Kalman Filter as Tool for the Real-time Detection of Fast
Displacements by the Use of Low-cost GPS Receivers
Paolo Dabove and Ambrogio Maria Manzino
Environment, Land and Infrastructure Department, Politecnico di Torino, Corso Duca degli Abruzzi 24, Turin, Italy
Keywords: Landslide Monitoring, GNSS NRTK Positioning, Mass-market Receivers, Kalman Filter, Accuracy.
Abstract: In this paper the problem of landslide monitoring and deformation analysis using the Kalman filter and results
obtained from a GPS mass-market receiver in real-time is addressed. Landslide monitoring and deformation
analysis are relevant aspects about the safety of human life in any terrain where landslides can impact human
activity. It is therefore necessary to monitor these effects in order to detect and prevent these risks. Very often,
most of this type of monitoring is carried out by using traditional topographic instruments (e.g. total stations)
or satellite techniques such as GNSS receivers, and many experiments were carried out considering these
types of mass-market instruments. In this context it is fundamental to detect whether or not deformation exists,
in order to predict future displacement. Filtering means are essential to process the diverse noisy
measurements (especially if low cost sensors are considered) and estimate the parameters of interest. In this
paper a particular version of Kalman Filter is considered in order to understand if there are any displacements
from a statistical point of view in real time. The tests, the algorithm and results are herein reported.
Deformation monitoring is the act of ordinary and
continuous observation of such variations that are
referred to as “deformation” (Sedlak and Jecny, 2004;
Chrzanowski et al., 1986).
Considering the types of network, deformation
survey techniques are classified as Absolute
Deformation Monitoring (some reference points
located in the area surrounding the object of interest,
i.e. dam, bridge, etc.) and Relative Deformation
Monitoring (where the reference points are located in
the structure and both the object and reference points
are subject to displacement) (Aharizad et al., 2012;
USACE, 2002). Methods of deformation monitoring
have changed considerably in principle over the past
few decades as newer data sources have come to be
used. In sparsely vegetated terrain, landslides are
routinely detected and mapped by a combination of
the interpretation of airphotos or multispectral digital
imagery and selective ground verification (Benoit et
al., 2014). However, it is quite difficult to use these
methods in rugged terrain covered with dense
vegetation. Also, landslide inventory mapping studies
typically focus on outlining boundaries and neglect
the wealth of information revealed by internal
deformation features (Cruden, 1991).
With regard to deformation analysis, it is possible
to consider two main categories (Szostak-
Chrzanowski et al., 2005): geometrical analysis,
which detects the location and the magnitude of the
deformation, and physical interpretation, which
determines the relationship between the deformation
and its causes. In this context, there are four types of
models that allow the analysis of deformation
(Welsch and Heunecke, 2001; Aharizad et al., 2012;
Brückl et al., 2013) These are the static, kinematic,
dynamic and congruence models.
This paper focuses attention on the second type of
model. Kinematic models describe deformation as a
function of time, including velocity and acceleration.
It is also possible to classify data processing
techniques into two main groups. The first consists of
robust methods, such as Iterative Weighted Similarity
Transformation (IWST) and tests (e.g. Chow test,
Chow, 1960; Bellone et al., 2016), while the second
one is composed of non-robust methods, e.g. Kalman
Filter (Li and Kuhlmann, 2008; Tasci, 2010; Simon,
2001; Gülal, 1999; Acar et al, 2004; Masiero et al,
2013). In this study attention is focused on these last
methods, and especially on the Kalman Filter, in
Dabove, P. and Manzino, A.
Kalman Filter as Tool for the Real-time Detection of Fast Displacements by the Use of Low-cost GPS Receivers.
In Proceedings of the 2nd International Conference on Geographical Information Systems Theory, Applications and Management (GISTAM 2016), pages 15-23
ISBN: 978-989-758-188-5
2016 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
order to perform a 3-D deformation analysis using a
low-cost single-frequency GPS data in real-time.
Some previous studies have also investigated the
accuracy obtainable with geodetic receivers and
antennas (Li and Kuhlmann, 2010 and 2012) while
some of them have also considered the mass-market
ones for landslide monitoring (Janssen and Rizos
2003; Squarzoni et al., 2005; Heunecke et al., 2011).
