Long baseline positioning array optimization deployment method, device and medium

Abstract

The invention discloses a long baseline positioning array optimization deployment method and device and a medium, and relates to the technical field of underwater positioning, and the method comprises the steps: firstly building a TOA or TDOA observation equation between a target and a transponder, and building a dynamic distance measurement error model in combination with underwater sound propagation characteristics; on the basis, constructing a Fisher information matrix and performing inversion to obtain a Cramer-Rao lower bound representing a theoretical precision lower limit; generating visual prediction information of positioning precision spatial distribution by gridding the target area and calculating the lower bound point by point; and finally, by taking optimization of the regional positioning precision as a target and taking the position of the transponder as a decision variable, constructing an optimization model based on a Cramer-Rao lower bound, and solving an optimal deployment scheme by adopting an intelligent algorithm. According to the method, theoretical precision prediction and automatic optimization of array configuration before deployment are realized, so that the positioning performance is improved, and the deployment cost and risk are reduced.

Description

Technical Field

[0001] This invention relates to the field of underwater positioning technology, and in particular to a method, equipment and medium for optimizing the deployment of a long baseline positioning array. Background Technology

[0002] Long baseline positioning systems in the field of underwater acoustic positioning technology typically achieve high-precision positioning by deploying transponder arrays on the seabed and using the acoustic signals between the array and the target for ranging. Currently, the actual deployment of long baseline positioning arrays largely relies on the practical experience of engineers or the use of simple geometric rules such as squares and triangles for layout. This method lacks quantitative and theoretical prediction methods for the system's achievable positioning accuracy before deployment. Regarding ranging methods, time of arrival (TOA) and time difference of arrival (TDOA) are two commonly used techniques, and their ranging estimation accuracy is comprehensively affected by a variety of complex factors, including array geometry, underwater acoustic ray propagation errors, and signal-to-noise ratio.

[0003] Due to the aforementioned situation, existing technologies suffer from the following limitations. First, the array deployment process is highly empirical and lacks quantitative theoretical basis. Actual positioning accuracy is often only known after deployment and testing. If the accuracy fails to meet requirements, subsequent adjustments will incur extremely high time and economic costs. Second, before physical deployment, there is a lack of effective methods to accurately predict and compare the theoretically optimal accuracy achievable by different array types in a specific working area, resulting in a lack of foresight in scheme selection. Furthermore, there is a lack of systematic optimization methods guided by theoretical performance boundaries for how to specifically improve positioning accuracy in a particular area of ​​interest by adjusting the specific position of the transponder. In addition, for specific application scenarios, it is difficult to determine before deployment whether time-of-arrival (TOA) or time-difference-of-arrival (TDOA) modes will yield superior positioning accuracy. Summary of the Invention

[0004] This invention provides a method, device, and medium for optimizing the deployment of a long baseline positioning array. The technical problem it aims to solve is: how to provide an effective solution that can theoretically predict and quantitatively evaluate the positioning accuracy of a long baseline positioning system in a specific water area before its actual seabed deployment, and use this to guide the optimization of the array configuration.

[0005] In a first aspect, embodiments of the present invention provide a method for optimizing the deployment of a long baseline positioning array, comprising: For a long baseline positioning system containing several transponders, an observation equation between the target position and the transponder position is established within the target area, and a dynamic ranging error model that varies with distance and environment is constructed based on the underwater acoustic propagation model. The observation equation is either the Time of Arrival (TOA) observation equation or the Time Difference of Arrival (TDOA) observation equation. Based on the observation equation and the dynamic ranging error model, a Fisher information matrix is ​​constructed to characterize the accuracy of positioning parameter estimation. By solving for the inverse of the Fisher information matrix, the Cramerlow lower bound of the target position estimation error is obtained. By gridding the target area and calculating the Cramerlow lower bound for each grid point, predictive information reflecting the spatial distribution of positioning accuracy is generated. With the goal of optimizing the positioning accuracy within the target area, the deployment location of the transponder is used as a decision variable. An optimization problem is constructed and solved based on the Cramer-Rao lower bound to obtain the optimized transponder deployment scheme.

[0006] Optionally, the ranging error variance of the dynamic ranging error model is the sum of the ranging error variance based on the signal-to-noise ratio and the ranging error variance based on the sound speed error; wherein, The standard deviation of the ranging error based on the signal-to-noise ratio is calculated according to the formula. Calculate, where σ t Here, SNR represents the standard deviation of the ranging error based on signal-to-noise ratio (SNR), c is the speed of sound, B is the signal bandwidth, and SNR is the received signal-to-noise ratio. The received signal-to-noise ratio (SNR) is calculated according to the sonar equation SNR=SL-TL-NL+DI-DT, where SL is the sound source level, TL is the propagation loss, NL is the ambient noise level, DI is the directivity gain of the receiving array, and DT is the detection threshold. The propagation loss TL is based on the formula Calculate, where K is the extension type coefficient, r is the propagation distance, and α is the absorption coefficient; The environmental noise level NL is determined based on a marine environmental noise spectrum model.

[0007] Optionally, the variance of the ranging error based on the sound speed error is determined according to the formula... Calculate, where σ c Here, represents the standard deviation of the ranging error based on the sound speed error, and t represents the signal propagation time. This represents the standard deviation of the sound speed measurement error.

[0008] Optionally, the process of constructing the Fisher information matrix includes: For the TOA observation mode, according to the formula Calculate the Fisher information matrix, where N is the number of transponders, σ i 2 Let g be the variance of the ranging error of the i-th transponder. i Let cosine be the direction vector from the target to the i-th transponder; For the TDOA observation mode, the first transponder is used as the reference transponder, according to the formula... Calculate the Fisher information matrix, where σi1 2 Let be the variance of the distance difference between the i-th transponder and the reference transponder.

[0009] Optionally, the lower bound of the Cramer-Rao formula is the positioning error covariance matrix, and the standard deviation of the horizontal positioning accuracy is determined according to the formula. Calculate, where σ xy σ represents the standard deviation of horizontal positioning accuracy. x 2 and σ y 2 These are the variances of the eastward position estimation error and the northward position estimation error extracted from the lower bound matrix of the Cramérod matrix, respectively.

[0010] Optionally, the optimization problem is formulated as follows: find a set P of transponder position coordinates to minimize a statistical index J(P) based on the lower bound of the Cramerograph for all grid points in the target area Ω, and satisfy P∈D, where D is a preset feasible deployment area; the statistical index J(P) is the average or maximum value of the standard deviation of the horizontal positioning accuracy of all grid points in the target area Ω.

[0011] Optionally, a particle swarm optimization algorithm is used to solve the optimization problem, wherein the position vector of each particle encodes the coordinates of all transponders; during the iteration process, the velocity v of the particle in the d-th dimension at the k-th iteration is... i,d and position x i,d Updated according to the following formula:

[0012]

[0013] Where w is the inertia weight, and c1 and c2 are learning factors. Let be the component of the particle's historical best position in the d-th dimension. Let r1 and r2 be the components of the global historical best position of the group in the d-th dimension, and r1 and r2 be random functions.

[0014] Optionally, the inertia weight w adopts a linear decreasing strategy, according to the formula Calculate, where w max and w min These are the preset maximum and minimum inertia weights, where k is the current iteration number, and K is the maximum and minimum inertia weights. max This represents the maximum number of iterations.

[0015] Secondly, embodiments of the present invention also provide a computer device, which includes a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the above-described method.

[0016] Thirdly, embodiments of the present invention also provide a computer-readable storage medium storing a computer program that, when executed by a processor, can implement the above-described method.

[0017] This invention provides a method, device, and medium for optimizing the deployment of a long baseline positioning array. The method includes: for a long baseline positioning system containing several transponders, establishing an observation equation between the target location and the transponder locations within a target area, and constructing a dynamic ranging error model that varies with distance and environment based on an underwater acoustic propagation model; the observation equation being either a Time of Arrival (TOA) observation equation or a Time Difference of Arrival (TDOA) observation equation; constructing a Fisher information matrix to characterize the accuracy of positioning parameter estimation based on the observation equation and the dynamic ranging error model; obtaining a Cramer-Rao lower bound for the estimation error of the target location by solving the inverse of the Fisher information matrix; generating predictive information reflecting the spatial distribution of positioning accuracy by gridding the target area and calculating the Cramer-Rao lower bound for each grid point; and constructing and solving an optimization problem based on the Cramer-Rao lower bound, with the goal of optimizing the positioning accuracy within the target area, using the deployment location of the transponders as a decision variable, to obtain an optimized transponder deployment scheme. By establishing a dynamic error model that integrates the characteristics of the underwater acoustic environment and performing prior quantitative calculations of positioning accuracy based on the Cramero lower bound theory, theoretical prediction and visual evaluation of the performance of long baseline arrays were achieved before physical deployment. Furthermore, using this theoretical accuracy limit as a clear optimization target, an intelligent algorithm automatically searches for the optimal transponder deployment location, transforming array design from an experience-dependent process to a model-driven rational optimization process, thereby systematically improving positioning performance and reducing deployment costs and risks. Attached Figure Description

[0018] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 A flowchart illustrating an optimized deployment method for a long baseline positioning array provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of the distribution of the lower boundary heat map of the entire region of Clamer-Rao, provided in an embodiment of the present invention; Figure 3 This is a schematic diagram illustrating the changes in the spatial distribution of transponders before and after optimization, according to an embodiment of the present invention. Figure 4 This is a schematic block diagram of a computer device provided in an embodiment of the present invention. Detailed Implementation

[0020] 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, not all, of the embodiments of the present invention. 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.

[0021] It should be understood that, when used in this specification and the appended claims, the terms "comprising" and "including" indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0022] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0023] It should also be further understood that the term "and / or" as used in this specification and the appended claims refers to any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0024] As used in this specification and the appended claims, the term "if" may be interpreted, depending on the context, as "when," "once," "in response to determination," or "in response to detection." Similarly, the phrase "if determined" or "if [described condition or event] is detected" may be interpreted, depending on the context, as "once determined," "in response to determination," "once [described condition or event] is detected," or "in response to detection of [described condition or event]."

[0025] Please see Figure 1 This invention provides a method for optimizing the deployment of a long baseline positioning array, which includes the following steps: S1. For a long baseline positioning system containing several transponders, an observation equation is established between the target position and the transponder position within the target area, and a dynamic ranging error model that varies with distance and environment is constructed based on the underwater acoustic propagation model. The observation equation is either the Time of Arrival (TOA) observation equation or the Time Difference of Arrival (TDOA) observation equation.

[0026] In practical implementation, the geographical boundaries of the target sea area, water depth data, the number of pre-set transponders, and sound velocity profiles need to be input. First, an observation model and a dynamic ranging error model are established. For the observation model, either TOA or TDOA mode is selected based on the system design. In TOA mode, the observation equation is the Euclidean distance between the target position vector and the position vector of the i-th transponder. In TDOA mode, the observation equation is the difference between the distance from the target to the i-th transponder and the distance to the first designated reference transponder. For the dynamic ranging error model, this method, based on the laws of underwater acoustics, pre-sets a function related to propagation distance, signal frequency, and environmental noise to calculate the initial value of the ranging error variance at different distances. This variance is not a fixed constant.

[0027] In this embodiment of the invention, by simultaneously establishing the TOA or TDOA observation equations between the target and the transponder within the physical context of underwater acoustic positioning, and constructing a dynamically changing ranging error model in conjunction with the underwater acoustic propagation laws, the simplistic assumption of using fixed empirical error values ​​in traditional methods is fundamentally changed. Factors such as the unavoidable geometric spread loss, medium absorption attenuation, and distance-varying marine environmental noise inherent in the propagation of acoustic signals in the actual marine environment are systematically incorporated into the ranging accuracy evaluation system. The resulting ranging error variance is no longer a constant, but a function of the geometric distance between the target and each transponder, as well as environmental parameters. This allows the subsequent accuracy prediction model to closely fit the physical reality of a specific sea area, significantly improving the authenticity and reliability of the prediction results and overcoming the risk of prediction failure due to model distortion.

[0028] In some preferred embodiments, the ranging error variance of the dynamic ranging error model is the sum of the ranging error variance based on the signal-to-noise ratio and the ranging error variance based on the sound speed error; wherein, The standard deviation of the ranging error based on the signal-to-noise ratio is calculated according to the formula. Calculate, where σ t Here, SNR represents the standard deviation of the ranging error based on signal-to-noise ratio (SNR), c is the speed of sound, B is the signal bandwidth, and SNR is the received signal-to-noise ratio. The received signal-to-noise ratio (SNR) is calculated according to the sonar equation SNR=SL-TL-NL+DI-DT, where SL is the sound source level, TL is the propagation loss, NL is the ambient noise level, DI is the directivity gain of the receiving array, and DT is the detection threshold. The propagation loss TL is based on the formula Calculate, where K is the extension type coefficient, r is the propagation distance, and α is the absorption coefficient; The environmental noise level NL is determined based on a marine environmental noise spectrum model; specifically, Where B is the signal bandwidth. This represents the baseline spectral level of marine environmental noise at the center frequency. The marine noise spectral level is approximated based on the Knudsen spectral curve. Then, the ambient noise level at the receiving end can be calculated. .

[0029] In practice, the ranging error component based on the signal-to-noise ratio (SNR) is calculated. This method uses typical values ​​of the sound source level, the directivity index of the receiving array, and the detection threshold, based on underwater acoustic engineering parameters. According to the geometric distance between the target point and the transponder, signal attenuation is calculated using the propagation loss formula based on the spread loss coefficient and absorption coefficient. Simultaneously, the ambient noise level is estimated based on classic ocean noise models such as the Knudsen spectrum, combined with the operating frequency band. The sound source level, the calculated propagation loss, the ambient noise level, the array gain, and the detection threshold are substituted into the sonar equations to solve for the received SNR. Subsequently, this SNR value, the known speed of sound, and the system signal bandwidth are substituted into the formula to directly calculate the standard deviation of the ranging error determined by the signal detection accuracy, and thus obtain its variance.

[0030] Furthermore, the ranging error component based on the sound velocity error is calculated. This method presupposes a standard deviation of the sound velocity measurement error, derived from the nominal accuracy of the sound velocity profiler used or statistical analysis of historical observation data. The propagation time required for the signal to travel from the target point to the corresponding transponder is calculated. This propagation time is used as a sensitivity coefficient, and substituted into the formula along with the standard deviation of the sound velocity measurement error to calculate the additional ranging error variance caused by the sound velocity uncertainty.

[0031] Furthermore, the total ranging error variance is synthesized. Since the two error sources mentioned above are independent, according to error propagation theory, the calculated ranging error variance based on signal-to-noise ratio and the ranging error variance based on sound speed error are directly added together. The result is the final dynamic total ranging error variance used on this propagation path. This variance value will be used in the subsequent construction of the Fisher information matrix.

[0032] The dynamic ranging error model defined in this embodiment significantly improves the realism and reliability of positioning accuracy prediction. This model abandons the simplistic assumption of treating ranging error as a fixed value, instead establishing a functional relationship between error and propagation distance, signal frequency, and marine environmental noise based on sonar equations and sound propagation theory. This allows the ranging error variance to naturally increase with the distance between the target and the transponder, simulating the actual physical processes of signal attenuation and noise accumulation. Simultaneously, the dynamic ranging error model independently considers the impact of the systematic error source of sound velocity measurement error. By synthesizing two independent error components, the resulting dynamic ranging error model more comprehensively and accurately reflects the uncertainties of the ranging process in complex underwater environments. Applying this refined model to the calculation of the Cramero lower bound makes the final predicted theoretical positioning accuracy lower limit closer to the performance boundary that the system may achieve in actual sea areas, thus providing a more reliable theoretical basis for pre-deployment scheme evaluation and optimization.

[0033] Furthermore, in some preferred embodiments, the ranging error variance based on the sound speed error is determined according to the formula... Calculate, where σ c Here, represents the standard deviation of the ranging error based on the sound speed error, and t represents the signal propagation time. This represents the standard deviation of the sound speed measurement error.

[0034] S2. Based on the observation equation and the dynamic ranging error model, construct the Fisher information matrix to characterize the accuracy of positioning parameter estimation.

[0035] In practice, a Fisher information matrix is ​​constructed. Based on the observation equation established in the previous step, the partial derivative of the target position vector with respect to the observation value is calculated, i.e., the Jacobian matrix or direction cosine vector. Simultaneously, using a dynamic ranging error model, the specific ranging error variance to each transponder under the current target position assumption is calculated. The direction cosine vector is combined with the corresponding inverse of the ranging error variance, and summed according to the matrix formula corresponding to the TOA or TDOA mode, thereby constructing a Fisher information matrix reflecting the positioning information under the current geometric configuration.

[0036] Specifically, in some preferred embodiments, the process of constructing the Fisher information matrix includes: For the TOA observation mode, according to the formula Calculate the Fisher information matrix, where N is the number of transponders, σ i 2 Let g be the variance of the ranging error of the i-th transponder. i Let cosine be the direction vector from the target to the i-th transponder; For the TDOA observation mode, the first transponder is used as the reference transponder, according to the formula... Calculate the Fisher information matrix, where σ i1 2 Let be the variance of the distance difference between the i-th transponder and the reference transponder.

[0037] In practical implementation, for the TOA observation mode, the ranging error variance from the target point to each transponder in the network is first calculated based on the dynamic ranging error model. Further, the unit direction vector from the target point to each transponder, i.e., the direction cosine vector, is calculated. For each transponder, the reciprocal of its ranging error variance is used as a weight and multiplied by the outer product matrix of the transponder's direction cosine vector and its transpose to obtain the transponder's contribution to the information matrix. Further, the contribution matrices of all transponders are spatially superimposed and summed; the resulting sum matrix is ​​the TOA mode Fisher information matrix at the target point.

[0038] For the TDOA observation mode, the first transponder is designated as the common reference station. The variance of the ranging error from the target point to each transponder (including the reference station) is calculated, and the variance of the distance difference error between each transponder and the reference station is calculated according to the error propagation law. Further, the direction cosine vector from the target point to each transponder and the reference station is calculated. Further, for each non-reference transponder, the difference between its direction cosine vector and the reference station's direction cosine vector is calculated. Further, the outer product matrix of this difference vector is multiplied by the reciprocal of the corresponding distance difference error variance as a weight. Further, the weighted outer product matrices of all non-reference transponders are summed to obtain the TDOA mode Fisher information matrix at the target point.

[0039] This embodiment explicitly defines the specific formulas for constructing Fisher information matrices for both TOA and TDOA, two mainstream observation modes, making this method universal for handling different system configurations. By providing precise matrix construction methods for each mode, the mathematical transformation process from observation model to theoretical accuracy assessment is ensured to be correct and complete. The formula for TOA mode directly reflects the information contribution of each independent distance observation to position estimation, while the formula for TDOA mode accurately captures the geometric constraint characteristics of distance difference observations. This clear distinction and definition allows users to evaluate the theoretical performance limits achievable using TOA or TDOA positioning under the same framework and for the same array configuration, thus providing a crucial theoretical basis for selecting the appropriate positioning mode based on accuracy requirements in practical engineering.

[0040] S3. By solving the inverse matrix of the Fisher information matrix, the Cramero lower bound of the target position estimation error is obtained.

[0041] In practice, the Cramer-Rao lower bound is calculated. The inverse operation is performed on the constructed Fisher information matrix. This inverse matrix is ​​the Cramer-Rao lower bound matrix, and its diagonal elements represent the theoretical minimum error variance achievable in the east, north, and sky directions when estimating the target's position at the current location.

[0042] In this embodiment of the invention, based on the aforementioned refined observation and error model, a Fisher information matrix is ​​constructed to evaluate the performance of parameter estimation, and its inverse matrix is ​​further solved to obtain the Cramer-Rao lower bound, which constitutes the theoretical core of this scheme. This embodiment transforms the complex positioning accuracy problem into a performance boundary analysis within a rigorous mathematical optimization framework. From an information theory perspective, the Cramer-Rao lower bound provides an absolute theoretical lower limit for the minimum variance achievable by unbiased estimation of the target position under given array geometry and observation error characteristics. This transforms the performance evaluation of any preset array configuration from subjective, qualitative empirical judgment to objective, quantitative theoretical calculation, thereby achieving accurate calibration of the system's potential positioning capability before physical deployment and completely solving the problem of being unable to quantify and predict the theoretically optimal accuracy before deployment.

[0043] In some preferred embodiments, the lower bound of the Cramer-Rao equation is the positioning error covariance matrix, and the standard deviation of the horizontal positioning accuracy is determined according to the formula... Calculate, where σ xy σ represents the standard deviation of horizontal positioning accuracy. x 2 and σ y 2 These are the variances of the eastward position estimation error and the northward position estimation error extracted from the lower bound matrix of the Cramérod matrix, respectively.

[0044] In practice, after obtaining the Cramer-Rao lower bound matrix through inversion, this matrix is ​​a 2×2 or 3×3 symmetric positive definite matrix. When focusing on horizontal positioning accuracy, the variance values ​​corresponding to the eastward position coordinate estimation error and the northward position coordinate estimation error are extracted from this matrix. These two variance values ​​are the elements in the first row and first column and the second row and second column of the matrix, respectively. Subsequently, the extracted eastward error variance and northward error variance are directly added together. Finally, the square root of the sum is taken, and the result is the standard deviation of the positioning accuracy in the horizontal plane at the target point. This value is a scalar, intuitively representing the theoretical minimum circular probability error radius measure when performing two-dimensional horizontal positioning at this point.

[0045] This embodiment transforms an abstract mathematical matrix into an intuitive performance indicator with clear physical meaning by defining a specific formula for extracting and synthesizing the standard deviation of horizontal positioning accuracy from the Cramérault lower bound matrix. The Cramérault lower bound matrix itself contains error information across multiple dimensions, while this step focuses on the horizontal positioning performance most relevant to engineering applications. By extracting the variances of the eastward and northward errors and calculating the square root of their sum of squares, the resulting standard deviation of horizontal positioning accuracy directly corresponds to the concepts of circular error or radial error commonly used to measure positioning accuracy. This greatly facilitates engineers' understanding and application of the prediction results, making performance comparisons between different array configurations or different regions readily apparent, and providing a concise and powerful quantitative tool for accuracy-based decision-making.

[0046] S4 generates predictive information reflecting the spatial distribution of positioning accuracy by gridding the target area and calculating the Cramer-Rao lower bound for each grid point.

[0047] In practice, the system generates prediction information on the spatial distribution of precision. First, based on preset resolution parameters, the target area is divided into grids on a horizontal plane. Specifically, the boundary coordinates of the target area are input, and the area is discretized into multiple continuous rectangular or square grid cells according to the specified grid spacing. The center point of each grid cell is defined as a grid point to be evaluated, and the set of east and north coordinates of all grid points is obtained.

[0048] Furthermore, for each point in the grid point set, the following calculation process is performed: Substitute the coordinates of the point into the pre-established observation equation and dynamic ranging error model to calculate the theoretical observation values ​​to each transponder and the corresponding ranging error variance; Based on this, construct the Fisher information matrix at the point; Perform the inversion operation on the Fisher information matrix to obtain the Cramer-Rao lower bound matrix at the point.

[0049] Furthermore, the variances of the eastward and northward position estimation errors are extracted from the Cramer-Rao lower bound matrix of each grid point, and the standard deviation of their horizontal positioning accuracy is calculated.

[0050] Furthermore, the standard deviation of the horizontal positioning accuracy of each grid point is correlated with its geographical coordinates to form a spatial discrete dataset covering the entire target area.

[0051] Furthermore, based on this spatial discrete dataset, the graphics generation module is invoked to generate a two-dimensional positioning accuracy distribution map through interpolation rendering, in which the accuracy values ​​are represented by color depth or contour lines. This completes the generation of predictive information reflecting the spatial distribution of positioning accuracy.

[0052] In this embodiment of the invention, the target working sea area is discretized into a grid, and the Cramero lower bound corresponding to each grid point is calculated one by one, thereby generating spatial distribution prediction information of positioning accuracy across the entire area (such as a heat map). This embodiment extends the theoretical accuracy assessment of a single point to the entire two-dimensional or three-dimensional working space of interest. The generated visualized accuracy distribution map can intuitively and panoramically reveal where the positioning accuracy is high and where there are areas of low accuracy or geometric dilution under a specific array configuration. This provides engineers with unprecedented forward-looking insight, enabling them to clearly identify the performance differences and risk areas of different array types (such as square, L-shaped, etc.) before deployment, providing a direct decision-making basis for scheme comparison and initial design elimination, and effectively avoiding subsequent engineering rework caused by blind selection.

[0053] S5. With the goal of optimizing the positioning accuracy within the target area, the deployment location of the transponder is used as the decision variable. An optimization problem is constructed and solved based on the Cramerlow lower bound to obtain the optimized transponder deployment scheme.

[0054] In practice, the transponder deployment scheme is optimized. An optimization objective function is defined, such as minimizing the maximum standard deviation of accuracy for all grid points within the entire target area (i.e., the accuracy of the worst-case region). The two-dimensional coordinates of all transponders are used as decision variables to be optimized. Constraints are set, such as transponders must be deployed on the seabed, maintain a minimum safe distance from each other, and be located within a workable rectangular area. A global optimization algorithm, such as a genetic algorithm or simulated annealing algorithm, is used to automatically and iteratively adjust the simulated positions of the transponders within the constraints. After each adjustment, the accuracy heatmap and objective function value for the entire area are recalculated and evaluated. Through numerous iterations, the algorithm ultimately searches for a set of transponder coordinates that optimize the objective function value, which is then output as the recommended optimized deployment scheme.

[0055] In this embodiment of the invention, the spatial coordinates of the transponder are used as decision variables. The optimization objective is to minimize a certain statistical indicator (such as average accuracy or worst-case accuracy) within the target area based on the Cramero lower bound. A mathematical optimization model is constructed and solved using intelligent algorithms. This embodiment transforms array deployment from a passive process relying on trial and error based on human experience into a proactive and automated design process guided by theoretical performance limits. Optimization algorithms (such as particle swarm optimization) can automatically and efficiently search the vast solution space for transponder coordinate combinations that optimize the theoretical boundary of the overall positioning performance of the target area under given deployment constraints. This not only systematically improves the expected positioning accuracy and robustness of key areas but also avoids the high costs and time delays caused by repeated array adjustments in actual sea areas because optimization is performed in a virtual environment. Furthermore, since this method integrates both TOA and TDOA models, it makes it possible to compare the theoretical performance of the two modes under the same environment and array conditions, thus providing a theoretical basis for prior judgment in selecting a better positioning mode for specific application scenarios.

[0056] The technical solution defined in this invention enables quantitative performance prediction and automation of long baseline positioning systems before deployment. This method overcomes the blindness of traditional experience-based array deployment by systematically constructing observation and error models and integrating the physical characteristics of underwater acoustic propagation into the theoretical evaluation framework of positioning accuracy. Specifically, different candidate array configurations can be digitally simulated before deployment, calculating and visualizing their theoretical accuracy distribution across the entire working sea area. This allows engineers to proactively identify areas with weak accuracy and compare the advantages and disadvantages of different schemes. Furthermore, this method uses the Cramero lower bound, the theoretical accuracy limit, as a clear optimization target, automatically searching for the optimal transponder location through intelligent algorithms, transforming array design from manual trial and error to a model-driven scientific decision-making process. This not only effectively improves the system's potential positioning performance in key areas but also avoids the high adjustment costs caused by substandard accuracy after deployment, enhancing the robustness and economy of the system design.

[0057] In some preferred embodiments, the optimization problem is formulated as: finding a set P of transponder location coordinates to minimize a statistical index J(P) based on the Cramerlow lower bound on all grid points within the target area Ω, satisfying P∈D, where D is a preset feasible deployment area; the statistical index J(P) is the average or maximum value of the standard deviation of the horizontal positioning accuracy of all grid points within the target area Ω.

[0058] In practice, firstly, a set of decision variables P is defined, which is a one-dimensional vector containing the eastward and northward coordinates of all transponders. Secondly, the feasible deployment area D is defined, which is usually a two-dimensional geographical constraint defined by polygon boundaries or maximum and minimum coordinate values. The coordinates of each transponder must be within D, and a minimum spacing constraint may be attached.

[0059] Furthermore, the objective function J(P) is defined. When calculating J(P), for a given array scheme P, the system automatically calculates the standard deviation of horizontal positioning accuracy σ_h at the grid points of the entire target area Ω. If J(P) is defined as the average, then the arithmetic mean of σ_h is calculated for all grid points; if it is defined as the maximum, then the maximum value of σ_h among all grid points is found.

[0060] Furthermore, the optimization problem is input into the optimization solver. The solver's task is to find the optimal coordinate set P* that minimizes J(P) by adjusting the components of P, given that P∈D.

[0061] This embodiment rigorously formulates the transponder deployment optimization problem as a constrained mathematical optimization model, laying the foundation for the application of automated algorithms. By explicitly defining the deployment coordinates as decision variables, geographical and engineering constraints as constraints, and defining the Cramer-Rao lower bound statistics reflecting overall positioning performance (such as regional average accuracy or worst-case accuracy) as the objective function, this mathematical optimization model fully and accurately characterizes the core requirements of engineering optimization. This formalized formulation transforms the complex deployment design problem into a mathematical problem that can be automatically solved by a computer. It makes the optimization objective no longer a vague "better performance" but a clear and calculable indicator, thereby enabling a systematic and efficient search for the truly optimal or near-optimal solution in a broad deployment scheme space, ensuring the scientific nature of the optimization process and the optimality of the results.

[0062] In some preferred embodiments, a particle swarm optimization algorithm is used to solve the optimization problem, wherein the position vector of each particle encodes the coordinates of all transponders; during the iteration process, the velocity v of the particle in the d-th dimension at the k-th iteration is... i,d and position x i,d Updated according to the following formula:

[0063]

[0064] Where w is the inertia weight, and c1 and c2 are learning factors. Let be the component of the particle's historical best position in the d-th dimension. Let r1 and r2 be the d-th dimension component of the global historical best position of the population, and let r1 and r2 be random functions. Specifically, r1 and r2 are functions that generate uniformly distributed random numbers in the range [0, 1).

[0065] In practice, the first step is to encode the problem. The particle swarm size is set, for example, 50 particles. Each particle is represented by a position vector, which has a dimension twice the number of transponders, storing the east and north coordinates of all transponders sequentially. Simultaneously, a velocity vector is randomly initialized for each particle.

[0066] Further, the population is initialized. Within the feasible deployment area D, the initial position and initial velocity of each particle are randomly generated. Then, iterative optimization begins. In each iteration, the following operations are performed on each particle: its position vector is decoded into specific responder coordinates, and the objective function value J(P) under the current deployment is calculated. The particle's own historical best position and the global best position found so far for the entire population are updated.

[0067] Furthermore, the particle's velocity and position vectors are updated according to the formula. The update formula comprises three parts: the inertial part maintains the original motion trend, the cognitive part drives the particle to the best position it previously found, and the social part drives the particle to the best position found by the population. A learning factor controls the weights of the latter two parts, and a random function increases the randomness of the search.

[0068] Further check if the new position exceeds the bounds; if so, perform a bounce or reset. Repeat the iterative process until the preset stopping condition is met, such as the maximum number of iterations or convergence of the objective function.

[0069] This embodiment employs the Particle Swarm Optimization (PSO) algorithm to solve the deployment optimization problem, effectively overcoming the difficulties posed by the problem's high dimensionality, nonlinearity, and potentially multimodal nature. PSO is a highly efficient swarm intelligence stochastic optimization algorithm. Its advantage lies in the fact that each particle updates its position by tracking individual and swarm extrema, possessing both global exploration and local development capabilities. Encoding the deployment scheme as particle positions allows the algorithm to simultaneously evaluate a large number of candidate schemes. Through information sharing and collaboration during the iteration process, the entire particle swarm can gradually converge towards the deployment region with better performance. Compared to traditional enumeration or gradient-based methods, PSO excels at finding globally optimal or high-quality solutions within complex feasible regions, thus ensuring that the final optimized deployment scheme theoretically significantly improves the overall or worst-case localization accuracy of the target region, providing a reliable and efficient automated design tool for practical engineering deployments.

[0070] In some preferred embodiments, the inertia weight w adopts a linear decreasing strategy, according to the formula Calculate, where w maxand w min These are the preset maximum and minimum inertia weights, where k is the current iteration number, and K is the maximum and minimum inertia weights. max This represents the maximum number of iterations.

[0071] In practice, before the optimization algorithm begins, the maximum and minimum values ​​of the inertia weight are preset, for example, set to 0.9 and 0.4 respectively. Simultaneously, the maximum number of iterations is set. At each step of the iteration process, the algorithm records the current iteration number. Based on the linear decreasing formula, the inertia weight value to be used in this iteration is calculated in real time using the maximum iteration number, the current iteration number, and the preset upper and lower weight limits. Specifically, the calculation involves subtracting an amount that increases linearly with the iteration progress from the maximum value; this increase is the product of the total range of weight changes and the proportion of the current iteration progress. The calculated weight value will be used to update the velocity of all particles in this iteration. As the iteration progresses from the initial stage to the later stage, this weight value will linearly decrease from the maximum value to the minimum value.

[0072] The linearly decreasing inertia weight strategy employed in this embodiment further optimizes the search performance of the particle swarm optimization algorithm, enabling it to better balance the two stages of global exploration and local fine-tuning search. In the early stages of iteration, a larger inertia weight grants particles higher flight inertia, allowing them to explore a broad feasible deployment area with larger step sizes, quickly locating regions where potentially high-quality solutions exist, effectively preventing the algorithm from prematurely falling into local optima. As the number of iterations increases, the inertia weight decreases linearly, weakening the inertia effect of the particles, and their motion is more influenced by the individual and swarm's historical optimal positions. This allows the particle swarm to perform a more refined, smaller-scale local search near discovered high-quality solution regions in the later stages of iteration, thereby fine-tuning the deployment coordinates to approximate the theoretically optimal solution. This adaptive weight adjustment mechanism makes the optimization process more intelligent, improving convergence accuracy and efficiency while ensuring search breadth, thus reliably obtaining high-quality optimized deployment schemes.

[0073] This invention proposes an optimized deployment method for long-baseline positioning arrays, comprising: establishing an observation equation between the target location and the transponder location within a target area for a long-baseline positioning system containing several transponders; constructing a dynamic ranging error model that varies with distance and environment based on an underwater acoustic propagation model; wherein the observation equation is a Time of Arrival (TOA) observation equation or a Time Difference of Arrival (TDOA) observation equation; constructing a Fisher information matrix to characterize the positioning parameter estimation accuracy based on the observation equation and the dynamic ranging error model; obtaining a Cramer-Rao lower bound for the target location estimation error by solving the inverse of the Fisher information matrix; generating predictive information reflecting the spatial distribution of positioning accuracy by gridding the target area and calculating the Cramer-Rao lower bound for each grid point; and constructing and solving an optimization problem based on the Cramer-Rao lower bound, with the goal of optimizing the positioning accuracy within the target area, using the transponder deployment location as a decision variable, to obtain an optimized transponder deployment scheme. By establishing a dynamic error model that incorporates underwater acoustic environment characteristics and performing prior quantitative calculations of positioning accuracy based on the Cramer-Rao lower bound theory, theoretical prediction and visual evaluation of the long-baseline array performance are achieved before physical deployment. Furthermore, by taking the theoretical accuracy limit as a clear optimization target, the optimal transponder deployment location is automatically searched through intelligent algorithms, transforming array design from an experience-dependent process to a model-driven rational optimization process, thereby systematically improving positioning performance and reducing deployment costs and risks.

[0074] Furthermore, to demonstrate the effectiveness of the proposed method, a specific embodiment is provided. This embodiment applies the method to a specific scenario: a long baseline positioning system containing four transponders, taking the optimization of positioning accuracy at a single specified target point as an example (i.e., the target area Ω degenerates into a single point), and uses a particle swarm optimization algorithm for layout optimization simulation. The optimization objective is to minimize the lower bound of the positioning error at that point, Cramer-Rao. The simulation settings are as follows: the initial layout of the transponders adopts a symmetrical geometry, the target point position is fixed at the origin of the coordinate system, and the positioning mode adopts the time-of-arrival method. To closely approximate the actual underwater acoustic environment, the simulation parameters of the ranging error are set according to the dynamic ranging error model, specifically: sound speed 1500 m / s, signal bandwidth 1 kHz, absorption coefficient 1.9 dB / km, ambient noise level 88 dB, source noise level 192 dB, and sound speed measurement error 0.2 m / s. The optimization algorithm parameters are set as follows: particle swarm size 30, maximum iteration count 100, and adaptively adjusted inertia weights and learning factors are used to balance the algorithm's global search and local exploitation capabilities.

[0075] In the simulation process, each particle encodes the planar coordinates of its four transponders using an eight-dimensional vector, representing a deployment scheme. At each iteration, the algorithm calculates the Cramer-Rao lower bound of each placement at the origin as a fitness function for evaluation, and updates the particle state based on the individual's historical best position and the swarm's global best position. To ensure the feasibility of the solution, a search range constraint is set for the transponder coordinates, and a boundary bounce strategy is used to handle out-of-bounds cases. The simulation monitors the convergence process in real time, outputting the current optimal solution every 10 iterations.

[0076] After optimization and simulation, the system outputs the optimal transponder layout coordinates, the minimum Cramer-Rao lower bound, and a detailed performance comparison analysis. The changes in transponder spatial distribution before and after optimization are visualized (see [link]). Figure 3 ) and the distribution of the lower boundary of the Cramero region in the heat map (see Figure 2 ).

[0077] Simulation results show that before optimization, the lower limit of the Cramer-Rao coordinate at the origin was 0.4163 square meters, which decreased to 0.0314 square meters after optimization, representing a theoretical accuracy improvement of 92.47%. This embodiment verifies that the proposed method can effectively optimize the transponder layout and significantly improve the theoretical positioning accuracy of key points under the specific acoustic field environment and single-point positioning requirements, providing a quantitative reference for practical engineering deployment.

[0078] Please see Figure 4 , Figure 4 This is a schematic block diagram of a computer device 500 provided in an embodiment of this application. The computer device 500 can be a terminal or a server, wherein the server can be a standalone server or a server cluster composed of multiple servers.

[0079] The computer device 500 includes a processor 502, a memory, and a network interface 505 connected via a system bus 501. The memory may include a non-volatile storage medium 503 and internal memory 504.

[0080] The non-volatile storage medium 503 may store an operating system 5031 and a computer program 5032. When the computer program 5032 is executed, it causes the processor 502 to execute a long baseline positioning array optimization deployment method.

[0081] The processor 502 provides computing and control capabilities to support the operation of the entire computer device 500.

[0082] The internal memory 504 provides an environment for the execution of the computer program 5032 in the non-volatile storage medium 503. When the computer program 5032 is executed by the processor 502, the processor 502 can execute a long baseline positioning array optimization deployment method.

[0083] The network interface 505 is used for network communication with other devices. Those skilled in the art will understand that the above structure is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device 500 to which the present application is applied. A specific computer device 500 may include more or fewer components than shown in the figures, or combine certain components, or have different component arrangements.

[0084] The processor 502 is used to run a computer program 5032 stored in the memory to perform the following steps: For a long baseline positioning system containing several transponders, an observation equation between the target position and the transponder position is established within the target area, and a dynamic ranging error model that varies with distance and environment is constructed based on the underwater acoustic propagation model. The observation equation is either the Time of Arrival (TOA) observation equation or the Time Difference of Arrival (TDOA) observation equation. Based on the observation equation and the dynamic ranging error model, a Fisher information matrix is ​​constructed to characterize the accuracy of positioning parameter estimation. By solving for the inverse of the Fisher information matrix, the Cramerlow lower bound of the target position estimation error is obtained. By gridding the target area and calculating the Cramerlow lower bound for each grid point, predictive information reflecting the spatial distribution of positioning accuracy is generated. With the goal of optimizing the positioning accuracy within the target area, the deployment location of the transponder is used as a decision variable. An optimization problem is constructed and solved based on the Cramer-Rao lower bound to obtain the optimized transponder deployment scheme.

[0085] Optionally, the ranging error variance of the dynamic ranging error model is the sum of the ranging error variance based on the signal-to-noise ratio and the ranging error variance based on the sound speed error; wherein, The standard deviation of the ranging error based on the signal-to-noise ratio is calculated according to the formula. Calculate, where σ t Here, SNR represents the standard deviation of the ranging error based on signal-to-noise ratio (SNR), c is the speed of sound, B is the signal bandwidth, and SNR is the received signal-to-noise ratio. The received signal-to-noise ratio (SNR) is calculated according to the sonar equation SNR=SL-TL-NL+DI-DT, where SL is the sound source level, TL is the propagation loss, NL is the ambient noise level, DI is the directivity gain of the receiving array, and DT is the detection threshold. The propagation loss TL is based on the formula Calculate, where K is the extension type coefficient, r is the propagation distance, and α is the absorption coefficient; The environmental noise level NL is determined based on a marine environmental noise spectrum model.

[0086] Optionally, the variance of the ranging error based on the sound speed error is determined according to the formula... Calculate, where σ c Here, represents the standard deviation of the ranging error based on the sound speed error, and t represents the signal propagation time. This represents the standard deviation of the sound speed measurement error.

[0087] Optionally, the process of constructing the Fisher information matrix includes: For the TOA observation mode, according to the formula Calculate the Fisher information matrix, where N is the number of transponders, σ i 2 Let g be the variance of the ranging error of the i-th transponder. i Let cosine be the direction vector from the target to the i-th transponder; For the TDOA observation mode, the first transponder is used as the reference transponder, according to the formula... Calculate the Fisher information matrix, where σ i1 2 Let be the variance of the distance difference between the i-th transponder and the reference transponder.

[0088] Optionally, the lower bound of the Cramer-Rao formula is the positioning error covariance matrix, and the standard deviation of the horizontal positioning accuracy is determined according to the formula. Calculate, where σ xy σ represents the standard deviation of horizontal positioning accuracy. x 2 and σ y 2 These are the variances of the eastward position estimation error and the northward position estimation error extracted from the lower bound matrix of the Cramérod matrix, respectively.

[0089] Optionally, the optimization problem is formulated as follows: find a set P of transponder position coordinates to minimize a statistical index J(P) based on the lower bound of the Cramerograph for all grid points in the target area Ω, and satisfy P∈D, where D is a preset feasible deployment area; the statistical index J(P) is the average or maximum value of the standard deviation of the horizontal positioning accuracy of all grid points in the target area Ω.

[0090] Optionally, a particle swarm optimization algorithm is used to solve the optimization problem, wherein the position vector of each particle encodes the coordinates of all transponders; during the iteration process, the velocity v of the particle in the d-th dimension at the k-th iteration is... i,d and position x i,d Updated according to the following formula:

[0091]

[0092] Where w is the inertia weight, and c1 and c2 are learning factors. Let be the component of the particle's historical best position in the d-th dimension. Let r1 and r2 be the components of the global historical best position of the group in the d-th dimension, and r1 and r2 be random functions.

[0093] Optionally, the inertia weight w adopts a linear decreasing strategy, according to the formula Calculate, where w max and w min These are the preset maximum and minimum inertia weights, where k is the current iteration number, and K is the maximum and minimum inertia weights. max This represents the maximum number of iterations.

[0094] It should be understood that in the embodiments of this application, the processor 502 may be a central processing unit (CPU), or it may be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or any conventional processor.

[0095] It will be understood by those skilled in the art that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program may be stored in a storage medium, which is a computer-readable storage medium. The computer program is executed by at least one processor in the computer system to implement the process steps of the embodiments of the above methods.

[0096] Therefore, the present invention also provides a storage medium. This storage medium can be a computer-readable storage medium. The storage medium stores a computer program. When executed by a processor, the computer program causes the processor to perform the following steps: For a long baseline positioning system containing several transponders, an observation equation between the target position and the transponder position is established within the target area, and a dynamic ranging error model that varies with distance and environment is constructed based on the underwater acoustic propagation model. The observation equation is either the Time of Arrival (TOA) observation equation or the Time Difference of Arrival (TDOA) observation equation. Based on the observation equation and the dynamic ranging error model, a Fisher information matrix is ​​constructed to characterize the accuracy of positioning parameter estimation. By solving for the inverse of the Fisher information matrix, the Cramerlow lower bound of the target position estimation error is obtained. By gridding the target area and calculating the Cramerlow lower bound for each grid point, predictive information reflecting the spatial distribution of positioning accuracy is generated. With the goal of optimizing the positioning accuracy within the target area, the deployment location of the transponder is used as a decision variable. An optimization problem is constructed and solved based on the Cramer-Rao lower bound to obtain the optimized transponder deployment scheme.

[0097] Optionally, the ranging error variance of the dynamic ranging error model is the sum of the ranging error variance based on the signal-to-noise ratio and the ranging error variance based on the sound speed error; wherein, The standard deviation of the ranging error based on the signal-to-noise ratio is calculated according to the formula. Calculate, where σ t Here, SNR represents the standard deviation of the ranging error based on signal-to-noise ratio (SNR), c is the speed of sound, B is the signal bandwidth, and SNR is the received signal-to-noise ratio. The received signal-to-noise ratio (SNR) is calculated according to the sonar equation SNR=SL-TL-NL+DI-DT, where SL is the sound source level, TL is the propagation loss, NL is the ambient noise level, DI is the directivity gain of the receiving array, and DT is the detection threshold. The propagation loss TL is based on the formula Calculate, where K is the extension type coefficient, r is the propagation distance, and α is the absorption coefficient; The environmental noise level NL is determined based on a marine environmental noise spectrum model.

[0098] Optionally, the variance of the ranging error based on the sound speed error is determined according to the formula... Calculate, where σ c Here, represents the standard deviation of the ranging error based on the sound speed error, and t represents the signal propagation time. This represents the standard deviation of the sound speed measurement error.

[0099] Optionally, the process of constructing the Fisher information matrix includes: For the TOA observation mode, according to the formula Calculate the Fisher information matrix, where N is the number of transponders, σ i 2 Let g be the variance of the ranging error of the i-th transponder. i Let cosine be the direction vector from the target to the i-th transponder; For the TDOA observation mode, the first transponder is used as the reference transponder, according to the formula... Calculate the Fisher information matrix, where σ i1 2 Let be the variance of the distance difference between the i-th transponder and the reference transponder.

[0100] Optionally, the lower bound of the Cramer-Rao formula is the positioning error covariance matrix, and the standard deviation of the horizontal positioning accuracy is determined according to the formula. Calculate, where σ xy σ represents the standard deviation of horizontal positioning accuracy. x 2 and σ y 2 These are the variances of the eastward position estimation error and the northward position estimation error extracted from the lower bound matrix of the Cramérod matrix, respectively.

[0101] Optionally, the optimization problem is formulated as follows: find a set P of transponder position coordinates to minimize a statistical index J(P) based on the lower bound of the Cramerograph for all grid points in the target area Ω, and satisfy P∈D, where D is a preset feasible deployment area; the statistical index J(P) is the average or maximum value of the standard deviation of the horizontal positioning accuracy of all grid points in the target area Ω.

[0102] Optionally, a particle swarm optimization algorithm is used to solve the optimization problem, wherein the position vector of each particle encodes the coordinates of all transponders; during the iteration process, the velocity v of the particle in the d-th dimension at the k-th iteration is... i,d and position x i,d Updated according to the following formula:

[0103]

[0104] Where w is the inertia weight, and c1 and c2 are learning factors. Let be the component of the particle's historical best position in the d-th dimension. Let r1 and r2 be the components of the global historical best position of the group in the d-th dimension, and r1 and r2 be random functions.

[0105] Optionally, the inertia weight w adopts a linear decreasing strategy, according to the formula Calculate, where w max and w min These are the preset maximum and minimum inertia weights, where k is the current iteration number, and K is the maximum and minimum inertia weights. max This represents the maximum number of iterations.

[0106] The storage medium is a physical, non-transient storage medium, such as a USB flash drive, external hard drive, read-only memory (ROM), magnetic disk, or optical disk, or any other physical storage medium capable of storing program code. The computer-readable storage medium can be non-volatile or volatile.

[0107] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0108] In the several embodiments provided by this invention, it should be understood that the disclosed apparatus and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative. For example, the division of each unit is merely a logical functional division, and there may be other division methods in actual implementation. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed.

[0109] The steps in the method of this invention can be adjusted, merged, or reduced in order according to actual needs. The units in the device of this invention can be merged, divided, or reduced according to actual needs. Furthermore, the functional units in the various embodiments of this invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0110] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, a terminal, or a network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention.

[0111] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0112] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Since these modifications and variations fall within the scope of the claims and their equivalents, this invention also intends to include these modifications and variations.

[0113] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and these modifications or substitutions should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for optimizing the deployment of a long baseline positioning array, characterized in that, include: For a long baseline positioning system containing several transponders, an observation equation between the target position and the transponder position is established within the target area, and a dynamic ranging error model that varies with distance and environment is constructed based on the underwater acoustic propagation model. The observation equation is either the Time of Arrival (TOA) observation equation or the Time Difference of Arrival (TDOA) observation equation. Based on the observation equation and the dynamic ranging error model, a Fisher information matrix is ​​constructed to characterize the accuracy of positioning parameter estimation. By solving for the inverse of the Fisher information matrix, the Cramerlow lower bound of the target position estimation error is obtained. By gridding the target area and calculating the Cramerlow lower bound for each grid point, predictive information reflecting the spatial distribution of positioning accuracy is generated. With the goal of optimizing the positioning accuracy within the target area, the deployment location of the transponder is used as a decision variable. An optimization problem is constructed and solved based on the Cramer-Rao lower bound to obtain the optimized transponder deployment scheme.

2. The method for optimizing the deployment of a long baseline positioning array according to claim 1, characterized in that, The ranging error variance of the dynamic ranging error model is the sum of the ranging error variance based on the signal-to-noise ratio and the ranging error variance based on the sound speed error; where, The standard deviation of the ranging error based on the signal-to-noise ratio is calculated according to the formula. Calculate, where σ t Here, SNR represents the standard deviation of the ranging error based on signal-to-noise ratio (SNR), c is the speed of sound, B is the signal bandwidth, and SNR is the received signal-to-noise ratio. The received signal-to-noise ratio (SNR) is calculated according to the sonar equation SNR=SL-TL-NL+DI-DT, where SL is the sound source level, TL is the propagation loss, NL is the ambient noise level, DI is the directivity gain of the receiving array, and DT is the detection threshold. The propagation loss TL is based on the formula Calculate, where K is the extension type coefficient, r is the propagation distance, and α is the absorption coefficient; The environmental noise level NL is determined based on a marine environmental noise spectrum model.

3. The method for optimizing the deployment of a long baseline positioning array according to claim 2, characterized in that, The variance of the ranging error based on sound speed error is calculated according to the formula. Calculate, where σ c Here, represents the standard deviation of the ranging error based on the sound speed error, and t represents the signal propagation time. This represents the standard deviation of the sound speed measurement error.

4. The method for optimizing the deployment of a long baseline positioning array according to claim 1, characterized in that, The process of constructing the Fisher information matrix includes: For the TOA observation mode, according to the formula Calculate the Fisher information matrix, where N is the number of transponders, σ i 2 Let g be the variance of the ranging error of the i-th transponder. i Let cosine be the direction vector from the target to the i-th transponder; For the TDOA observation mode, the first transponder is used as the reference transponder, according to the formula... Calculate the Fisher information matrix, where σ i1 2 Let be the variance of the distance difference between the i-th transponder and the reference transponder.

5. The method for optimizing the deployment of a long baseline positioning array according to claim 1, characterized in that, The lower bound of the Cramérod equation is the positioning error covariance matrix, and the standard deviation of horizontal positioning accuracy is determined according to the formula. Calculate, where σ xy σ represents the standard deviation of horizontal positioning accuracy. x 2 and σ y 2 These are the variances of the eastward position estimation error and the northward position estimation error extracted from the lower bound matrix of the Cramérod matrix, respectively.

6. The method for optimizing the deployment of a long baseline positioning array according to claim 1, characterized in that, The optimization problem is formulated as follows: find a set P of transponder position coordinates to minimize a statistical index J(P) based on the lower bound of the Cramérault for all grid points in the target area Ω, and satisfy P∈D, where D is a preset feasible deployment area; the statistical index J(P) is the average or maximum value of the standard deviation of the horizontal positioning accuracy of all grid points in the target area Ω.

7. The method for optimizing the deployment of a long baseline positioning array according to claim 6, characterized in that, The optimization problem is solved using a particle swarm optimization algorithm, where the position vector of each particle encodes the coordinates of all transponders; during the iteration process, the velocity v of the particle in the d-th dimension at the k-th iteration is... i,d and position x i,d Updated according to the following formula: Where w is the inertia weight, and c1 and c2 are learning factors. Let be the component of the particle's historical optimal position in the d-th dimension. Let r1 and r2 be the components of the global historical best position of the group in the d-th dimension, and r1 and r2 be random functions.

8. The method for optimizing the deployment of a long baseline positioning array according to claim 7, characterized in that, The inertia weight w adopts a linear decreasing strategy, according to the formula... Calculate, where w max and w min These are the preset maximum and minimum inertia weights, where k is the current iteration number, and K is the maximum and minimum inertia weights. max This represents the maximum number of iterations.

9. A computer device, characterized in that, The computer device includes a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the method as described in any one of claims 1-8.

10. A computer-readable storage medium, characterized in that, The storage medium stores a computer program that, when executed by a processor, can implement the method as described in any one of claims 1-8.

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