A method for measuring the configuration of a towed array based on underwater acoustic differential positioning

Abstract

A towed array formation measurement method based on underwater acoustic differential positioning is presented, belonging to the field of underwater acoustic engineering. This method addresses the technical challenge of achieving stable and high-precision relative positioning in complex acoustic environments using existing long-baseline positioning methods. By utilizing the seabed sound velocity, the positions of various seabed reference points, and the time delay from each reference point to each array element, an observation equation is constructed for each element. A differential origin array element is selected, and an inter-element differential positioning model is built using the observation equations between the differential origin element and other array elements, along with a target function. The initial coordinates of each element are corrected by solving the target function, yielding the coordinate calculation results for each element. This reconstructs the spatial morphology of the towed array, ultimately completing the formation measurement. This method is primarily used for towed array formation measurement.

Description

Technical Field

[0001] This invention relates to the field of underwater acoustic engineering, and specifically to a method for measuring towed array configurations. Background Technology

[0002] A towed array is a hydrophone array consisting of multiple hydrophones arranged at fixed intervals along flexible cables, towed into the water by the stern of a vessel or other carrier. It is mainly used for long-range underwater acoustic detection. High-precision estimation and reconstruction of the three-dimensional spatial formation of the towed array is a prerequisite for ensuring the beamforming efficiency and far-field azimuth resolution of large-aperture towed arrays, and is key to maintaining high-performance passive detection and target identification under complex sea conditions and platform maneuvering.

[0003] Because flexible towed arrays can reach kilometer scales, the ranging system error of the seabed reference exhibits heterogeneous influence with the spatial distribution of array elements. When using the conventional point-to-point positioning mode of long baseline positioning to perform high-precision estimation of the three-dimensional spatial configuration of the towed array, problems such as sound velocity disturbances, multipath effects, and base station position drift arise, leading to positioning deviations, time delay processing errors, and system positioning errors. These errors are strongly coupled and globally correlated, making it difficult for long baseline positioning systems to achieve stable and high-precision relative positioning in complex acoustic environments. Summary of the Invention

[0004] To overcome the technical problem that existing long baseline positioning methods are difficult to achieve stable and high-precision relative positioning in complex acoustic environments, this invention provides a towed array measurement method based on underwater acoustic differential positioning.

[0005] A method for measuring the array configuration of a towed array based on underwater acoustic differential positioning includes:

[0006] S1: Obtain the position of each seabed reference, obtain the sound velocity between each seabed reference and each element of the towed array, and obtain the propagation delay between each seabed reference and each element of the towed array.

[0007] S2: Construct the observation equation for each array element using the data obtained in S1;

[0008] S3: Select one array element that meets the preset conditions from each array element of the dragging array as the differential origin array element, and subtract the observation equation of the non-differential origin array element from the observation equation of the differential origin array element to obtain the differential positioning model between array elements.

[0009] S4: Based on the differential positioning model between array elements, construct the objective function for estimating the formation of the towed array based on differential positioning;

[0010] S5: Solve the objective function of the towed array formation estimation based on differential positioning to obtain the correction amount of the initial coordinate point of each array element; based on the correction amount, correct the initial coordinate point of each array element to obtain the coordinate solution result of each array element, and complete the towed linear array formation measurement.

[0011] Furthermore, the observation equation for each array element is:

[0012] ;

[0013] In the formula, This represents the Euclidean norm, i.e., spatial distance. As a seabed reference number, , The total number of seabed references, ; Indicates the first Seabed reference position coordinates , , and They represent the first A seabed datum in a geodetic coordinate system axis, shaft and Axis coordinates; For the first The position coordinates of each dragging array element. , , and They represent the first The three-dimensional coordinates of each dragged array element in the geodetic coordinate system; For the first The first seabed benchmark to the first Measured sound velocity of each array element; For the first The first seabed benchmark and the first Propagation delay between array elements; For dragging array element labels, , The total number of dragging array elements. .

