AUV Localization Using a Single Transponder Acoustic Positioning System

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1 AUV Localization Using a Single Transponder Acoustic Positioning System Igor N. Burdinsky, Semen A. Otcheskiy Department of Computer Science Pacific National University Khabarovsk, Russia igor_burdinsky@mail.ru, semgog@mail.ru Abstract The article considers the problem of autonomous underwater vehicle navigation using a single transponder and proposes a new method for calculating the underwater vehicle coordinates based on the particle filter. A comparison of the new method with the known method of underwater vehicle s positioning based on the Kalman filter is given in the article. Keywords navigation, underwater acoustic positioning systems, autonomous underwater vehicle, Kalman filter, particle filter. I. INTRODUCTION Hardware and software for positioning in the marine environment are of great importance for autonomous underwater vehicles (AUV as a successful execution of the vehicle mission depends on the reliability and accuracy of its navigation system [,]. Today long base-line (LBL acoustic positioning systems are considered to be the best means of determining the AUV coordinates because of a wide range of operation (from hundreds of meters to tens of kilometers and high accuracy [3,4]. In these systems the object position is determined in real time on the basis of measured distances to a set of reference beacons-transponders with known coordinates [5]. Despite their reliability and accuracy, the classic LBL systems have significant drawbacks: Low mobility. Installing the positioning system implies deploying at least three transponders around the area, in which underwater works will be carried out. Since the distance between the beacons can be up to tens of kilometers, it can take a lot of time and must be done in advance before the launch of an AUV. A similar situation is with LBL system dismounting. Due to low mobility, such systems are usually installed once and for a long-term operation in a given area. High cost. The acoustic transponders used in LBL systems are complex autonomous technical aggregates, which cost tens and hundreds of thousands of dollars. It is impossible to deploy positioning system beacons without vessels, the operation of which also requires considerable financial expenses. Restricted use. There can be such conditions, when it is difficult or impossible to deploy a navigation system consisting of several transponders, separated by long distances. For example, when using AUV in ice conditions [6]. These drawbacks can be eliminated if a single reference transponder is used. However, in this LBL system configuration the position of the object cannot be determined with a single range measurement. There are two approaches to solving this problem. The first approach is the use of classical LBL system algorithms under special conditions: a series of range measurements to the reference beacon is carried out from different AUV positions; the AUV movement trajectory between these positions is tracked with maximum precision. This solution is presented in [7] and is based on the use of a high-precision dead reckoning system. This approach has the following drawbacks: Providing high precision AUV motion parameters is a difficult task, and solving this task leads to a substantial increase in the cost of onboard systems. Since it is impossible to achieve an absolute measurement precision, there still remains an unsolved problem of the error accumulation in dead reckoning systems, because of which it is necessary to periodically correct the AUV position using other navigation tools (the position can be determined using satellite navigation after the surfacing of the AUV. The second approach to the problem of providing navigation using a single transponder is to develop new algorithms [8-0]. The main advantage of this approach is that it is universal, i.e. the obtained solution can be applied to most existing AUVs and LBL systems. The purpose of this paper is the research and development of algorithms for calculating the AUV position using a single LBL system transponder. II. THE KALMAN FILTER Most algorithms for computing the AUV position with a single transponder are based on the idea of correction of the coordinates obtained by an onboard dead reckoning system according to the measured ranges between the AUV and the transponder. Typically, these algorithms are based on the ISBN:

2 Kalman filter [0-] due to its precision and low computational complexity. Now we will consider a simplified version of the algorithm proposed in [0]. Step. Initialization of the Kalman filter. Setting statistical filter parameters E, E (set once before launching the AUV: E δv s 0, ( 0 δvs E δτ where δv s is the expected standard deviation of the sound velocity in the marine environment from the real value; δτ is the expected standard deviation of the measured navigation signal propagation time (time during which a sound wave of the signal ers the distance between the AUV and the transponder. The following steps of the algorithm focus on calculating the AUV position and they are executed each time the navigation signal from the reference transponder is received by the AUV. Step. Measurement of the AUV motion parameters by means of onboard sensors. The following parameters are measured: the duration of the navigation