阅读说明：本技术 一种二维声呐基阵运动姿态自校准方法 (Two-dimensional sonar array motion attitude self-calibration method ) 是由 魏波 李海森 周天 朱建军 徐超 陈宝伟 那万凯 于 2020-11-19 设计创作，主要内容包括：本发明提供一种二维声呐基阵运动姿态自校准方法,首先对声呐基阵接收到的回波信号进行脉冲压缩处理,分别估计“声亮点”距离基阵各顶点的整数倍时延及小数倍时延,结合二维基阵孔径建立非线性超定方程组。针对获得的非线性超定方程组构造目标函数,利用梯度法迭代求解方程组的最小二乘解,从而获得当前采样位置处的二维基阵中心、平移误差以及四顶点位置。利用系统旋转矩阵再次建立非线性超定方程组,迭代求解获得姿态误差。本方法通过对回波信号的时延估计和基阵结构建立几何方程,能够实现二维基阵运动姿态的六自由度运动误差联合自校准过程,具有不依赖于昂贵的外部辅助设备、时延估计精确高、算法实时性良好等技术优势。(The invention provides a self-calibration method for the motion attitude of a two-dimensional sonar array, which comprises the steps of firstly carrying out pulse compression processing on echo signals received by the sonar array, respectively estimating integral multiple time delay and decimal time delay of a sound and light spot from each vertex of the array, and establishing a nonlinear overdetermined equation set by combining with the aperture of the two-dimensional array. And constructing a target function aiming at the obtained nonlinear over-determined equation set, and iteratively solving a least square solution of the equation set by using a gradient method so as to obtain a two-dimensional matrix center, a translation error and a four-vertex position at the current sampling position. And (5) establishing a nonlinear over-determined equation set again by using the system rotation matrix, and iteratively solving to obtain an attitude error. According to the method, a geometric equation is established for the time delay estimation and the array structure of the echo signal, the six-degree-of-freedom motion error joint self-calibration process of the two-dimensional array motion attitude can be realized, and the method has the technical advantages of independence on expensive external auxiliary equipment, high time delay estimation accuracy, good algorithm instantaneity and the like.)

1. A two-dimensional sonar array motion attitude self-calibration method is characterized by comprising the following steps: the method comprises the following steps:

the method comprises the following steps: selecting receiving elements at three vertex positions of a two-dimensional matrix, performing pulse compression processing on received echo signals, selecting three 'sound bright point' targets in a detection area, respectively estimating integral multiple time delay and decimal multiple time delay from the targets to the vertex positions, and calculating target slant distance;

step two: establishing a nonlinear overdetermined equation set according to a geometric relation and constructing a target function by using the obtained target slant distance and the receiving aperture of the two-dimensional array, and solving a least square solution of the nonlinear overdetermined equation set by a gradient method;

step three: estimating the geometric center of the matrix and the four-vertex coordinates thereof according to the least square solution obtained in the step, thereby calculating the translation error of the matrix;

step four: and (4) establishing a nonlinear over-determined equation set again by using the system rotation matrix and the vertex coordinates and the translation errors estimated in the steps, and obtaining attitude errors of the matrix by solving, thereby jointly estimating the six-degree-of-freedom motion errors of the system.

2. The two-dimensional sonar array motion attitude self-calibration method according to claim 1, characterized in that: the first step is specifically as follows: the system selects a linear frequency modulation signal as a detection signal, and the emission signal is as follows:

where N is the width of the transmitted signal pulse, f₀Is the signal center frequency, f_sThe sampling rate of the system is shown, and n is a sampling sequence number; the number of received signal delay points can be represented as t + Δ t, wherein the number of integer multiple delay points t can be obtained by calculating a correlation peak, and the received signal form is as follows:

the correlation function after the pulse compression process is expressed as:

extracting the phase P of the cross-correlation signal r (m), and then estimating the residual error of the number of delay points at the time when m is equal to N, the relationship is as follows:

solving the root of the unitary quadratic equation to obtain the number delta t of the time delay estimation residual error points, namely the decimal time delay:

3. the two-dimensional sonar array motion attitude self-calibration method according to claim 2, characterized in that: the second step is specifically as follows: establishing a nonlinear overdetermined equation set according to a geometric relationship by using the obtained target slant distance and the receiving aperture of the two-dimensional array; the motion error self-calibration method based on the 'acoustic bright points' estimates the position of the current array by using the position of the last array, so that the time delay from an independent bright point target to the three top points of the array is estimated firstly; setting the detection area to have three independent bright spots E (x)₁,y₁,z₁)，F(x₂,y₂,z₂) And G (x)₃,y₃,z₃) Initial position P of the carrier₀Selecting three vertexes A with known positions₀(x₀₁,y₀₁,z₀₁)，B₀(x₀₂,y₀₂,z₀₂) And C₀(x₀₃,y₀₃,z₀₃) Carrier offset position P₁Selecting three vertexes A to be estimated₁(x₁₁,y₁₁,z₁₁)，B₁(x₁₂,y₁₂,z₁₂) And C₁(x₁₃,y₁₃,z₁₃) Two-dimensional array track real aperture d_yAnd the horizontal direction real aperture d_xThe method comprises the following steps of (1) knowing;

at the initial position P of the carrier₀From the correlation function, the carrier can be determined at the offset position P₁Bright spots E to A at the time of treatment₁、B₁And C₁Distance at three verticesAndand has the distance relation:

there is also a relationship for bright spots E and F:

for a receiving array with a two-dimensional area array structure, any three vertexes of the receiving array are positioned on a right triangle, and the following relations are provided:

the system of established relational equations F (ξ) according to the above is:

4. the two-dimensional sonar array motion attitude self-calibration method according to claim 3, characterized in that: constructing a target function in the step two, and solving a least square solution of a nonlinear overdetermined equation set through a gradient method; the target function is like:

the gradient iteration is carried out according to the following steps:

(1) setting three vertex coordinates of the array at the initial position as an iteration initial value, and setting xi^kAn estimate obtained for the kth iteration;

(2) calculating the target function G (xi)^k) If G (ξ)^k) If epsilon is less than xi, then xi at this moment is considered^kFor the least squares solution found, otherwise the iterative solution needs to be modified, for the objective function G (ξ)^k) The gradient of (d) can be obtained by partial derivation of xi;

(3) iterative solution of iterative correctionUntil meeting convergence accuracy (G)₁ ^k+1,G₂ ^k+1,…,G₁₂ ^k+1) < ε, the calculation is terminated.

5. The two-dimensional sonar array motion attitude self-calibration method according to claim 4, is characterized in that: the third step is specifically as follows: estimating the geometric center of the matrix and the four-vertex coordinates thereof according to the least square solution obtained in the step, thereby calculating the translation error of the matrix; estimating the carrier P by the gradient iteration method₁Three vertex coordinates at locationAndand calculating to obtain the center O' of the matrix and the position of the fourth vertex

6. The two-dimensional sonar array motion attitude self-calibration method according to claim 5, characterized in that: the fourth step is specifically as follows: establishing a nonlinear overdetermined equation set again by using the system rotation matrix and the vertex coordinates and the translation errors estimated in the step, and obtaining the attitude error of the matrix through solving; wherein the rotation matrix is defined as M_{＜α,β,γ＞}And has the following relation:

the constraint is a nonlinear over-determined system of equations with 3 unknowns and 9 equations, and the gradient method can be used to iteratively search a least squares solution to estimate the attitude errors (Δ α, Δ β, Δ γ) of the carrier.

Technical Field

The invention relates to a self-calibration method for a motion attitude of a two-dimensional sonar array, and belongs to the field of sonar signal processing.

Background

Imaging sonar is currently the most common technical means for detecting underwater topography and landform, has developed a number of technical branches, and has received extensive research and attention from academic institutions and sonar equipment manufacturers. Common imaging sonar equipment mainly includes side scan sonar, multi-beam sounding sonar, synthetic aperture sonar and the like. These imaging sonar equipment realize two-dimentional or three-dimentional imaging process to the detection area through launching and receiving acoustic signal. Motion attitude estimation and compensation of a sonar array carrier are important factors of sonar imaging and imaging post-processing, and accurate attitude estimation and compensation are important guarantees of stable imaging and image splicing. The navigation of the carrier in the three-dimensional space can generate motion errors with six degrees of freedom, including: lateral, longitudinal, heave and roll, pitch, yaw. Wherein, the lateral shift, longitudinal shift and heave deviation of the translation along the horizontal axis, the track axis and the depth axis are called as position errors; roll, pitch, and heading deviations about the horizontal, track, and depth axes are referred to as attitude errors. The imaging sonar with different array structures and detection principles has different sensitivities to errors with six degrees of freedom, for example, for a single-line array multi-beam sounding sonar, the rolling is the main factor influencing the imaging effect, the pitching and heading deviation mainly influence the imaging uniformity, and the position errors of the traversing, the longitudinal moving and the heaving mainly influence the spatial homing of the imaged figure, so that the single-line array multi-beam sounding sonar imaging effect is considered to be sensitive to the rolling, and the influence on other factors is slightly weak, so that the compensation after the imaging of the motion error can be carried out. For example, in a single-element synthetic aperture sonar or a multi-subarray receiving system arranged along a certain direction, the imaging effect is mainly affected by position errors, and attitude rotation in certain dimensions only affects the directivity of a receiving array element and the spatial homing of a transmitting beam, and does not affect the spatial position of the array element, namely, does not affect the acoustic path difference of an echo. With the continuous development of imaging sonar technology research, the two-dimensional sonar array is gradually applied to an imaging system, better array gain can be provided, the system surveying and mapping efficiency can be improved, and new mechanisms and new equipment gradually emerge, such as two-dimensional multi-beam image sonars and multi-beam synthetic aperture sonars.

Therefore, for the new detection mechanism of various imaging sonars, the joint estimation of the motion errors with six degrees of freedom is particularly important, and the refined detection technology is sensitive to the motion errors in the three-dimensional space. The existing imaging sonar motion estimation technology is divided into two types: hardware estimation and software estimation. The hardware estimation mainly refers to an estimation method based on external motion estimation auxiliary equipment such as an attitude instrument, a compass, a GPS and the like, and has the advantages of good estimation real-time performance, high upper limit of precision and the defects of high price, large occupied space and incapability of being used in an underwater small-space closed cabin body, and limits the application in an underwater unmanned environment; software estimation mainly carries out motion attitude estimation in a synthetic aperture sonar system in a target echo self-focusing mode, then carries out imaging compensation, has the advantages of cost saving, no need of additionally increasing external auxiliary equipment and the defect that the existing method is not completely suitable for a two-dimensional sonar array structure.

Aiming at the defects of the existing method, the invention discloses a self-calibration method for the motion attitude of a two-dimensional sonar array, aiming at better estimating the motion attitude error of the two-dimensional sonar array. The six-degree-of-freedom combined self-calibration process of the two-dimensional array motion attitude can be realized, and the method has the technical advantages of independence on expensive external auxiliary equipment, high time delay estimation accuracy, good algorithm real-time performance and the like.

Disclosure of Invention

The invention aims to realize the six-degree-of-freedom combined self-calibration process of the motion attitude of a two-dimensional array by matching with a new mechanism of multi-beam synthetic aperture sonar detection, and aims to improve the time delay estimation precision and ensure the real-time performance of an algorithm without depending on expensive external auxiliary equipment.

The purpose of the invention is realized as follows: the method comprises the following steps:

the method comprises the following steps: selecting receiving elements at three vertex positions of a two-dimensional matrix, performing pulse compression processing on received echo signals, selecting three 'sound bright point' targets in a detection area, respectively estimating integral multiple time delay and decimal multiple time delay from the targets to the vertex positions, and calculating target slant distance;

step two: establishing a nonlinear overdetermined equation set according to a geometric relation and constructing a target function by using the obtained target slant distance and the receiving aperture of the two-dimensional array, and solving a least square solution of the nonlinear overdetermined equation set by a gradient method;

step three: estimating the geometric center of the matrix and the four-vertex coordinates thereof according to the least square solution obtained in the step, thereby calculating the translation error of the matrix;

step four: and (4) establishing a nonlinear over-determined equation set again by using the system rotation matrix and the vertex coordinates and the translation errors estimated in the steps, and obtaining attitude errors of the matrix by solving, thereby jointly estimating the six-degree-of-freedom motion errors of the system.

The invention also includes such structural features:

1. the first step is specifically as follows: the system selects a linear frequency modulation signal as a detection signal, and the emission signal is as follows:

where N is the width of the transmitted signal pulse, f₀Is the signal center frequency, f_sThe sampling rate of the system is shown, and n is a sampling sequence number; the number of received signal delay points can be represented as t + Δ t, wherein the number of integer multiple delay points t can be obtained by calculating a correlation peak, and the received signal form is as follows:

the correlation function after the pulse compression process is expressed as:

extracting the phase P of the cross-correlation signal r (m), and then estimating the residual error of the number of delay points at the time when m is equal to N, the relationship is as follows:

solving the root of the unitary quadratic equation to obtain the number delta t of the time delay estimation residual error points, namely the decimal time delay:

2. the second step is specifically as follows: establishing a nonlinear overdetermined equation set according to a geometric relationship by using the obtained target slant distance and the receiving aperture of the two-dimensional array; the motion error self-calibration method based on the 'acoustic bright points' estimates the position of the current array by using the position of the last array, so that the time delay from an independent bright point target to the three top points of the array is estimated firstly; setting the detection area to have three independent bright spots E (x)₁,y₁,z₁)，F(x₂,y₂,z₂) And G (x)₃,y₃,z₃) Initial position P of the carrier₀Selecting three vertexes A with known positions₀(x₀₁,y₀₁,z₀₁)，B₀(x₀₂,y₀₂,z₀₂) And C₀(x₀₃,y₀₃,z₀₃) Carrier offset position P₁Selecting three vertexes A to be estimated₁(x₁₁,y₁₁,z₁₁)，B₁(x₁₂,y₁₂,z₁₂) And C₁(x₁₃,y₁₃,z₁₃) Two-dimensional array track real aperture d_yAnd the horizontal direction real aperture d_xThe method comprises the following steps of (1) knowing;

at the initial position P of the carrier₀From the correlation function, the carrier can be determined at the offset position P₁Bright spots E to A at the time of treatment₁、B₁And C₁Three-vertexDistance of (A) toAndand has the distance relation:

there is also a relationship for bright spots E and F:

for a receiving array with a two-dimensional area array structure, any three vertexes of the receiving array are positioned on a right triangle, and the following relations are provided:

the system of established relational equations F (ξ) according to the above is:

3. constructing a target function in the step two, and solving a least square solution of a nonlinear overdetermined equation set through a gradient method; the target function is like:

the gradient iteration is carried out according to the following steps:

(1) given a base array three at an initial positionThe vertex coordinate is used as an iteration initial value, and xi is set^kAn estimate obtained for the kth iteration;

(2) calculating the target function G (xi)^k) If G (ξ)^k) If epsilon is less than xi, then xi at this moment is considered^kFor the least squares solution found, otherwise the iterative solution needs to be modified, for the objective function G (ξ)^k) The gradient of (d) can be obtained by partial derivation of xi;

(3) iterative solution of iterative correctionUntil meeting convergence accuracy (G)₁ ^k+1,G₂ ^k+1,…,G₁₂ ^k+1) < ε, the calculation is terminated.

4. The third step is specifically as follows: estimating the geometric center of the matrix and the four-vertex coordinates thereof according to the least square solution obtained in the step, thereby calculating the translation error of the matrix; estimating the carrier P by the gradient iteration method₁Three vertex coordinates at locationAndand calculating to obtain the center O' of the matrix and the position of the fourth vertex

5. The fourth step is specifically as follows: by using the system rotation matrix and the vertex coordinates and the translation errors estimated in the steps, the nonlinear over-determined equation set is established again, and the attitude errors of the matrix are obtained by solving(ii) a Wherein the rotation matrix is defined as M_{＜α,β,γ＞}And has the following relation:

the constraint is a nonlinear over-determined system of equations with 3 unknowns and 9 equations, and the gradient method can be used to iteratively search a least squares solution to estimate the attitude errors (Δ α, Δ β, Δ γ) of the carrier.

Compared with the prior art, the invention has the beneficial effects that:

1. the six-degree-of-freedom joint error of the two-dimensional array is estimated through the least square method, and the method has better engineering applicability compared with the error estimation of single degree of freedom.

2. The time delay estimation precision from the target to the matrix is improved in a mode of combining integral multiple estimation and decimal multiple estimation, and therefore the accuracy of six-degree-of-freedom joint estimation is improved.

3. And a software motion error estimation method aiming at the target echo is adopted, and the self-calibration process of the motion attitude of the carrier is realized by utilizing the echo signals received by the two-dimensional array and the geometric relationship thereof. High cost and requirements on loading space brought by hardware estimation are avoided, and the method is suitable for the engineering application scene of the underwater unmanned small space.

Drawings

FIG. 1 is a schematic diagram of six-degree-of-freedom joint error estimation

FIG. 2 is a schematic diagram of a motion error trajectory of a carrier and an estimation result thereof

FIG. 3 deviation between carrier position estimation result and preset value

FIG. 4 deviation between carrier attitude estimation result and preset value

FIG. 5 imaging results before motion error estimation and compensation

FIG. 6 imaging results after motion error estimation and compensation

Detailed Description

The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.

As shown in FIG. 1, the invention relates to a two-dimensional sonar array motion attitude self-calibration method, which comprises the following steps:

step (1): selecting receiving elements at three vertex positions of a two-dimensional matrix, performing pulse compression processing on received echo signals, selecting three 'sound bright point' targets in a detection area, respectively estimating integral multiple time delay and decimal multiple time delay from the targets to the vertex positions, and calculating target slant distance.

Step (2): and establishing a nonlinear over-determined equation set according to the geometric relation and constructing a target function by using the obtained target slant distance and the receiving aperture of the two-dimensional array, and solving the least square solution of the nonlinear over-determined equation set by a gradient method.

And (3): and estimating the geometric center of the matrix and the four-vertex coordinates thereof according to the least square solution obtained in the step, thereby calculating the translation error of the matrix.

And (4): and (4) establishing a nonlinear over-determined equation set again by using the system rotation matrix and the vertex coordinates and the translation errors estimated in the steps, and obtaining attitude errors of the matrix by solving, thereby jointly estimating the six-degree-of-freedom motion errors of the system.

In the step (1), the receiving elements at the three vertex positions of the two-dimensional array are selected, the received echo signals are subjected to pulse compression processing, and three 'sound and bright point' targets in a detection area are selected, as shown in fig. 1. And selecting three bright spot positions in the three-dimensional space, and estimating the distances between the bright spots and three vertexes of the two-dimensional array so as to determine the array position. The six-degree-of-freedom motion error joint estimation method based on the 'acoustic bright points' estimates the position of the current array by using the position of the last array, so that the time delay from an independent bright point target to the three vertex positions of the array is estimated firstly. Setting the detection area to have three independent bright spots E (x)₁,y₁,z₁)，F(x₂,y₂,z₂) And G (x)₃,y₃,z₃) Initial position P of the carrier₀Selecting three vertexes A with known positions₀(x₀₁,y₀₁,z₀₁)，B₀(x₀₂,y₀₂,z₀₂) And C₀(x₀₃,y₀₃,z₀₃) Carrier offset position P₁Selecting three vertexes A to be estimated₁(x₁₁,y₁₁,z₁₁)，B₁(x₁₂,y₁₂,z₁₂) And C₁(x₁₃,y₁₃,z₁₃) Two-dimensional array track real aperture d_yAnd the horizontal direction real aperture d_xAre known. For a discrete chirp signal, the transmit signal may be expressed as:

where N is the width of the transmitted signal pulse, f₀Is the signal center frequency, f_sIs the system sampling rate, and n is the sampling sequence number. When the transmitted signal is reflected back to the receiving element by the target, the number of time delay points can be represented as t + Δ t, wherein the number of time delay points of integral multiple t can be calculated from the correlation peak, so that the estimated residual Δ t is only considered, and the signal form is:

when the received signal is subjected to the matched filtering process, a discrete signal expression can be obtained as shown below, and it is observed that when m is equal to N + Δ t, r (m) has the maximum amplitude value and the phase term at this time is 0. Therefore, the phase value of the signal correlation peak can be used for solving the time delay point residual error delta t, and the phase change of the point residual error delta t is within the main value interval without the phase ambiguity problem because the point residual error delta t is constantly smaller than a time gate corresponding to one sampling point.

Extracting the phase P of the cross-correlation signal r (m), and then estimating the residual error of the number of delay points at the time when m is equal to N, the relationship is as follows:

the time delay estimation residual point number delta t can be obtained by solving the root of the unitary quadratic equation:

the equation has two square roots, and an effective solution can be determined according to a constraint condition | delta t | < 1, so that an accurate time delay value tau between a target and an array element can be calculated by utilizing a related peak and a time delay point number estimation residual error thereof, and a slant distance l from an independent bright point to a receiving array element can be calculated according to a sound velocity.

In the step (2), a nonlinear overdetermined equation set is established according to the geometric relation and an objective function is constructed by using the obtained target slant distance and the receiving aperture of the two-dimensional array, and the least square solution of the nonlinear overdetermined equation set is solved through a gradient method.

As shown in fig. 1, at the initial position P of the carrier₀Can be according to the bright spots E to A₀、B₀And C₀The coordinate positions of the three vertexes are uniquely determined by the distances of the three vertexes, and the offset position P of the carrier can be determined according to the correlation function₁Bright spots E to A at the time of treatment₁、B₁And C₁Distance at three verticesAndand has the distance relation:

similarly, for bright spots E and F there is also the relationship:

in addition, for a receiving array with a two-dimensional area array structure, any three vertexes of the receiving array are positioned on a right triangle, and the following relations are provided:

for computational convenience, the above equation set is rewritten as follows:

the above equation set has 9 unknowns of three vertex coordinates and a limiting condition of 12 equations, and the limiting condition is a quadratic equation set, so that an analytic solution thereof may not exist, and the three vertex coordinates need to be solved by solving a least square solution of a nonlinear over-determined equation set. For solutions of a non-linear over-determined system of equations, it is first necessary to convert them into the appropriate system of equations, and then solve for the unknowns by iterative methods. Constructing an objective function g (x), solving a least squares solution of the function by using a gradient method:

starting from a certain point, the direction in which the function descends most quickly at the point is taken as the searching direction, and then the direction of the negative gradient is the direction in which the function descends most quickly at the point. Therefore, the problem can be converted into a group of target functions searched along the direction of negative gradientAnd (4) counting the optimal solution. For the objective function G (xi), xi is found to be the minimum, i.e. the least squares solution found, where the unknown xi is (x ═ x)₁₁,y₁₁,z₁₁,x₁₂,y₁₂,z₁₂,x₁₃,y₁₃,z₁₃). An iteration threshold epsilon is set, and when the k-th iteration is performed, the set of solution xi^kCan satisfy G (xi)^k) If epsilon is less than epsilon, the iteration is terminated.

The gradient iteration is carried out according to the following steps:

(1) given three vertex coordinates xi of the matrix at the initial position⁰＝(x₀₁,y₀₁,z₀₁,x₀₂,y₀₂,z₀₂,x₀₃,y₀₃,z₀₃) As an iteration initial value, ξ is set^kThe estimate obtained for the k-th iteration.

(2) Calculating the target function G (xi)^k) If G (ξ)^k) If epsilon is less than xi, then xi at this moment is considered^kFor the least squares solution found, otherwise the iterative solution needs to be modified as follows:

for the objective function G (ξ)^k) The gradient of (d) can be obtained by partial derivation of xi:

wherein the content of the first and second substances,h controls the convergence constant.

(3) Iterative solution of iterative correctionUntil meeting convergence accuracy (G)₁ ^k+1,G₂ ^k+1,…,G₁₂ ^k+1) < ε, the calculation is terminated.

And (3) estimating the geometric center of the matrix and the coordinates of four vertexes of the matrix according to the least square solution obtained in the step, thereby calculating the translation error of the matrix. Through the gradient iteration method in the steps, the carrier P can be estimated₁Three vertex coordinates at locationAndand the center of the matrix and the position of the fourth vertex can be calculated:

in the step (4), a nonlinear overdetermined equation set is established again by using the system rotation matrix and the vertex coordinates and the translation errors estimated in the step, and the attitude error of the matrix is obtained by solving. As for the center of the carrier, the position thereof is not affected by the change in the attitude, and therefore the change in the position thereof reflects the translation error of the carrier, whereby the position error (Δ x, Δ y, Δ z) of the carrier can be obtained. According to the positions of four vertexes of the two-dimensional array and the designed array element spacing of the array, the actual spatial positions of all receiving elements can be obtained step by step. In addition, the attitude error of the carrier can be obtained through a three-dimensional space transformation inverse matrix, wherein P is_r0 ^-1Is an initial position P_r0The generalized inverse of (1).

M_{＜α,β,γ＞}＝(P_r1-P_Δ)×P_r0 ^-1

By rotating the matrix M_{＜α,β,γ＞}＝M_αN_βQ_γThe constraint relation can be obtained:

the constraint is a nonlinear over-determined system of equations with 3 unknowns and 9 equations, and the gradient method can be used to iteratively search for a least squares solution, thereby estimating the attitude errors (Δ α, Δ β, Δ γ) of the carrier.

The present application is described in more detail below with reference to a specific application simulation of the method of the present application: selecting a two-dimensional multi-beam synthetic aperture sonar system array structure and a system signal center frequency f₀150kHz, 10ms and 10cm are adopted as signal bandwidth B, 10ms is adopted as pulse width T, and 10cm is adopted as emission array element real aperture size D. The number of horizontal array elements is 32, the spacing between the array elements is 5mm, the number of track array elements is 4, and the spacing between the array elements is 11 cm. The movement speed of the carrier is set to be 0.2m/s, and the theoretical movement track is uniform linear movement along the track direction. And (3) superposing an error curve on the theoretical motion track, setting the position error of the carrier to change according to a sine wave with the amplitude of 1m, and setting the attitude error to change according to a sine wave with the amplitude of 10 degrees. The motion trail and the motion deviation of the carrier are estimated by using the two-dimensional array attitude self-calibration method provided by the application, the motion trail of the carrier is shown in figure 2, and the position of the central point of the array is used as the motion trail of the carrier. It can be observed that the carrier center position after least square estimation has good goodness of fit with the carrier center position when a motion error is preset, and the actual position of the carrier can be accurately reflected.

The position error and the attitude error of six degrees of freedom are jointly estimated by using the two-dimensional matrix attitude self-calibration method provided by the application, and the deviation between the algorithm estimation result and the preset result is shown in fig. 3 and 4. The six-degree-of-freedom error changes along with the track direction sampling position, the estimation deviation of the position error is kept in the centimeter magnitude, the estimation deviation of the attitude error is kept in the range of 0.05 degrees, and the algorithm simulation result proves the effectiveness of the six-degree-of-freedom joint error estimation algorithm. In addition, an iterative algorithm simulation is carried out by using a DSP device TMS320C6678 with 8 operation cores, the running time of the motion error estimation algorithm is about millisecond magnitude under the condition that a CPU works in a single core and at a master frequency of 1GHz, and a certain acceleration ratio can be obtained after the device is subjected to parallelization processing, so that the calculation time can be further reduced, and the operation real-time performance of the joint estimation algorithm under the engineering application condition is ensured.

Fig. 4 and 5 show the imaging effect when the accuracy of the simulation hardware attitude estimation method is insufficient and the imaging result by the self-calibration method proposed in the present application, respectively, given simulation conditions, the carrier sails at a speed of 0.5m/s, an error curve is superimposed on a theoretical motion trajectory, the position error of the carrier is set to change according to a sine wave with an amplitude of 1m, and the attitude error is set to change according to a sine wave with an amplitude of 10 °. Setting 30 independent point targets on a plane with the depth value of 15m and the target distance of 20cm, and performing three-dimensional imaging on a detection area by using a multi-beam synthetic aperture sonar imaging algorithm. Firstly, simulating an imaging result under the condition that the hardware compensation precision is insufficient, controlling the preset carrier position precision range within 2cm, controlling the posture precision within 0.2 degrees, and cutting the posture information. Comparing fig. 4 with fig. 5, it can be found that although the imaging effect of the region where the target is located is basically correct, and no serious image defocusing occurs, the number and positions of the targets are aliased, and the imaging effect does not reach the theoretical effect. The self-calibration method provided by the application jointly estimates the six-degree-of-freedom motion error, the target position and the distance are displayed to be consistent with the theoretical preset value for the obtained imaging effect after the motion error compensation, the energy gathering degree of the target position is good, the expected effect is achieved, and the effectiveness of the method provided by the application is proved.

The method uses a least square estimation method to calculate the six-degree-of-freedom joint error of the two-dimensional array, and has better engineering applicability compared with the error estimation of single degree of freedom. The time delay estimation precision from the target to the matrix is improved in a mode of combining integral multiple estimation and decimal multiple estimation, and therefore the accuracy of six-degree-of-freedom joint estimation is improved. And a software motion error estimation method aiming at the target echo is adopted, and the self-calibration process of the motion attitude of the carrier is realized by utilizing the echo signals received by the two-dimensional array and the geometric relationship thereof. High cost and requirement limitation on loading space caused by hardware estimation are avoided, and the method is suitable for the engineering application scene of the underwater unmanned small space.

In conclusion, the invention discloses a self-calibration method for the motion attitude of a two-dimensional sonar array. Firstly, the echo signals received by a sonar array are subjected to pulse compression processing, integral multiple time delay and decimal time delay of the distance between the 'sound bright point' and each vertex of the array are respectively estimated, and a nonlinear over-determined equation set is established by combining the aperture of a two-dimensional array. And constructing a target function aiming at the obtained nonlinear over-determined equation set, and iteratively solving a least square solution of the equation set by using a gradient method so as to obtain a two-dimensional matrix center, a translation error and a four-vertex position at the current sampling position. And (5) establishing a nonlinear over-determined equation set again by using the system rotation matrix, and iteratively solving to obtain an attitude error. According to the method, a geometric equation is established for the time delay estimation and the array structure of the echo signal, the six-degree-of-freedom motion error joint self-calibration process of the two-dimensional array motion attitude can be realized, and the method has the technical advantages of independence on expensive external auxiliary equipment, high time delay estimation accuracy, good algorithm instantaneity and the like.