Those studies used both post-processing (Cina and
Piras, 2014) and real-time (Bellone et al., 2016)
approaches in order to analyze the various types of
landslide phenomena. In both cases, the most notable
feature of these instruments is that they provide
centimeter or sub-centimeter accuracy in real time
when phase ambiguity is adjusted (Manzino and
Dabove, 2013). This is also observed in considering
different GNSS positioning techniques (Othman et al.
2011a; Othman et al. 2011b) such as static (Brunner
et al. 2007), rapid-static (Hastaoglu and Sanli 2011),
and real-time kinematic (RTK - Wang 2011)
A practical case study will show the reliability of
the results obtained through the Kalman filter as a
statistical tool to detect and predict displacements in
real-time. A brief comparison of the results obtained
by this method and those obtained with the modified
Chow test (Bellone et al., 2016) will conclude this
Nowadays, many types of GNSS instruments are
available functioning in a variety of frequencies,
constellations and accuracies obtainable both in real-
time and post-processing (Dabove et al., 2014;
Dabove and Manzino, 2014). As previously stated,
GPS/GNSS instruments are very often used for
landslides monitoring (Eyo Etim et al., 2014) and are
frequently coupled with other instruments such as
theodolite, Electronic Distance Measurement (EDM)
(Günther et al., 2008), levels, total station (Rizzo,
2002), inclinometers (Calcaterra et al., 2012), and
wire extensometers (Bertachini et al. 2009; Coe et al.
2003; Gili et al., 2000; Malet et al., 2002; Moss, 2000;
Tagliavini et al., 2007).
In other studies GPS instruments were integrated
with other surveying techniques, such as terrestrial
laser scanning, Synthetic Aperture Radar (SAR)
interferometry (Peyret et al., 2008; Rott and Nagler
2006), and photogrammetry (Mora et al., 2003), to
investigate landslide phenomena (Wang and Soler,
2012). Some studies have also investigated the
accuracy of low-cost single-frequency GPS receivers
for landslide monitoring (Janssen and Rizos, 2003;
Squarzoni et al. 2005) both in post-processing, (Cina
and Piras, 2014), and in real-time approaches
(Bellone et al., 2016) in order to analyze various types
of landslide phenomena (landslides with low constant
velocity or with an unexpected and sudden
displacement). Considering the first approach, raw
GNSS measurements are acquired and post-
processed in a single- or multi-base solution with one
or more GNSS permanent stations or Virtual Rinex
while, considering the second one, differential
corrections provided by CORSs networks are used to
determine the rover position in real-time. In this paper
we focus our attention only on this last approach,
analysing displacements in real-time.
Table 1: Characteristics of GPS receiver and antenna.
uBlox LEA EVK-5T
Evaluation kit
Garmin GA38
GPS& Glonass L1
Constellation: GPS (50
Constellation: GPS +
C/A L1, Doppler, S/N
Gain 27 dB on the average
Cost: about 250 € Cost: about 50 €
The employment of mass-market receivers and
antennas is due to the fact that there is an high
probability to lose these instruments if an unexpected
displacement occurs: in this context, the amount of
cost is less than 1000 € for each receiver + antenna
that is an order of magnitude less than geodetic
instruments. For this study, an u-blox EVK-5T
receiver (Table 1- left) with an external antenna
(Garmin GA38, Table 1 - right) was used. This
receiver has a cost of about 350 € (including a patch
antenna) while the cost of the Garmin antenna is
about 50 €. One of the features of this receiver is that
it is able to receive in input the differential corrections
obtained from a Continuous Operating Reference
Stations (CORSs) network.
GISTAM 2016 - 2nd International Conference on Geographical Information Systems Theory, Applications and Management
The experiments using this mass-market receivers for
Network Real Time Kinematic (NRTK) positioning
were performed within the Regione Piemonte
CORSs network (Figure 1). The network product
used is the VRS
stream broadcasted by the network
software SpiderNet of the Leica Geosystems
Figure 1: The GNSS CORSs network of Regione Piemonte.
In previous studies (Bellone et al., 2016) it was
possible to analyze the performances obtainable
considering a static positioning using both real-time
and post-processing approaches with this type of
receiver and antenna.
The antenna was mounted on a sledge (Figure 2)
composed by a complex system of micrometric
screws that allow small and controlled displacements,
in order to verify the quality of the positioning and the
reliability of the statistic tests that were to be
The movements are set by means of a hand-wheel,
which moves the sledge along the rail. It is therefore
possible with a millimetre tape to obtain direct and
visual information about the movements in order to
compare the imposed movements against those
measured by GNSS instruments. With this sledge,
horizontal and vertical movements up to 1.30 m and
0.4 m respectively are possible.
As stated in previous studies (Cina et al., 2014;
Bellone et al., 2016), there is always a precision of the
sledge movement of about 1mm. Therefore it is
possible to consider this value as the “scale
resolution” of this support.
The patch antenna was mounted on this sledge as
shown in Figure 2. The positioning results were
obtained with a frequency of 1 Hz, considering
displacements equal to 1 cm both in planimetry and
in altimetry which were provided manually at 30
second intervals.
Figure 2: The sledge where the GNSS antenna was
To perform the NRTK positioning, the routines
RTKLIB V. 2.4.2 (http://www.rtklib.com/) were used
(Takasu and Yasuda, 2009). This software was
chosen because it supports standard and precise
positioning algorithms with GPS, Global'naja
Navigacionnaja Sputnikovaja Sistema (GLONASS)
and Quasi-Zenith Satellite System (QZSS)
constellations, considering also different positioning
modalities for both real-time and post-processing
approaches: single-point, DGPS/DGNSS, Kinematic,
Static, Moving-baseline, Fixed, etc. Moreover the
software is able to manage both the proprietary
messages (e.g. u-blox LEA-4T, 5T, 6T) and external
communication via serial, TCP/IP, NTRIP etc. of
several GNSS receivers. In particular, the RTKNAVI
tool was used for these experiments. This tool allows
the input of both the raw data (pseudorange and
carrier-phase measurements) of the u-blox receiver
and the stream data coming from a network with
NTRIP authentication (Weber et al., 2006). For this
reason the receiver was connected to a laptop to
enable Internet connection and to store the NMEA
sentences (Manzino and Dabove, 2013). Another
peculiarity of this software is that it allows the fixing
of the phase ambiguity for real-time kinematic
positioning, even if the receiver uses only the L1 GPS
Kalman Filter as Tool for the Real-time Detection of Fast Displacements by the Use of Low-cost GPS Receivers
The Kalman Filter (KF) was designed to estimate
linear dynamic systems (Kalman, 1960; Kalman and
Bucy, 1961). According to Grewal and Andrews
(1993), the Kalman Filter is an estimator for what is
called the linear-quadratic Gaussian (according to
Linear Quadratic Gaussian – LQG) (Mäkilä, 2004),
while Maybeck (1979) claims that the Kalman Filter
is simply an optimal recursive data processing
The intuition of this filter is represented by the
possibility of updating an estimate of the least squares
adjustment due to the introduction of new
observations, without recalculating the entire system.
The Kalman filter consists of two steps (Welch
and Bishop, 2003): filtering and smoothing. The first
allows the best parameter estimation at the current
epoch to be determined, while the second, starting
from the last epoch of measurement, allows the best
parameter estimation of the previous epochs to be
determined. For the real-time purposes of this study,
only the filtering process is applicable.Unlike the
sequential least squares method, one characteristic of
the Kalman filter is represented by the fact that it can
be used for dynamic problems (Wei et al., 2010).
For this reason, the vector containing the
parameters to be estimated will be called the state
This vector, which contains, for example, the
position and speed of an aeroplane, is not the same at
the time i and at the time i-1. It is possible to assume,
however, the existence of a simple relationship (e.g.
linear), among the state parameters of two following
epochs, the said state equation:
|1 1 1|1ii i i i i
is the system transition matrix,
1| 1ii
are the state vectors at different epochs.
The measurement equation, similar to that
commonly used in the least squares method, should
now be added:
Hx e
is the measurement vector and
is the
observation matrix at epoch i.
As it is possible to see from (1), the state equation
includes the errors
, which assumes zero mean and
known dispersion matrix
. On the other side, the
measurement equation (2) includes the measurement
, that also, in this case, are assumed to have
zero mean and known dispersion matrix
. Another
hypothesis is given by the fact that it is assumed that
the measurement errors are independent with respect
to the state errors.
Given these preliminary remarks relating to the
classic version of the filter, it is necessary to analyze
in which way the measurement and state equations
can be modified if there is bias. The first applications
dates to Teunissen (1998) and Tiberius (1998) where
the goal was the detection and resolution "on the fly"
of cycle slips, or rather with a moving receiver. The
authors in fact apply to the KF a well-known
procedure that has already been previously applied,
called DIA. The acronym indicates the three steps of
the process: Detection, Identification and Adaptation.
This procedure can also be considered for the
detection of movements or displacements, especially
if these movements are quick (i.e. occuring within
only two epochs), and if the accuracy of the
instruments allows their observation.
In this case, equation (1) can be written as
|1 1|1 1|1ii i i i i
xTx Bb
|1 | |ii ii ii
is a vector that identifies the position and
the velocity of the point with respect to the initial
position while
is a scalar value that represents the
difference between the coordinates estimated at
epoch i and i-1. The
term represents the biases,
such that the possible displacements occurred
between two consecutive epochs. If one considers
only the height component (called z) the relationship
can be written as:
where z is the position and v the velocity of the point
is the bias of the position and
the bias of the
velocity) considering only the up component. So
01 01
under the hypothesis of a constant and known
velocity motion,
become scalar values, then:
GISTAM 2016 - 2nd International Conference on Geographical Information Systems Theory, Applications and Management
= and
So, equations (1) and (2) can be written as:
|1 1|1
ii i i
ii ii
yH e
22 22 22
22 22 22 22
00 00
xx x
xx xx
where I (in the first equation) represents the identity
matrix and C
is the var-covariance matrix of
parameters. If the mean velocity is set equal to zero,
previous equations can be written as:
|1 1|1
ii i i
 
 
 
ii ii ii
yH e
The var-covariance matrices in these experiments are
chosen respectively as:
10 0
10 0
The weights were chosen according to both the
accuracy of the measurements and the expected
displacements (that have an order of magnitude of 1
cm) in an adaptive way.
As it is known, at every period it is possible to test
the predicted residuals. If these last are defined as:
with their var-covariance matrix
it is possible to identify the displacement as an outlier,
according to the
test. The
represents the var-
covariance matrix of parameters estimated at epoch i.
Since, in this case, there is only one measurement
equation but two unknowns, the DIA does not provide
reliable results, as is known in the literature (Baarda,
1968; Teunissen and Salzmann, 1989; Salzmann
1995). However, by using the Kalman filter, the
solution can also be obtained in this case.
Accordingly, the Thomson test can be used in
order to define if a displacement occurs:
represents the significance level (in our
case equal to 10 % that represents the probability of
rejecting the null hypothesis when it is true) and
is the degree of freedom of the system, that in this
case can be determined as the trace of the redundancy
ii ee
dof tr R tr I H Q H C
So if
it can be assumed that the obtained
values are the positioning results, otherwise there is
the possibility that a displacement occurs. In this case,
the Minimum Detectable Bias (MDB) is
calculated in order to verify if this value is a real
The method previously described is applied to two
real-time datasets that simulates a landslide. As
previously stated, the system was composed as shown
in Figure 2. The positioning results were obtained
with a frequency of 1 Hz, considering displacements
equal to 1 cm both in planimetry and in altimetry
provided manually every 30 seconds. This can be
seen in Figure 4, where two cases, one with good
(number of satellites greater than 7) and another one
with low (only 5 satellites) satellite visibility, are
considered. The results shown in this paper will refer
only to the second case, that represents the worst
available possibility.
Kalman Filter as Tool for the Real-time Detection of Fast Displacements by the Use of Low-cost GPS Receivers
Figure 3: Altimetric profile of displacements with good
(more than 7 satellites - left) satellite visibility.
Figure 4: Altimetric profile of displacements with poor
(only 5 satellites - right) satellite visibility.
Figure 5: Planimetric trend (up) and estimated bias (down).
The goal is to estimate the most probable value of
the bias (the occurred shift) and to add it to the value
of the bias of the previous period.
As it is possible to see from Figure 5, despite some
errors in the estimation of discontinuities (in the
circle), the solution seems to be correct. If the
detected displacements are analyzed, a success rate of
96.1% is obtained (i.e. real displacements detected
correctly). As well, 1.3% of undetected displacements
(i.e. real displacements not detected) and 2.6% of
false alarms (it means that the filter has declared a
displacement that it has not occurred) are identified.
An example of undetected or correctly detected
displacements can be seen in Figure 7, where also a
summary of obtained results can be found. Must to be
underlined that no significant differences in terms of
success rate can be obtained according to the number
of visible satellites, even if the quality of the
positioning changes as it is possible to see from
Figure 3. The reported tests were made considering
from 5 up to 7 satellites while all results shown in this
work are obtained with a number of satellites equal to
6, that is a reasonable number of satellites visible with
mass-market receivers, also in hard-environment
Figure 6: Altimetric trend (up) and estimated bias (down).
Also the root mean square (RMS) values of the
solution and biases are evaluated. As can be seen
from Figure 8, the accuracy of the solution is very
high. This means that the Kalman filter can be
considered as a useful tool to detect displacements
with this type of receivers and that the tuning of the
filter was correctly achieved.
Figure 7: Results obtained with the Kalman filter.
If the tuning is carried out correctly, this filter
allows both to decrease the accidental error of RTK
positioning and to control the possible gross-errors or
outliers that can be due to a false fix of the phase
GISTAM 2016 - 2nd International Conference on Geographical Information Systems Theory, Applications and Management
ambiguity and not to an unexpected displacement (in
this case this error goes to zero at the next epoch).
Figure 8: RMS of estimated biases and solution.
This can be affirmed considering the previous
results (Figure 8) and those obtained if a planimetric
positioning error of 24 hours is considered (Figure 9).
Figure 9: Planimetric positioning error (the dotted line
represents the significance level equal to 95%).
In fact, in the first case the RMS of positioning
(less than 2 cm) is better than those obtained in the
following graph (5 cm at 95% of reliability).
Finally, these results were compared with those
obtained in a previous study based on a modified
Chow test. Applying the methods described in the
literature (Bellone et al., 2016), and considering a 10-
element sample size (meaning that a sample
composed of 10 epochs = 10 seconds of latency of
alarm at 1 Hz of acquisition rate), this method
correctly identified 93.1% of the displacements, with
a very low rate of false alarms equal to 3.3%. Anyway
these values are greater than those estimated with the
Kalman filter, that has shown the best performances
in terms of both false alarms (2.6%) and undetected
displacements (1.3%).
In this study, the Kalman filtering technique has been
applied for kinematic deformation analysis
procedure. A GPS data set that simulates a landslide
movement was collected and the proposed method
has been tested. The two methods (Kalman filter and
modified Chow test) produced comparable results,
even though the proposed version of the Kalman filter
has shown the best performance. Interesting results
have been obtained in real-time also by employing a
mass-market GPS receiver. In this context, the results
have shown the possibility of using this type of
receivers for this kind of application.
The employment of these receivers on a landslide
site could be useful also from an economic point of
view. The total cost of receiver, antenna, transmission
system and power supply (solar panel and battery) is
about € 600. The advantage is that the economic
damage in case of an unexpected event is less than
could occur if a geodetic GNSS instrumentation is
utilized. At the same time, it is possible to calculate
the position of the receivers in a similar way to the
CORS network, with obvious advantages in the
precision and accuracy of the results and the landslide
This study has considered static motion but it is
also possible to suppose a motion where the bias is
the change of velocity between two points.
Considering some preliminary results, in this last
case the Kalman filter appears to provide better
results with respect to statistical tests. This aspect will
be investigated subsequently.
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