interval dt (the time interval between the current and the previous registration of the navigation signal by the AUV; the average speed of the AUV in relation to the seabed during the navigation interval v AUV ; the resultant displacement vector α. Step 3. Calculating the current AUV position by the onboard dead reckoning system. xi xi + x, ( yi yi + y where x i-, y i- are the AUV coordinates at the end of the previous navigation interval; is a resultant displacement, which is calculated by the formula: x vauv dt cos( α. (3 y vauv dt sin( α Step 4. Calculation of the filtration parameters. a Calculation of the expected value of ariance matrix E E + E, (4 for the first navigation interval E equals 0. b Calculation of the filtration vector V k V k P P AUV AUV Pb, (5 P v where P AUV is a vector containing the AUV coordinates, taken by the onboard dead reckoning system; P b is a vector containing the coordinates of the reference transponder; v s is a mean value of sound velocity in the marine environment. c Calculation of the Kalman gain vector C k : s T Ck EV, (6 k C where С is a coefficient, calculated by the following formula: T k EVk + E C V. (7 d Calculation of the difference Err between the measured (τ values and the calculated (τ est in relation to the obtained by the dead reckoning system position values of the sound wave propagation time between the AUV and the reference transponder. Step 5. Calculation of the AUV position: Err τ τ est. (8 a Correction of the coordinates, obtained in Step. kxi xi + Ck ( Err, (9 kyi yi + Ck ( Err where kx i, ky i is the algorithm result, final AUV coordinates. b Recalculation of the ariance matrix for calculation of the coordinates of the next navigation signal registration: E I CkVk where I is a x identity matrix. ( E, (0 In the given algorithm the calculation of the current AUV coordinates is done by correcting the data of the dead reckoning system using the Kalman filter. Thus precise coordinates of the starting point are required for the correct operation of the algorithm. This is due to the fact that deadreckoning systems accumulate error and if there is an error in the initial stage it will increase in the course of the mission. The Kalman filter restrains the error accumulation and allows preserving navigation precision for quite a long time, but it cannot eliminate the error of the first initialization. The drawback of the algorithm is that in case of the loss of navigation, which can be caused by the accumulation of errors as well as by impulse noise, the starting position coordinates must be calculated again for the further AUV functioning. Precise initialization usually requires: the AUV s surfacing for determination of the coordinates using satellite navigation systems; usage of specialized acoustic positioning systems installed on the support vessel; bringing the AUV to the point ISBN:

3 with known coordinates (for example, to a reference transponder [3]. The first two variants are difficult to implement in ice conditions, where the possibilities of AUV s surfacing and of the ship movement are limited. Therefore, the necessity of precise starting position coordinates can be the cause of mission cancellation and it can expose the AUV to danger when operating in extreme conditions. III. THE PARTICLE FILTER To eliminate the described drawback, a new method for calculating the AUV coordinates on the basis of the particle filter was developed. Below is the description of the method algorithm: Step. The particle filter initialization. Setting the filter (set once before launching the AUV: a Creation of two arrays xp [xp..xp npart ], yp [yp..yp npart ] containing the coordinates of the possible AUV positions (npart is the number of positions in the local coordinate system of the AUV. b Initialization of the created arrays with the coordinates of the points uniformly distributed in a given area (for example, the area of AUV deploying or the area of supposed underwater work. c Creation of an array of probability of possible positions p [p..p npart ]. d At the initial time all possible positions can be the AUV real position with equal probability. Therefore, the array of probability of possible positions p is filled with /npart values. e Calculation of the vector с [с..с npart ] which contains the cumulative probability function p. f Calculation of the starting position as the mathematical expectation of all possible positions. The following steps of the algorithm focus on calculating the AUV coordinates and are executed each time the AUV receives the navigation signal from the reference transponder. Step. Resampling. Each possible position..npart is replaced by a new one. a A random number r is generated in the range [0..] according to a uniform probability distribution law. b The first element с [с..с npart ] satisfying the following condition is found: c i < r, ( i > min c the pair of coordinates (xp(, yp( is taken as the new possible position. Step 3. Displacement of possible positions: a A determined displacement of possible positions takes place: xp( yp( xp( yp( i.. npart j j j j + x, ( + y where xp( j-, yp( j- are the coordinates of i-th possible position; is the displacement, which is calculated by the following formula: x vauv dt cos( α, (3 y vauv dt sin( α where v AUV is the average speed of the AUV in relation to the seabed during the navigation interval; dt is the duration of the navigation interval; α is the resultant displacement vector. b A random displacement of the possible positions is added: xp( xp( + wxp(, (4 yp( yp( + wyp( i.. npart where wxp( is a random variable generated under the normal law with the expectation value xp( and standard deviation sigma (chosen depending on the predicted errors of course measurement and the AUV speed; wyp( is a random variable generated under the normal law with the expectation value yp( and standard deviation sigma (chosen depending on the predicted errors of course measurement and the AUV speed. Step 4. The formation of AUV coordinates estimation. a Recalculation of the array of probability of possible positions p [p..p npart ]. The probability is calculated relative to the following parameters. d ( τ vs ( sigmaτ pτ ( e, (5 π sigmaτ dτ dτ est ( sigmadτ pdτ ( e π sigmadτ dα dαest ( sigmaα pα( e π sigmaα i.. npart where pτ( is probability relative to the measured propagation time for the i-th possible position; pdτ( is probability relative to propagation time change for the i-th possible position; pα( is probability relative to the change of course for the i-th possible position; d( is the distance between the i-th possible position and the reference transponder; v s is the sound velocity in water; τ is the measured propagation time; sigmaτ is the coefficient of the standard deviation in τ; dτ is the change of the measured propagation time relative to the previous event; dτ est is the change of the calculated propagation time relative to the previous event; sigmadτ is the coefficient of the standard deviation in dτ; dα is the change of the measured propagation time relative to the previous event; dα est is the change of the ISBN:

4 T0 T T T3 Figure. Solving the AUV positioning task. calculated propagation time relative to the previous event; sigmadα is the coefficient of the standard deviation in dα; ( pτ ( + pdτ ( + pα( p( npart p( i i.. npart. (6 b Estimation of the AUV coordinates is calculated as a mathematical expectation of all possible positions: x( y( npart i.. npart xp( yp( p(. (7 i npart i p( c Recalculation of the vector с [с..с npart ]. A software model was developed and a series of numerical experiments was carried out to test the effectiveness of the presented method and to compare it with the method of the coordinates calculation based on the Kalman filter. The simulation was performed taking into account the instrumental errors of the measuring equipment, with which the modern AUVs and LBL systems made by the Institute of Marine Technology Problems FEB RAS are equipped [4,5]. IV. THE SIMULATION RESULTS The main advantage of the particle filter is that, thanks to its properties, it can solve the problem of positioning, i.e. it allows determining the object position in the given area. Figure shows the solution of the AUV positioning task using the developed method for calculating coordinates. The following symbols are used in the figure: asterisk (the position of the reference acoustic transponder; square (the real position of the AUV; circle (the calculated position of the AUV; plus (one of the possible positions. The real and the calculated tracks of the AUV are also shown in the figure. ISBN:

5 Error (m Error (m t (c Figure. Comparison of single transponder navigation methods. t (c At the moment of time T 0 the possible positions (particles are uniformly distributed in the area of AUV functioning. The AUV starts circular motion. On their way particles gather in clouds (areas where the AUV is more likely to be positioned. At the moment of time T four such clouds were formed. Later the clouds merge into one. This resultant cloud concentrates around the real AUV position at T. Since the estimation of the AUV coordinates is the mathematical expectation of all possible positions, the calculated position can be considered correct as soon as the particles form a single cloud around the real position T 3. Along with the further AUV movement the cloud continues to concentrate around the real position and the accuracy of the calculated coordinates also increases. The developed method of the AUV position calculation using a single transponder does not require initial initialization. The starting position can be determined with the help of a setup movement. Thus, in case of navigation loss, there is no need to interrupt the execution of the mission, to perform an emergency surfacing or to involve the support vessel. Figure shows the simulation results of the developed AUV coordinates calculation method based the particle filter (on the left and the method of calculating the AUV coordinates based on the Kalman filter (on the right. The upper graphs show the real and the calculated tracks of the AUV. The lower graphs show the distribution of time errors for each method (deviation from the real AUV position in meters. A preliminary circular setup movement followed by track consists of parallel legs was used as a model of motion. Analysis of the results shows that the developed method excels the position calculation method based on the Kalman filter in accuracy. The developed method has the following statistical error parameters: the mean value is 0.8 m, the standard deviation is 0. m; for the method based on the Kalman filter the parameters are m and 0.5 m, respectively. It is worth mentioning that to accelerate the particle filter setting the possible positions were placed uniformly in the area around the point of AUV submergence within a radius of 0 meters. It means that initially a cloud of particles was created, within which there was an AUV. The cloud concentrated on its way, increasing the accuracy of the calculated coordinates. The drawback of this method is its high computational complexity. Processing of each possible position (one particle requires twice as much operations with the floating point as it is used in the Kalman filter for each iteration. Fluctuations of accuracy of the values obtained by using the particle filter depend on the number of particles. 50 possible positions were used in the simulation. Thus, to compute one pair of coordinates the developed method required 300 times more floating point operations than the method based on the Kalman filter. This complexity can become a serious obstacle to the introduction of this method into the existing AUV models, as their computational powers are often severely limited. However, the structure of the developed method algorithms shows that almost all operations with particles (step 3, step 4 (a do not influence each other s results and can be executed in a parallel way. Today the development of microprocessor technology allows to effectively organize parallel computing to rationalize the particle filter. V. CONCLUSION The developed method of AUV positioning by a single transponder based on the particle filter has the following advantages: High reliability. The method does not require the initial position data on board the AUV that allows the AUV to operate without emergency surfacing caused by the loss of navigation. ISBN:

6 Maintenance of the positioning accuracy level throughout the AUV s mission. The method does not use the dead reckoning system, the main drawback of which is the accumulation of errors. Universality. The method can be used to navigate any underwater vehicle equipped with acoustic transceiver equipment by software (if AUV computing resources are sufficient and hardware upgrade. At present we work on testing and improvement of the developed method taking into account the dynamic motion of an underwater vehicle. REFERENCES [] I.N. Burdinsky, D.S. Chemeris The guidance and positioning system based on the video processing The First Russia and Pacific Conference on Computer Technology and Applications (Russia Pacific Computer 00 Russian Academy of Sciences, Far Eastern Branch, Vladivostok, Russia, 00, pp , 6 9 September 00. [] I.N. Burdinsky, A.V. Myagotin, AUV positioning model employing acoustic and visual data processing OCEANS'0 IEEE Sydney, 00, pp. -6, 4-7 May 00. [3] J.C. Kinsey, R.M. Eustice, L.L. Whitcomb A survey of underwater vehicle navigation: Recent advances and new challenges IFAC Conference of Manoeuvering and Control of Marine Craft, 006. [4] J.J. Leonard, A.A. Bennett, C.M. Smith, H. Feder Autonomous underwater vehicle navigation IEEE ICRA Workshop on Navigation of Outdoor Autonomous Vehicles, January 998. [5] I.N. Burdinsky, A.V. Myagotin A framework of an acoustic navigation network servicing multiple autonomous underwater vehicles Proceedings of the IASTED Internatio nal Conference on Auto mation, Control, and Information Technology Information and Communication Technology, ACIT- ICT 00, pp [6] A.V. Inzartsev, A.V. Kamornyi, L.V. Kiselev,.V. Matvienko, A.M. Pavin, N.I. Rylov, et al. The integrated navigation system of an autonomous underwater vehicle and the experience from its application in high arctic latitudes Gyroscopy and Navigation, 00. Vol..,. pp [7] M.B. Larsen Synthetic long baseline navigation of underwater vehicles OCEANS 000 MTS, IEEE Conference and Exhibition. IEEE, 000., Vol. 3., pp , -4 September 000. [8] A.P. Scherbatyuk The AUV positioning using ranges from one transponder LBL OCEANS'95. MTS, IEEE. Challenges of Our Changing Global Environment. Conference Proceedings. 995, Vol. 3. pp , 9- October 995. [9] I.N. Burdinsky Guidance algorithm for an autonomous unmanned underwater vehicle to a given target Optoelectronics, Instrumentation and Data Processing. 0. Vol pp [0] P. Baccou, B. Jouvencel Homing and navigation using one transponder for AUV, postprocessing comparisons results with long base-line navigation Robotics and Automation, 00. Proceedings. ICRA'0. IEEE International Conference, 00., Vol. 4. pp , -5 May 00. [] S.E. Webster, R.M. Eustice, H. Singh, L.L. Whitcomb Advances in single-beacon one-way-travel-time acoustic navigation for underwater vehicles The International Journal of Robotics Research, 3(8, pp [] J.A. Saude, A.P Aguiar Single Beacon Acoustic Navigation for an AUV in the presence of unknown ocean currents In Proc. of MCMC09-8th IFAC Conference on Manoeuvring and Control of Marine Craft. Guaruja (SP, Brazil., 009, pp [3] F.V. Bezruchko, I.V. Burdinsky, A.V. Myagotin Global extremum searching algorithm for the auv guidance toward an acoustic buoy OCEANS, 0 IEEE-Spain. IEEE, 0, pp. -7, 6-9 June 0. [4] V.E. Gornak, A.V. Inzartsev, O.U. Lvov,.V. Matvienko, A.PH. Scherbatyuk MMT small AUV of new series of IMTP FEB RAS OCEANS 006 Boston, MA, 8- September 006. [5] I.V. Karabanov, M.A. Linnik, I.N. Burdinskiy Threshold Methods of Sonar Pseudonoise Phase-shift Signal Detection The First Russia and Pacific Conference on Computer Technology and Applications (Russia Pacific Computer 00 Russian Academy of Sciences, Far Eastern Branch, Vladivostok, Russia, 00, pp , 6 9 September 00. ISBN: