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GNSS定姿态_各种方法评估1
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Received November 25, 2019, accepted January 8, 2020, date of publication January 28, 2020, date of current version February 10, 2020.
Digital Object Identifier 10.1109/ACCESS.2020.2970083
GNSS-Based Attitude Determination
Techniques—A Comprehensive Literature Survey
ALMAT RASKALIYEV
1
, SAROSH HOSI PATEL
1
, TAREK M. SOBH
1
, AND AIDOS IBRAYEV
2
1
Robotics, Intelligent Sensing and Control (RISC) Laboratory, School of Engineering, University of Bridgeport, Bridgeport, CT 06604, USA
2
Department of Mechanical Engineering, Faculty of Mathematical Engineering, Al-Farabi Kazakh National University, Almaty 050061, Kazakhstan
This work was supported by the University of Bridgeport.
ABSTRACT GNSS-based Attitude Determination (AD) of a mobile object using the readings of the
Global Navigation Satellite Systems (GNSS) is an active area of research. Numerous attitude determination
methods have been developed lately by making use of various sensors. However, the last two decades have
witnessed an accelerated growth in research related to GNSS-based navigational equipment as a reliable
and competitive device for determining the attitude of any outdoor moving object using data demodulated
from GNSS signals. Because of constantly increasing number of GNSS-based AD methods, algorithms, and
techniques, introduced in scientific papers worldwide, the problem of choosing an appropriate approach, that
is optimal for the given application, operational environment, and limited financial funding becomes quite
a challenging task. The work presents an extensive literature survey of the methods mentioned above which
are classified in many different categories. The main aim of this survey is to help researchers and developers
in the field of GNSS applications to understand pros and cons of the current state of the art methods and
their computational efficiency, the scope of use and accuracy of the angular determination.
INDEX TERMS Attitude determination, GNSS, angular resolution, ambiguity resolution.
I. INTRODUCTION
The attitude of any object is its spatial orientation with
respect to the object’s mass center. This parameter is usu-
ally represented by Euler angles, Rodriguez parameters,
and quaternion or direction cosine matrix. Attitude Deter-
mination is an operation of attitude computation of the
object relative to some inertial reference frame or Earth.
AD is usually provided by sensors installed on the object
and mathematical computations made on the microcon-
troller. Algorithms and techniques applied and computational
power of the processing unit usually define the accuracy
constraints. Attitude determination subsystems are widely
implemented in satellites, vehicles, boats, aircrafts and other
mobile objects. Inertial Measurement Units (IMU), GNSS
receivers, magnetometers, digital compasses, gyroscopes,
and accelerometers might be used as sensors in AD subsys-
tems. Then, point to point or recursive attitude determination
algorithms process readings from the sensors in order to
estimate the attitude by means of kinematic and dynamic
models.
The associate editor coordinating the review of this manuscript and
approving it for publication was Masood Ur-Rehman .
Recent studies have proved that the GNSS can take an
important place in numerous applications, including attitude
determination, because of its stable operation, cost effective-
ness and low power consumption. Computational methods
and algorithms developed for solving problems in the area of
GNSS-based AD are described in a great amount of scientific
reports and journals that is why strong demand for providing
well-structured reviews of these methods arises.
In [1], the authors provide a short overview of GNSS-
based methods and models for AD of a spacecraft by means
of phase measurements. The authors of [2] compare distinct
methods, constrained Least-squares Ambiguity Decorrela-
tion Adjustment (LAMBDA) and multivariate constrained
LAMBDA, which represent two different approaches in the
area of GNSS-based AD. The researchers in [3] make a
comparison between methods based on single and double
differenced carrier phase measurements. Baroni and Kuga
in [4] made theoretical and experimental analysis that com-
pared Least-Squares Ambiguity Search Technique (LSAST)
and LAMBDA algorithms using quaternion formulation. The
same researchers in [5] made a comparison between LSAST
and LAMBDA methods providing their findings in analy-
sis of the computational process of ambiguity resolution.
VOLUME 8, 2020
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see http://creativecommons.org/licenses/by/4.0/
24873
A. Raskaliyev et al.: GNSS-Based AD Techniques—Comprehensive Literature Survey
However, the works mentioned above do not encompass all
contemporary methods of GNSS-based AD in a single entity
written in some structured way.
With the background presented in Section 1, the second
section provides an overview and classification of current
mathematical algorithms and techniques utilized in the pro-
cess of GNSS-based AD. It outlines roughly three algorith-
mic steps of attitude determination and ambiguity resolution
during computational operations, as well as baseline and
attitude approaches in constructing GNSS-based AD meth-
ods. The third section elaborates on the interrelation between
the sensors used for AD and corresponding computational
techniques. The forth section discusses optimal ways of pro-
cessing GNSS measurements depending on the mathematical
model chosen for solving an attitude determination prob-
lem. This section also explains positioning and geometry
free GNSS models that are used while employing various
types of GNSS readings. In the fifth section, we describe the
methods applied based on various dynamic and kinematic
models of the moving object given in the problem. Finally,
we make some conclusions and illustrate a representative list
of research articles to emphasize the performance of GNSS-
based AD methods.
