A Design Method for USBL Systems with Skew Three-element Arrays

Transcription

1 A Design Metho for USBL Sstems with Skew Three-element Arras MIKHAIL ARKHIPOV Department of Postgrauate Stuies Technological Universit of the Mixteca Carretera a Acatlima Km. 2.5, Huajuapan e Leon, Oaxaca, MEXICO mikhail@mixteco.utm.mx Abstract: - This paper escribes a esign metho for ultra-short baseline (USBL) sstems where the location of the unerwater object is efine b utilizing of orthogonal an non-orthogonal (skew) basic (three-element) measuring sstems. The case of calculation of the Cartesian coorinates of the object in the reference coorinate sstem boune up with the USBL sstem s carrier is consiere. The propose esign metho an the algorithm are base on the utilization of multiple rotations of the basic (three-element) USBL receiving arras (orthogonal an non-orthogonal) aroun the horizontal an vertical axes associate with the carrier coorinate sstem. In the article the case of a five-element USBL sstem is investigate. The propose construction of the receiving arra allows it to obtain ifferent spatial orientations of the basic USBL arras an to increase the consistenc an reliabilit of object coorinate etermination. It is suppose that the spatial orientation of the receiving USBL arra is controlle b the measurement of its pitch an roll angles. The coorinate etermination algorithm for the propose USBL sstem is esigne an teste with the assumption that the USBL arra can have significant inclination. Ke-Wors: - Ultra-short baseline (USBL) sstem, unerwater object, transponer, carrier coorinate sstem, local coorinate sstem, skew coorinate sstem, pitch an roll angles. Introuction The central problem of the USBL sstem esign is the unerwater object location etermination with high accurac in real marine conitions. The principle of operating of the USBL sstems is well known an is escribe in etail in [,2]. Object position etermination with this metho is realize b means of the measuring of the istance to the object an its angular position relative to the measuring sstem location. During the last ecaes, numerous stuies an investigations for improvements in accurac an reliabilit of object position etermination with use of the USBL sstems were realize [3-7]. To improve the reliabilit of the USBL sstems various special signal processing techniques were emploe. In particular the chirp signals an greater inter-element arra separation [3] were use. Also the acoustic igital sprea spectrum [4] an moulate Barker-coe signals [5] were applie. In [6] the USBL sstem with frequenchoppe pulses was investigate. The problem of improvement in accurac in the case of instabilit of the position of the receiving USBL arra was stuie in etail in [7]. In [8,9] the problem of low precision in coorinate etermination for the case of the object foun in the plane of receiving bases is stuie. In [0,] the esign metho of multi-element USBL sstems is propose. The iea of this esign metho was to increase the accurac of coorinate etermination with use of the supplementar receiving elements of the USBL arra. The iea of the esign metho in the present article is to use not onl orthogonal receiving bases of antenna arra. It allows the utilization at the most the latent reserves of receiving antenna. The ambiguit of coorinate etermination with these non-orthogonal three-element sstems can be resolve with the use of other elements of antenna. 2 Problem Formulation 2. Basic USBL Sstem The measuring of the object coorinates is realize as the following. The USBL sstem transmitter sens an interrogation acoustical impulse in the propagation meium where the object is locate at an accessible istance. The object must be equippe with a transponer that receives the interrogation impulse an sens an acoustical impulse in repl. The istance to the object is etermine b the measurement of the values of propagation times of the interrogation impulse an the transponer response pulse. The angular position of the object is etermine b the measurement of the phase ifference of the transponer pulse carrier frequenc ISBN:

