Journal of Global Positioning Systems (2008)

Vol. 7, No. 1 : 1-8

GPS RTK Performance Characteristics and Analysis

Yanming Feng
Faculty of Information Technology, Queensland University of Technology, Australia

Jinling Wang
School of Surveying and Spatial Information Systems, The University of New South Wales, Australia

Abstract
involved in the positioning operations. Single Point
Global Navigation Satellite Systems (GNSS) provide Positioning (SPP) produces navigation solutions with
various types of positioning state solutions, such as pseudorange measurements from a single receiver and a
single point positioning (SPP), precise point positioning single epoch. Precise Point Positioning (PPP) solutions
(PPP), differential GPS (DGPS) and real time kinematic are obtained using both code and phase measurements
(RTK) solutions. These solutions are obtained involving from a single receiver, but a period of observations, e.g.,
different data types, receivers, samples, serving different tens of minutes to hours, regardless of kinematic or static
classes of users. Previous studies on performance user applications. Differential GPS (DGPS) solutions are
characteristics have mainly focused on SPP solutions for based on code measurements from a single epoch as
safety-of-life navigation applications. This paper defines well, but using the differential corrections from a
various useful performance characteristics for carrier reference station or network. Real Time Kinematic
phase Ambiguity Resolution (AR) and Position (RTK) positioning makes use of carrier phase
Estimation (PE) solutions in the RTK context. These measurements in the differential positioning mode,
parameters, including base-rover distance, time-to-first ideally, from a single epoch. Practically, multiple epochs
fix (TTFF), AR reliability, RTK accuracy, availability or a short period of observations are often involved to
and integrity, etc, effectively represent the performance achieve reliable AR, while the RTK solutions are derived
of a commercial RTK system and can be used to from the current epochs.
evaluate RTK systems and algorithms, and processing
strategies through extensive experimental results. Different characteristics are required to evaluate various
Statistical results from extensive field experiments were GNSS solutions, to address positioning performance
obtained using a commercial RTK system, requirements for various applications. Code based SPP
demonstrating convincing overall system performance in and DGPS navigation are the simplest and most robust
different perspectives. Experimental results from three positioning modes, but, evaluation of code based
baselines were also analysed using a version of research- navigation solutions has been a quite involved problem.
oriented RTK software, showing that AR performance The parameters of accuracy, availability, continuity and
improvement of using Wide-lane (WL) and Narrow-lane integrity are defined to evaluate the performance of
(NL) signals with respect to the original L1 and L2 navigation solutions in aviation navigation (Langley,
signals when the baselines exceed 20 kilometres. 1999). For instance, availability is an instantaneous
performance characteristic defined as a percentage of
Key words: GNSS, real time kinematic (RTK) time during which the service is available at a certain
positioning, performance characteristics, ambiguity accuracy. Integrity relates to the level of trust that can be
resolution (AR), RTK integrity. placed in the information provided by the navigation
system. It includes the ability of the navigation system to
provide timely and valid warnings to users when the
1. Introduction system must not be used for the intended operation or
phase of flight. GPS does not provide integrity
Global Navigation Satellite Systems (GNSS) positioning information to users.
may be classified into several different types, depending
on (i) the types of measurements used in the positioning In the context of integrity, three parameters, integrity
estimation, (ii) the data epochs or data arcs required to risk, time to alert and alarm-limit are defined.
create a set of solutions, and (iii) the number of receivers Furthermore, various methods for monitoring the
 Feng et al: GPS RTK Performance Characteristics and Analysis
2

integrity of GPS SPP solutions have been proposed (i) 2. Performance Characteristics of a RTK
external monitoring, which relies on a number of ground System
stations, where a faulty individual satellite is identified
and a warning is sent to users within the time-to-alert A RTK system consists of a continuous operating
required. The typical example is the Wide Area reference station network and data links between a
Augmentation Systems (WAAS) (Enge et al, 1996; network server and reference stations and between the
Walter, 2002), (ii) Receiver Autonomous Integrity server and user-terminals. The reference network
Monitoring (RAIM) (Brown, 1996), which is applicable comprises a minimum of one reference station and a
within a user receiver to autonomously determine system network server with a data processing facility. Data links
integrity. The method attempts to detect the existence of set up between the network server and user receivers
faulty measurements and identification of unhealthy provide or deliver the differential corrections to user-
satellites. terminals. The user terminal is generally equipped with a
GNSS RTK receiver and a communication device and a
RTK positioning is a much more complicated and user control/interface unit where RTK solutions are
vulnerable process, aiming to achieve the accuracy as integrated or interfaced with a particular application. To
high as centimetres with as few as possible data epochs completely assess the performance of a RTK system, the
in real time for any user kinematics. Therefore a greater following parameters should be considered (Feng &
care has to be taken of to characterise the performance Wang, 2007):
and to address the concerns of liability-critical
professional positioning users, such as surveying, data Base-rover distance, which is the maximum radius of
acquisitions, machine automation in precision circle coverage, where a signal base station can serve
agriculture, mining and construction and future safety- effectively, allowing the users to receive the RTCM
related vehicle navigation. In many applications, users messages within certain latency and obtain its RTK
are concerned about not only accuracy, but also solutions epoch-by-epoch. A relevant concept is the
availability and integrity of the solutions. For instance, in inter-station distance in the network-based RTK case. As
an open cut mine, the cost of every hour of RTK service shown in Fig. 1, the base-rover distance D is
outages to the productions would reach the level of one approximately equivalent to 0.5774 times of the inter-
million (Higgins, 2007). station distance S. For instance in the Virtual Reference
Station (VRS) system where the maximum inter-station
However, RTK performance characteristics are much spacing is S=70 km, the equivalent maximum base-rover
less studied and understood than those of the SPP distance is about 40 km. The distance limitation is
solutions. This paper presents a systematic review for mainly caused by the strong dependence of the
RTK performance characteristics and then evaluates the ionospheric biases on the separation of two receivers.
GNSS ambiguity resolution (AR) and RTK performance The next distance-dependent error factor is the residual
with GPS measurements in terms of the various RTK tropospheric errors after modelling corrections. The
performance parameters, which may not necessarily be effect of broadcast orbital errors is relatively small and
suitable for real time quality control purposes. In the may be ignored. The system performance is considered
following sections, we first present the definitions of more desirable if a longer base-rover distance is allowed.
various performance parameters for AR and RTK
solutions in order to comprehensively evaluate Timeliness of RTCM message, which is defined as the
performance of a RTK system. Next, we outline the time latency of the latest RTCM message available for
linear equations for AR and Position Estimation (PE) users with respect to the user time instant at which the
with the specific WL and NL signals, to conceptually user states are needed to compute. Users will need to
demonstrate the dependence of performance on the predict the ranging corrections to the most current time
models and algorithms. In the forth section, we will first instant when the user-terminal produce RTK solutions.
examine the statistical results for the different This latency is the sum of delays caused by data
performance parameters of a commercial RTK system, processing at the base station/network centre and data
HD-RTK2TM, according to its extensive data sets of transmissions from base stations to network centre, and
different baselines. Utilising the research version of the messages from the network server to users, typically one
QUT-RTK software, we then compare AR performance to a few seconds. This parameter is obtainable from
improvement of the WL and NL signals with respect to statistical results for a given operational environment
the use of the original L1 and L2 signals. In this analysis, and communication links.
three 24-h RINEX data sets over the baselines of 21, 56 Another related parameter is the communication rates,
and 74 km will be analysed. Finally, the major results of for instance, 1Hz, or 5Hz and 10Hz. The higher
RTK performance characterisations and extensive communication rates are required for higher position
numerical analyses are outlined. update rates and control of position accuracy.
 Feng et al: GPS RTK Performance Characteristics and Analysis
3

provided by a RTK processing unit.

AR reliability (AR success rate). This is defined as the

percentage of the total correctly fixed DD integers over
the total number of DD integers. In some studies, the AR
success rate was implicitly defined as the total number of
epochs, when all the ambiguity integers are correctly
fixed, with respect to the total number of epochs of the
data session.

