Proceedings of the International Conference “Underwater Acoustic Measurements: Technologies & Results” Heraklion, Crete, Greece, 28th June - 1st July 2005

ROBUST AUTOPOSITIONING FOR AN AUV-MOUNTED SAS - A COMPARATIVE STUDY

Alex Cederholma , Mattias J¨onssona , Peter Karlssona , John Robinsona , Ilkka Karasaloa a

Swedish Defence Research Agency, SE-172 90 Stockholm, Sweden

Alex Cederholm, Swedish Defence Research Agency, SE-172 90 Stockholm, Sweden, fax: +46 8 55 50 35 43, email: [email protected] Abstract: Synthetic Aperture Sonar (SAS) constitutes an important enhancement of the capability of an Autonomous Underwater Vehicle (AUV) in mine hunting with respect to detection and classification. In this context, a SAS systems operational performance is dependent on accurate navigation data. Methods for robust autopositioning are developed with the aim to reduce the sensitivity to navigation errors. The developed methods are time-, frequency- or image-based, and their performance is addressed in a comparative study. The study encompasses analysis of both experimental and simulated sonar data. Keywords: synthetic aperture sonar, autonomous underwater vehicle, autopositioning 1. INTRODUCTION Mine-hunting systems must be able to detect, localise and classify mines with high probability and accuracy. An Autonomous Underwater Vehicle (AUV) will minimise personal risk and handle ”dull, dirty or dangerous” missions, where the system could be sent out to a designated area and deliver detected, localised and classified targets together with the Synthetic Aperture Sonar (SAS) image through a communication link. The SAPPHIRES (Synthetic APerture Processing HIgh REsolution Sensor) project aims at proving in real time how such a system should be designed and how it would improve the Swedish mine-hunting capability. The SAPPHIRES system consists of an AUV equipped with SAS and autopositioning capabilities. Autopositioning in this context means correcting navigation data using the sonar echoes themselves, alternative terms for such methods are autofocusing or micro navigation.

The project is a collaboration between the Swedish Defence Research Agency (FOI) and Saab Underwater Systems (SUS) lead by the Swedish Defence Procurement Office (FMV). The SAS technique is an established discipline today, see [1], and several AUV systems have been reported lately in the literature. [3] reports of three different SAS/AUV systems, where one of the systems is in the early stages of development with on board SAS processing, automated target detection and classification and the possibility to communicate results during operation. The vision of an autonomous network of cooperative AUVs and the need for communication between the AUVs is addressed as well. [4] reports of trials with a SAS/AUV at range over 250 m in shallow water. The key to a successful SAS system is accurate positioning of the sonar for the pings building the synthetic aperture. Moreover, [5] suggests using autopositioning as part of the platform navigation loop and [6] describes multi-path interference at SAS/AUV mine hunting in shallow water. Research in applications of SAS in shallow water at FOI was initiated in the mid 90’s, encompassing development of algorithms for SAS imaging and autopositioning, as well as experimental assessment, with a focus on mine-hunting applications [2]. In this paper one image-enhancing method and three autopositioning methods of the SAPPHIRES system are presented, where the autopositioning methods are based on beam correlation, phase increment and highlight tracking respectively. 2. SONAR DATA SETS The sonar system is composed of an uniform receiver array with n e = 24 elements and a transmitter displaced in the close vicinity of the receiver. In this trial the source signal is a linearly frequency modulated pulse with center frequency f c = 25 kHz and bandwidth B = 10 kHz. The sonar system is positioned at a specific water depth and is then moved along a straight track, during which pings are registered with a sampling frequency f s = 100 kHz. The sound velocity is c = 1450 m/s throughout the water column. In the present study the performance of the autopositioning methods is analysed by applying them to one measured and one simulated data set. Measurements were conducted in the waters of the Stockholm archipelago late spring of 2004, see [7]. The transmitter and the receivers were placed on a waggon, which then were moved along a water submerged rail. Orientation and positions of the sonar system were carefully registered for each ping. For the SAS processing in this paper a data set was selected with np = 43 pings, which focused on two targets on the seafloor, a styrofoam ball with two weights, and a corner reflector. These two targets were displaced approximately 1.5 m from each other. For the simulated data set, the echoes from the targets and the seabed are modelled using ray-path approximations. The targets are modelled as acoustically impenetrable spherical objects with different radius and positioned close to the bottom. The acoustic intensity of the echo contribution from a target to a receiver is computed in two steps. In the first step the reflection point at the target r tar , for the ray travelling between source-target-receiver, is computed by minimising the raylength with respect to all points r at the target surface. The acoustic intensity for the echo contribution at the receiver Itar is obtained as Itar =

I [1 + 2γt Rt (r tar )][1 + 2γr Rr (r tar )]

,

(1)

where I is the intensity of the transmitted signal at r tar and where γt and γr are the principal radii of curvature of the target surface at r tar . The quantities Rt (r) and Rr (r) in (1), are the lengths of the transmitted and the reflected ray segments. The bottom is modelled with

several point reflectors positioned randomly with an uniform distribution at the bottom plane. With respect to the vertical axis the reflectors are restricted to a small interval 0-0.2 m, 1.0 m beneath the targets. The echo contributions from the reflectors are added to the receivers with arrival times according to their corresponding raylengths. In particular the maximum acoustic intensity of bottom-reflector contributions are adjusted to -30 dB in comparison to the maximum acoustic intensity of the target-echo contributions. 3. AUTOPOSITIONING METHODS To test the autopositioning methods, navigation errors are introduced in the positioning data, that is errors in the two coordinates of the horizontal plane (x,y) and the yaw angle (ϕ). The estimate of each parameter P˜ ∈ {x, y, ϕ} is modelled as P˜ = P0 + V˜ ∆t

, V˜ = (1 + Egain )V + Ebias + Erand

.

(2)

In (2), P0 denotes the original value of the parameter at the first ping, and ∆t is the elapsed time. The quantities V˜ and V are the estimated and original values of either the velocity in the x- or y-direction or the angular velocity in the ϕ-direction. The parameters E gain , Ebias and Erand are assumed to have a normal distribution, where Egain and Ebias are randomly selected at the first ping and Erand is randomly selected at each ping. 3.1 PROMINENT POINT PROCESSING - PPP Prominent Point Processing (PPP) is incorporated in the SAS imaging algorithm. For each ping a physical aperture image is formed. The SAS image is then formed by adding these images along the synthetic aperture. If an isolated strong reflector is present in the target, this gives rise to a point-spread function in each physical aperture image with peak brightness at the pixel corresponding to the reflector location. Phase coherence for this reflector is then forced by phase-shifting the whole physical aperture image so that the phase of the bright pixel is zero before adding it into the SAS image. The phase shift corrects for both along and across-heading errors resolved along the line of sight to the selected pixel in the target area, and thus for the whole image if the area is sufficiently small. The bright pixel location is carefully selected, since the brightest pixel may move from one ping to the next. The strategy used here is to select the location of the brightest pixel in the uncompensated SAS image. 3.2 BEAM CORRELATION AUTOPOSITIONING - BCA Beam Correlation Autopositioning (BCA) is a Displaced Phase-Center Array (DPCA) method. DPCA methods correlate echoes from the seabed between two successive pings to determine change of position and heading between pings. N correlation points are uniformly distributed over the image area. For each correlation point the phase-center array is determined where each phase-center array element is placed on the line going through the correlation point and the point mid-way between transmitter and corresponding receiver element. Moreover, the phase-center element is placed at the location giving the same round trip propagation time as the bistatic transmitter-reflector-receiver configuration. Thus, the phase center is placed slightly behind the mid-point between the transmitter and the receiver element. Only the parts of the phase-center arrays that overlap between the two pings are considered and the overlapping parts are divided into M subarrays. Beams pointing at the correlation point are formed from the subarrays and the beam-series are limited in range. Then beams

from overlapping subarrays are correlated and their displacements are determined. A first order polynomial is fitted to the displacements in a least-squares sense, where the slope of the line yields the heading correction. The heading is corrected and new phase centers are determined. Beams are formed and correlated and the displacements are again determined as above. Mean displacement then gives range correction. The procedure is repeated for each given correlation point. The heading correction is taken as the mean heading correction and the position correction is given by a weighted least-squares solution from the determined range corrections. 3.3 PHASE INCREMENT AUTOPOSITIONING - PIA The Phase Increment Autopositioning (PIA) method is a frequency domain method for autopositioning in the slant plane. For each physical sensor in the array, the received and range gated time series xk (t), k = 1, . . . , M is Fast Fourier Transformed (FFT) to yield Xk (ω), k = 1, . . . , M , where ω belongs to a set Ω of discrete FFT frequencies. A subset ˜ ⊆ Ω of frequencies is selected such that the frequencies in Ω ˜ are distributed over the main Ω ˜ the phase of Xk (˜ frequency support of the transmitted pulse. For each frequency ω ˜ ∈ Ω ω) as a function of sensor index k is computed. The phase progression of X k (˜ ω ) as a function of k is compared with the corresponding phase progression at the previous ping. Under the idealised assumption of a small target in the far field of the array, the phase of X k (˜ ω ) should be an affine function of the sensor index k. The ping-to-ping change in the affine function parameters gives the ping-to-ping change in radial distance and azimuth, for each frequency ˜ The result from the phase progression is weighted together to form a single estimate, ω ˜ ∈ Ω. ˜ The estimated changes in range and azimuth are as an average over all the frequencies in Ω. compared to those reported by the Inertial Navigation System (INS) and corrections in the slant plane to INS data are computed. 3.4 HIGHLIGHT TRACKING - HIT The HIghlight Tracking (HIT) method assumes that the received echoes are dominated by highlights from one or more targets, the number of which remains fixed during the SAS recording. After matched filtering and beamforming, a pre-determined number N (e.g. N = 3) of highlights at time points tk , k = 1, ...k are identified with the N largest values of maxj |B(tk , θj |, where B(tk , θj ) is the signal in beam direction θj at time tk . Each highlight k is assumed to be caused by a point reflector, corresponding to the two way travel time t k . For each highlight k, a preliminary estimate of the bearing to the point reflector is computed, as well as high-resolution estimates of the arrival time τki at each receiver i. Then a highresolution estimate pk of the position of the k’th point reflector is computed by minimising X (Ti (p) − τki )2 (3) i

as a function of p, where Ti (p) is the theoretical travel time source-p-receiver i. If the position estimate for highlight k at the previous ping is denoted by q k , a one to one map m(k) ˆ k of between q k and pk is derived as follows: First the navigation-data-predicted positions p the reflectors at ping j, in a vessel-fixed coordinate system, are computed ˆj) . ˆ = P (δˆj )(ˆ p q −h (4) k

k

ˆ j are the changes in the angle and the position of the sonar P is a rotation matrix and δˆj and h system. The map m(k) is then selected to the permutation of [1, ..., k], for which the sum of

ˆ m(k) | is minimised. The estimates δ and h of the increments in yaw angle the distances |pk − p and position are then obtained by minimising X |rk − P (δ)(q m(k) − h)|2 (5) k

as a function of h and δ. This minimisation problem is solved by eliminating h analytically and then finding δ with an algorithm for one-dimensional non-linear optimisation. 4. COMPARATIVE STUDY The resulting SAS image with PPP for the measured data is found in Fig. 1, with the styrofoam ball and weights at around position (x,y) = (110.5,666.5) m and the corner reflector at position (x,y) = (112.5,665.5) m. A target constellation derived from the SAS image based on measured data, is modelled according to section 2 and the resulting SAS image with PPP is also found in Fig. 1. As can be seen in the simulated SAS image, the main features of the image from the measurements are kept. In addition the bottom echo contribution is set to be larger in the simulated case. The last image in Fig. 1 shows the resulting SAS image without PPP when introducing navigation errors of the form depicted in section 3 with values three times as large as the SAPPHIRES AUV navigation performance. As can be seen in the SAS image, the target information is severely degraded. The autopositioning methods are applied to the measured data, with navigation errors introduced. The corrected tracks are then used for SAS processing with PPP. The resulting three images are found in Fig. 2. y [m]

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Fig. 1: Left - SAS+PPP image for measured data, Middle - SAS+PPP image for simulated data, Right - SAS image for measured data with navigation error.

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Fig. 2: SAS+PPP images for measured data with navigation errors and autopositioning methods applied. Left - BCA, Middle - PIA, Right - HIT.

5. CONCLUSIONS The SAPPHIRES system can generate SAS images with high resolution and AUV introduced navigation errors can be corrected using one of the three autopositioning methods. All three methods are under development and more tuning is needed before they can be used autonomously. However the results here indicate that they are capable of correcting errors three times as large as predicted SAPPHIRES vehicle navigation performance. By correcting is here meant improving image quality and retrieving as much target information as possible. Another aspect that has not yet been considered is combining the methods. E.g. BCA is better at estimating range errors than heading errors, while PIA is better at estimating heading errors than range errors. The range estimation from BCA combined with the heading estimation from PIA would probably improve the performance. The echo modelling within the SAPPHIRES project is capable of describing almost any target scene. This gives an option to test the methods in conditions where experimental data is lacking. In addition, the modelling facility is also considered for classification. Given a SAS image with unknown objects and a bank of mine geometries, a SAS template of each mine can be produced using the present track. The template that gives the highest correlation with the given image then indicates the best classification of the object. REFERENCES [1] M.P. Hayes, P.T. Gough, Synthetic aperture sonar: A maturing discipline, In The Seventh European Conference on Underwater Acoustics, Delft, The Netherlands, D.G. Simons, volume 2, pp. 1101-1106, 2004. [2] G. Shippey, M. J¨onsson, E. Parastates, J. Phil, The problem of heading estimation in synthetic aperture sonar, In World Conference on Ultrasonics, Paris, France, D. Cassereau, pp. 673-676, 2003. [3] J.E. Fernandez, A.D. Matthews, D.A. Cook, J.S. Stroud, Synthetic aperture sonar development for autonomous underwater vehicles, In MTS/IEEE Oceans 2004, Kobe, Japan, volume 4, pp. 1927-1939, 2004. [4] T.J. Sutton, H.D. Griffiths, S.A. Chapman, R. Crook, M. Way, Optimizing a threestage autofocus system for synthetic aperture imaging using a UUV, In MTS/IEEE Oceans 2003, San Diego, USA, volume 5, pp. 2433-2437, 2003. [5] R.E. Hansen, T.O. Sæbø, K. Gade, S. Chapman, Signal processing for AUV based interferometric synthetic aperture sonar, In MTS/IEEE Oceans 2003, San Diego, USA, volume 5, pp. 2438-2444, 2003. [6] M. Pinto, A. Bellettini, L. Wang, P. Munk, High and low frequency synthetic aperture sonar for AUV based minehunting, In The Seventh European Conference on Underwater Acoustics, Delft, The Netherlands, D.G. Simons, volume 2, pp. 1145-1150, 2004. ˚ [7] M. J¨onsson, J. Phil, M. Aklint, Imaging of buried objects by low frequency SAS, In MTS/IEEE Oceans 2005, Brest, France, (in press).