Aided Inertial Navigation in GPS-denied
Environments Using Synthetic Aperture
Processing
Prepared by:
J. Dillon
National Research Council Canada, Flight Research – Aerospace Portfolio
1200 Montreal Road, U-61, Ottawa, ON K1A 0R6
NRC MOU Annex Number: DND/NRC/AERO/2015-13
Technical Authority: Vince Myers, Defence Scientist
The scientific or technical validity of this Contract Report is entirely the responsibility of the Contractor and the contents do
not necessarily have the approval or endorsement of the Department of National Defence of Canada.
Contract Report
DRDC-RDDC-2016-C200
March 2016
© Her Majesty the Queen in Right of Canada, as represented by the Minister of National Defence, 2016
© Sa Majesté la Reine (en droit du Canada), telle que représentée par le ministre de la Défense nationale,
2016
Flight Research – Aerospace Portfolio
Aided Inertial Navigation in GPS-denied
Environments Using Synthetic Aperture
Processing
CR-FRL-2016-0034
March 2016
Authors/Auteurs : J. Dillon
FLIGHT RESEARCH LABORATORY
Aided Inertial Navigation in GPS-Denied
Environments Using Synthetic Aperture
Processing
Report No.: CR-FRL-2016-0034
Date: March 2016
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CR-FRL-2016-0034
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ABSTRACT
The focusing of a Synthetic Aperture Radar or Sonar (SAR/SAS) provides a precise measurement of the
trajectory of the host platform over the length of the synthetic aperture. Although GPS is a widely used
navigation sensor for unmanned systems, many operations either occur or could potentially occur in GPSdenied environments such as hostile airspace or covert underwater operations. In this report, the position
measurement from an Inertial Navigation System (INS) is corrected using the integrated pulse-to-pulse
displacement from synthetic aperture correlation processing. Results were obtained using data collected
from a DRDC autonomous underwater vehicle operating in the Arctic during the 2014 Victoria Strait
Expedition. The performance of the SAS was compared with conventional Doppler velocity aiding to
evaluate the accuracy improvement of synthetic aperture aided navigation. While the motion estimate is
ideal for focusing an image over the length of the synthetic aperture (on the order of 10 m for SAS), this
precision does not necessarily translate into an improvement in long term navigation accuracy unless the
sensors are carefully aligned and calibrated.
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RÉSUMÉ
La focalisation d’un radar à synthèse d’ouverture ou sonar (SAR/SAS) fournit une mesure précise de la
trajectoire de la plateforme hôte sur toute la longueur de l’ouverture synthétique. Bien que le GPS
constitue un capteur de navigation largement utilisé pour les systèmes sans pilote, plusieurs opérations
sont menées ou pourraient prendre place dans des environnements sans service GPS, tel qu’un espace
aérien ennemi ou lors d’opérations sous-marines secrètes. Dans ce rapport, les mesures de positionnement
provenant du système de navigation par inertie (INS) ont été corrigées à l’aide du déplacement à
impulsions intégré résultant du traitement par corrélation des mesures d’ouverture synthétique. Les
résultats s’appuient sur les données recueillies à l’aide d’un véhicule sous-marin autonome de RDDC en
activité dans l’Arctique durant l’expédition dans le détroit de Victoria de 2014. La performance du SAS a
été comparée à celle d’un détecteur de vitesse Doppler conventionnel pour évaluer l’amélioration de
l’exactitude de la navigation avec un dispositif à ouverture synthétique. Bien que l’estimation du
mouvement demeure idéale pour focaliser une image sur toute la longueur de l’ouverture synthétique (de
l’ordre de 10 m pour le SAS), cette précision n’entraîne pas automatiquement une amélioration à long
terme de l’exactitude de la navigation, à moins que les capteurs ne soient soigneusement alignés et
étalonnés.
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Table of Contents
1.0
INTRODUCTION........................................................................................................................... 9
2.0
THEORY ....................................................................................................................................... 10
2.1
Principles of acoustic velocity logs ............................................................................................. 10
2.2
Sources of error ........................................................................................................................... 11
2.3
SAS motion estimation ............................................................................................................... 12
3.0
EXPERIMENT ............................................................................................................................. 13
3.1
2014 Victoria Strait Expedition .................................................................................................. 13
3.2
Arctic Explorer AUV .................................................................................................................. 14
3.3
AquaPix InSAS ........................................................................................................................... 14
4.0
RESULTS ...................................................................................................................................... 15
4.1
AUV deployment ........................................................................................................................ 15
4.2
DVL aiding ................................................................................................................................. 16
4.3
SAS aiding .................................................................................................................................. 17
4.4
Velocity integration .................................................................................................................... 18
5.0
DISCUSSION ................................................................................................................................ 19
6.0
CONCLUSION ............................................................................................................................. 21
REFERENCES .......................................................................................................................................... 21
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List of Figures
Figure 1: Displaced phase centre antenna. (Source: [13]) .......................................................................... 12
Figure 2: 2014 Victoria Strait Expedition search areas. (Map: Thomas Herbreteau/Canadian Geographic.