II. GNSS-BASED ATTITUDE DETERMINATION METHODS
Current GNSS-based methods employed in AD algorithms
can be generally divided into three operational groups, which
are aimed for line bias/baseline computation, integer ambi-
guity resolution (IAR) and estimation of attitude angles [6].
‘‘Line biases commonly occur due to the differences in cable
lengths between antennas and the receiver’’ [7] or differences
in radio frequency (RF) front ends in the receiver [8] or a
combination of both. These parameters are generally given
as constant variables and calibrated using some technique
before launching a custom AD algorithm in GNSS attitude
determination receivers, for example, Trimble’s TANS (Trim-
ble Advanced Navigation Sensor) Vector [6] and Space Sys-
tems/Loral’s GPS Tensor. Another method is that the line
biases are treated as components of the state vector of the
system, and therefore, estimated along with other state com-
ponents (for example [8]).
A GNSS receiver is able to measure only the fractional
part of the carrier phase. The integer number of wavelengths
between an antenna and a satellite cannot be measured
directly. This is a well-known problem of integer ambi-
guity. Two main approaches have evolved to resolve the
problem of integer ambiguity in the area of GNSS-based
attitude determination. The approaches are either motion-
based (for instance, [7]) or search-based (for example, ( [9]).
Motion-based methods require acquiring measurements for a
period of time during which considerable changes of a visible
navigational satellites constellation or the antenna platform
motion have happened. The search-based algorithms utilize
only single epoch readings to retrieve the most likely solution
that is why they are sometimes subject to incorrect solutions
because of measurement noise. Two search-based techniques
have been developed. In the first technique, the search is
conducted in a real number domain. The search domain is
composed of all potential grid points in the coordinate system
of solution parameters. These parameters might be the actual
length and azimuth angle of a baseline (for instance, [9])
or Euler angles of the antenna platform [10]. In the second
search-based technique, the search environment is chosen in
the integer number domain. ‘‘The search domain is composed
of all potential combinations of integer ambiguity candi-
dates’’ [9].
In scientific publications, various integer ambiguity reso-
lution methods have been elaborated [1], like Least-Squares
Ambiguity Search Technique (LSAST) [11], Fast Ambigu-
ity Resolution Approach (FARA) [12], Modified Cholesky
decomposition [13], most widely applied Least-squares
Ambiguity Decorrelation Adjustment (LAMBDA) [14], Null
method [15], Fast Ambiguity Search Filter (FASF) [16],
Three Carrier Ambiguity Resolution (TCAR) [17], Inte-
grated TCAR [18], Optimal Method for Estimating GPS
Ambiguities (OMEGA) [19] and Cascade Integer Resolution
(CIR) [20]. A comparison of LAMBDA with CIR, TCAR,
ITCAR and the Null-method is provided in [21] and [22].
Nowadays the LAMBDA method is a common method for
solving GNSS integer ambiguity resolution problems with
unconstrained baselines. For nonlinearly constrained ambi-
guity resolution problems, the single baseline constrained
LAMBDA method [23] was introduced and the newly
suggested The Multivariate Constrained LAMBDA method
([24] and [25]) determines the integer ambiguities and Euler’s
angles in an integral manner.
The third operational group of AD algorithms, implemented
in the procedure of attitude angles estimation, is composed of
three consecutive steps [26]. Firstly, a typical least-squares
adjustment is employed in order to achieve the so-called
float solution. All unknown parameters are evaluated to be
real-valued. In the second step, the integer constraint on
the ambiguities is taken into account. This implies that the
float ambiguities are mapped to integer parameters. Various
options of the mapping function are viable. The float ambi-
guities can merely be rounded to the closest integer values or
rounded to some extent so that the correlation between the
ambiguities reaches its minimum. Application of the integer
least-squares estimator becomes optimal, that increases the
probability of valid integer estimation. In the third step,
after fitting the ambiguities to their integer counterparts, the
remaining unknown parameters are resolved based on their
correlation with the fixed ambiguities [27].
Among IAR methods, the integer estimators widely uti-
lized in GNSS applications [28] are Integer least squares
(ILS) [29] Integer Bootstrapping (IB) [30], and Integer
Rounding (IR) [31]. They present various options of mapping
to integer parameters.
From the point of view of measurement processing,
the techniques for attitude angles estimation can be approxi-
mately divided into the following two types: (a) point estima-
tion techniques (for example [7]) and (b) stochastic filtering
24874 VOLUME 8, 2020
A. Raskaliyev et al.: GNSS-Based AD Techniques—Comprehensive Literature Survey
techniques (for instance [32]). There are two categories of
point estimation techniques. The first category of point esti-
mation technique employs vectorized measurements [33] and
can be regarded as a two-level optimal estimation problem,
the least squares problem and Wahba’s problem [34]. The sec-
ond category of point estimation techniques is related to
the differenced carrier phase measurements directly. It either
utilizes a non-linear, least-square fit (NLLSFit) method [35]
or transforms the problem interchangeably into Wahba’s
problem [7].