The other concern is the performance of RTK

positioning with the ambiguities-resolved double-
differenced (DD) phase measurements. To this end, the
RTK position estimation is similar to the code-based
SPP solutions. Therefore, we can similarly introduce the
Fig. 1 Relation of Inter-station distance S and equivalent SPP performance parameters to define the performance
base-rover distance D=0.5774S of the RTK solutions:

The above two parameters are used to evaluate the RTK accuracy. This is defined as the degree of
performance at the system level. At the user terminal, conformance of an estimated RTK position at a given
performance of a RTK system may be evaluated using time to a defined reference coordinate value (or ‘true’
the following characteristics, which may vary with the value) which is obtained from an independent approach,
system performance parameters. preferably at higher level of accuracy. As usual, the RTK
accuracy can be specified versus the rover-base
Time To First-Fix (TTFF). This is referred to the time distances, for instance, σ=1.0 cm + 0.5 ppm.
period required to resolve or fix sufficient integer
ambiguities of the linear equation system, then perform RTK availability (in term of accuracy). This is defined
position estimation.. In some literature, this parameter is as the percentage of time during which the RTK
known as “Time To Ambiguity-Fix (TTAF)” or solutions are available at a certain accuracy using the
“initialisation time” of the RTK system. However, TTAF ambiguity-fixed and/or ambiguity-float phase
is more suitable for more general situations where all the measurements.
integer parameters are resolved and fixed independently
at each epoch, involving measurements from single or RTK availability (in term of AR reliability). This
multiple most recent epochs. It is most desirable if the characteristic is be defined as the percentage of time, of
RTK system always fix the ambiguity integers for all the which PE is based on all the phase measurements whose
double-differenced phase measurements of the current integers have been correctly fixed at each epoch,
epoch in the linear equation system, to minimise the assuming all the ambiguity-fixed solutions will give
discontinuity of the RTK solutions after any phase required accuracy.
breaks. However, one can also define the TTAF based on
the partial ambiguity resolution (PAR) concept RTK integrity. This relates to the confidential level that
developed by Teunissen (1999). The question is wether can be placed in the information provided by the RTK
the DD phase measurements with partially resolved system. It includes the ability of the RTK navigation
ambiguities are sufficient for PE to support the RTK system to provide timely and valid warnings to users
services. when the system must not be used for the intended
operation. For instance, the RTK system with the
AR fixed rate. This instantaneous performance integrity capacity can inform users when the actual
characteristic is defined as the fixed rates of the integer positional errors of the RTK solutions have exceeded
estimation results. The system may be unavailable for Horizontal/Vertical Protection Levels (HPL/VPL) within
AR, when the geometry is too week, or satellites in view a certain Time-To-Alert (TTA) period at a given
are too few, or the effects of various errors are too Integrity Risk (IR). RTK Integrity Risk is defined as the
strong. AR fixed rate can be calculated by the ratio of the probability that the system claims its normal operational
total number of fixed DD integers to the total number of status while actually being in an abnormal status, e.g.,
DD integers over a continuously operating session. The the ambiguities being incorrectly fixed and positional
fixed integers are these that have passed the validation errors having exceeded the given HPL.
tests in the integer search process. The problem is that
the validation process may include incorrect integers and RTK continuity. This is defined as RTK availability
exclude correct integers. This parameters can be over a certain operational period and conditions. Both
 Feng et al: GPS RTK Performance Characteristics and Analysis
4

TTAF and AR availability will affect the RTK L(4,-3) instead, in order to minimise the effects of the
continuity. This parameter is provided to address user larger ionospheric errors for AR over longer ranges.
requirement for the tolerable service down-time over a
certain operational period, such as 24 hours and 7 days. P(1,1)= (f1P1+f2P2)/(f1+f2); (2)
For instance in mining and civil construction, user
tolerable down-time is about 1 to 2 minutes per day, L(1,-1) =(f1L1-f2L2)/(f1-f2); (3)
corresponding a 99.9% of continuity requirement of
services (Positioning one consulting, 2008). L(4,-3) =(4f1L1-3f2L2)/(4f1-3f2); (4)

Those parameters may be either all or selectively used to where f1 and f2 stand for the frequencies for L1 and L2
evaluate performance of a RTK system, although carrier respectively. In (2) to (4), the subscript (i, j)
variations and modifications to these definitions are still represents the integer values of the coefficients of the
possible. Of these parameters, the base-rover distance, combined measurements. L(1,-1) and L(4,-3) have the
time to ambiguity fix, AR reliability, RTK availability wavelengths of λ(1,-1)=86.2 cm, and λ(4,-3)=11.45 cm,
and RTK accuracy may be of most concerns to most respectively. As a result, we have the following linear
professional users. The concept of RTK integrity is also equations,
important from the liability-critical users’ perspective. In
farming machine automation applications, the HPL is ⎡ δP1,1 ⎤ ⎡A⎤ ⎡ 0 0 ⎤ ⎡ εP(1,1) ⎤
about 10 centimetres while for civil construction ⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎡N1 ⎤ ⎢ ⎥ (5)
machine automation, the requirement for VPL would be ⎢δL(4,−3) ⎥ = ⎢A⎥ δX− ⎢λ(4,−3)I − λ(4,−3)I⎥⎢N ⎥ + ⎢εL(4,−3) ⎥
as high as a few centimetres ((Positioning one consulting, ⎢δL(1,−1) ⎥ ⎢⎣A⎥⎦ ⎢λ(1,−1) I − λ(1,−1)I⎥⎣ 2 ⎦ ⎢εL(1,−1) ⎥
⎣ ⎦ ⎣ ⎦ ⎣ ⎦
2008). However, few existing commercial RTK systems
provide sufficient performance parameters in their
specifications. Obviously, more detailed performance where δP(1,1) , δL ( 4, −3) and δL (1, −1) are the residual
information would indeed help the users choose a vectors between the observed and computed range vector
desirable RTK system to meet the performance ρ or the n×1 double-differenced P(1,1), L(1,-1) and L(4,-3)
requirements, including integrity requirements. measurement vectors; I is the n×n identity matrix; εp1,1,
εL(1,-1), εL(4,-3), are the noise vectors for P(1,1), L(1,-1) and
3. Linear equations for ambiguity resolution L(4,-3) measurements, respectively. n=k-1 where k is the
with wide-lane and narrow-lane phase number of satellites used in computation.
measurements
For convenience, Equations (1) and (2) are rewritten as
For a typical single-base RTK problem, the standard follows,
linearised observation equations for the n×1 double- δY j = AjδX j + B j N j + ε j (6)
differenced pseudoranges P1 (or C/A) and P2, carrier
phases L1 and L2 can be written as follows (Misra and E (ε j ) = 0;Var (ε j ) = σ 2W j−1 (7)
Enge, 2004)
where the subscript j represents the jth epoch; δY is the
⎡ δP1 ⎤ ⎡ P1 − ρ ⎤ ⎡A⎤ ⎡0 0⎤ ⎡εP1 ⎤ m×1 observation vector; A is the m×3 matrix; δX is the
⎢δP ⎥ ⎢P − ρ⎥ ⎢ ⎥ ⎢0 0⎥ N ⎢ ⎥
⎥⎡ 1 ⎤ + ⎢εP2 ⎥ (1)
3×1 state vector; and B is the m×p matrix, N is the p×1
⎢ 2 ⎥ = ⎢ 2 ⎥ = ⎢A⎥ δX − ⎢
⎢δL1 ⎥ ⎢L1 − ρ⎥ ⎢A⎥ ⎢λ1I 0 ⎥⎢⎣N2 ⎥⎦ ⎢εL1 ⎥ ambiguity vector; in which m=3(k-1) and p=2(k-1) with
⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ dual-frequency GPS measurements.
⎣δL2 ⎦ ⎣L2 − ρ⎦ ⎣A⎦ ⎣ 0 λ2I⎦ ⎣εL2 ⎦
The above equations are provided for each measurement
where ρ is the n×1 computed double-differenced range epoch, implying that the state and ambiguity parameters
are estimated and fixed with the measurements at the
vector; A is the n×3 observational matrix; δX is the 3×1 current epoch only, which yields desirable kinematic
user state vector; the carrier phases L1 and L2; have the position solutions without imposing the assumptions of
wavelengths λ1 and λ2 and the integer ambiguities phase measurement continuity and sample intervals.
N1 and N 2 respectively; εp1, εp2, εL1 and εL2 are the noise Modelling is always the first key process for a RTK
vectors for the respective measurement vectors system. This includes the processes of combining and
differencing measurements, imposing constraints such as
δP1 , δP2 δL1 and δL 2 . known coordinates and integers, applying ionosphere
and troposphere corrections etc. The stochastic models
Feng and Rizos (2007) and Feng (2008) suggested the (7) give the statistical knowledge or assumptions on the
use of the Wide-Lane (WL) L(1,-1) and Narrow-Lane (NL) residual errors and measurement noises, such as zero
 Feng et al: GPS RTK Performance Characteristics and Analysis
5

mean white noise, correlations between the accuracy in horizontal and vertical direction is illustrated
measurements of different epochs (Wang, 2000; Wang et in Fig. 3, confirming the formal horizontal and vertical
al., 2002) accuracy within 1cm+0.5ppm and 2cm+1ppm
respectively.
The next key process is to complete AR and PE
following one of the AR methods, such as the Least-
50
squares ambiguity decorrelation adjustment (LAMBDA)
method (Teunissen, 1995; Teunissen et al., 1997), 45
Minima Search (LMS) method (Pratt et al., 1997). Any 40
improved version of the methods will be an additional 35

T T F F (s e c o n d )
advantage. The process basically consists of a Least- 30
Squares estimator and an Integer Search Engine. The 25
estimator provides initial real values for both state 20
parameters and ambiguity parameters and their 15
covariance matrix for the AR integer search, and then 10
final PE after ambiguities are fixed to their correct 5
integer values. The integer search engine performs a 0
statistical search over the potential ambiguity candidates 0 5 10 15 20 25 30 35
to find and validate the best set of integer candidates.
Baseline (km)

Implementation of efficient multipath mitigation Fig. 2 TTFF (seconds) plotted against baseline lengths
approaches, quality control and quality assurance
procedures in the above modeling and estimation Thanks to HandyNav (2005), we were also able to
processing is also important. It is fairly the case that the examine AR availability and AR reliability against
success of a RTK system depends on detailed processing different baselines. The GPS data sets were obtained
techniques. Some software systems implement a more from 16 static baselines over 2 to 45 kilometres from 60
efficient integer search algorithm, whilst others are to 400 hours. Each data set was processed separately
superior in deterministic and/or stochastic modeling. The every 300 seconds, producing over 250,000 sets of
most successful AR software takes good care of the results and solutions. Therefore the AR availability and
detailed elements, this being especially true in the reliability results can more definitively represent the
current GPS system, where only L1 and L2 carriers are performance characteristics of the tested RTK system.
available for AR.

4. Performance Analysis of Experimental RTK 0.06

Solutions North
0.05 East
Up
This section will provide numeral analysis results for the
P o s itio n a l S T D v a lu e (m )

1cm+0.5ppm
performance of RTK solutions obtained from a 0.04 2cm+1ppm

commercial RTK system and the new algorithms

described in Section 3, according to the performance 0.03

characteristics defined in Section 2.

0.02
TM
4.1 HD-RTK2 Performance
0.01
TM
A commercial RTK system, HD-RTK2 , developed by
HandyNav Inc (HandyNav, 2005), was provided to the 0
0 5 10 15 20 25 30 35
first author for this performance analysis, so that we can Baseline (km)

demonstrate some of the performance parameters and Fig. 3 RTK positioning (STD) accuracy vs base-rover
how the different parameters are obtained through distances
experiments and are related to each other. Using two
NovAtel OEM4 receivers, the GPS testing data were Fig. 4 illustrates the AR availability varying with
collected for seven static baselines over 2.5 to 31 baseline lengths, while Fig. 5 plots the AR reliability
kilometres in Brisbane and processed using the HD- against the baseline length, showing the difference and
RTK2TM software. similarity between the two indicators. We see that AR
reliability is not necessarily worse than AR availability.
Fig. 2 shows the TTFF (seconds) versus the baselines in But, in general, the longer the baseline is, the lower the
km in the above tests. The RTK standard deviation (STD) AR availability and AR reliability are.
 Feng et al: GPS RTK Performance Characteristics and Analysis
6

demonstrated in Feng and Rizos (2007) and Feng (2008).