Source: G. Hobson [16]) ............................................................................................................................. 13
Figure 3: Deployment of the Arctic Explorer AUV during the 2014 Victoria Strait Expedition. (Photo:
Nick Walker [18]) ....................................................................................................................................... 14
Figure 4: AquaPix interferometric SAS with dual-row design for multipath suppression. (Source: [24]) . 15
Figure 5: Vehicle survey track relative to the dive location of N 6927’05” W 9933’18”. Approximately
10 minutes of pre-dive and post-surfacing motion are also shown. ............................................................ 16
Figure 6: Example SAS image from outbound survey leg showing a scour mark across an otherwise flat
sandy bottom. The actual seabed image is reversed left-to-right since the image was acquired from the
sonar array on the port side of the vehicle. ................................................................................................. 16
Figure 7: Latitude correction from GPS position measurement when vehicle surfaces after completing
mission plan with DVL-aided inertial navigation. The magnitude of the latitude correction was 16.3 m. 17
Figure 8: Longitude correction from GPS position measurement when vehicle surfaces after completing
mission plan with DVL-aided inertial navigation. The magnitude of the longitude correction was 24.6 m.
.................................................................................................................................................................... 17
Figure 9: Comparison of SAS and INS+DVL velocity time series during outbound survey leg. .............. 18
Figure 10: Comparison of SAS and INS+DVL velocity time series during return survey leg. .................. 18
Figure 11: Integration of velocity error in the body frame during the outbound survey leg. ...................... 19
Figure 12: Integration of velocity error in the body frame during the return survey leg. ........................... 19
Figure 13: Integration of velocity error in the body frame during the outbound and return survey legs. ... 20
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List of Tables
Table 1: RDI Workhorse Navigator 300 kHz DVL specifications ............................................................. 10
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1.0 INTRODUCTION
GPS and other satellite-based systems have been widely used for navigation due to their accuracy, low
cost of receiver equipment, and global coverage. Here, we use the generic term GPS to refer to global
satellite-based navigation systems such as NAVSTAR (USA), GLONASS (Russia) and Galileo
(European Union) [1]. However, these technologies are vulnerable to disruption by electromagnetic
interference and they are also ineffective for underwater navigation because electromagnetic waves are
strongly attenuated by seawater. For both civilian and military applications, one must therefore consider
the problem of navigation in a GPS-denied environment such as scenarios due to hostile actions
(intentional jamming, spoofing), inadvertent interference (unintentional jamming), signal blockage (inside
buildings) or operation of Autonomous Underwater Vehicles (AUVs) and submarines where GPS is
unavailable below the sea surface. Inertial sensing is another widely used technology for navigation
which has the advantage of being self-contained in the sense that no radio-navigation aids are required.
However, the position error of an INS tends to drift in the absence of input from an aiding sensor. For
inertial navigation to be effective without aiding measurements, the sensor must either be of an extremely
high quality, such as those used in nuclear-powered submarines where long-term covert operation is
essential, or the duration of navigation must be sufficiently short for accumulated errors to remain
acceptably small, as is the case with some types of missiles and guided weapons.
Several alternatives to GPS exist. For instance, the precursors to GPS navigation include aviation radionavigation aids such as beacons (VOR/DME) and LORAN, which require an extensive infrastructure
network and lack global coverage. Many vision-based or optical sensors are also in development,
especially for land vehicle and aerial applications [2]. However, optical systems tend to lack the allweather day/night coverage of GPS and other radio signals. Also, optical systems tend to have extremely
limited range in the ocean, even in the case where the vehicle provides its own illumination of the
environment in the form of lighting or laser scanning. For underwater applications, there are acoustic
positioning systems that consist of either a network of beacons on the ocean or a surface vessel that
transmits an acoustic signal to a vehicle below the surface. These systems effectively extend the range of
GPS by taking position measurements at the surface and relaying them to a receiver below the surface
using time-of-flight or time-difference-of-arrival techniques for localization [3]. However, there is a cost
associated with the time required to deploy and recover the beacons (or a cost of operating the support
vessel). The most successful combination for underwater navigation has therefore been to combine
inertial sensing with velocity measurement from an acoustic velocity sensor that measures speed from
echoes reflected from the seafloor [4].
Velocity sensors exploiting the Doppler principle have been widely used for both aviation (Doppler radar)
and underwater applications using a Doppler Velocity Log (DVL). For inertial navigation, position is
obtained by twice integrating the signals from linear accelerometers. An accelerometer bias therefore
causes a position error that grows quadratically with time. With velocity aiding, the position error growth
is reduced to a linear function. In other words, velocity aiding provides a navigation improvement but it
does not completely solve the problem of accurate navigation for missions of long duration.
The mission for many AUVs and Unmanned Air Vehicles (UAVs) consists of mapping the environment
using a high resolution sensor such as Synthetic Aperture Radar (SAR) or Synthetic Aperture Sonar
(SAS) [5]. The focusing of a SAR or SAS provides a precise measurement of the trajectory of the host
platform over the length of the synthetic aperture. In previous work, the synthetic aperture motion
estimate has been combined with inertial sensing to improve image focusing, especially for low frequency
systems with relatively long wavelengths [6], [7]. However, the synthetic aperture correction can also be
fed back to the vehicle navigation system in post-processing to improve the position measurement used
for image georeferencing [8]. In this report, the motion estimate from a high frequency synthetic aperture
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sonar is compared with data from a DVL-aided INS for an AUV operating below the surface in the
absence of GPS. The principles of acoustic velocity sensing and SAS motion estimation are outlined in
Section 2.0, followed by a description of the data collection in Section 3.0. Results are presented in
Section 4.0 followed by a detailed discussion in Section 5.0.
