autonomous

vehicle indoor/outdoor naviga-

tion applications. His current research interests include integration of

GNSS, INS, and pseudolite (Locata), altitude determination, GNSS

receiver technique and its application to navigation, and optimal

estimation/filtering theory and applications.

Chris Rizos is Professor of

Geodesy and Navigation,

School of Civil & Environmen-

tal Engineering, the University

of New South Wales, Sydney,

Australia. Chris is president of

the International Association of

Geodesy (IAG), a member of

the Executive and Governing

Board of the International

GNSS Service (IGS), and co-

chair of the Multi-GNSS Asia

Steering Committee. Chris is a

Fellow of the IAG, a Fellow of

the Australian Institute of Nav-

igation, a Fellow of the U.S. Institute of Navigation, and an honorary

professor of Wuhan University, China. Chris has been researching the

technology and applications of GPS since 1985 and is an author/co-

author of over 600 journal and conference papers.

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