We now examine the AR and positioning estimation (PE)
performance using data sets of three different baselines.
In principle, this advantage may be more evident for
longer baseline and when the AR is performed instantly
with measurements from single epochs. Hence, the
following experimental results will focus on a few key
performance parameters such as AR reliability and RTK
availability and RTK accuracy, based on single-epoch
ambiguity resolution.

Three 24-h GPS data sets were collected on 1 January

2007 from US Continuously Operating Reference
Stations network (http://www.ngs.noaa.gov/CORS). All
Fig. 4 AR availability variation Vs base-rover distances
three baselines are South-North directions, sampled at 15
second intervals.
In summary, with these extensive experimental results,
we conclude that the HD-RTM2TM system can provide
Tables 1 and 2 summarise the performance statistical
instant RTK solutions for distance of up to 20 km, and
results obtained with the models (1) and (2),
ambiguity-fixed solutions for distance of up to 50km.
respectively, for three baselines of 21, 56 and 74 km. It
The AR reliability of the fixed solutions is above 99%
is noted that the AR reliability and RTK availability of
for 20km baselines and 98% for 50 km baselines. The
the model (1) are evidently higher than those of the
position accuracy for integer-fixed solutions is
model (2), especially for the longer baselines. It is
1cm+0.5ppm (horizontal) and 2cm+1pmm (vertical). It
important to note that the above performance results are
is believed that these performance specifications would
obtained purposely to reflect the benefits of a new
be more convincing to users than the specifications given
algorithm under the same circumstance and do not
in the most commercial RTK systems
represent the potential performance of the RTK system
in use. In fact, we have intentionally removed some
modelling process like known integer constraints and
advanced stochastic modelling procedures, which could
change the AR and RTK performance results. On the
other hand, the proposed characteristics may also be
effective to assess different stochastic models and
particular processing strategies, similarly through
extensive numerical studies.

Table 1 Performance results of the model (5), with WL

L(1,-1) and NL L(4,-3) observables for three baselines
P478- P473-P478 P473-474
P474 56km 74km
21km
Fig. 5 AR reliability variation Vs base-rover distances. Total No of epochs 5760 5760 5758
Number of epochs 82 727 1309
4.2 Performance Analysis of Proposed RTK with wrong integers
Number of DD phase 72562 72452 72310
Models and Algorithms
measurements
Number of wrong 12/180 134/2487 143/4668
Using the research version of the QUT-RTK software, WL/NL integers
we are able to test performance of different models, AR success rates for 99.97% 99.63% 99.60%
algorithms and statistical conditions and processing WL/NL signals 99.50% 93.13% 87.09%
strategies in terms of various characteristics defined in Overall(average) 99.74% 96.38% 93.35%
Section 2. In this context, we examine the performance RTK availability 98.58% 87.38% 77.27%
advantages of the model (5), using the WL L(1,-1) and NL (correct integer-fix)
L(4,-3), with respect to the model (1), using L1 and L2 RTK availability 98.44% 84.81% 68.41%
signals directly. Theoretically, the AR with the model (5) (0.025,0.025,0.05cm) 99.79% 90.73% 84.00%
may perform better than the model (1) when over longer 94.53% 90.90% 77.56%
RTK accuracy (STD 0.008m 0.009m 0.009m
baselines where the effects of ionospheric delay is
in North 0.006m 0.007m 0.008m
minimized with respect to the wavelengths, as East and Up (m) 0.025m 0.020m 0.030m
 Feng et al: GPS RTK Performance Characteristics and Analysis
7

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