[0014] Furthermore, the method for selecting the differential origin array element is as follows: select array elements that receive all seabed reference acoustic signals from all array elements as candidate array elements, perform single-point long baseline positioning on the candidate array elements, and select the array element with the smallest positioning residual as the differential origin array element.

[0015] Furthermore, if the m-th array element is used as the differential origin array element, then the expression for the differential positioning model between array elements is:

[0016] ;

[0017] In the formula, This represents the position coordinates of the element in the difference lattice. , , and These represent the three-dimensional coordinates of the finite difference lattice element in the geodetic coordinate system; Indicates the first Measured sound velocity from a seabed reference point to a differential lattice element For the first The propagation delay from the seabed reference to the differential origin lattice element.

[0018] Furthermore, the expression for the objective function of towed array configuration estimation based on differential positioning is as follows:

[0019] .

[0020] Furthermore, the least squares method is used to solve the objective function for estimating the towed array configuration based on differential positioning.

[0021] Furthermore, the steps for solving the objective function of towed array configuration estimation based on differential positioning include:

[0022] S51: The objective function is written in the following form:

[0023] ;

[0024] S52: Apply the function described in S51 to a non-difference origin lattice element. initial point Performing a Taylor expansion at the given point yields the following linear equation in matrix form:

[0025] ;

[0026] In the formula, Represents non-difference original lattice elements The corresponding residual matrix, , Represents non-difference original lattice elements Corresponding to the The residuals of the observation equations for each seabed reference; Represents non-difference original lattice elements The corresponding Jacobian matrix, , Represents non-difference original lattice elements Corresponding to the Jacobian matrix of the observation equations for a seabed reference; As the initial point The amount of correction; , and These represent the three-dimensional coordinates of the initial point in the geodetic coordinate system;

[0027] S53: Using the least squares method to initialize the point Correction amount Solve for the problem using the following formula:

[0028] ;

[0029] In the formula, Representing the Jacobian matrix transpose, express The inverse matrix;

[0030] S54: Utilizing Correction Amounts For non-difference original lattice elements initial point After correction, the non-differential original lattice elements are obtained. Location ; ;

[0031] S55: Based on the methods described in S51-S54, determine the positions of all non-differential origin lattice elements to complete the towed array formation measurement.

[0032] Furthermore, the non-difference original lattice elements Corresponding to the Jacobian matrix of observation equations for a seabed reference The specific form is:

[0033] .

[0034] Furthermore, the non-difference original lattice elements Corresponding to the The observation equation residuals of the seabed benchmark The specific form is:

[0035] .

[0036] Furthermore, the sound velocity between each seabed reference and each element of the towed array is obtained by measuring the sound velocity profiler.

[0037] The beneficial effects of this invention are:

[0038] By utilizing the sound velocity on the seabed, the positions of various seabed reference points, and the time delay from each reference point to each array element, an observation equation is constructed for each array element. A differential origin array element is selected, and a differential positioning model between array elements is built using the observation equations between the differential origin array element and other array elements, along with a target function. The initial coordinate points of each array element are corrected by solving the target function, resulting in the coordinate calculation results for each element. The spatial morphology of the towed array is reconstructed, ultimately completing the array shape measurement. The differential positioning model constructed in this invention utilizes the homogeneous propagation error characteristics to allow complex error sources to cancel and compensate for each other in the differential domain, effectively reducing or eliminating systematic errors and achieving stable, high-precision relative positioning in complex acoustic environments. Attached Figure Description

[0039] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0040] Figure 1 This is a schematic diagram of differential localization model construction in one embodiment of the method of the present invention. Detailed Implementation

[0041] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0042] Due to factors such as seabed reference errors, marine environmental errors, and platform motion, the geometric configuration of existing long baseline positioning models changes frequently with time delays and interruptions, leading to inconsistent error propagation links between different array elements and making it difficult to achieve stable and high-precision relative positioning. To address these issues, this application provides a towed array configuration measurement method based on underwater acoustic differential positioning, applicable to a system including a towed array, a seabed reference array, and a calculation terminal.

