An artificial lateral array optimization method for underwater vehicle attitude estimation

Abstract

The present invention relates to the field of artificial lateral line optimization layout, and specifically to an artificial lateral line array optimization method for underwater vehicle attitude estimation, comprising: step 1: forming a quaternion model, obtaining vector parameters, and deriving a rotated vector; step 2: forming an artificial lateral line array and constructing an underwater vehicle pressure field model; step 3: deriving the relative root mean square error to obtain an effective estimation range of the vector parameters; step 4: determining the value range of the quaternion model vector parameters and determining the artificial lateral line array layout parameter constraints; step 5: determining the optimization target; and step 6: verifying the reliability of the optimization method. By integrating the artificial lateral line array and the quaternion model, based on a quantitative evaluation index system for array attitude estimation performance, the problem of cumulative error existing in the integral operation process of the inertial sensor system is effectively avoided, and the universal joint deadlock problem during Euler angle calculation is overcome.

Description

Technical Field

[0001] The present invention relates to the field of artificial lateral line optimization layout, and in particular to an artificial lateral line array optimization method for underwater vehicle attitude estimation. Background Art

[0002] Fish and aquatic amphibians possess a unique sensory system—the lateral line—that senses the hydrodynamics of their surroundings, enabling complex locomotion. On the one hand, the biomimetic lateral line system offers a new approach to underwater vehicle attitude estimation, effectively overcoming the inherent cumulative errors inherent in inertial sensor systems during integration. On the other hand, while Euler angles can intuitively represent the vehicle's attitude, their computation suffers from gimbal lock. Using a quaternion model can effectively reduce computational complexity. Therefore, a quantitative performance evaluation metric for attitude estimation using an artificial lateral line array is proposed. This metric can be used to assess the performance of array layouts and optimize their layout, which is crucial for improving the accuracy of underwater vehicle attitude estimation. Summary of the Invention

[0003] In response to the problems existing in the prior art, the purpose of the present invention is to propose a new attitude estimation method that integrates artificial lateral line sensing and quaternion model based on the aquatic biological perception mechanism to improve the shortcomings of traditional inertial sensing systems in attitude estimation and enhance the accuracy of underwater vehicle motion control. A quantitative evaluation index for the attitude estimation performance of artificial lateral line arrays is proposed based on the Cramer-Rao lower bound, thereby achieving the optimal design of artificial lateral line arrays for underwater vehicles.

[0004] To achieve the above-mentioned object, the present invention provides a technical solution: an artificial lateral array optimization method for underwater vehicle attitude estimation, comprising the following steps:

[0005] Step 1: According to the rotation angle α and the unit rotation vector u Composing quaternion model q , obtain the vector parameters when the underwater vehicle attitude is represented by the quaternion model, and any vector to be rotated by the underwater vehicle v Derive the rotated vector in matrix representation v ';

[0006] Step 2: Based on the lateral line sensing principle, select pressure sensors to form an artificial lateral line array, determine the array layout and initial layout positions of the pressure sensors, construct an underwater vehicle pressure field model, and form an array signal model;

[0007] Step 3: Based on the array signal model, derive the Cramer-Rao lower bound of the quaternion model vector parameters considering Gaussian white noise. Based on the Cramer-Rao lower bound, derive the relative root mean square error of the quaternion model vector parameter estimation. This is used as a quantitative evaluation indicator for the array attitude estimation performance. The effective estimation range of the vector parameters is obtained to determine whether the array meets the attitude estimation requirements.

[0008] Step 4: Determine the value range of the quaternion model vector parameters and determine the layout parameter constraints of the artificial lateral array based on the underwater vehicle model parameters;

[0009] Step 5: Determine the optimization goal and optimize the artificial lateral array layout parameters to obtain the simplest array that meets the attitude estimation requirements;

[0010] Step 6: Based on the obtained minimal array layout parameters, a randomized simulation analysis framework is constructed using Monte Carlo simulation. The least squares method is integrated to estimate the vector parameters of the quaternion model. The average relative root mean square error under simulation conditions is obtained and compared with the theoretical calculated value in S4 to complete the reliability verification of the optimization method.

[0011] In the above-mentioned artificial side line array optimization method for underwater vehicle attitude estimation, in step 1, the basic form and matrix form of the quaternion model vector parameters are:

[0012] , , ,in: q 1 is the real part parameter, q 2. q 3. q 4 is the imaginary part parameter, i 、 j 、 k are three mutually orthogonal imaginary unit vectors, sin is the sine function, and cos is the cosine function;

[0013] The basic form of the rotated vector v′ is: ,in, q * represents the conjugate of the quaternion. According to the matrix form of the quaternion model, the rotated vector v′ is expressed using matrix multiplication as follows: .

[0014] In the above-mentioned artificial side line array optimization method for underwater vehicle attitude estimation, step 2 comprises:

[0015] Step 2-1: Set the center of gravity of the underwater vehicle to coincide with the origin of the coordinate system. The head array elements of the underwater vehicle are arranged in a cross pattern, and the main array elements are arranged in a linear pattern. The array consists of M=4M1+4M2+1 array elements. Obtain the static pressure at each array element position of the artificial side line array.p The water depth of the array element d The relationship between: ,in, p 0 is atmospheric pressure, r is the density of seawater, g is the acceleration due to gravity;

[0016] Step 2-2: Combined with the rotated vector v′ obtained by matrix multiplication in step 1, the static pressure at each element position of the array after rotation can be expressed as:

[0017] ,in,[ p 1, p 2, … , p M ] T is the static pressure at each array element position, d 0 is the depth of the underwater vehicle's center of gravity, [ v 1, v 2, … , v M ] T is the rotation vector represented by each array element, and T represents transpose;

[0018] Step 2-3: According to step 2-2, the artificial lateral line array signal model is obtained as follows: ,in: z [ n ] is the array observation signal, p [ n ; i ] is the array theory signal containing the vector parameters of the quaternion model, i =[ u x u y u z α ] T is the vector parameter to be estimated, w [ n ] has a mean of zero and a variance of s 2 Gaussian white noise.

[0019] In the above-mentioned artificial sideline array optimization method for underwater vehicle attitude estimation, the Cramer-Rao lower bound of the quaternion model vector parameters considering Gaussian white noise is derived based on the array signal model in step 3, including:

[0020] Step 3-1: Set the likelihood function of Gaussian white noise P ( z ; i ) satisfies the regularity condition, which can be expressed as:

[0021] , where exp is a real number e An exponential function with base ;

[0022] Step 3-2: According to the Cramer-Rao lower bound theory, for vector parameters i Any unbiased estimator of The estimated variance of Satisfy the following formula:

[0023] ,in, I ( i ) is a vector parameter i The Fisher information matrix, whose inverse is the characterization vector parameter i Cramer-Rao lower bound of the estimated variance, E[] means finding the mathematical expectation, ∂ means finding the partial derivative, and ln means finding the logarithm;

[0024] Step 3-3: For quaternion model vector parameters i , its Fisher information matrix I ( i ) is expressed as:

[0025] ,

[0026] Vector parameters i Cramer-Rao lower bounds for each component The diagonal elements corresponding to the inverse of the Fisher information matrix are expressed as:

[0027] ,in: C ( u x ), C ( u y ), C ( u z ), C ( α ) are parameters u x 、 u y 、 u z 、 α The Cramer-Rao lower bound of I -1 ( i ) is the inverse matrix of the Fisher information matrix, and diag[] represents the diagonal elements of the extraction matrix.

[0028] In the above-mentioned artificial side line array optimization method for underwater vehicle attitude estimation, step 3 further includes:

[0029] Step 3-4: According to the vector parameters i The Cramer-Rao lower bounds of each component, the relative root mean square errors of the unit rotation vector and rotation angle of the quaternion model can be expressed as:

[0030] ,

[0031] , where ReRMSE( u ) is the relative root mean square error of the unit rotation vector estimation, ReRMSE( α ) is the relative root mean square error of the rotation angle estimation, | u ∣ is the modulus of the unit rotation vector;

[0032] Step 3-5: Use the relative root mean square error of the quaternion model unit rotation vector and rotation angle estimation as the evaluation indicator of the array attitude estimation performance. Using a relative root mean square error of 10% as the judgment basis, obtain the effective estimation range of the quaternion model unit rotation vector and rotation angle. Based on the size of the effective estimation range, determine whether the array meets the attitude estimation requirements.

[0033] In the above-mentioned artificial side line array optimization method for underwater vehicle attitude estimation, step 4 further includes:

[0034] Step 4-1: Determine the range of the rotation angle. The unit rotation vector in the spherical coordinate system is determined by the polar angle ψ and azimuth f express:

[0035] ;

[0036] Step 4-2: Based on the size limitations of the sensor itself and the underwater vehicle physical model, the artificial sideline array is laid out according to the constraints, which include the number of array elements, array element spacing, array element position, array length, and array attitude estimation performance.

[0037] In the above-mentioned artificial side line array optimization method for underwater vehicle attitude estimation, step 5 comprises:

[0038] Step 5-1: Set N h =4M1+1 head array element and N b =4M2 main array elements form an array, and the array satisfies the constraint condition;

[0039] Step 5-2: According to the geometric characteristics of the underwater vehicle physical model, the array head elements are arranged along a curve and the main body elements are arranged along a straight line. The main body elements are randomly generated to meet the element spacing constraint conditions. Δd , and judge whether the main array meets the array length constraint condition. If not, then according to the length of the underwater vehicle body L And one quarter of the main array elements M2 are used to correct it. The correction formula is:

[0040] , in order to avoid repeated constraints, the head array element spacing angle β It can be calculated from the arc length of the head half-arm array and the number of array elements M1: ;

[0041] Step 5-3: The total number of array elements M = N h +N b The optimization goal is to minimize and optimize the array attitude estimation performance, set a reasonable weight ratio between the total number of array elements and the array attitude estimation performance, and use the archived micro-genetic algorithm for multi-objective optimization;

[0042] Step 5-4: When the termination condition of the iteration is met, the simplest array that meets the posture estimation requirements is obtained, and the array layout parameters are output.

[0043] In the above-mentioned artificial side line array optimization method for underwater vehicle attitude estimation, step 6 comprises:

[0044] Step 6-1: Based on the layout parameters of the simplest array obtained in step 5, random noise interference is introduced and 1000 sets of simulation data are generated using Monte Carlo simulation;

[0045] Step 6-2: Based on the generated simulation data, use the least squares method to estimate the vector parameters of the quaternion model, and calculate the estimation errors of all Monte Carlo simulation samples to obtain the relative root mean square error of the unit rotation vector and rotation angle estimation of the simulation quaternion model;

[0046] Step 6-3: Compare the relative root mean square errors of the vector parameter simulation and theoretical estimation. If the deviation is within the preset confidence interval, it proves that the above optimization method is statistically reliable, thereby achieving closed-loop verification of the artificial side line array optimization method.

[0047] The present invention provides an artificial sideline array optimization method for underwater vehicle attitude estimation, which has the following beneficial effects: by integrating the artificial sideline array and the quaternion model, a quantitative evaluation index system for array attitude estimation performance based on the Cramer-Rao lower bound is proposed, which effectively avoids the cumulative error problem existing in the integral operation process of the inertial sensor system and overcomes the universal joint deadlock problem during Euler angle calculation; by combining the underwater vehicle pressure field model and the quaternion model rotation matrix, an artificial sideline array signal model is constructed, and the Cramer-Rao lower bound theory is used to achieve quantitative characterization of underwater vehicle attitude parameter estimation, providing a quantitative basis for array layout parameter optimization; finally, through Monte Carlo simulation and least squares estimation, a reliability evaluation system for the artificial sideline array optimization design method from theoretical derivation to simulation verification is improved, and the simplest array layout parameters that meet the constraints are obtained while ensuring the accuracy of attitude estimation, significantly reducing the computational complexity and design cost, improving the robustness and real-time performance of vehicle attitude estimation in complex underwater environments, and laying a theoretical and methodological foundation for the scientific design, development and engineering application of artificial sideline arrays for underwater vehicle attitude estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 Schematic diagram of vector parameters of a quaternion model in an embodiment of the present invention;

[0049] Figure 2 Schematic diagram of the side line array of an underwater vehicle in an embodiment of the present invention;

[0050] Figure 3 Schematic diagram of a unit rotation vector in a spherical coordinate system according to an embodiment of the present invention;

[0051] Figure 4 This is a flowchart of the array layout optimization of the archived micro genetic algorithm in an embodiment of the present invention;

[0052] Figure 5 Flowchart of the artificial lateral line array layout optimization design method in an embodiment of the present invention. DETAILED DESCRIPTION

[0053] In order to enable those skilled in the art to better understand the technical solution of the present invention, the technical solution of the present invention is described below in conjunction with specific implementation methods and drawings.

[0054] Example 1

[0055] An artificial side line array optimization method for underwater vehicle attitude estimation includes the following steps.

[0056] S1, construct an underwater vehicle attitude representation method based on quaternion model.

[0057] S2, based on the lateral line perception principle, selects pressure sensors to form an artificial lateral line array, determines the array layout and the initial layout position of the pressure sensors, constructs the underwater vehicle pressure field model, and forms the array signal model.

[0058] S3, derive the Cramer-Rao lower bound of the quaternion model vector parameters considering Gaussian white noise based on the array signal model.

[0059] S4: Based on the Cramer-Rao lower bound, the relative root mean square error of the quaternion model vector parameter estimation is derived, which is used as a quantitative evaluation indicator of the array attitude estimation performance. The effective estimation range of the vector parameters is obtained to determine whether the array meets the attitude estimation requirements.

[0060] S5. Determine the value range of the quaternion model vector parameters, and determine the layout parameter constraints of the artificial side line array based on the underwater vehicle model parameters. The array elements of the artificial side line array need to be arranged on the underwater vehicle based on parameters such as quantity and spacing. The constraints are used to limit the various constraints on the arrangement of the array elements on the vehicle. For example, the quantity constraint limits the upper and lower limits of the number of array elements, and the spacing constraint limits the spacing between array elements to a minimum of not less than the size of a sensor and a maximum of not more than certain parameters of the vehicle, etc.

[0061] S6, determine the optimization target, optimize the layout parameters of the artificial side line array, and obtain the simplest array that meets the attitude estimation requirements.

[0062] In S7, based on the obtained simplest array layout parameters, a randomized simulation analysis framework was constructed using Monte Carlo simulation. The least squares method was integrated to estimate the vector parameters of the quaternion model. The average relative root mean square error under simulation conditions was obtained and compared with the theoretical calculated value in S4 to complete the reliability verification of the above optimization method.

[0063] Example 2

[0064] like Figure 1-Figure 5 As shown, an artificial side line array optimization method for underwater vehicle attitude estimation includes the following steps.

[0065] Step 1: Construct an underwater vehicle attitude representation method based on the quaternion model.

[0066] The underwater vehicle attitude estimation has three degrees of freedom, and the quaternion model has four parameters and one constraint, which can effectively avoid the singularity problem when representing the three-dimensional attitude. q By a rotation angle α and a unit rotation vector u =( u x , uy , u z ), the vector parameters when the quaternion model is used to represent the underwater vehicle attitude are as follows Figure 1 As shown, its basic form and matrix form are as follows:

[0067] (1),

[0068] (2),

[0069] (3), where: q 1 is the real part parameter, q 2. q 3. q 4 is the imaginary part parameter, i 、 j 、 k are three mutually orthogonal imaginary unit vectors, sin is the sine function, and cos is the cosine function.

[0070] For any vector to be rotated for the underwater vehicle v =( v x , v y , v z ), its rotated vector v ' can be expressed by the following formula: (4),

[0071] in: q * indicates the conjugate of a quaternion.

[0072] To facilitate subsequent model derivation, according to the matrix form of the quaternion model, using matrix multiplication, the matrix form of equation (4) can be expressed as:

[0073] (5).

[0074] Step 2: Based on the lateral line sensing principle, pressure sensors are selected to form an artificial lateral line array, the array layout and the initial layout positions of the pressure sensors are determined, a pressure field model of the underwater vehicle is constructed, and an array signal model is formed.

[0075] According to the lateral line perception principle of fish, the neuromast can respond sensitively to the pressure field changes caused by weak underwater flow, so pressure sensors are selected to form an artificial lateral line array. Figure 2As shown in the figure, assuming that the center of gravity of the underwater vehicle coincides with the origin of the coordinate system, the array elements at the head of the vehicle are arranged in a cross pattern, the array elements in the main body are arranged in a linear pattern, and the overall pattern is arranged in an axisymmetric pattern, then the array consists of a total of M=4M1+4M2+1 array elements. p The water depth of the array element d The following relationship exists: (6), where: p 0 is atmospheric pressure, r is the density of seawater, g is the acceleration due to gravity.

[0076] Combined with the quaternion model rotation matrix obtained by matrix multiplication in step 1, the static pressure at each element position of the array after rotation can be expressed as:

[0077] (7), where: [ p 1, p 2, … , p M ] T is the static pressure at each array element position, d 0 is the depth of the underwater vehicle's center of gravity, [ v 1, v 2, … , v M ] T is the rotation vector represented by each array element, and T represents transpose.

[0078] Then the artificial side line array signal model can be expressed as: (8), where: z [ n ] is the array observation signal, p [ n ; i ] is the array theory signal containing the vector parameters of the quaternion model, i =[ u x u y u z α ] T is the vector parameter to be estimated, w [ n ] has a mean of zero and a variance of s 2 Gaussian white noise.

[0079] Step 3: Derived the Cramer-Rao lower bound of the quaternion model vector parameters considering Gaussian white noise based on the array signal model.

[0080] Assuming Gaussian white noise likelihood functionP ( z ; i ) satisfies the regularity condition, which can be expressed as: (9), where exp is a real number e An exponential function with base .

[0081] According to the Cramer-Rao lower bound theory, for vector parameters i Any unbiased estimator of The estimated variance of Satisfy the following formula:

[0082] (10), where: I ( i ) is a vector parameter i The Fisher information matrix, whose inverse is the characterization vector parameter i Estimate the Cramer-Rao lower bound of the variance. E[] represents the mathematical expectation, ∂ represents the partial derivative, and ln represents the logarithm.

[0083] For quaternion model vector parameters i , its Fisher information matrix I ( i ) can be expressed as:

[0084] (11).

[0085] Vector parameters i Cramer-Rao lower bounds for each component The diagonal elements corresponding to the inverse of the Fisher information matrix can be expressed as:

[0086] (12), where: C ( u x ), C ( u y ), C ( u z ), C ( α ) are parameters u x 、 u y 、 u z 、 α The Cramer-Rao lower bound of I -1 ( i) is the inverse matrix of the Fisher information matrix, and diag[] represents the diagonal elements of the extraction matrix.

[0087] Step 4: Based on the Cramer-Rao lower bound, the relative root mean square error of the quaternion model vector parameter estimation is derived, and this is used as a quantitative evaluation indicator of the array attitude estimation performance. The effective estimation range of the vector parameters is obtained to determine whether the array meets the attitude estimation requirements.

[0088] Quaternion model vector parameters i The estimation accuracy can be characterized by the relative root mean square error ReRMSE of the unit rotation vector and rotation angle estimation respectively. i The Cramer-Rao lower bounds of each component, the relative root mean square errors of the unit rotation vector and rotation angle of the quaternion model can be expressed as:

[0089] (13),

[0090] (14), where: ReRMSE( u ) is the relative root mean square error of the unit rotation vector estimation, ReRMSE( α ) is the relative root mean square error of the rotation angle estimation, | u ∣ is the modulus of the unit rotation vector.

[0091] The relative root mean square error of the quaternion model unit rotation vector and rotation angle estimation is used as the evaluation index of the array attitude estimation performance. Based on the 10% relative root mean square error, the effective estimation range of the quaternion model unit rotation vector and rotation angle is obtained. According to the size of the effective estimation range, it is determined whether the array meets the attitude estimation requirements.

[0092] Step 5: Determine the value range of the quaternion model vector parameters and determine the artificial side line array layout parameter constraints based on the underwater vehicle model parameters.

[0093] Considering the symmetry of the underwater vehicle's attitude transformation, first, the range of the rotation angle is determined to be 0~90°; Figure 3 As shown, the unit rotation vector in the spherical coordinate system can be expressed by the polar angle ψ and azimuth f The polar angle is determined by ψ and azimuth f The value range is 0~90°. Unit rotation vector and polar angle in spherical coordinate system ψ and azimuth f The conversion relationship can be expressed as: (15).

[0094] Considering the size limitations of the sensor itself and the physical model of the underwater vehicle, the layout parameters of the artificial side line array must meet certain constraints. The specific constraints on the number of array elements, array element spacing, array element position, array length, and array attitude estimation performance are shown in Table 1.

[0095] Table 1 Constraints on the layout parameters of artificial lateral arrays

[0096] .

[0097] in, R is the head radius of the underwater vehicle; L is the main body length of the underwater vehicle; b is the diameter of the array element; M1 is the number of half-arm array elements in the head; M2 is the number of one-quarter main body array elements; Δd and β are the array element spacing distance and spacing angle respectively; ( x h , y h , z h ) is the layout coordinate of the head pressure sensor; ( x b , y b , z b ) is the layout coordinate of the main pressure sensor; d is the offset distance of the underwater vehicle's head center relative to its center of gravity; V u 、 V α They are the effective estimation ranges of the unit rotation vector and rotation angle of the quaternion model respectively; T u 、 T α are the actual estimated total ranges of the quaternion model unit rotation vector and rotation angle respectively; or Lower bound for array pose estimation performance.

[0098] Step 6: Determine the optimization target and optimize the layout parameters of the artificial side line array to obtain the simplest array that meets the attitude estimation requirements.

[0099] Archived micro genetic algorithm artificial lateral array layout optimization process Figure 4 shown.

[0100] First, suppose the array consists of N h =4M1+1 head array element and N b =4M2 main array elements, and the array element quantity constraint is satisfied.

[0101] For the main array element, randomly generate the main array element spacing that meets the array element spacing constraint condition. Δd , and judge whether the main array meets the array length constraint condition. If not, then according to the length of the underwater vehicle body L And one quarter of the main array elements M2 are used to correct it. The correction formula is as follows: (16).

[0102] To avoid repeated constraints, the head element spacing angle β It can be calculated from the arc length of the head half-arm array and the number of array elements M1, that is:

[0103] (17).

[0104] According to the geometric characteristics of the underwater vehicle physical model, the array head elements are arranged along a curve and the main body elements are arranged along a straight line. The generated array element coordinates must meet the array element position constraints.

[0105] Assume that the Cramer-Rao lower bound of the relative root mean square error of the quaternion model unit rotation vector and rotation angle estimation is less than 10%, which is considered a valid estimation. Calculate the valid estimation range of the unit rotation vector and rotation angle respectively, and take 90% as the lower limit of the array attitude estimation performance. Then, the ratio of the valid estimation range of the unit rotation vector and rotation angle to the actual total estimation range must meet the array attitude estimation performance constraint.

[0106] Finally, the total number of array elements M=N h +N b The optimization goal is to minimize and maximize array attitude estimation performance. A reasonable weighting ratio between the total number of array elements and array attitude estimation performance is set, and an archived micro-genetic algorithm is used for multi-objective optimization. When the termination conditions are met, the simplest array that meets the attitude estimation requirements is obtained, and the array layout parameters are output.

[0107] In step 7, based on the obtained simplest array layout parameters, a randomized simulation analysis framework is constructed using Monte Carlo simulation, and the least squares method is integrated to estimate the vector parameters of the quaternion model. The average relative root mean square error under simulation conditions is obtained and compared with the theoretical calculation value in S4 to complete the reliability verification of the above optimization method.

[0108] Based on the layout parameters of the simplest array obtained in step 6, such as the number of array elements, array element spacing, and array element position, random noise interference is introduced, and Monte Carlo simulation is used to generate 1000 sets of simulation data.

[0109] According to the generated simulation data, the least squares method is used to estimate the vector parameters of the quaternion model, and the estimation errors of all Monte Carlo simulation samples are counted to obtain the relative root mean square error of the unit rotation vector and rotation angle estimation of the simulation quaternion model.

[0110] By comparing the relative root mean square errors of vector parameter simulation and theoretical estimation, if the deviation is within the preset confidence interval, it proves that the above-mentioned optimization design method is statistically reliable, thereby realizing closed-loop verification of the artificial lateral line array optimization design method.

[0111] The overall process of the artificial lateral array layout optimization design method is as follows Figure 5 shown.

[0112] The above embodiments are intended only to illustrate the structural concepts and features of the present invention. Their purpose is to enable those skilled in the art to understand the present invention and implement it accordingly. They are not intended to limit the scope of protection of the present invention. Any equivalent changes or modifications made based on the essence of the present invention should be included in the scope of protection of the present invention.

Claims

1. An artificial lateral array optimization method for underwater vehicle attitude estimation, characterized in that: The following steps are involved: Step 1: According to the rotation angle α and the unit rotation vector u Composing quaternion model q , obtain the vector parameters when the underwater vehicle attitude is represented by the quaternion model, and any vector to be rotated by the underwater vehicle v Derive the rotated vector in matrix representation v '; Step 2: Based on the lateral line sensing principle, select pressure sensors to form an artificial lateral line array, determine the array layout and initial layout positions of the pressure sensors, construct an underwater vehicle pressure field model, and form an array signal model; Step 3: Based on the array signal model, derive the Cramer-Rao lower bound of the quaternion model vector parameters considering Gaussian white noise. Based on the Cramer-Rao lower bound, derive the relative root mean square error of the quaternion model vector parameter estimation. This is used as a quantitative evaluation indicator for the array attitude estimation performance. The effective estimation range of the vector parameters is obtained to determine whether the array meets the attitude estimation requirements. Step 4: Determine the value range of the quaternion model vector parameters and determine the layout parameter constraints of the artificial lateral array based on the underwater vehicle model parameters; Step 5: Determine the optimization goal and optimize the artificial lateral array layout parameters to obtain the simplest array that meets the attitude estimation requirements; Step 6: Based on the obtained minimal array layout parameters, a randomized simulation analysis framework is constructed using Monte Carlo simulation. The least squares method is integrated to estimate the vector parameters of the quaternion model. The average relative root mean square error under simulation conditions is obtained and compared with the theoretical calculated value in S4 to complete the reliability verification of the optimization method.

2. The artificial side line array optimization method for underwater vehicle attitude estimation according to claim 1, characterized in that: In step 1, the basic form and matrix form of the quaternion model vector parameters are: , , ,in: q 1 is the real part parameter, q 2. q 3. q 4 is the imaginary part parameter, i 、 j 、 k are three mutually orthogonal imaginary unit vectors, sin is the sine function, and cos is the cosine function; The basic form of the rotated vector v′ is: ,in, q * represents the conjugate of the quaternion. According to the matrix form of the quaternion model, the rotated vector v′ is expressed using matrix multiplication as follows: .

3. The artificial side line array optimization method for underwater vehicle attitude estimation according to claim 2, characterized in that: The step 2 includes: Step 2-1: Set the center of gravity of the underwater vehicle to coincide with the origin of the coordinate system. The head array elements of the underwater vehicle are arranged in a cross pattern, and the main array elements are arranged in a linear pattern. The array consists of M=4M1+4M2+1 array elements. Obtain the static pressure at each array element position of the artificial side line array. p The water depth of the array element d The relationship between: ,in, p 0 is atmospheric pressure, ρ is the density of seawater, g is the acceleration due to gravity; Step 2-2: Combined with the rotated vector v′ obtained by matrix multiplication in step 1, the static pressure at each element position of the array after rotation can be expressed as: ,in,[ p 1, p 2, … , p M ] T is the static pressure at each array element position, d 0 is the depth of the underwater vehicle's center of gravity, [ v 1, v 2, … , v M ] T is the rotation vector represented by each array element, and T represents transpose; Step 2-3: According to step 2-2, the artificial lateral line array signal model is obtained as follows: ,in: z [ n ] is the array observation signal, p [ n ; θ ] is the array theory signal containing the vector parameters of the quaternion model, θ =[ u x u y u z α ] T is the vector parameter to be estimated, w [ n ] has a mean of zero and a variance of σ 2 Gaussian white noise.

4. The artificial side line array optimization method for underwater vehicle attitude estimation according to claim 3, characterized in that: In step 3, the Cramer-Rao lower bound of the quaternion model vector parameters considering Gaussian white noise is derived based on the array signal model, including: Step 3-1: Set the likelihood function of Gaussian white noise P ( z ; θ ) satisfies the regularity condition, which can be expressed as: , where exp is a real number e An exponential function with base ; Step 3-2: According to the Cramer-Rao lower bound theory, for vector parameters θ Any unbiased estimator of The estimated variance of Satisfy the following formula: ,in, I ( θ ) is a vector parameter θ The Fisher information matrix, whose inverse is the characterization vector parameter θ Cramer-Rao lower bound of the estimated variance, E[] means finding the mathematical expectation, ∂ means finding the partial derivative, and ln means finding the logarithm; Step 3-3: For quaternion model vector parameters θ , its Fisher information matrix I ( θ ) is expressed as: ， Vector parameters θ Cramer-Rao lower bounds for each component The diagonal elements corresponding to the inverse of the Fisher information matrix are expressed as: ,in: C ( u x ), C ( u y ), C ( u z ), C ( α ) are parameters u x 、 u y 、 u z 、 α The Cramer-Rao lower bound of I -1 ( θ ) is the inverse matrix of the Fisher information matrix, and diag[] represents the diagonal elements of the extraction matrix.

5. The artificial side line array optimization method for underwater vehicle attitude estimation according to claim 4, characterized in that: The step 3 further comprises: Step 3-4: According to vector parameters θ The Cramer-Rao lower bounds of each component, the relative root mean square errors of the unit rotation vector and rotation angle of the quaternion model can be expressed as: ， , where ReRMSE( u ) is the relative root mean square error of the unit rotation vector estimation, ReRMSE( α ) is the relative root mean square error of the rotation angle estimation, | u ∣ is the modulus of the unit rotation vector; Step 3-5: Use the relative root mean square error of the quaternion model unit rotation vector and rotation angle estimation as the evaluation indicator of the array attitude estimation performance. Using a relative root mean square error of 10% as the judgment basis, obtain the effective estimation range of the quaternion model unit rotation vector and rotation angle. Based on the size of the effective estimation range, determine whether the array meets the attitude estimation requirements.

6. The artificial side line array optimization method for underwater vehicle attitude estimation according to claim 5, characterized in that: The step 4 further comprises: Step 4-1: Determine the range of the rotation angle. The unit rotation vector in the spherical coordinate system is determined by the polar angle ψ and azimuth φ express: ； Step 4-2: Based on the size limitations of the sensor itself and the underwater vehicle physical model, the artificial sideline array is laid out according to the constraints, which include the number of array elements, array element spacing, array element position, array length, and array attitude estimation performance.

7. The artificial side line array optimization method for underwater vehicle attitude estimation according to claim 6, characterized in that: The step 5 comprises: Step 5-1: Set N h =4M1+1 head array element and N b =4M2 main array elements form an array, and the array satisfies the constraint condition; Step 5-2: According to the geometric characteristics of the underwater vehicle physical model, the array head elements are arranged along a curve and the main body elements are arranged along a straight line. The main body elements are randomly generated to meet the element spacing constraint conditions. Δd , and judge whether the main array meets the array length constraint condition. If not, then according to the length of the underwater vehicle body L And one quarter of the main array elements M2 are used to correct it. The correction formula is: , in order to avoid repeated constraints, the head array element spacing angle β It can be calculated from the arc length of the head half-arm array and the number of array elements M1: ; Step 5-3: The total number of array elements M = N h +N b The optimization goal is to minimize and optimize the array attitude estimation performance, set a reasonable weight ratio between the total number of array elements and the array attitude estimation performance, and use the archived micro-genetic algorithm for multi-objective optimization; Step 5-4: When the termination condition of the iteration is met, the simplest array that meets the posture estimation requirements is obtained, and the array layout parameters are output.

8. The artificial side line array optimization method for underwater vehicle attitude estimation according to claim 7, characterized in that: The step 6 comprises: Step 6-1: Based on the layout parameters of the simplest array obtained in step 5, random noise interference is introduced and 1000 sets of simulation data are generated using Monte Carlo simulation; Step 6-2: Based on the generated simulation data, use the least squares method to estimate the vector parameters of the quaternion model, and calculate the estimation errors of all Monte Carlo simulation samples to obtain the relative root mean square error of the unit rotation vector and rotation angle estimation of the simulation quaternion model; Step 6-3: Compare the relative root mean square errors of the vector parameter simulation and theoretical estimation. If the deviation is within the preset confidence interval, it proves that the above optimization method is statistically reliable, thereby achieving closed-loop verification of the artificial side line array optimization method.

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