III. SENSORS USED IN GNSS-BASED AD
To solve the problem of attitude determination of the mov-
ing object, one can use only GPS and other satellite nav-
igation systems (standalone GNSS AD), make integration
of GNSS receivers with INS (for example accelerometer
and gyroscope), as well as integrate with other navigational
sensors (for instance magnetic antenna, digital compass and
magnetometer).
Standalone GNSS AD may require integration of GPS
receivers with other satellite navigation sensors such as
GLONASS, Russian Global Navigation Satellite System,
Galileo, Europe’s own global navigation satellite system,
and Compass (Chinese second-generation satellite navigation
system also known as Beidou-2). GNSS-based AD may be
categorized as dedicated or non-dedicated. In the dedicated
AD system, a single exclusively focused GNSS receiver is
used while in the non-dedicated AD system, a set of indepen-
dent, general-purpose GNSS receivers is used for the attitude
determination of the object. Many companies that manufac-
ture GNSS receivers like Trimble [36], [37]; Texas Instru-
ments [38], [39]; Ashtech [40]–[42]; Adroit Systems [43],
and others have been designing dedicated GNSS receivers
with multiple antennas for attitude determination.
If we consider measurement types used for standalone
GNSS-based AD, then they are divided as L1 frequency
and L1/L2 frequency GNSS receivers. Double frequency
receivers have much higher cost, but they lead to improve-
ment of ambiguity resolution because of tackling the disper-
sive ionosphere delays.
The number of GNSS antennas, used for AD, might also
vary. There are computational methods that use only one
GNSS antenna (for instance [44], [45]), two GNSS anten-
nas [46]–[48] that lead to a single computational baseline
and three or more GNSS antennas. Employing one or two
antennas usually provides an opportunity to calculate with
good precision only two of three attitude angles.
GNSS receivers can also be divided as sensors able to
register code phase (code) and carrier phase measurements
or only code measurements. Furthermore, the majority of
GNSS receivers provide code and carrier phase measure-
ments. Because of the nature of these readings, AD based on
carrier phase measurements can result in much more accu-
racy in comparison with code (pseudo range) measurements.
That is why a centimeter level GNSS-based AD requires
GNSS receivers that can measure carrier phase with a good
precision. However, code measurements are often utilized
in code-phase smoothing and cycle slip detection and repair
algorithms, while utilization of carrier phase measurements
requires implementation of IAR algorithm.
IV. GNSS-BASED ATTITUDE DETERMINATION MODELS
An overview of GNSS models and their applications in
different areas [1] are presented in textbooks such as
[49]–[54]) GNSS models have two main types: non-
positioning or geometry-free models and the positioning or
geometry-based models. Furthermore, various GNSS models
might be distinguished by virtue of the differencing utilized.
By differencing, we mean to take the differences between
measurements from different receivers and/or different satel-
lites. It is usually used in order to get rid of several error
types from the observation equations [23]. The single dif-
ference and double-difference methods are discussed in [3].
Unconstrained baselines are baselines for which preliminary
information about the length is not known and constrained
baselines are baselines for which the length is a-priori known
and constant [55].
In general, all GNSS baseline models can be put in the fol-
lowing formula of linearized observation equations according
to a Gauss-Markov model [56]:
E(y) = Aa + Bb; D(y) = Q
yy
(1)
where y is the known vector of GNSS observables, a and
b are the unknown parameter vectors of integer ambigui-
ties and real-valued baselines correspondingly. E(:) and D(:)
denote the expectation and dispersion operators, and A and B
are the given design matrices which bound the data vector
to the unknown parameters. Matrix A includes the carrier
wavelengths and the geometry matrix B includes the receiver-
satellite unit line-of-sight vectors. The variance matrix of y is
set to the positive definite matrix Q
yy
.
The model defined by (1) is referred as the unconstrained
model and its Integer Least Squares (ILS) solution is found
in [56]. For GNSS-based attitude determination applications,
one often may take advantage of the knowledge of the addi-
tional constraint on the baseline vector length, so that the
Integer Least-Squares minimization problem can be reorga-
nized as a Quadratically Constrained Integer Least-Squares
(QC-ILS) problem [56].
After applying double differencing, the model (1) can be
converted into a single-epoch, multi-frequency GNSS array
model in a multivariate form as:
E(Y ) = MX + NZ , X ∈ R
3×r
, Z ∈ Z
fs×r
, (2)
with r number of baselines, f number of GNSS frequencies,
s+1 number of GNSS satellites tracked, Y the 2fs × r data
matrix of double-differenced observables, (M, N ) the 2fs ×
(3 + fs) design matrix, X ∈ R
3×r
the unknown real-valued
baseline matrix in the reference frame and Z ∈ Z
fs×r
the
unknown integer ambiguity matrix.
Depending from the types of constraints employed,
the model (1) can be developed into a general GNSS attitude
VOLUME 8, 2020 24875
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