2.0 THEORY
2.1 Principles of acoustic velocity logs
Acoustic velocity sensors exploit the principle that seabed echoes from successive pulses are correlated
when two or more closely spaced pulses are transmitted. The majority of in-service acoustic velocity logs
exploit the Doppler principle, which is the frequency shift of the seabed or seawater echoes due to the
relative motion of the sonar. A typical DVL consists of four narrow beams steered in the fore/aft and
port/starboard directions to estimate the 3D velocity vector from Doppler shifts associated with each
beam. The beams are steered downward approximately 30 from vertical in a compromise between
operating near nadir to maximize seabed echo strength, while also requiring a non-zero Doppler shift
when measuring the horizontal component of velocity.
Another acoustic technology for underwater velocity measurement is known as the Correlation Velocity
Log (CVL). Originally proposed in the 1950s for use with radar, it was used with sonar with some
success in the 1970s. The fundamental concept is still best described in the words of the pioneers Dickey
and Edward [9]: “The objective, in the correlation system, is to transmit two identical signals separated by
a known time interval and then to search for a separation vector and a time delay for which the correlation
(of the received signal) is a maximum.”
A CVL transmits pulses vertically downward with a much broader beam than used for DVLs. The
reflected signal is recorded by two or more receivers separated by a few centimeters. Two variations
exist: a temporal log searches for the time delay that maximizes the correlation between a pair of
receivers, whereas a spatial log finds a receiver pair that maximizes the correlation for a fixed time delay
(typically the time interval between successive pulses). In either case, the velocity estimate is found by
dividing the known distance between receiver elements by the correlation time delay.
An important advantage of the CVL over the DVL is that the measurement of velocity in the plane of the
array (i.e., the horizontal component, in the absence of pitch or roll) does not depend on the speed of
sound [10]. By its principle of operation, a CVL measures a 2D displacement vector between two receiver
channels for successive pulses, so that the corresponding velocity measurement is given simply by the
displacement divided by the time interval between pulses, with no need for a sound speed measurement.
Table 1: RDI Workhorse Navigator 300 kHz DVL specifications
Bottom Velocity
Standard deviation at 1 m/s
Standard deviation at 3 m/s
Standard deviation at 5 m/s
Velocity bias
Long term accuracy
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Value
0.4 cm/s
0.7 cm/s
0.9 cm/s
±0.2 cm/s
±0.4%
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2.2 Sources of error
The measurement from an acoustic velocity sensor consists of the true sonar velocity plus a measurement
error that is best modeled as a random variable. For example, the presence of electrical noise at the
receiver input introduces a random component in the echoes from successive pulses. In the ocean, there
can also be environmental noise in the frequency band of the sonar which can either be uncorrelated from
pulse to pulse, or correlated with a different time delay than the seabed echoes. At the relatively high
frequencies used by DVLs (>100 kHz), environmental noise is primarily due to thermal fluctuations in
the water column at the molecular scale [11]. Another source of error is due to the random distribution of
scatterers within the beam footprint. When the sonar is moving, the seabed echoes are recorded from
different spatial locations. Since the seabed echo is the sum of contributions from many scatterers within
the beam footprint, there is a pulse-to-pulse decorrelation that is well described by the van Cittert-Zernike
theorem from statistical optics [12]. Therefore, even in the limit of perfect receiver electronics, it is not
possible to eliminate the random nature of acoustic velocity measurements.
The statistics of the velocity error are usually described by specifying a single ping standard deviation
(e.g. assuming a zero-mean Gaussian distribution), a bias velocity, and a long term drift as a percent of
distance travelled. It should be noted that this description does not fully characterize the error distribution
because the bias and long term drift are typically time-varying with a mixture of random and deterministic
components. For example, one could specify a correlation time to model slowly varying errors as random
walks, or describe the power spectrum of velocity error by specifying standard deviations in a series of
frequency bands, or include directional information such as comparing the magnitudes of along track and
across track errors.
The measurement errors for a widely used DVL are specified by the manufacturer as shown in Table 1
[14]. If the velocity measurements were integrated directly (i.e., without an INS), the integration of the
single ping random error would result in a random walk position error that grows as the square root of the
integration time. However, in an aided INS, it is the accelerometer and rate gyroscope outputs of the
inertial sensor that are integrated to give position, velocity, and attitude, while the aiding measurement is
processed by a Kalman filter to correct the offsets of the inertial sensors. The single ping standard
deviation of the velocity aid therefore only affects the tuning and rate of convergence of the Kalman filter,
whereas the bias velocity and long term drift determine the position accuracy of the integrated navigation
system. For a vehicle travelling at 1.5 m/s, an accuracy of 0.4% of distance travelled corresponds to a
velocity error of 0.6 cm/s.
The bias velocity causes a position error that grows linearly with time independent of the motion of the
vehicle. The effect of the velocity bias can therefore be minimized by travelling quickly to make the bias
small relative to the vehicle speed. However, in practice, it is the long term error (percent of distance
travelled) that is the dominant effect. For example, using values in Table 1 for an eight hour mission, the
position error due to the bias velocity is 58 m. For comparison, if the vehicle speed is 3 knots, the long
term error as a percentage of distance travelled is 174 m. Therefore, for AUV survey missions, there is
only a small improvement in navigation accuracy when the survey speed is increased. The choice of
survey speed is dictated by hydrodynamic efficiency and operational requirements.
The long term error specified in terms of percent of distance travelled is typical of error sources that affect
the scale factor of the measurement. For DVLs, these include errors in the sound speed measurement,
uncertainty in the DVL beam angle, a bias caused by sloping terrain, and clock drift in the receiver
electronics [15]. Another source of across track scale factor error is a misalignment angle between the
INS and DVL, which is not a DVL error per se, but affects the position accuracy nonetheless. If the
misalignment angle 𝛿𝜓 is small, then the along track velocity error is proportional to (1 − cos 𝛿𝜓 ) ≈ 0,
whereas the across track error is V𝛿𝜓 where V is the vehicle forward speed. When integrated over time T,
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the across track error is VT𝛿𝜓 . In other words, the misalignment angle in radians translates directly into a
position error as a percentage of distance travelled.
Acoustic velocity sensors measure velocity in the body frame, e.g. along the forward and lateral axes of
the vehicle, whereas positioning is performed in a navigation frame such as North/East/Vertical or the
XYZ axes of an Earth-centered Earth-fixed frame. Therefore, velocity aiding relies on a heading
measurement from the INS to transform measurements between the body and navigation frame. The
navigation error due to heading is similar to the misalignment error described above. Heading error results
in an across track error that is proportional to distance travelled. Heading error is observable by the
Kalman filter when the vehicle is maneuvering with measurements available in the navigation frame (e.g.
with GPS) [1]; however, the heading error is unobservable when aiding is performed using body axis
velocity measurements only.
2.3 SAS motion estimation
The major challenge in synthetic aperture imaging is to estimate the platform trajectory with subwavelength accuracy (on the order of 0.1 mm for high resolution sonar). This accuracy requirement is
generally beyond the capabilities of inertial measurement technologies. The most effective technique for
SAS has been a data-driven approach based on the Displaced Phase Centre Antenna (DPCA) principle
[13]. The image is divided into a series of range segments and the Line Of Sight (LOS) displacement is
estimated from cross-correlation of the received echoes using overlapping phase centres from subsequent
pings, as illustrated in Figure 1. The figure illustrates ping-to-ping surge, sway and rotation of a SAS
array in the slant range plane with overlapping phase centres indicated by the shaded regions. Ping-toping rotation is measured by an angular rate sensor, and the LOS direction can either be determined from
platform altitude (assuming a flat seabed) or from an angle of elevation measurement using two vertically
displaced receiver arrays. The projection of the rotation vector in the LOS plane determines a
displacement correction that is required to accurately focus the image.
Figure 1: Displaced phase centre antenna. (Source: [13])
In DPCA processing, only the LOS displacement is sensed in each range window rather than resolving
both sway and heave because it is only the LOS displacement that is required for focusing the SAS image.
Dual-sided navigation allows sway and heave to be resolved using a simple geometric technique [19].
Kalman filtering has also been applied to DPCA measurements to improve the robustness of image
focusing [20]. A different approach is taken in the INSIGHT SAS processing software from Kraken Sonar
Systems [21] which uses an interferometric technique to sense the seabed slope in both along track and
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across track directions. The filter combines displacements, angular rate measurements, and seabed slope
information to derive a 3D velocity vector using the principles of Kalman smoothing [22]. Velocity
estimation is possible using a single-sided sonar configuration, which allows for real-time processing
where port and starboard data streams are processed independently. The velocity output from the SAS
provides a measurement that can potentially improve the accuracy of the platform navigation system.
For example, the Cramér-Rao lower bound of the DPCA sway measurement is given in [17]. Assuming
one overlapping phase centre (the minimum for ping-to-ping correlation), the velocity standard deviation
is
𝜎𝑣 =
𝜆
1
1
1
√ + 2
4𝜋𝑇 √𝐵𝑊 𝜌 2𝜌
(1)
where  is the acoustic wavelength, T is the pulse repetition interval, B is the bandwidth of the transmit
pulse, W is the sum of the durations (in seconds) of the DPCA range windows, and  is the signal-to-noise
ratio. For typical values of a 300 kHz SAS, (1) gives a velocity standard deviation of 0.002 cm/s, which is
more than two orders of magnitude more precise than the corresponding values for a 300 kHz DVL in
Table 1. It should be noted that the sway measurement of a SAS depends on a sound speed measurement,
e.g. through the acoustic wavelength 𝜆 = 𝐶 ⁄𝑓0 in (1), where C is the sound speed and 𝑓0 is the centre
frequency of the transmit pulse.
A SAS array can also be used to measure the along track ping-to-ping displacement [23]. The procedure
is entirely analogous to a one dimensional CVL array with a fully populated (non-sparse) array. The surge
displacement is obtained by cross-correlating overlapping phase centres and applying peak fitting
techniques (e.g. parabolic interpolation) to refine the estimate of the correlation peak location. As with a
CVL, the surge velocity measurement is independent of sound speed because velocity is calculated by
dividing a displacement along the array by the known pulse repetition interval.
3.0 EXPERIMENT
3.1 2014 Victoria Strait Expedition
Beginning in 2007, Parks Canada initiated a series of annual search expeditions that culminated in the
discovery of the wreck of HMS Erebus in September 2014. The 2014 Victoria Strait Expedition included
several Government of Canada departments and private organizations while showcasing the latest
technologies such as AUVs and synthetic aperture sonar. The 2014 search areas are indicated in Figure 2.
Figure 2: 2014 Victoria Strait Expedition search areas.
(Map: Thomas Herbreteau/Canadian Geographic. Source: G. Hobson [16])
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3.2 Arctic Explorer AUV
The Arctic Explorer is a 7.4 m long AUV manufactured by International Submarine Engineering in Port
Coquitlam, BC. Two vehicles were acquired by the Government of Canada for Project Cornerstone, a
Canadian effort to map the Arctic continental shelf under the auspices of the United Nations Convention
on the Law of the Sea (UNCLOS) [25].
The vehicle navigation payload consists of an iXSEA PHINS III inertial navigation system, a Teledyne
RDI Workhorse Navigator 300 kHz DVL, a Sound Ocean Systems GPS receiver (L1 band), a
Paroscientific depth sensor, and a Sonardyne ultra-short baseline (USBL) acoustic positioning system.
The USBL system was not used during the 2014 Victoria Strait Expedition. Therefore, on the surface,
position measurements were obtained from GPS, whereas while submerged, the positioning system
consisted of a DVL-aided INS. The PHINS unit includes a navigation Kalman filter to incorporate GPS
and DVL aiding measurements in real-time. Heading accuracy of the PHINS is specified as 0.02 secant
latitude while submerged, which equals 0.06 uncertainty at a latitude of 70.
Figure 3: Deployment of the Arctic Explorer AUV during the 2014 Victoria Strait Expedition.
(Photo: Nick Walker [18])
The Arctic Explorer vehicles are operated by the Atlantic research lab of Defence Research and
Development Canada (DRDC) on behalf of the Government of Canada. During the 2014 Victoria Strait
Expedition, the AUV was deployed from the polar research vessel One Ocean Voyager (registered name
Akademik Sergey Vavilov) as shown in Figure 3.
3.3 AquaPix InSAS
AquaPix is a wideband 300 kHz Interferometric SAS (InSAS) manufactured by Kraken Sonar Systems
featuring a dual-row design for multipath suppression [26]. A dual-sided AquaPix InSAS system was
purchased by DRDC and integrated into one of the Arctic Explorer vehicles. In Figure 3, the black
rectangle aft of the vehicle nose is the port-side InSAS installed in a free-flooding payload section, with a
second identical InSAS system installed on the starboard side. Prior to the 2014 Victoria Strait
Expedition, the vehicle and sonar were extensively tested during deployments from a jetty at the Bedford
Institute of Oceanography for a research project on repeat-pass interferometry [27], [28].
Each side of the InSAS consists of one transmitter module and four receiver modules, as shown in Figure
4. Each receiver module has a length of 53.3 cm, which is divided into 16 acoustic elements along track.
Included in each module (both transmitter and receivers) are two rows of ceramic elements that are
operated in distinct frequency bands. The short row (labelled “High Frequency” in Figure 4 is angled
down at a depression angle of 17.5 relative to horizontal, whereas the taller row (“Low Frequency”) has
a depression angle of 5.7. Each row surveys roughly half of the range swath of the sonar, with the short
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row covering a range of 2 to 5 times altitude and the tall row covering a range of 5 to 10 times altitude.
The centre frequency and bandwidth for each row are programmable in software. The bandwidth is
typically set to 40 kHz, resulting in a nominal range resolution of 1.9 cm. The short and tall rows are
operated at centre frequencies of 337 and 240 kHz, respectively, to ensure that seabed echoes from each
row do not interfere.
Figure 4: AquaPix interferometric SAS with dual-row design for multipath suppression. (Source: [24])
As shown in Figure 4, the four receiver modules are arranged in two rows of two modules. The vertically
separated modules form an interferometer that provides a precise measurement of the angle of arrival of
seabed echoes in the vertical plane. For example, cross-correlating the complex SAS images from each
row of modules results in measurements of seabed bathymetry.
4.0 RESULTS
4.1 AUV deployment
The Arctic Explorer AUV was deployed by crane from the deck of One Ocean Expedition as shown in
Figure 3 during the 2014 Victoria Strait Expedition. The mission chosen for analysis consists of AUV and
SAS data collected on September 5, 2014. Data recording for the SAS was initiated over a WiFi link
while the vehicle was on the surface. The vehicle track is shown in Figure 5, which consists of some
surface motion during mission configuration, a dive to an altitude of 25 m above the seabed (in water
depth of 38 m), an outbound linear segment of length 4 km, two 90 left turns, and a return linear segment
followed by surfacing. While submerged, the vehicle speed was 1.44 m/s. The outbound and return legs
were along true headings of 85 and 263, respectively.
The SAS data acquisition system logged sonar data continuously for the duration of the mission while
navigation data was recorded onboard the AUV. The sonar and vehicle systems operate asynchronously.
However, clocks were synchronized to within approximately 10 ms using an NTP time server onboard the
vehicle. Also, the DVL transmit pulse was triggered by the SAS to prevent interference (the 300 kHz
DVL is sufficiently broadband that DVL pulses would otherwise appear in the SAS data at 240 and 337
kHz). An example SAS seabed image is shown in Figure 6.
Measurements from sensors onboard the vehicle indicated a water temperature of -0.6C and a sound
speed of 1436 m/s. The sonar was programmed to transmit linear frequency-modulated pulses of duration
5 ms and bandwidth 40 kHz simultaneously from short and tall rows with centre frequencies of 337 and
240 kHz. A pulse repetition interval of 0.34 s resulted in a theoretical maximum range of 240 m.
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Figure 5: Vehicle survey track relative to the dive location of N 6927’05” W 9933’18”. Approximately
10 minutes of pre-dive and post-surfacing motion are also shown.
Figure 6: Example SAS image from outbound survey leg showing a scour mark across an otherwise flat
sandy bottom. The actual seabed image is reversed left-to-right since the image was acquired from the sonar
array on the port side of the vehicle.
4.2 DVL aiding
The PHINS inertial navigation system accepts and processes GPS and DVL measurements in real-time.
Navigation data recorded onboard the AUV therefore consisted of the aided INS outputs including
position, body velocity components, Euler angles and angular rates at a sample rate of 10 Hz. GPS
position measurements were also recorded at 10 Hz although position is only updated at 1 Hz by the GPS
receiver. Raw acceleration and DVL measurements were not available. While the vehicle is at the ocean
surface, GPS signals are received by an antenna located on a mast that protrudes above the water.
However, GPS availability is lost immediately when the vehicle dives below the surface.
During the submerged mission, the vehicle follows a pre-programmed set of waypoints using the DVLaided INS for navigation. When the vehicle surfaces at the completion of the mission, GPS reception is
regained and the navigation Kalman filter updates its position and error states based on the position error
between GPS and the inertial position, which may have drifted during the mission. The GPS
measurements and corresponding INS position correction during surfacing are shown in Figure 7 and
Figure 8. The time axis in Figure 7 and subsequent figures refers to the number of seconds since the time
when the vehicle dove to begin the mission.
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Figure 7: Latitude correction from GPS position measurement when vehicle surfaces after completing
mission plan with DVL-aided inertial navigation. The magnitude of the latitude correction was 16.3 m.
Figure 8: Longitude correction from GPS position measurement when vehicle surfaces after completing
mission plan with DVL-aided inertial navigation. The magnitude of the longitude correction was 24.6 m.
4.3 SAS aiding
SAS processing was performed for the port side data of the outbound and return linear segments resulting
in a sequence of images where each image covers an along track distance of approximately 50 m, as
shown in Figure 6. During processing, the images were focused using the DPCA principles outlined in
Section 2.3 with a three-dimensional velocity vector output for each ping. The DVL-aided inertial
velocities and SAS velocity components are compared in Figure 9 and Figure 10 for the outbound and
return legs, respectively. Surge refers to the forward component of the body velocity vector whereas sway
refers to the lateral component. The INS and SAS data sets are well synchronized and both sensors
measure similar vehicle dynamics. However, a small bias on the order of 1 cm/s is evident for both the
outbound and return legs.
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Figure 9: Comparison of SAS and INS+DVL velocity time series during outbound survey leg.
Figure 10: Comparison of SAS and INS+DVL velocity time series during return survey leg.
4.4 Velocity integration
In Figure 11 and Figure 12, the INS velocity data was interpolated to match the sample times of the SAS
velocity output. The resulting velocity error (SAS velocity minus INS velocity) was then integrated in
both the along track (surge) and across track (sway) directions. For both legs, the integrated sway error
was approximately linear with a slope of 0.8 cm/s for the outbound leg and 1.2 cm/s for the return leg.
In Figure 13, the integrated velocity error for each leg is transformed into the geographic frame using the
outbound and return heading angles as measured by the INS. For comparison, the GPS position correction
during surfacing (from Figure 7 and Figure 8) is also shown.
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Figure 11: Integration of velocity error in the body frame during the outbound survey leg.
Figure 12: Integration of velocity error in the body frame during the return survey leg.
5.0 DISCUSSION
The first observation to make is that the SAS data collected on September 5, 2014 was generally of a very
high quality. Due to the cold Arctic water temperatures, acoustic absorption was low, resulting in a high
signal-to-noise ratio across the entire swath. During the outbound and return segments, the vehicle motion
was stable, as expected for a large AUV operating below the surface. As a result, all of the SAS images
such as Figure 6 were well focused, which implies that the SAS motion estimation was measuring pingto-ping displacements with sub-wavelength precision.
The second observation is that the SAS velocity has exceptionally low measurement noise, as predicted
by the theoretical calculation in Section 2.3. Typically, the velocity measurement from a DVL or GPS
receiver is much noisier than the inertial velocity that is obtained by integrating the accelerometer and rate
gyroscope outputs. However, the inertial velocity tends to drift with time because of the unknown biases
on the accelerometer and gyroscope outputs. A navigation-grade INS such as the iXSEA PHINS would
typically have sensor biases on the order of 100 µg and 0.01/h for linear acceleration and angular rates,
respectively [1]. The navigation Kalman filter is therefore tuned to act like a complementary filter where
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the inertial measurement provides high frequency information and the aiding sensor supplies the low
frequency content. The Kalman filter tracks errors with a relatively slow time constant by making small
updates to the error states for each new aiding measurement that is processed [1]. The results of Section
4.2 demonstrate that if aiding information was supplied by the SAS, it would be possible to tune the
Kalman filter for faster convergence because each velocity measurement from the SAS has less noise than
the corresponding DVL measurement.
Figure 13: Integration of velocity error in the body frame during the outbound and return survey legs.
The time series of INS+DVL and SAS velocity in Section 4.3 show that the data sets are synchronized
and both sensors capture the oscillations in the vehicle dynamics. Small biases on the order of 1 cm/s
were observed between the SAS and the DVL-aided INS. When the velocity error was integrated, the
position correction did not move toward the GPS position correction when the vehicle surfaced. In fact,
integrating the SAS velocity actually moved the position 10 m away as shown in Figure 13. There are
several possible explanations.
The GPS update upon surfacing represents a correction to the errors accumulated during the entire
mission. In addition to the two survey legs, errors also accumulate during the dive, the two 90 turns, and
the surfacing maneuver, whereas the SAS processing only occurs during the straight survey legs. If the
raw inertial and DVL measurements were available, a more thorough analysis could be obtained by
reprocessing the data with a Kalman smoother [22] and propagating the effect of SAS velocity aiding
through the turning and surfacing maneuvers.
The GPS correction also includes an error due to the GPS measurement itself. At high latitudes, GPS
receivers suffer from dilution of precision due a reduced number of visible satellites. The effect of GPS
uncertainty could be reduced by using a GPS+GLONASS receiver, especially since the GLONASS
constellation is well suited for high latitudes. Also, the use of a dual-frequency L1/L2 receiver would
reduce the position error arising from the unknown propagation delay through the ionosphere [1].
Differential GPS processing using a fixed ground station would further improve the accuracy. With
carrier phase processing and dual-frequency receivers, accuracies on the order of 1 cm are typical.
In Figure 11 and Figure 12, the sway error is consistently negative and larger than the surge error. This
suggests misalignment of the SAS as a possible error source. When the vehicle is assembled, the INS and
DVL are carefully aligned by mounting both units in close proximity using a common structural element.
By comparison, the SAS is located several metres away from the INS using a mounting frame that is only
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linked to the INS via the fibreglass hull of the payload section. The average sway velocity error of 1 cm/s
would be induced by a misalignment angle of 0.4. DVLs are typically mechanically aligned to within
about 0.1 using alignment pins and the residual misalignment is estimated and corrected in postprocessing [15]. A calibration of the SAS alignment could be performed by surveying a common seabed
area from opposite directions and using image co-registration techniques to estimate the heading
misalignment. Calibration would also improve the accuracy of georeferencing when SAS pixels are
mapped to geographic coordinates during image post-processing.
In Figure 13, it is seen that the outbound and return errors tend to cancel because of the change in
direction of the vehicle body frame. In fact, this is one advantage of performing “lawnmower” survey
patterns. However, for the purpose of evaluating navigation accuracy, the ideal mission would consist of
long straight segments with surfacing for a GPS update at the end of each leg. The inertial data could be
reprocessed to simulate one long submerged mission by only applying initial and terminal GPS updates,
with the intermediate GPS measurements used to measure the rate of position error growth. A longer
mission results in a larger inertial position drift, so the effect of GPS position error becomes relatively
less significant.
As presently implemented, the SAS processor produces a velocity time series for each image, or roughly
every 30 seconds for a vehicle travelling at 3 knots. The main challenge for ping-to-ping processing is to
unwrap the phase of the DPCA correlation, which can be done robustly when an entire image is processed
at once. However, the results from DPCA ping-to-ping correlation could in principle be output as each
new ping is acquired, producing a velocity update with a latency of about 0.3 seconds for real-time
navigation.
6.0 CONCLUSION
The results of this study show that SAS processing produces a velocity time series with measurement
noise roughly two orders of magnitude lower than a DVL operating at a similar frequency. While the
DPCA motion estimate is ideal for focusing an image over the length of the synthetic aperture (on the
order of 10 m for SAS), this precision does not necessarily translate to an improvement in long term
navigation accuracy. To realize the full potential for SAS-aided navigation, sensor alignment and
calibration must be at least as accurate as the INS/DVL alignment. Recommendations for future work
include recording raw inertial measurements for post-processing and analysis, conducting long straight
survey legs with surfacing for a GPS update at the end of each leg, and developing robust ping-to-ping
DPCA software for real-time SAS-aided navigation.
REFERENCES
[1]
P. D. Groves, Principles of GNSS, Inertial, and Multisensor Integrated Navigation Systems.
Boston, MA: Artech House, 2008.
[2]
J. Collier et al., “Autonomous navigation and mapping in GPS-denied environments at Defence
R&D Canada,” Defence Research and Development Canada, Medicine Hat, AB, Canada, Tech.
Rep. NATO RTO-MP-SET-168, 2012.
[3]
B. Jalving and K. Gade, “Positioning accuracy for the HUGIN detailed seabed mapping UUV,” in
Proc. IEEE OCEANS, vol. 1, Nice, France, Sep. 1998, pp. 108–112.
[4]
H. J. Callow, P. E. Hagen, R. E. Hansen, T. O. Sæbø, and R. B. Pedersen, “A new approach to
high-resolution seafloor mapping,” J. Ocean Technology, vol. 7, no. 2, pp. 13–22, 2012.
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[5]
M. P. Hayes and P. T. Gough, “Synthetic aperture sonar: A review of current status,” IEEE J.
Ocean. Eng., vol. 34, no. 3, pp. 207–224, 2009.
[6]
M. Legris, M. Amate, and A. Hétet, “Navigation data fusion for low frequency synthetic aperture
sonar focusing,” in Proc. 7th Workshop on Underwater Acoustics (JASM’04), Brest, France, Oct.
2004, pp. 1–8.
[7]
W. Xu, F. Sun, and J. Li, “Integrated navigation for an autonomous underwater vehicle carrying
synthetic aperture sonar,” IET Radar Sonar Navig., vol. 6, no. 9, pp. 905–912, 2002.
[8]
R. E. Hansen, H. J. Callow, T. O. Sæbø, and S. A. V. Synnes, “Challenges in seafloor imaging and
mapping with synthetic aperture sonar,” IEEE Trans. Geosci. Remote Sens., vol. 49, no. 10, pp.
3677–3687, 2011.
[9]
F. R. Dickey and J. A. Edward, “Velocity measurement using correlation sonar,” in Proc. IEEE
Conference on Position, Location and Navigation, vol. 255, San Diego, CA, USA, Nov. 1978, p.
264.
[10] P. N. Denbigh, “Ship velocity determination by Doppler and correlation techniques,” IEE
Proceedings Part F, vol. 131, no. 3, pp. 315–326, 1984.
[11] G. M. Wenz, “Acoustic ambient noise in the ocean: Spectra and sources,” J. Acoust. Soc. Am., vol.
34, no. 12, pp. 1936–1956, 1962.
[12] R. Mallart and M. Fink, “The van Cittert-Zernike theorem in pulse echo measurements,” J. Acoust.
Soc. Am., vol. 90, no. 5, pp. 2718–2727, 1991.
[13] A. Bellettini, M. Pinto, L. Wang, and R. Hollett, “Synthetic aperture sonar micronavigation using a
gyrostabilized displaced phase center antenna,” NATO SACLANTCEN, La Spezia, Italy, Tech.
Rep. SR-378, 2004.
[14] Teledyne RD Instruments. (2013) Workhorse Navigator Doppler Velocity Log (DVL). [Online].
Available: http://www.rdinstruments.com/product/dvl/workhorse-navigator-dvl
[15] B. Jalving, K. Gade, K. Svartveit, A. Willumsen, and R. Sørhagen, “DVL velocity aiding in the
HUGIN 1000 integrated inertial navigation system,” Modeling, Identification and Control, vol. 25,
no. 4, pp. 223–236, 2004.
[16] T. Herbreteau. (2014) Victoria Strait Expedition search areas. [Online]. Available:
http://www.canadiangeographic.ca/franklin-expedition/assets/victoriastrait-expedition-map
[17] A. Bellettini and M. Pinto, “Theoretical accuracy of synthetic aperture sonar micronavigation using
a displaced phase-center antenna,” IEEE J. Ocean. Eng., vol. 27, no. 4, pp. 780–789, 2002.
[18] N. Walker. (2014) The Voyager crane lifts the AUV into the water on a four-hour test mission.
[Online]. Available: http://www.canadiangeographic.ca/franklin-expedition/search-focus-on-queenmaud-gulf-article.asp
[19] H. Schmaljohann, J. Groen, U. Hölscher-Höbing, and W. Jans, “Dual-sided micronavigation for
synthetic aperture sonar,” in Proc. Underwater Acoustics, Corfu, Greece, Jun. 2013, pp. 119–126.
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[20] J. D. Campbell and J. R. Pearson, “A synthetic aperture sonar micronavigation Kalman filter,” in
Proc. Inst. Acoust. Int. Conf. SAS/SAR, vol. 28, no. 5, Lerici, Italy, Sep. 2006, pp. 183–190.
[21] D. Shea, D. Dawe, J. Dillon, and S. Chapman, “Real-time SAS processing for high-Arctic AUV
surveys,” in Proc. IEEE/OES Autonomous Underwater Vehicles (AUV 2014), Oxford, MS, USA,
Oct. 2014, pp. 1–5.
[22] A. Gelb, Ed., Applied Optimal Estimation. Cambridge, MA: The MIT Press, 1974.
[23] J. W. Oeschger, “Estimating along-track displacement using redundant phase centers,” in Proc.
Inst. Acoust. Int. Conf. SAS/SAR, vol. 28, no. 5, Lerici, Italy, Sep. 2006, pp. 160–167.
[24] A. N. Mirkin, J. DiCecco, and T. A. Merchant, “Operation of a synthetic aperture sonar from a
REMUS 600 autonomous underwater vehicle,” Naval Undersea Warfare Center, Newport, RI,
Tech. Rep. NUWC-NPT 13-013, 2013.
[25] T. Crees et al., “UNCLOS under ice survey – An historic AUV deployment in the Canadian high
Arctic,” in Proc. IEEE OCEANS, Seattle, WA USA, Sep. 2010, pp. 1–8.
[26] M. Pinto, “Interferometric synthetic aperture sonar design optimized for high area coverage
shallow water bathymetric survey,” in Proc. Underwater Acoustic Measurements, Kos, Greece,
Jun. 2010, pp. 1–7.
[27] J. Dillon and V. Myers, “Baseline estimation for repeat-pass interferometric synthetic aperture
sonar,” in Proc. 10th European Conference on Synthetic Aperture Radar (EUSAR 2014), Berlin,
Germany, Jun. 2014, pp. 1–4.
[28] J. Dillon and V. Myers, “Coherence estimation for repeat-pass interferometry,” in Proc. IEEE
OCEANS, St. John’s, Canada, Sep. 2014, pp. 1–5.
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