POSITIONING OF AUV USING GPS AND ACOUSTIC MEASUREMENTS full report
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01-04-2010, 03:06 PM
1.1 AUTONOMOUS UNDER WATER VEHICLE
Autonomous underwater vehicles (AUVs) provide marine researchers with new forms of access to the ocean. AUVs are platforms for a variety of sensors: acoustic, magnetic, gravimetric and chemical. One acoustic-based sensor, a multibeam swath mapper, can map seafloor bathymetry with the resolution of a few centimeters. This resolution is sufficient for detecting and measuring seafloor deformation associated with geophysical phenomena, e.g., mid ocean ridge evolution.
This AUV is allowed to move along the ocean floor and as it does so it collects information about the ocean floor via its numerous sensors.
1.2 NEED FOR POSITIONINIG OF AUV
To exploit the sub centimetre resolution of AUVs for underwater studies requires AUV navigation approaching the meter-level and localization to the decimetre-level. To be practical, the sensor platformâ„¢s position must be repeatable at discrete time intervals over multiple years to detect seafloor changes and extend over an areal expanse of several square kilometers. In fact, it is desirable to link together studies in separate regions of an oceanic plate that are several hundred kms apart, e.g., midocean ridge and subduction zone.
This is so because all the processes going under the ocean are very slow to occur. So to provide the marine researchers with some useful information about the ocean floor the AUV must tell them how different parameters of the ocean floor changes with time. And this time interval is huge due to the low pace of under water phenomena.
Thus to make the AUV retrace the path it once traced the instantaneous position of the AUV must be known for which we have to position the AUV.
The positioning can be done using different methods two of which are explained in the following chapters. Both methods make use of Global Positioning System (GPS). But GPS signals cannot be obtained under water. So some other technique has to go with GPS to complete the positioning task. Using these, the AUV is positioned in a global reference frame like the ITRF2000.
ITRF stands for International Terrestrial Reference Frame. The ITRF is a result of combination of global terrestrial reference frames (stations positions and velocities) provided by 5 space geodesy techniques: Very Long Baseline Interferometry (VLBI), Lunar and Satellite Laser Ranging (LLR and SLR), Global Positioning System (GPS) and Doppler Orbitography Radio-positioning Integrated by Satellite (DORIS).
The International Terrestrial Reference Frame (ITRF) is a set of points with their 3-dimensional cartesian coordinates which realize an ideal reference system, the International Terrestrial Reference System (ITRS), as defined by the IUGG resolution No. 2 adopted in Vienna, 1991.
The International Terrestrial Reference System (ITRS) constitutes a set of prescriptions and conventions together with the modelling required to define origin, scale, orientation and time evolution of a Conventional Terrestrial Reference System. The ITRS is an ideal reference system, as defined by the IUGG resolution No. 2 adopted in Vienna, 1991. The system is realised by the International Terrestrial Reference Frame (ITRF) based upon estimated coordinates and velocities of a set of stations observed by VLBI, LLR, GPS, SLR, and DORIS. The ITRS can be connected to the International Celestial Reference System (ICRS) by use of the IERS Earth Orientation Parameters (EOP).
1.3.1 History and Goals of ITRF
Since 1988, the International Earth Rotation Service has been computing stations coordinates and velocities (to take into account global plate tectonics) of ITRF sites on a yearly basis. This is only possible through a worldwide international scientific cooperation of fundamental geodetic observatories, geodetic archiving data centres and a large number of analysis groups to make full profit of all exiting satellite geodetic data present and past.
1.3.2 Current precision of ITRF co ordinates
The latest version of ITRF is ITRF-2000, which is used for a wide variety of applications: from coordinates of satellite altimetry tracking stations to national primary geodetic networks. The present estimated accuracy of ITRF coordinates is about 2 to 5 mm for the best stations in position
and 1 to 2 mm per year in velocity. However, due to the uncertainty in the velocity determination, coordinates error will tend to grow in the future (as it will be an extrapolation using data from the past).
1.3.3 The ITRF co ordinates:
The ITRF system has its origin at the Earth centre of mass, Z axis pointing towards the North Pole, X pointing towards the Prime Meridian (which crosses Greenwich), and Y at right angles to X and Z to form a right-handed orthogonal coordinate system.
Figure shows the ITRF co ordinate system
International Terrestrial Reference Frame network showing collocations of VLBI, SLR, GPS, DORIS techniques:
How the researchers position the AUV in the ITRF2000 reference frame using GPS and other positioning techniques is explained in the coming chapters. A brief overview of GPS is provided in the very next chapter.
GLOBAL POSITIONING SYSTEM
2.1 THE BASIC IDEA
GPS positioning is based on trilateration, which is the method of determining position by measuring distances to points at known coordinates. At a minimum, trilateration requires 3 ranges to 3 known points. GPS point positioning, on the other hand, requires 4 pseudoranges to 4 satellites.
Time that the signal is transmitted from the satellite is encoded on the signal, using the time according to an atomic clock onboard the satellite. Time of signal reception is recorded by receiver using an atomic clock. A receiver measures difference in these times:
pseudorange = (time difference)*(speed of light)
Note that pseudorange is almost like range, except that it includes clock errors because the receiver clocks are far from perfect.
Correcting the clock errors
Satellite clock error is given in Navigation Message, in the form of a polynomial. The unknown receiver clock error can be estimated by the user along with unknown station coordinates. There are 4 unknowns; hence we need a minimum of 4 pseudorange measurements.
How do we know position of satellites
A signal is transmitted from each satellite in the direction of the Earth. This signal is encoded with the Navigation Message, which can be read by the userâ„¢s GPS receivers. The Navigation Message includes orbit parameters (often called the broadcast ephemeris), from which the receiver can compute satellite coordinates (X,Y,Z). These are Cartesian coordinates in a geocentric system, known as WGS-84,
which has its origin at the Earth centre of mass, Z axis pointing towards the North Pole, X pointing towards the Prime Meridian (which crosses Greenwich), and Y at right angles to X and Z to form a
right-handed orthogonal coordinate system. The algorithm which transforms the orbit parameters into WGS-84 satellite coordinates at any specified time is called the Ephemeris Algorithm.
2.2 THE GPS SEGMENTS
There are four GPS segments:
Â¢ The Space Segment, which includes the constellation of GPS satellites, which
transmit the signals to the user;
Â¢ The Control Segment, which is responsible for the monitoring and operation of the
Â¢ The User Segment, which includes user hardware and processing software for
positioning, navigation, and timing applications;
Â¢ The Ground Segment, which includes civilian tracking networks that provide the User Segment with reference control, precise ephemerides, and real time services.
2.2.1 The Space Segment
The satellite constellation is designed to have at least 4 satellites in view anywhere, anytime, to a user on the ground. For this purpose, there are nominally 24 GPS satellites distributed in 6 orbital planes. According to Keplerâ„¢s laws of orbital motion, each orbit takes the approximate shape of an ellipse, with the Earthâ„¢s centre of mass at the focus of the ellipse. For a GPS orbit, the eccentricity of the ellipse is so small (0.02) that it is almost circular. The semi-major axis (largest radius) of the ellipse is approximately 26,600 km, or approximately 4 Earth radii. The 6 orbital planes rise over the equator at an inclination angle of 55o to the equator. The point at which they rise from the Southern to Northern Hemisphere across the equator is called the Right Ascension of the ascending node. Since the orbital planes are evenly distributed, the angle between the six ascending nodes is 60o.
2.2.2 Satellite Hardware
There are nominally 24 GPS satellites, but this number can vary within a few satellites at any given time, due to old satellites being decommissioned, and new satellites being launched to replace
them. All the prototype satellites, known as Block I, have been decommissioned. Between 1989 and 1994, 24 Block II (1989-1994) were placed in orbit. From 1995 onwards, these have started to be
replaced by a new design known as Block IIR. The nominal specifications of the GPS satellites are as follows:
Â¢ Life goal: 7.5 years
Â¢ Mass: ~1 tonne (Block IIR: ~2 tonnes)
Â¢ Size: 5 metres
Â¢ Power: solar panels 7.5 m2 + Ni-Cd batteries
Â¢ Atomic clocks: 2 rubidium and 2 caesium
2.2.3 The Control Segment
The Control Segment, run by the US Air Force, is responsible for operating GPS. Several ground stations monitor the satellites L1 and L2 signals, and assess the health of the satellites. As outlined previously, the Control Segment then uses these signals to estimate and predict the satellite orbits and clock errors, and this information is uploaded to the satellites. In addition, the Control Segment can control the satellites; for example, the satellites can be manoeuvred into a different orbit when necessary. This might be done to optimise satellite geometry when a new satellite is launched, or when an old satellite fails. It is also done to keep the satellites to within a certain tolerance of their nominal orbital parameters (e.g., the semi-major axis may need adjustment from time to time). As another example, the Control Segment might switch between the several on-board clocks available, should the current clock appear to be malfunctioning.
2.3 THE GPS SIGNALS
The signals from a GPS satellite are fundamentally driven by an atomic clocks (usually cesium, which has the best long-term stability). The fundamental frequency
is 10.23 Mhz. Two carrier signals, which can be thought of as sine waves, are created from this signal by multiplying the frequency by 154 for the L1 channel (frequency = 1575.42 Mhz; wavelength = 19.0 cm), and 120 for the L2 channel (frequency = 1227.60 Mhz; wavelength = 24.4 cm). The reason for the second signal is for self-calibration of the delay of the signal in the Earthâ„¢s ionosphere. Information is encoded in the form of binary bits on the carrier signals by a process known as phase modulation. (This is to be compared with signals from radio stations, which are typically encoded using either frequency modulation, FM, or amplitude modulation, AM). The
binary digits 0 and 1 are actually represented by multiplying the electrical signals by either +1 or -1, which is equivalent to leaving the signal unchanged, or flipping the phase of the signal by 180o. We come back later to the meaning of phase and the generation of the binary code. There are three types of code on the carrier signals:
Â¢ The C/A code
Â¢ The P code
Â¢ The Navigation Message
The C/A (Course Acquisition) code can be found on the L1 channel. This is a code sequence which repeats every 1 ms. It is a pseudo-random code, which appears to be random, but is in fact generated by a known algorithm. The carrier can transmit the C/A code at 1.023 Mbps. The Chip Length or physical distance between binary transitions (between digits +1 and -1), is 293 metres. The basic information that the C/A code contains is the time according to the satellite clock when the signal was transmitted (with an ambiguity of 1 ms, which is easily resolved, since this corresponds to 293 km). Each satellite has a different C/A code, so that they can be uniquely identified. The P (Precise) code is identical on both the L1 and L2 channel. Whereas C/A is a courser code appropriate for initially locking onto the signal, the P code is better for more precise positioning. The P code repeats every 267 days. In practice, this code is divided into 7 day segments; each weekly segment is designated a PRN number, and is designated to one of the GPS satellites. The carrier can transmit the P code at 10.23 Mbps, with a chip length of 29.3 metres. Again, the basic information is the satellite clock time or transmission, which is identical to the C/A information, except that it has ten times the resolution. Unlike the C/A code, the P code can be encrypted by a process known as anti-spoofing. The Navigation Message can be found on the L1 channel, being transmitted at a very slow rate of 50 bps. It is a 1500 bit sequence, and therefore takes 30 seconds to transmit. The Navigation Message includes information on the Broadcast Ephemeris (satellite orbital parameters), satellite clock corrections, almanac data (a crude ephemeris for all satellites), ionosphere information, and satellite health status. On the base of the overview of GPS given here the following chapters describe how an AUV is positioned using GPS and other techniques.
POSITIONING OF AUV
3.1 METHODS OF POSITIONING OF AUV
Basically, there are two methods of positioning an Autonomous Underwater Vehicle. They are,
1. Using GPS and IMU
2. Using GPS and Acoustic based measurements
The first method is explained in brief:
3.2 POSITIONING OF AN AUTONOMOUS UNDERWATER VEHICLE USING GPS AND IMU:
What is done in this approach is to acquire GPS ties when the AUV is surfaced at the start and end of a subsurface track and integrate vehicle acceleration, velocity and/or rotation into position during the subsurface segment. For this purpose, an Inertial Measurement Unit (IMU) is used. An IMU is basically an adder. It can find parameters like acceleration, velocity and/or rotation relating to the Autonomous Underwater Vehicle. And the values of these parameters are added to the initial position of the AUV obtained using GPS at every instant to obtain the instantaneous position of the AUV.
3.3 DISADVANTAGES OF IMU
As IMU is an adder, position errors accumulate with distance travelled at a rate dependent on the quality of the inertial measurement unit (IMU). Given that typical low-grade IMUs incur positional errors in excess of 1% of distance travelled, errors of 10m would be expected for the nominal 1-km-long AUV tracks in this experiment. To eliminate this factor of error concerning the use of IMUs we may use high-grade high precision IMUs that are now available. But these IMUs are
usually very costly, very heavy and are of huge size. The AUV is preferred to be a light and compact vehicle to facilitate its easy movement under the ocean. So the heavy and huge IMUs prove to be
unfit for use in AUV. Thus, another method which makes use of GPS and acoustic based measurements is preferred over this method which is explained in the next chapter.
POSITIONING OF AUV USING GPS AND ACOUSTIC MEASUREMENTS
4.1 BASIC CONCEPTS
In this method of positioning of an Autonomous Underwater Vehicle, an array of transponders are used which are fixed on the ocean floor near the intended track of the AUV. These transducers are positioned in a globally referenced frame. Now by finding the position of the vehicle with respect to the transponders will yield the co ordinates of the AUV in the reference frame. As GPS signals cannot be used under water acoustic signalling methods are employed.
Figure showing AUV, transponder array and the surface ship
Advances in two technologies make use of this method possible: precise underwater acoustic ranging and kinematic GPS positioning. Precision underwater ranging is based upon precision travel time measurement. Decimeter resolution of geometric distances up to a few km is routinely achievable by combining the precise time measurements with detailed modelling of the sound speed and geometric environment. The method uses GPS receivers and processing methods to locate surface platforms (ships, buoys) with subdecimeter resolution for distances 1000s km from shore
based reference sites. The first step in this approach uses kinematic GPS to provide subdecimeter level positioning of a transducer aboard a ship. By collecting precision underwater ranges from this transducer to seafloor transponders, the transponders are tied to an absolute, globally referenced coordinate frame. The limiting factor is the accuracy of the sound speed and because its error contribution increases with water depth, uncertainties of few cms might be expected in shallow water. With the transponder array globally referenced, the second step is to locate the vehicle relative to the transponders. Knowing the transponder positions in the global frame should permit vehicle positioning in ITRF2000 coordinates with submeter accuracy, depending on water depth.
The basic requirements for this method are- a surface ship carrying GPS antennae on its board, a transducer to receive the acoustic signals used for under water ranging and an array of transponders that are embedded on the sea floor near the intended track of the AUV.
4.2 STEPS INVOLVED
The various steps involved in this method are:
Step 1: Using kinematic GPS the transducer aboard a ship is positioned to sub decimeter level.
Step 2: By collecting precision underwater ranges from this transducer to seafloor transponders ,the transponders are tied to an absolute, globally referenced coordinate frame.
For positioning the transducer, the surface ship circles around it at a radii approximately equal to the depth of the sea floor transponder collecting simultaneously acoustic signals from the transponder and GPS data. By calculating the time delay between transmission and reception of acoustic signals the distance between ship and transducer can be calculated. And by processing these information along with the GPS data collected by the antennae on the ship board, the position of the transponder in the reference frame can be obtained.
Locating the transponder
Step 3: Now after locating the transponders the next step is to locate the vehicle relative to the transponders. Knowing the transponder positions in the global frame should permit vehicle positioning in ITRF2000 coordinates with sub meter accuracy, depending on water depth.
For this purpose there are two methods:
1. Direct mode
2. Indirect mode
This method is also known as two way travel time mode. Here, the time taken for acoustic signal to travel from AUV to sea floor transponder and back is calculated from which the distance between them can be found. For using this method an acoustic source must be present in the AUV.
This method is also known as the time differencing mode. In this method the time difference between the arrivals of acoustic signals at the transducer directly from the AUV and from AUV through the transponder is measured by using which the distance between the AUV and the transponder can be calculated.
Step 4: after step 3 the horizontal position of the AUV is obtained. But to get the full picture of the AUV its depth must be known. For this, a pressure gauge is employed using which the depth of the AUV can be measured.
4.3 ACOUSTIC SIGNAL DETAILS
Structure of the acoustic signal
The structure of the signal used for acoustic ranging is shown in the figure. The signal consists of 1 ms of 9 kHz leader, 4 ms of 8 kHz, 4 ms of 12 kHz, a 2-ms space, and 3.5 ms of 11.5 kHz, which acts as a unique identification tag. There will be unique identification tags corresponding to each of the transponders and the AUV so that the receiver can identify the signal from each. The identification tag is attached to the end of the signal as shown in the figure.
To illustrate this method of AUV positioning, Marine Physical Laboratory, USA conducted an experiment which is explained in the next chapter.
5.1 THE BASIC DETAILS
A practical implementation of this method of positioning an AUV using GPS and acoustic based measurements was experimented by the Marine Physical Laboratory, USA. The experiment was conducted some 50 km offshore the coast of San Diego. It was done at a nominal depth of 300m. A surface ship, the R/V Robert Gordon Sproul, carrying three GPS antennae and a navigation transducer hanging at the end of a 4m pole pointing towards the ocean was used. The transponder array consisted of three transponders that were deployed in a triangular fashion on the ocean floor, each separated by a distance of 500-700m. The acoustic source for the synthetic aperture experiment was aboard the floating laboratory instrument platform (FLIP) moored nearby. The primary receiving unit for this source was a hydrophone array mounted along the sides of a Bluefin Oddessy-IIb AUV. Also mounted on the AUV were a navigation transducer and a pressure gauge. Transponders deployed to form a triangular array separated by 500â€œ700 m. Another navigation transducer was aboard the R/V Robert Gordon Sproul mounted to a pole and lowered on the port side to a depth of approximately 4 m. Aboard the ship were three dual frequency GPS receiver/antennas mounted on towers. Mounted on the deck of the ship was a total station land surveying instrument that measured angles in two orthogonal planes and distances to reflective prisms. The measurements obtained from the total station were then used to determine the offsets between prisms mounted atop the transducer pole and below the GPS antennas. A temporary GPS reference station was established ashore (RITT) to provide a reference tie for the shipboard GPS data. The three transponders were referred to as PXP1, PXP2 and PXP3. In shrinking this system for AUVs, both the transmitter and
receiver components must ultimately reside within the AUV to collect the usual two-way travel time measurements between the AUV and the navigation transponders (Fig. 1). However, to validate the approach without completing the entire transition of electronic components to the AUV, we proceeded with an intermediate step that first incorporated only the transmitter in the AUV and retained the receiver aboard the ship.
The picture shows the basic setup of the experiment:
5.2 GPS DATA PROCESSING
The 1-Hz shipboard antenna positions were solved for kinematically holding the shore station RITT fixed. GPS data from the ship antennas and the shore site were combined and processed using NASA Jet Propulsion Laboratoryâ„¢s GIPSY/OASIS-II software with modeling approaches developed at SIO , . Shipboard GPS antenna positions were determined to cm (2- ) in ITRF2000 coordinates by forming an ionosphere-free double-differenced phase observable between shore and shipboard receivers and solving for the integer ambiguity . The ITRF2000 coordinates for each antenna were estimated independently, and as a check on the resolution, were differenced to estimate the baseline between shipboard antennas (Fig. 6). Each baseline shows a scatter of cm, indicating the stability of the solutions. The propagated uncertainty (Fig. 7) for the GPS antenna positions is 6cm during the transit of the ship ahead of the AUV. Results are similar when the ship drove a circle around the transponders.
5.3 POSITIONING THE TRANSDUCER ACOUSTIC PHASE CENTER IN A GLOBAL REFERENCE FRAME
The ultimate aim of the GPS positioning is to realize globally referenced coordinates underwater. This requires the position of the shipboard transducer in ITRF2000 coordinates during transmission and reception of acoustic signals to/from seafloor transponders and during reception from the manoeuvring AUV. Because the GPS antennas were atop the ship to observe the satellite signals and the acoustic transducer was underwater below the ship to receive the acoustic energy, GPS cannot directly position the shipboard transducer, but requires an intermediate connection. The connection is through static vectors between the corner cube reflectors attached to each GPS antenna and to the top of the transducer mounting pole. These vectors can be determined using a survey instrument that measures angles in two orthogonal planes and distances with an electromagnetic distance measurement system (EDM). Combining these vectors with offsets between prisms and the phase centers of antennas and transducer, a sequence of rotations can transform the ITRF2000 positions from the GPS antennas to the transducer.
5.3.1 Dockside Survey
Prior to the shipboard installation, offsets were determined between three prisms attached to the top of the mounting pole and the transducer phase center (Fig), as well as, between the GPS antenna phase center and prism mounted beneath the antenna. Determining the offsets between the three prisms atop the transducer pole and the transducer phase center required an intermediate survey conducted in the laboratory. Angles and ranges were measured to the prisms attached to the top of the mounting pole and to prisms bracketing the transducer phase center. These polar coordinates were transformed into a Cartesian frame using
Where dd is the slope distance between the EDM and each corner cube reflector, ad is the angle perpendicular to a horizontal plane, and is an angle in a horizontal plane from an arbitrary reference. The origin of this system was at the surveying instrument with aligned with the local vertical, aligned with the prism atop the mounting pole, and forming a right-hand system. The sole purpose of these arbitrary coordinates was to provide a reference tie (i.e., the three prisms) between
the phase centers of the transducer and GPS antennas, because once the mounting pole was installed aboard the ship, the transducer was no longer observable.
5.3.2 Shipboard Survey
After the GPS antenna towers were erected and the transducer pole deployed, the survey instrument was mounted in a lateral position to a post on the main deck. Angles and distances between antenna and the pole prisms were observed. These polar coordinates were transformed into another Cartesian frame using
where is the slope distance obtained from the EDM,as and ÃƒÅ¸s are angles in orthogonal planes measured with the total station. The origin was located at the total station with the
axis project and implimentationing from the top of the survey instrument (i.e., roughly port-to-starboard). The Xs Zs plane was perpendicular to the axis and the axis was realized by referencing the horizontal angles to the port antenna. The initial survey frame (Xs) is a coordinate frame of convenience for setting up and operating the survey instrument which could not be easily aligned to the standard axes defining the usual heading, pitch, and roll conventions.
Alignment to the standard axes was achieved using a series of orthogonal rotations to transform this arbitrary reference frame into the shipâ„¢s body frame: Xb defined Xb with parallel to the keel and positive forward, Yb a beam and positive to port and the Zb positive up. In the first transformation step, the Yr axis is aligned with the vector between the two aft antennas by rotation about the Xs axis and then the Xs axis
where Xr coordinates are aligned with the Yb axis of the shipboard body frame and is from (2). The rotation angles were calculated using
Where Xs, Ys and Zs are the differences between the starboard and port antennas in Xs. next the XrYr plane was rotated parallel to the shipâ„¢s deck by
And Hp is the height difference between the port antenna prism and the survey instrument base (measured prior to set-up). A final rotation about the Zrr by
completed the transformation of the GPS antenna and transponder pole prisms into alignment with the shipboard body frame. Several assumptions were used in this transformation: 1) the flatness of the deck; 2) the perpendicularity of the three antenna towers to the deck; 3) the height of the two aft antenna prisms were the same relative to the deck. Finally, the GPS antenna phase centers were brought into the shipboard body frame by adding the antenna-prism offsets to the coordinates of each prism. This permitted a comparison between the GPS-only derived baseline distances between antenna phase centers and the values determined by the survey instrument (Table I).
The consistency between these measurements is about Ã‚Â±2mm, within the respective uncertainties of the two measurement approaches. Next, the transducer phase center was transformed into the shipâ„¢s body frame using the three transducer-pole prisms whose coordinates were known in both the laboratory frame and the shipboard-aligned frame. The transformation is defined using some algebraic method.
5.3.2 Transducer Positioning Precision
The uncertainties in the ITRF2000 coordinates of the transducer positions were calculated by propagating the uncertainties for each 1-Hz solution of the GPS antenna positions along with the survey measurement uncertainties through the coordinate transformations. The GPS antenna position
uncertainties Ã‚Â±3cm were obtained as part of solutions discussed in Section III and shown in Fig. 7. The survey instrument uncertainties were Ã‚Â±5arc seconds angular and Ã‚Â±.003m distance. The uncertainty propagation through (1)â€œ(12) were calculated through successive applications of a general relation. Fig. shows the results of the error propagation for the ITRF2000 coordinates of the transducer: Ã‚Â±10cm uncertainties for the horizontal position. Mounting the transducer at the bottom of the pole which was attached to the side of the ship increased the transducer positioning error in two ways. First, the inaccessible location of the transducer required additional measurements and transformations. Also, the cantilever effect between the three prisms atop the mounting pole and the transducer~ 5 m away amplified the uncertainty in the prism positions. All these contributed to increasing the uncertainty in transferring the GPS positions to the hydrophone. Second, because the pole was mounted along the side of the ship, it was exposed to stresses from currents, course and speed changes of the ship. These resulted in flexing of thepole, by up to 15 cm. On a larger ship, we implemented an improved approach using a hollow tube, mounted within the shipâ„¢s hull in an instrument well, as the mounting device. Here, a prism was placed on the backside of the transducer just above a water tight seal. This reduced the lever arm from about 5m in the case of the installation used in this experiment to ~30cm. The propagated error reduces to a few mm maintaining Ã‚Â±6cm positioning uncertainty on the transducer. However, for the following analysis we will retain the more conservative value of Ã‚Â±10cm uncertainty on the transducer ITRF2000 coordinates.
5.4 UNDERWATER ACOUSTIC RANGING
The accurate determination of underwater ranges relies on the ability to measure: 1) the time of travel of the acoustic pulse; and 2) the rate at which the acoustic energy travels.
5.4.1 Travel Time
Travel-time resolution was achieved using a pulse compression technique consisting of an 8-ms-long code with 4-kHz bandwidth, a transponder with a fixed delay
line stable to a few microseconds and a matched filter . Cross correlation of the two-tone signal containing four 180 phase flips (Fig. 10) provided sufficient processing gain to ensure that the main lobe peak could be resolved from the peaks of the adjacent side lobes (Fig.)
The incoming acoustic signals were sampled at a rate of 1-MHz with time slaved to a GPS receiver. The signal was decimated and then cross correlated with a replica of the transmittedsignal. Any correlation amplitudes crossing a manually set arbitrary threshold triggered a cross correlation of the full (undecimated)1-MHz data segments with the replica signal. The peak of this correlogram was picked based on maximum normalized magnitude and was resolvable to Ã‚Â±5Ã‚Âµs. The individual signal paths were identified by the frequency tag attached to the end of each signal with frequencies: 9, 10, and 11 kHz corresponding to transponders; PXP1, PXP2, and PXP3 and 11.5 kHz to the AUV.
In the case of the transponder location survey, the signal was sent at an integer second from a waveform generator to both the transducer (after amplification) and to a computer
where it was digitally stored to be used in the cross-correlation process. A total in-the-water travel time for the acoustic signal was obtained from the elapsed time between the peaks of the transmit and receive correlograms minus the transponder delay. The two-way travel time formed the observable for positioning the seafloor transponder. In the case of the AUV survey, the outgoing pulses were generated in the AUV and because these signals were not stored, a replica of the signal was correlated with the incoming signals aboard the
surface ship. The time difference of arrivals between the three transponder replies and the direct signal were calculated by differencing the respective correlogram peaks and subtracting the transponder delay (Fig.).
These travel times, along with the AUV depth measured with a pressure gauge, formed the observables for positioning the AUV.
5.4.2 Sound Speed
Given the ability to resolve time measurements to a resolution of a few microseconds, the limiting factor in underwater ranging is the ability to accurately measure the sound speed field. The uncertainty in sound speed comes from three main sources: 1) accuracy of the state equation; 2) accuracy of the measurable parameters conductivity (salinity), temperature, and pressure; and 3) temporal and spatial undersampling of the sound speed variability. The state-equation from which sound speed is calculated is based on the laboratory derived relationship between conductivity, pressure, and temperature. Analysis and at-sea tests have shown that these equations are consistent with accuracies of Ã‚Â±0.05ms with depth <1000m.
Absolute positioning of an underwater vehicle using an LBLapproach requires: 1) locating the seafloor transponders in a global reference frame, 2) positioning the vehicle relative to the transponders. Both steps utilize a similar nonlinear least squares estimation approach. This approach is first described in general terms and followed by details specific to the two implementations of the model. Determining precise positions for the seafloor transponders or the AUV begins with initial, approximate positions . These are then used to calculate model predictions of the travel times which are then differenced with the actual observed travel times also known as the observed values of the observables to form residuals . The residuals are project and implimentationed into corrections to the initial approximate positions. This procedure of computing travel times based on a position estimate and correcting the
position is repeated until the corrections fall below a threshold of 1 cm. To implement this procedure a function is defined that relates the desired unknown positions to the adjusted observables.
5.5.1 Locating the sea floor transponder
To locate the seafloor transponders (referred to as PXPs), travel times were collected from ship to transponder and back to the ship as it circled each transponder. The acoustic signal was transmitted on an integer second allowing the transducerâ„¢s phase centre position to be known directly from the GPS-derived transducer positions. The received signal reception times, which were not typically at integer seconds, required the interpolation of transducer positions. A known, fixed delay for the transponder was then removed to yield the time of flight of the signal. The unknown position of the PXP is related to the observables; the positions of the shipboard transducer at transmit and reception, the travel times from ship to PXP to ship, and the sound speed by a function. Now, this function was solved for the unknown ITRF2000 coordinates of the transponder. Hence, by following this method, all the transducers were positioned relative to a globally referenced frame.
5.5.2 Positioning the vehicle
1) Time-Differencing: To locate the AUV as it transited near the seafloor array, the AUV recorded its depth every second and pinged every 6 s, while the shipboard transducer recorded signals that consisted of the direct path (AUV to ship) and three indirect paths (AUV to seafloor transponder to ship). In this case, the unknown position of the AUV at transmit is related to the observables: AUV depth, shipboard transducer position, travel times from AUV to ship and AUV to PXP to ship and the sound speed using a function when solved gave the coordinates corresponding to the position of the AUV in the reference frame.
2) Two-Way Travel Time: In this experiment we were limited to the time-difference approach because the receiver electronics were not on the AUV. However, we can use the internal consistency of the errors validated in the time-difference approach to simulate the improvement in AUV from: 1) moving the AUV track to within the transponder array; 2) replacing the time-difference approach with direct travel-time measurements between PXPs and the AUV. First, the geometry defined by the experiment is used for the simulation. Next, an AUV track passing through the middle of the transponder array is simulated. Here, the unknown is position of the AUV at transmit and observables are PXP position, travel times of AUV-PXP-AUV, sound speed and the relative motion of the AUV from transmit to reception. These are related by a function and solved for AUV position.
Site map showing location of acoustic source (FLIP), seafloor transponders (PXP), and AUV track. Inset shows location of experiment site and shore GPS reference station.
An AUV horizontal position accuracy of Ã‚Â±1m was achieved using globally referenced seafloor transponders and a time-difference mode which met the requirements of the synthetic aperture experiment. Using this actual data error source validation, a simulation shows that Ã‚Â± 30cm horizontal position uncertainty is possible by measuring directly travel times seafloor transponders that are known in the global frame. Using geodetic quality GPS measurements to position a shipboard antenna array and carefully transferring these position to the shipboard transducer permits Ã‚Â± 8cm uncertainty on locating seafloor transponders in shallow water <500m.
Future work is planned to migrate the receiver portion to the AUV and incorporate a doppler velocity log and INS. Then we plan to conduct tests of the LBL approach to independently validate the system precisions and accuracies. Decimeter-level positioning of the AUV would then have applications to repeat mapping and change detection, an emerging topic of importance in geo-referenced, active acoustic mapping of the seafloor.
 IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 30, NO. 1, JANUARY 2005, Neil H. Kussat, C. David Chadwell and Richard Zimmerman
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