[0043] The towed array includes several array elements, each of which is equipped with an acoustic receiver. Each array element transmits signals to the solution terminal via a cable.

[0044] The seabed reference array includes at least four time-synchronized seabed references, each equipped with a high-precision atomic clock. The atomic clock has a high-precision timekeeping function and can respond to preset acoustic modulation commands to achieve remote acoustic control, so that the time of each seabed reference is synchronized. Each seabed reference is deployed on the seabed. A surface vessel tows the array to its stern and navigates along the array area formed by the seabed references.

[0045] The solution terminal is deployed on a ship on the water.

[0046] In this embodiment of the application, the towed array includes 1280 array elements; the seabed reference array includes 6 time-synchronized seabed references.

[0047] The towed array formation measurement method based on underwater acoustic differential positioning includes the following steps:

[0048] Step S1: Obtain the position of each seabed reference, obtain the sound velocity between each seabed reference and each element of the towed array, and obtain the propagation delay between each seabed reference and each element of the towed array.

[0049] In this step, the sound speed is obtained by placing a sound speed profiler in the sea area to be measured.

[0050] In this step, the position of the seabed reference is obtained in the following way:

[0051] The surface vessel travels at a speed of no more than 2 knots, and during the voyage, it simultaneously records the surface vessel's position data acquired by the shipborne GNSS, the hull attitude data collected by the attitude sensor, and the round-trip propagation delay data of the acoustic signal between the surface vessel and the seabed reference.

[0052] First, the surface vessel position data is converted to the origin of the vessel coordinate system. Then, based on the vessel attitude data, the spatial offset of the transducer relative to the origin is compensated to obtain the true spatial coordinates of the shipborne transducer in the geodetic coordinate system. Subsequently, combining the spatial coordinates with acoustic distance observations, the absolute coordinates of the seabed reference point in the geodetic coordinate system are calculated using a spatial resection algorithm.

[0053] The navigation track includes navigation track one and navigation track two:

[0054] The navigation trajectory one is a circular trajectory with the seabed reference as the center and the sea depth value at the center position as the radius;

[0055] The second navigation trajectory is a cross-shaped trajectory that passes through the first navigation trajectory.

[0056] In this step, the propagation delay between each seabed reference and each element of the towed array is obtained in the following way: each seabed reference synchronously transmits underwater acoustic signals at a preset time period, the acoustic receiver on the towed array element collects the underwater acoustic signals, and transmits the underwater acoustic signals to the calculation terminal through a cable. The calculation terminal calculates the time delay between each seabed reference and each element in parallel based on the underwater acoustic signals.

[0057] In this embodiment of the application, the preset time period is 4 seconds.

[0058] Step S2: Based on the sound speed, the position of each seabed reference, and the propagation delay between each seabed reference and each array element, construct the observation equation for each array element.

[0059] Taking the j-th element as an example, the observation equation is:

[0060] (1)

[0061] In the formula, This represents the Euclidean norm, i.e., spatial distance. As a seabed reference number, , The total number of seabed references, ; Indicates the first Seabed reference position coordinates , , , They represent the first A seabed datum in a geodetic coordinate system axis, axis, Axis coordinates; For the first The position coordinates of each dragging array element. , , , They represent the first The three-dimensional coordinates of each dragged array element in the geodetic coordinate system; For the first The first seabed benchmark to the first Measured sound velocity of each array element; For the first The first seabed benchmark to the first The propagation delay of each array element; For dragging array element labels, , The total number of dragging array elements. .

[0062] In this embodiment, the total number of seabed references The total number of dragging array elements .

[0063] Step S3: Select an element from the towed array elements that meets the preset conditions as the differential origin element. Subtract the observation equation of the non-differential origin element from the observation equation of the differential origin element to obtain the differential positioning model between elements. Please refer to... Figure 1 , Figure 1 This is a schematic diagram of the differential localization model construction.

[0064] In this step, the differential origin array element is selected as follows: array elements that can receive all seabed reference acoustic signals are selected from all array elements as candidate array elements, single-point long baseline positioning is performed on the candidate array elements, and the array element with the smallest positioning residual is selected as the differential origin array element.

[0065] Assuming the m-th array element is the origin element of the differential array, the expression for the differential positioning model between array elements is:

[0066] (2)

[0067] In the formula, Indicates the position coordinates of the origin of the difference. , , , These represent the three-dimensional coordinates of the origin of difference in the geodetic coordinate system, which are derived from the conventional long baseline positioning spherical intersection principle. Indicates the first The measured sound velocity from the seabed reference point to the origin of the difference point For the first The propagation delay from the seabed reference point to the origin of the difference.

[0068] This represents the theoretical value. This represents the observed value.

[0069] By utilizing the strong spatial correlation of signal propagation paths and the common source characteristics of similar propagation errors, differential time delay observation equations between array elements are established, so that the errors of the coupled system composed of complex error sources such as sound speed disturbance, multipath time delay and reference drift can cancel and compensate each other in the differential domain.

[0070] Step S4: Based on the inter-element differential positioning model, construct the objective function for estimating the towed array formation based on differential positioning. Specifically, by minimizing the sum of squared residuals between the observed and theoretical values ​​of the non-differential origin array elements, the objective function for estimating the towed array formation based on differential positioning is constructed, expressed as:

[0071] (3)

[0072] Step S5: Solve the objective function of the towed array formation estimation based on differential positioning to obtain the correction amount of the initial coordinate point of each array element; based on the correction amount, correct the initial coordinate point of each array element to obtain the coordinate solution result of each array element, and complete the towed linear array formation measurement.

[0073] In this step, the least squares method is used to solve the objective function for the towed array formation estimation based on differential positioning. The steps include:

[0074] Step S51: The objective function for estimating the towed array formation based on differential positioning is written in the following functional form:

[0075] make:

[0076] (4)

[0077] Step S52: Apply the function described in step S51 to the non-difference origin lattice elements. initial point Performing a Taylor expansion at the given point yields the following linear equation in matrix form:

[0078] (5)

[0079] In the formula, Represents non-difference original lattice elements The corresponding residual matrix, , Represents non-difference original lattice elements Corresponding to the The residuals of the observation equations for each seabed reference; Represents non-difference original lattice elements The corresponding Jacobian matrix, , Represents non-difference original lattice elements Corresponding to the Jacobian matrix of the observation equations for a seabed reference; As the initial point The amount of correction; , and These represent the three-dimensional coordinates of the initial point in the geodetic coordinate system.

[0080] non-differential origin array element Corresponding to the Jacobian matrix of observation equations for a seabed reference The specific form is:

[0081] (6)

[0082] non-differential origin array element Corresponding to the The observation equation residuals of the seabed benchmark The specific form is:

[0083] (7)

[0084] Step S53: Use the least squares method to apply the formula (6) to the equation. Solve for the problem using the following formula:

[0085] (8)

[0086] In the formula, Representing the Jacobian matrix transpose, express The inverse matrix.

[0087] Step S54: Utilize the correction amount For non-difference original lattice elements initial point After correction, the non-differential original lattice elements are obtained. Location .

[0088] The corrected expression is:

[0089] (9)

[0090] Step S55: Based on the methods described in S51-S54, determine the positions of all non-differential origin lattice elements to complete the towed array formation measurement.

[0091] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0092] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for measuring the configuration of a towed array based on underwater acoustic differential positioning, characterized in that, include: S1: Obtain the position of each seabed reference, obtain the sound velocity between each seabed reference and each element of the towed array, and obtain the propagation delay between each seabed reference and each element of the towed array. S2: Construct the observation equation for each array element using the data obtained in S1; S3: Select one array element that meets the preset conditions from each array element of the dragging array as the differential origin array element, and subtract the observation equation of the non-differential origin array element from the observation equation of the differential origin array element to obtain the differential positioning model between array elements. S4: Based on the differential positioning model between array elements, construct the objective function for estimating the formation of the towed array based on differential positioning; S5: Solve the objective function of the towed array formation estimation based on differential positioning to obtain the correction amount of the initial coordinate point of each array element; based on the correction amount, correct the initial coordinate point of each array element to obtain the coordinate solution result of each array element, and complete the towed linear array formation measurement.

2. The towed array formation measurement method based on underwater acoustic differential positioning according to claim 1, characterized in that, The observation equation for each array element is: ； In the formula, This represents the Euclidean norm, i.e., spatial distance. As a seabed reference number, , The total number of seabed references, ; Indicates the first Seabed reference position coordinates , , and They represent the first A seabed datum in a geodetic coordinate system axis, shaft and Axis coordinates; For the first The position coordinates of each dragging array element. , , and They represent the first The three-dimensional coordinates of each dragged array element in the geodetic coordinate system; For the first The first seabed benchmark to the first Measured sound velocity of each array element; For the first The first seabed benchmark and the first Propagation delay between array elements; For dragging array element labels, , The total number of dragging array elements. .

3. The towed array formation measurement method based on underwater acoustic differential positioning according to claim 2, characterized in that, The method for selecting the differential origin array element is as follows: select array elements that receive all seabed reference acoustic signals from all array elements as candidate array elements, perform single-point long baseline positioning on each candidate array element, and select the array element with the smallest positioning residual as the differential origin array element.

4. The towed array formation measurement method based on underwater acoustic differential positioning according to claim 3, characterized in that, If the m-th element is taken as the origin element of the difference array, then the expression for the differential positioning model between elements is: ； In the formula, This represents the position coordinates of the element in the difference lattice. , , and These represent the three-dimensional coordinates of the finite difference lattice element in the geodetic coordinate system; Indicates the first Measured sound velocity from a seabed reference point to a differential lattice element For the first The propagation delay from the seabed reference to the differential origin lattice element.

5. The towed array formation measurement method based on underwater acoustic differential positioning according to claim 4, characterized in that, The expression for the objective function of towed array configuration estimation based on differential positioning is as follows: 。 6. The towed array formation measurement method based on underwater acoustic differential positioning according to claim 5, characterized in that, The objective function for estimating the formation of a towed array based on differential positioning is solved using the least squares method.

7. The towed array formation measurement method based on underwater acoustic differential positioning according to claim 6, characterized in that, The steps to solve the objective function for towed array configuration estimation based on differential positioning include: S51: The objective function is written in the following form: ； S52: Apply the function described in S51 to a non-difference origin lattice element. initial point Performing a Taylor expansion at the given point yields the following linear equation in matrix form: ； In the formula, Represents non-difference original lattice elements The corresponding residual matrix, , Represents non-difference original lattice elements Corresponding to the The residuals of the observation equations for each seabed reference; Represents non-difference original lattice elements The corresponding Jacobian matrix, , Represents non-difference original lattice elements Corresponding to the Jacobian matrix of the observation equations for a seabed reference; As the initial point The amount of correction; , and These represent the three-dimensional coordinates of the initial point in the geodetic coordinate system; S53: Using the least squares method to initialize the point Correction amount Solve for the problem using the following formula: ； In the formula, Representing the Jacobian matrix transpose, express The inverse matrix; S54: Utilizing Correction Amounts For non-difference original lattice elements initial point After correction, the non-differential original lattice elements are obtained. Location ; ; S55: Based on the methods described in S51-S54, determine the positions of all non-differential origin lattice elements to complete the towed array formation measurement.

8. The towed array formation measurement method based on underwater acoustic differential positioning according to claim 7, characterized in that, non-differential origin array element Corresponding to the Jacobian matrix of observation equations for a seabed reference The specific form is as follows: 。 9. A towed array formation measurement method based on underwater acoustic differential positioning according to claim 7, characterized in that, non-differential origin array element Corresponding to the The residuals of the observation equations for the seabed benchmark The specific form is as follows: 。 10. The towed array formation measurement method based on underwater acoustic differential positioning according to claim 1, characterized in that, The sound velocity between each seabed reference and each element of the towed array is obtained by measuring the sound velocity profiler.

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