2 on the receiving arra outputs. The minimum number of receiving elements for the USBL sstem for object coorinate etermination is three []. To improve the reliabilit an accurac of coorinate etermination the number of elements of receiving USBL arra can be increase. In general the propagation meium is non-homogeneous. Furthermore, in this paper we assume that the propagation meium is homogeneous an the multipath interference is absent. We consier briefl the principle of coorinate etermination for the case of the three-element orthogonal USBL arra. Let Σ=(0,x,,z) be the sea-surface associate reference frame with the origin in the point O (see Fig.). Let the plane x coincie with the sea surface (it is suppose that the sea surface is not perturbe) an the positive irection of the z axis run own. It is suppose that the carrier an the carrier coorinate sstem Σ carrier =(0,x carrier, carrier,z carrier ) coincies with the Σ=(0,x,,z) when the carrier oes not have pitch an roll inclinations. Also it is suppose that in such the x-coorinate axis coincies with the carrier longituinal axis L-L' (the positive irection coincies with the irection of the straight arrowe line), the -coorinate coincies with the carrier lateral axis B-B', an z axis goes ownwars. Now we can efine the USBL arra orientation in the introuce carrier coorinate sstem. Let Σ 23 =(0,x 23, 23,z 23 ) be the local coorinate sstem for the consiere USBL sstem (with receiving elements,2,3). It is assume that the origin of the USBL coorinate sstem coincies with the origin of the carrier coorinate sstem, the angle between the -axis an base -2 is 35, an the angle between the -axis an the base 3-2 is 45. It is also suppose that the receiving USBL arra is rigil mounte on the carrier hull. The geometr of the introuce sea-surface associate coorinate sstem Σ=(0,x,,z) an the receiving three-element USBL coorinate sstem Σ 23 =(0,x 23, 23,z 23 ) is presente in Fig.. The reference gri is shown onl for the USBL coorinate sstem. In Fig. we specif the angles (α, β an γ) that efine the position of the unerwater object (locate in point P) in the Σ 23 =(0,x 23, 23,z 23 ) coorinate sstem. We also assume that the USBL sstem is equippe with a special unit to measure the pitch an roll angles of the carrier (the pitch an roll angles of the USBL arra are the same as for the carrier). Let angles ξ an ζ be pitch an roll angles corresponing to the receiving USBL antenna (in the figure these angles show the rotations relative to the carrier lateral B-B' axis an the carrier longituinal L-L' axis). Let that the interrogation impulse has been sent an x x ξ 23 L' B' 3 ξ x 23 x ξ,ζ 23 3 USBL antenna 3 ξ,ζ ξ ξ,ζ α z ξ,ζ 23 O2 z ξ 23 z 23 z γ β ζ L R Repl impulse ξ 23 ξ,ζ ξ B Interrogation impulse P(X,Y,Z) Fig.. Geometr of the receiving antenna an the carrier longituinal an lateral axes. the repl impulse is being receive b antenna. The istance to the object is efine b measuring the propagation times of the interrogation an repl pulses. Time elas on receiving elements efine the object s angular position. The time elas τ 2 an τ 32 of the signal on the outputs of the receiving elements of the base -2 an the base 3-2 (it is suppose that R>>) can be expresse in the following wa: τ 2 =(/c)cosβ an τ 32 =(/c)cosα, where c is the spee of the soun in the water. With /c efine as τ we can write the irection cosines cosα=τ 32 /τ an cosβ=τ 2 /τ. The thir irection cosine is efine as: cosγ= ( τ / τ ) ( τ / τ ). Cartesian coorinates of the point P in the Σ 23 =(0,x 23, 23,z 23 ) coorinate sstem are: X 23 =Rcosα, Y 23 =Rcosβ, Z 23 =Rcosγ. To obtain the coorinates of point P in the Σ=(0,x,,z) coorinate sstem (point P(X,Y,Z) in Fig.) it is necessar to carr out the corresponing transformation of obtaine coorinates X 23, Y 23, Z 23. Let that the pitch an roll rotations of the receiving antenna take place. The pitch an roll rotations of the elemental three-element USBL antenna are shown in Fig.. After the first rotation on pitch angle ξ relative to B-B' axis the receiving elements are isplace to points ξ an 3 ξ respectivel. After the secon rotation on the angle ζ relativel L-L' axis the receiving elements are isplace to point ξ,ζ an 3 ξ,ζ respectivel (see Fig.). With the rotations of receiving bases the corresponing transformations of coorinate sstems from Σ 23 =(0,x 23, 23,z 23 ) to Σ ξ 23=(0,x ξ 23, ξ 23,z ξ 23) an to Σ ξ,ζ 23=(0,x ξ,ζ 23, ξ,ζ 23, z ξ,ζ 23) have taken place. Calculation expressions for the case of the pitch an roll of the three-element receiving antenna with introuce orientation relative to the carrier have been obtaine in [8,9]. So we escribe the calculation ISBN:

3 proceure here ver briefl. If we introuce vectors: p ξ,ζ 23=[X ξ,ζ 23, Y ξ,ζ 23, Z ξ,ζ 23] T ([X ξ,ζ 23, Y ξ,ζ 23, Z ξ,ζ 23] T represents the transpose of the vector [X ξ,ζ 23, Y ξ,ζ 23, Z ξ,ζ 23]) an p ξ 23=[X ξ 23, Y ξ 23, Z ξ 23] T (vector p ξ,ζ 23 represents the coorinates of the object in Σ ξ,ζ 23 coorinate sstem an vector p ξ 23 represents the coorinates of the object in Σ ξ 23 coorinate sstem) an the transformation matrix B=B[ζ,,η 23,,χ 23,,ν 23 ] with irection cosines η 23 =cos(x ξ 23,L), χ 23 =cos( ξ 23,L), ν 23.=cos(z ξ 23,L) (matrix B transforms vector p ξ 23 to vector p ξ,ζ 23) we can write the equation: p ξ 23= B - p ξ,ζ 23. If we introuce vector p 23 =[X 23, Y 23, Z 23 ] T ( vector p ξ 23 represents the coorinates of the object in Σ 23 coorinate sstem) an the transformation matrix A= A[ξ,η 23,χ 23,ν 23 ] with irection cosines η 23 =cos(x 23,B), χ 23 =cos( 23,B), ν 23 =cos(z 23,B) (matrix A transforms vector p 23 to vector p ξ 23) we can write the equation: p 23 =A - p ξ 23. These two transformations can be combine in the equation p 23 = A - B - p ξ,ζ 23. In orer to obtain the coorinates of the object in the Σ=(0,x,,z) coorinate sstem (we will have the same coorinates of the object in the carrier coorinate sstem Σ carrier =(0,x carrier, carrier,z carrier ) an in the seasurface associate coorinate sstem Σ=(0,x,,z) if the carrier is not incline) it is necessar to make one more rotation of the coorinate sstem Σ 23 aroun the axis z on the angle of 35 (see Fig.). For the Σ=(0,x,,z) coorinate sstem, we have the following irection cosines for the z-axis: cos(x,z)=0, cos(,z)=0, cos(z, z)=. If we introuce vector p=[x, Y, Z] T (vector p represents the coorinates of the object in Σ=(0,x,,z) coorinate sstem) an the transformation matrix C (matrix C transforms vector p to vector p 23 ) the final equation to fin vector p will be the following: p=c - A - B - p ξ,ζ 23. Thus to fin the coorinates in the Σ=(0,x,,z) coorinate sstem we write the final matrix equation: p=c - A - B - p ξ,ζ 23. () 2.2 Five-element USBL sstem Articles [8,9] note the problem of the low precision coorinate etermination for the cases when the controlle object is foun in planes of receiving bases of elemental USBL sstems. To resolve this problem a five-element USBL sstem with ifferent spatial orientation of receiving bases was propose. Also the special algorithm was esigne an investigate an significant accurac improvement was obtaine. In [0,] the aitional moernization of the antenna construction an improvement of the coorinate etermination algorithm were propose. In particular the number of transucers of the receiving arra was increase to nine. As a result the new USBL arra ha a larger number of elemental USBL arras with ifferent spatial orientations an a higher reliabilit of sstem was obtaine. The main goal of the present investigation is to check the possibilit of obtaining similar results with a smaller number of receiving arra elements. If we analze the construction of the five-element USBL arra investigate in [8],[9] we can see that besies having orthogonal three-element basic arras this USBL antenna also has a non-orthogonal threeelement basic arras. We can also see that these nonorthogonal USBL arras have spatial orientations similar to the orientations of the aitional orthogonal three-element USBL arras of the nineelement arra (mentione above an have been investigate in [0] an []). 3 Problem Solution 3. Skew three-element USBL sstem We will investigate the propose esign metho for the five-element USBL arra that has been stuie in [8,9]. The construction of the foregoing five-element USBL arra is shown in Fig.2. The USBL arra has the following orthogonal three-element USBL sstems: USBL 23, USBL 234, USBL 34, USBL 42, USBL 53, USBL 254. The aitional non-orthogonal three-element USBL sstems presente in this construction are: USBL 52, USBL 253, USBL 354, USBL 45 (in this particular case all of these nonorthogonal three-element arras form equilateral triangles). Our proposal is to utilize these non-orthogonal (skew) three-element arras as a part of the USBL measuring sstem. We will emonstrate the propose metho in etail onl for the case of the skew USBL 52 sstem. For the rest of the skew threeelement USBL sstems the sequence of necessar x x ξ x ξ,ζ 52 ξ 52 ξ,ζ x ξ,ζ 2 ξ,ζ 52 52_90 ξ,ζ ξ ξ z ξ,ζ 52 3 z ξ,ζ 4 52_90 D' 5 z ξ 52 z ξ C 52 O C' ζ D Fig.2. Five-element USBL arra ξ,ζ 52_90 ISBN:

4 operational steps will be similar. Let Σ 52 =(0,x 52, 52,z 52 ) be the local coorinate sstem for the consiere USBL 52 sstem (with receiving elements,5,2). The origin of the Σ 52 coorinate sstem is locate at the point of the placement of receiving element number 5. Before representing the sequence of algorithm steps we will introuce two new axes to obtain easier examination of USBL 52 arra pitch an roll inclinations. Let the C-C' be the axis that is parallel to the lateral axis B-B' an let the axis C-C' pass through the point 5 (the point of location of the receiving element number 5). Let the D-D' be the axis that is parallel to the longituinal axis L-L' an let the axis D-D' pass through the point 5 (the point of location of the receiving element number 5). After the introuction of these axes the rotation of the USBL 52 arra aroun the lateral axis B-B' on the pitch angle can be replace b the rotation aroun the axis C-C' an the rotation aroun the longituinal axis L-L' on the roll angle can be replace b the rotation aroun the axis D-D'. For further consieration all rotations of the USBL 52 coorinate sstem will take place aroun its origin. 3.2 Calculation expressions for skew threeelement USBL sstem We will consier the erivation of the calculation expressions for USBL 52 sstem in etail. Then we will present the expressions for the other skew threeelement USBL sstems (USBL 253, USBL 354, USBL 45 ). For convenience to get the calculation expressions we will firstl consier the case of location of the three-element USBL 52 sstem on a horizontal plane. Let Σ 52 =(0,x 52, 52,z 52 ) be the local skew coorinate sstem for the consiere USBL sstem (with receiving elements,5,2). The angle between the axis x 52, an axis 52 is efine b the electe construction of receiving antenna. We will esignate this angle as ν (for the propose antenna esign ν=60 ). The origin of the coorinate sstem coincies with the receiving element 5. We also assume that the axis z forms a right angle with the axes x 52, an 52. We will suppose that the object is locate in the point P. Geometr of the receiving antenna an location of the object are represente in Fig.3. Direction cosines cosα an cosβ are efine in the same wa as in the case of orthogonal axes: cosα=τ 5 /τ ; cosβ=τ 25 /τ. (2) x 52_90 x 52 X 52_90 X 52_covar O _90 ν R h β α β α 52 Z 52_covar z 52 z 52_90 γ R Y 52_90 Y 52_covar Fig.3. Skew three-element USBL arra To obtain the thir irection cosine cosγ (or angle γ) we nee to solve the next sstem of equations: R h =R cosα/cosα ; R h =R cosβ/cosβ ; R h =R sinγ; α +β =ν, (3) where R h is the istance to the object in horizontal plane; α an β are the angles that efine the angular position of the object in the horizontal plane. Fore the solution of (3) we can write the expression for α an β as follows: cosβ α = arctg cosν sinν cosα ; cosα β = arctg cosν. (4) sinν cos β The angle γ is efine as follows: cosα cos β γ = arcsin = arcsin. (5) cosα cos β P The covariant coorinates X 52_covar, Y 52_covar an Z 52_covar in skew coorinate sstem Σ 52 =(0,x 52, 52,z 52 ) are efine b the expressions: X 52_covar =Rcosα ; Y 52_covar =Rcos β ; Z 52_ covar = Rcosγ. (6) The contrvariant coorinates X 52_ccntr, Y 52_ccntr an Z 52_contr in skew coorinate sstem Σ 52 =(0,x 52, 52,z 52 ) are efine b the expressions: X 52_ccntr = X 52_covar R sinα ctgν; Y 52_ccntr = Y 52_covar Rsinβ ctgν; ISBN:

5 Z 52_ contr = Z 52_ covar = Rcosγ. (7) After measuring the coorinates of the object in the skew coorinate sstem (in this particular case in the Σ 52 =(0,x 52, 52,z 52 ) coorinate sstem) we must transform these coorinates to regular Cartesian coorinates. We can o this transformation in this stage. It will allow us to make the further coorinate transformations b using the alrea esigne proceures (the rotations of Cartesian coorinate sstems aroun earlier efine axes b pitch an roll angles). So now we efine the coorinates of the object in the Cartesian coorinate sstem Σ 52_90 =(0,x 52_90, 52_90,z 52_90 ). The z-axis in the new coorinate sstem will not change. The Cartesian coorinates in the new coorinate sstem will be efine with the expressions: X 52_90 = X 52_ccntr cos345 + Y 52_ccntr cos285 ; Y 52_90 = X 52_ccntr cos75 + Y 52_ccntr cos5 ; Z 52_90 = Z 52_ contr = Rcosγ. (8) To obtain the coorinates of point P in the Σ=(0,x,,z) coorinate sstem (point P(X,Y,Z) in Fig.) it is necessar perform the corresponing transformations of obtaine coorinates X 52_90, Y 52_90, Z 52_90. Let the pitch an roll rotations of the receiving antenna take place. The pitch an roll rotations of the three-element USBL arras are shown in Fig.,2. The ifference of the consieration of the rotation of the USBL 23 coorinate sstem from the rotation of USBL 52_90 coorinate sstem is in the following: in the first case the rotation is realize aroun the origin that is locate in point 2 an in the secon case the rotation is realize aroun the origin that is locate in point 5. The first rotation on pitch angle ξ relative to C-C' axis the receiving elements are isplace to points ξ an 2 ξ respectivel. After a secon rotation on the angle ζ relativel D-D' axis the receiving elements are isplace to point ξ,ζ an 2 ξ,ζ respectivel (see Fig.2). In our algorithm we will carr out the rotations with orthogonal coorinate sstems. With this assumption the corresponing transformations of coorinate sstems from Σ 52_90 =(0,x 52_90,, 52_90, z 52_90 ) to Σ ξ 52_90=(0,x ξ 52_90,, ξ 52_90,, z ξ 52_90) an to Σ ξ,ζ 52_90=(0,x ξ,ζ 52_90,, ξ,ζ 52_90,,z ξ,ζ 52_90) have taken place. Calculation expressions for the case of the pitch an roll of the orthogonal three-element receiving antenna with ifferent orientation relative to the carrier have been obtaine in [8,9]. After the transformation of the skew coorinates to the orthogonal coorinates in the Σ ξ,ζ 52_90 the further proceure of the calculation of the coorinates of the object in the Σ=(0,x,,z) coorinate sstem is accomplishe in the same wa as it is mae for the other orthogonal three-element USBL sstems. Using a similar sequence of steps as was applie to the orthogonal USBL 23 sstem we will have the final equation for the object s coorinates in the Σ=(0,x,,z) coorinate sstem efine with the USBL 52 sstem: ξ, ς USBL52 52_90 52_90 52_90 52_90 52_90 52_90 p =C D F A B p, (9) where p ξ,ζ 52_90=[X ξ,ζ 52_90,,Y ξ,ζ 52_90,,Z ξ,ζ 52_90] T is the vector that represents the coorinates of the object in Σ ξ,ζ 52_90 coorinate sstem; B 52_90 is the matrix that transforms vector p ξ 52_90 to vector p ξ,ζ 52_90; A 52_90 is the matrix that transforms vector p 52_90 to vector p ξ 52_90; F - 52_90 is the matrix that transforms vector p 52_90 to vector p 52_90_vert (p 52_90_vert is the vector in the vertical oriente coorinate sstem Σ 52_90 ); D - 52_90 is the matrix that transforms vector p 52_90_vert to vector p 52_53 (p 52_53 is the vector in the vertical oriente coorinate sstem Σ 53 ); C - 52_90 is the matrix that transforms vector p 52_53 to vector p. USBL Calculation expressions for five-element USBL sstem In the case of the five-element USBL arra, the sstem consists of ten basic USBL sstems with ten ifferent spatial orientations: USBL 23, USBL 234, USBL 34, USBL 42, USBL 53, USBL 254, USBL 52, USBL 253, USBL 354, an USBL 45. The coorinates of the object are etermine iniviuall in each elemental USBL sstem. The USBL 234, USBL 34 an USBL 42 sstems iffer from the USBL 23 sstem in their own values of the pitch an roll angles an in their own angles of rotation of each USBL antenna aroun the z-axis. The coorinate etermination for the USBL 53 sstems is almost the same as for the USBL 23 sstem. The ifference is that one aitional step is require to reuce the USBL 53 sstem coorinates to a horizontal plane (b rotation the USBL 53 sstem on a 90 angle). We have to o the same with coorinates obtaine with the USBL 254 sstem. To accomplish these aitional rotations for the USBL 53 an USBL 254 arras we introuce for each sstem the transformation matrix (matrix D). The USBL 253, USBL 354 an USBL 45 sstems iffer from the USBL 52 in their own irection cosines, in their own values of the pitch an roll angles an in their own angles of rotation of each USBL arra aroun the z- ISBN:

6 axis (see Fig.2). So for the USBL 253, USBL 354 an USBL 45 sstems we have to accomplish the all steps that have been implemente for USBL 52 sstem. In orer to istinguish the results of the measure coorinates b ifferent basic USBL sstems we introuce the consequent esignations for the vectors an transformation matrixes for each particular USBL sstem: ξ, ς USBL ξ, ς USBL ξ, ς USBL ξ, ς USBL ξ, ς p =C D A B p ; USBL ξ, ς p =C D A B p ; USBL ξ, ς USBL52 52_90 52_90 52_90 52_90 52_90 52_ ξ, ς USBL _90 253_90 253_90 253_90 253_90 253_ ξ, ς USBL _90 354_90 354_90 354_90 354_90 354_ ξ, ς USBL45 45_90 45_90 45_90 45_90 45_90 45_90 p =C D F A B p ; p =C D F A B p ; p =C D F A B p ; p =C D F A B p. (0) The final stage of the algorithm implies the calculation of the means of the object coorinates in the Σ=(0,x,,z) coorinate sstem with reliable ata obtaine b the elemental USBL sstems. 4 Conclusion In this article we have consiere the metho of esign of USBL sstems both utilizing of orthogonal an non-orthogonal (skew) basic three-element arras. A case for the esign of a five-element USBL sstem is presente. The paper focuse on the problem of exploiting the latent resources of the receiving USBL arra (skew three-element arras) for accurate coorinate etermination in conitions when the receiving antenna can have significant inclinations an the location of the object is arbitrar. The propose algorithm accomplishes the selection of reliable elemental USBL arras (orthogonal an non-orthogonal) utilizing the analsis of the values of latitue angles to the object for each elemental arra. The presente algorithm is a significantl moifie version of the algorithm esigne for the fiveelement USBL sstem where onl orthogonal elemental three-element arras have been utilize [9]. Algorithm simulation was realize for a variet of the mutual positions of the USBL sstem an object in a wie range of pitch an roll of receiving arras (pitch an roll angles ξ an ζ are assume to be in the range from -40 to +40 ). For all teste angular receiving arra positions an object locations the esigne algorithm showe reliable operation. References: [] P.H. Milne, Unerwater Acoustic Positioning Sstem, Gulf Publishing Compan, 983. [2] K. Vicker, Acoustic positioning sstems, A practical overview of current sstems. Proceeings of the 998 Workshop on Autonomous Unerwater Vehicles, 998, p.5-7. [3] M. Watson, C. Loggins, Y.T. Ochi, A New High Accurac Super Short Base Line (SSBL) Sstem, Unerwater Technolog, Proceeings of 998 International Smposium, 998, pp [4] D. Thomson, S. Elson, New generation acoustic positioning sstems, Proceeings of Oceans '02 MTS/IEEE, Vol.3, 2002, pp [5] F.V.F. Lima, C.M. Furukawa, Development an Testing of an Acoustic Positioning Sstem - Description an Signal Processing, Ultrasonics Smposium, Proceeings, 2002 IEEE, Vol., 2002, pp [6] P.P.J. Beaujean, A.I. Mohame, R. Warin, Acoustic Positioning Using a Tetraheral Ultrashort Baseline Arra of an Acoustic Moem Source Transmitting Frequenc-hoppe Sequences, The Journal of the Acoustical Societ of America, Vol.2, No., 2007, pp [7] D.R.C. Philip, An Evaluation of USBL an SBL Acoustic Sstems an the Optimisation of Methos of Calibration - Part, The Hrographic Journal, No.08, 2003, pp [8] M. Arkhipov, A Coorinate Determination Algorithm for USBL Sstems. Proceeings of the 2n WSEAS International Conference on CIRCUITS, SYSTEMS, SIGNALS an TELECOMMUNICATIONS (CISST 08), Acapulco, Mexico, 2008, pp [9] M. Arkhipov, An Algorithm for Improving the Accurac of Z-Coorinate Determination for USBL Sstems. WSEAS TRANSACTIONS on SYSTEMS, Vol.7, No.4, 2008, pp [0] M. Arkhipov, A Design Metho an Coorinate Determination Algorithm for Multi-element USBL Sstems. Proceeings of the 3th WSEAS International Conference on SYSTEMS, Roos, Greece, Jul 22-24, 2009, pp [] M. Arkhipov, An Approach for Design of Multi-element USBL Sstems. WSEAS TRANSACTIONS on SYSTEMS, Vol.8, No.8, 2009, pp ISBN: