CN110346783A - Sound ray modification method based on the equivalent ranging model of power series - Google Patents

Abstract

The invention discloses a sound ray correction method based on a power series equivalent distance measurement model, which solves the problem of distance measurement inaccuracy caused by the measurement time being longer than the straight line propagation time under the influence of sound ray bending. The main steps of the method include: collecting time delay and slant distance fitting samples, fitting data to determine the power series form of the equivalent ranging model, and using the equivalent ranging model to convert the measured time delay into a straight-line slant distance. Among them, according to the different situations of whether there is a sound velocity profile, there are two methods of PF and MF to obtain the fitting samples. The PF method simulates and calculates the sound ray channel model based on the sound velocity profile data to generate simulation samples; the MF method uses the known transponder, GPS and measured values of slant distance to form samples. In the case that the sound velocity profile is also required, the PF method achieves the high-precision effect of the sound ray tracing method, and greatly saves the amount of calculation. In the case of no sound velocity profile, the sound ray tracing method cannot be carried out, and MF can well complete the task of sound ray correction.

Description

Sound Ray Correction Method Based on Power Series Equivalent Ranging Model

technical field

The invention belongs to the technical field of underwater acoustic detection and positioning, and in particular relates to a sound ray bending fast correction method based on an equivalent ranging model.

Background technique

Both underwater detection and positioning require underwater acoustic ranging, and the geometric position is determined by slant distance. When the acoustic signal propagates underwater, it is subject to different salinity, temperature, depth and pressure, and its propagation speed is also different. Different sound velocities cause sound waves to no longer propagate in a straight line in water. From the perspective of the section, the sound ray between the source and the hydrophone is a curve instead of a straight line. Not only the length of the sound ray becomes larger, but also the time elapsed becomes longer. . How to use the time delay of the curved sound ray and the varying speed of sound to calculate the real straight-line distance—the slant distance is a practical problem that must be faced in all underwater acoustic engineering. The accuracy of distance measurement directly affects underwater detection and positioning. accuracy.

It is obviously not accurate enough to multiply the measured time delay by a fixed empirical sound velocity, and will introduce a huge error. The current existing method is to collect the sound velocity profile data in the water area, establish a sound ray channel model, correct the actual trajectory of the sound ray through the method of sound ray tracking, and calculate the straight-line slant distance. Whether it is constant velocity sound ray correction, equal gradient sound ray correction or equivalent sound velocity correction, there are inevitably several problems: (1) It is necessary to search for the initial grazing angle of the sound ray, and the search step size is too large The eigenrays may be skipped, and the search step size is too small to consume too much time. (2) The equipment has to repeat this process when calculating the slope distance at each position, and the workload is huge. (3) Due to the errors in the sound velocity profile and other errors in the system, the sound ray model cannot be completely consistent with the actual sound ray, and these errors will also affect the slant distance estimation. (4) The traditional method completely relies on the sound velocity profile, and cannot correct the influence of sound ray bending when there is no sound velocity profile data.

Contents of the invention

Purpose of the invention: Aiming at the deficiencies of traditional methods, the present invention proposes a new sound ray correction method, which can predict the equivalent ranging model in the entire plane area. The sound velocity distribution in this model is continuous and changing. After the time delay is measured, the corrected sound velocity can be obtained directly, which is very convenient. More importantly, when there is no sound velocity profile data, the present invention can also implement sound velocity correction through other means.

Technical solution: A sound ray correction method based on a power series equivalent ranging model according to the present invention comprises the following steps:

(1) According to the presence or absence of sound velocity profile data, different methods are used to obtain the delay-slope distance mapping, including slope range samples and time delay samples. In the case of sound velocity profile data, the underwater sound ray channel model is established , to calculate the maximum horizontal effective distance, referred to as PF (Profile Fitting) method; in the absence of sound velocity profile data, by calibrating the position of the transponder, performing actual measurement sampling and calculation to obtain delay samples and slant distance samples, referred to as MF (Measurement Fitting) Law;

(2) Select delay samples and slant distance samples;

(3) According to the continuity correction relationship between time delay and slant distance, a power series function of the equivalent ranging model is established;

(4) Using the power series function of the equivalent ranging model to convert the measured time delay into a slant distance to realize sound ray correction.

Further, in the step (1), in the case of sound velocity profile data, the PF method is executed, and the calculation of the maximum horizontal effective distance by establishing an underwater sound ray channel model includes:

Given the time delay t _j measured by the sounding head of the measuring ship, the GPS position p _j (x _j ,y _j ,0) of the measuring ship, the sound velocity profile c(z) of the water area, and the depth H of the transponder, for a The sound rays incident at the initial grazing angle θ ₀ are modeled according to the equal-gradient sound ray tracing method as follows:

R is the horizontal distance of the sound ray, and t is the time delay; c _i =c( _zi ) indicates the sound velocity value of each layer in the sound velocity profile; g _i =( _ci+1 -ci _{)/Δz i is} the sound velocity of each layer Gradient, Δz _i is the layer height, and there is p=cosθ ₀ /c ₀ , which is the snell coefficient; m represents the number of samples;

When sinθ ₀ =0, the sound ray shoots out horizontally, and the horizontal distance reached at this time is the maximum horizontal effective distance R _max , which is expressed as:

Further, in the step (1), in the absence of sound velocity profile data, the MF method is executed, and the actual measurement sampling and calculation are performed by calibrating the position of the transponder to obtain time delay samples and slant distance samples including:

Obtain the calibrated reference transponder position or use the long baseline calibration method to calibrate the transponder position, denoted as p _s (x _s , y _s , H), (x _s , y _s ) is the GPS coordinate of the transponder, and H is transponder depth;

The survey ship circles above the transponder, and records its GPS position p _k (x _k ,y _k ,0) while measuring the time delay;

According to the GPS position and the calibrated position of the transponder, the slant distance r _k =||p _k -p _s || is obtained.

Further, the step (2) includes:

In the PF method, N initial grazing angles are selected within (0,90°), and N horizontal distance samples R _k and time delay samples t _k (k=1,2,3,…,N) are calculated, Then get N slant distance samples

In the MF method, the time delay sample t _k and N slant range samples r _k are randomly selected from the actual sampled samples.

Further, the step (3) includes:

According to the equivalent gradient tracking method, there is a functional relationship between the time delay t and the horizontal distance R and the initial grazing angle θ ₀ t=f(θ ₀ ), R=g(θ ₀ ), and the slope distance r and the time delay t The functional relationship of: H is the transponder depth;

Express the continuous function in the form of power series, let h(t)=a ₀ +a ₁ t+a ₂ t ² +a ₃ t ³ +…+a _n t ⁿ , then the equivalent speed of sound is expressed as where n represents the order of the power series;

Let A _n = [a ₀ a ₁ ... a _n ] ^T , h _N = [r ₁ r ₂ ... r _N ] ^T , Then there is h _N = T _N×n A _n , and the coefficient matrix A _n is calculated by the least square method:

Further, the step (4) includes: for any time delay t _j within the maximum horizontal effective distance R _max , obtain the corresponding slant distance correction result r _j :

Beneficial effects: the present invention can compensate the distance measurement error caused by sound ray bending under the condition of both the acoustic profile data and the non-acoustic profile data, and effectively improve the accuracy of underwater acoustic distance measurement. According to the received measurement delay, the equivalent sound velocity is accurately estimated and the slope distance is calculated. The accuracy of the slope distance obtained by this method reaches the current advanced level, which is better than the result before compensation. With the support of accurate acoustic profile data, the slant distance error in the effective area (direct sound ray, no reflected sound ray) can be compensated to less than 0.1%, the calculation process is significantly simplified, the overall accuracy reaches the highest level at present, and the local accuracy exceeds the existing method. Without the support of acoustic section data, the invention improves the accuracy by 40% compared with the empirical sound velocity method. The method has the advantages of simplicity, stability, applicability and high accuracy.

Description of drawings

Fig. 1 is a flow chart of the sound ray correction method according to the present invention;

Fig. 2 is a geometrical schematic diagram of sound rays according to the present invention;

Fig. 3 is a schematic diagram of a sound velocity profile according to an embodiment;

Fig. 4 is a comparison diagram of different sound ray correction methods according to an embodiment;

Fig. 5 is a schematic diagram of a traveling path of a measuring ship according to an embodiment;

Fig. 6 is a comparison diagram of the slope distance error corrected according to the sampling path of Fig. 5;

Fig. 7 is a comparison diagram of the slant range error of the No. 1 transponder after verification and correction according to Fig. 5 .

Fig. 8 is a comparison diagram of the slant distance error of the No. 2 transponder corrected according to the verification of Fig. 5 .

Detailed ways

The technical solution of the present invention will be further described below in conjunction with the accompanying drawings. It should be understood that the embodiments provided below are only intended to disclose the present invention in detail and completely, and fully convey the technical concept of the present invention to those skilled in the art. The present invention can also be implemented in many different forms, and does not Limited to the embodiments described herein. The terms used in the exemplary embodiments shown in the drawings do not limit the present invention.

With reference to Fig. 1, a kind of sound ray correction method based on power series equivalent ranging model proposed by the present invention comprises the following steps:

Step 1. According to the presence or absence of sound velocity profile data, different methods are used to obtain the delay-slope distance mapping, including slope distance samples and time delay samples.

(1) In the case of sound velocity profile data, the PF method is used for correction.

The known variables when using the PF method include: the time delay t _j measured by the sounding head of the measuring ship (the subscript indicates different measurement results), the sound velocity profile c(z) of the water area, and the depth H of the transponder. For any The sound ray incident at the initial grazing angle θ ₀ can always uniquely determine its trajectory, including horizontal distance R, slant distance r and time delay t. The geometric relationship is shown in Figure 2.

According to the isogradient acoustic ray tracing method, the relationship is as follows:

In the formula, c _i =c( _zi ) represents the sound velocity value of each layer in the sound velocity profile; g _i =( _ci+1 -ci _{)/Δz i is} the sound velocity gradient of each layer; p=cosθ ₀ /c ₀ , is the snell coefficient; Δz _i is the layer height, and

When sinθ ₀ ＝0, the sound ray shoots out horizontally, and the horizontal distance R _max reached at this time is the maximum horizontal effective distance. Beyond this range, there will be no direct sound ray, and the sound ray will go through at least one reflection, time delay and oblique There is an obvious mismatch in the distance, so it is not considered. Only the case within the maximum horizontal effective distance R _max is considered. _Rmax is expressed as:

(2) In the absence of sound velocity profile data, the MF method is used for correction. By calibrating the position of the transponder, the time delay sample and the slant distance sample are obtained through actual measurement sampling and calculation.

When there is no sound velocity profile data, the maximum effective horizontal radius, slant distance samples and time delay samples cannot be obtained through modeling. Therefore, it is necessary to calibrate the position of the transponder, or find out that there is a pre-calibrated reference transponder in the water area, and set p _s (x _s ,y _s ,H). The calibration method of p _s adopts the long baseline calibration method, the survey ship circles above the transponder, and records the GPS position p _j (x _j ,y _j ,0) while measuring the time delay t _j . It can be seen from relevant theories that the horizontal position of the transponder calibrated by this method is unbiased, and the depth is provided by the depth gauge, so the calibration result is credible.

The survey ship travels in the area above the transponder, and the route covers the entire area as much as possible, so that the sample points can reflect the characteristics of this area as much as possible. During this process, the time delay sample t _k and the slope distance sample r _k are recorded, where The distance sample is obtained from the GPS position and the calibrated position of the transponder, r _k =||p _k -p _s || (the subscript k represents the sample selected in j). It should be noted that although the GPS is provided and the transponder can be calibrated, it does not mean that the two can be used to directly calculate the slope distance throughout the whole process. For example, the equivalent ranging model calculated based on the reference transponder can be used in the ranging of other unknown transponders; another example is that the robot carrying the transponder is still under water during calibration, and the equivalent ranging model is completed after the calibration is completed. It is possible to start underwater activities. At this time, the position has changed, and sound head ranging is required for positioning detection.

Step 2, select delay samples and slant distance samples.

In the PF method, N initial grazing angles are selected within (0,90°), which can be selected according to θ ₀ =arcsin(-0.0093k ² +0.2135k-0.1934), so that the horizontal distances obtained are evenly spaced. Calculate N horizontal distance samples R _k and delay samples t _k (k=1,2,3,...,N), and then get N slant distance samples

In the MF method, the time delay sample t _k and N slant range samples r _k are randomly selected from the actual sampled samples.

Step 3. According to the continuity correction relationship between time delay and slant distance, a power series equivalent ranging model is established.

When the sound velocity profile and depth are constant, the time delay t, the horizontal distance R, the slope distance r, and the initial grazing angle θ ₀ are all in one-to-one correspondence within R _max . It is not difficult to see from the equivalent gradient tracking method that t=f(θ ₀ ), R=g(θ ₀ ). So there are:

There is a functional correspondence between slant distance and time delay, and the function is continuous. However, the functional relationship is very complicated, and the specific form cannot be obtained. Considering that any continuous function can be approximated by a power series, let:

h(t)＝a ₀ +a ₁ t+a ₂ t ² +a ₃ t ³ +…+a _n t ⁿ

The equivalent speed of sound is then:

Where n represents the order of the power series, the larger n is, the higher the approximation of the function is, and in the hydroacoustic positioning model, n=3 or 4 usually meets the requirements. The low-order model has a weak fitting degree to the sample, changes slowly, is less affected by the error, and has high stability; the high-order model has a strong fitting degree to the sample, is greatly affected by the error, and is less affected by the change in the sample interval. Sensitive, estimates outside the sample interval are prone to distortion.

Let A _n = [a ₀ a ₁ ... a _n ] ^T , h _N = [r ₁ r ₂ ... r _N ] ^T , Then there are:

h _N ＝T _N×n A _n

The coefficient matrix A _n is calculated by the least square method:

Step 4. According to the power series function of the equivalent ranging model, the time delay is converted into a straight-line slant distance to realize sound ray correction.

For any time delay t _j within the horizontal distance R _max , the corresponding slant distance correction result r _j can be obtained:

The effect of PF and MF is verified through two specific examples below.

Example 1:

The simulation test is carried out on the environment with a water depth of 2800m. The sound velocity profile is shown in Figure 3, and the sample space is 30. The maximum effective horizontal distance under this experimental condition is 10580m. 6. The coefficients of the equivalent model are shown in Table 1:

Equivalent model coefficients in Table 1 Example 1

10 sound rays with different grazing angles within 0-90° were tested. During the test, the correction of sound rays by the present invention was compared with the other two methods, which were weighted average sound velocity correction and constant sound velocity tracking method correction. , the weighted average sound velocity calculated by the acoustic profile is 1450.9m/s, and the comparison results are shown in Figure 4. The error of the weighted average sound velocity method increases sharply with the distance. The PF method and the acoustic ray tracking method have obvious correction effects on ranging, and the ranging error does not increase when the distance is long. The maximum error of the 4th and 6th order does not exceed 1.7m. As a linear model, the first-order PF is also better than the weighted average sound velocity, which shows that its equivalent sound velocity is more accurate, and the constant coefficient plays a better compensation role. The second order and even higher orders show smaller error fluctuations, which indicates that a nonlinear model is necessary. The higher the order, the better the error control. The structure of line tracing, which shows that the PF method can achieve the same effect as sound ray tracing, and the order does not need to be very high. In terms of calculation, PF obviously has a better advantage.

Example 2:

This example is a no-sonic profile test carried out on Qiandao Lake. The position calibration of the underwater transponder is known, the water depth is 15.75m, and the estimated sound velocity is 1493.82m/s. The measuring ship travels within the range of 100m×100m on the water surface, the track is shown in Figure 5, and the signal propagation delay and GPS position are recorded during the driving process.

The data collected by the grid trajectory is used as a sample to fit the equivalent ranging model. The fitting results of each order are shown in Table 2, and χ is the fitting residual. The residual results are shown in Figure 6.

Fitting coefficients of each order in table 2 embodiment 2

The No. 2 transponder is released at the same place, and the data of the two transponders are collected simultaneously on the dot trajectory, and the fitted equivalent ranging model is substituted for comparison. The results are shown in Figure 7 and Figure 8. Under the effect of MF, the overall error is reduced by about 0.4m compared with the constant sound velocity ranging method. When the order is higher than 2, the effect of MF is better than that of the 1st order. Among them, the No. 1 transponder is at the 62nd data position, and the No. 2 transponder has a large deviation at the 40th data position. This is because the position of this position is beyond the coverage of the sample, which shows that the high-order model has a large impact on the sample. Unexpected predictive control is poor. For this case, it is recommended to use a low-order model. In this experiment, the 4th-order MF is the best.

The experimental results show that the equivalent ranging model fitted by the samples is suitable for sound velocity correction at different positions in the region. It fully proves that the present invention can still successfully complete the sound velocity correction under the condition of no sound velocity profile.

In summary, the present invention solves the practical problem that the sound ray bends in underwater acoustic detection and positioning and cannot accurately correct the slant distance according to the measurement time delay. The method of sound ray tracking simulation or actual measurement sampling is used to establish a power series in advance The equivalent ranging model obtains the continuous correction relationship between time delay and slant distance, which provides convenience for correcting the sound velocity in subsequent use. Compared with the traditional method, the invention has simple steps, easy calculation, higher precision, less conditional restrictions, is suitable for use in various occasions, and is highly efficient and reliable.

Claims (8)

1. a kind of sound ray modification method based on the equivalent ranging model of power series, which is characterized in that the method includes following steps It is rapid:

(1) according to whether there is or not Sound speed profile data, time delay-oblique distance is sought by different methods and is mapped, including oblique distance sample and when Prolong sample, wherein, by establishing underwater sound ray channel model, it is effective to calculate maximum horizontal in the case where there is velocity of sound cross-sectional data Distance, abbreviation PF method；In the case where no Sound speed profile data, by demarcating transponder location, actual measurement sampling and meter are carried out Calculation obtains time delay sample and oblique distance sample, abbreviation MF method；

(2) time delay sample and oblique distance sample are chosen；

(3) according to the continuous modification relationship of time delay and oblique distance, the equivalent ranging model of power series is established；

(4) time delay measured is converted into oblique distance using equivalent ranging model Exponential series function, realizes sound ray amendment.

2. the sound ray modification method according to claim 1 based on the equivalent ranging model of power series, which is characterized in that described In step (1) in the case where there is velocity of sound cross-sectional data, PF method is executed, by establishing underwater sound ray channel model, is calculated most Big horizontal effective distance includes:

The time delay t that known surveying vessel transmitting-receiving sound head measures_j, surveying vessel GPS location p_j(x_j,y_j, 0), the Sound speed profile c in the waters (z), the depth H of transponder, for one with initial glancing angle θ₀The sound ray of injection establishes mould according to constant gradient Ray-Tracing Method Type is as follows:

R is sound ray horizontal distance, and t is time delay；c_i=c (z_i) indicate each layer of Sound speed profile acoustic velocity value；g_i=(c_i+1-c_i)/Δ z_i, it is the sound velocity gradient of each layer, Δ z_iIt is layer height, and hasP=cos θ₀/c₀, it is snell coefficient；M indicates sample Number；

Work as sin θ₀When=0, sound ray level is projected, and the horizontal distance reached at this time is maximum horizontal effective distance R_max, indicate are as follows:

3. the sound ray modification method according to claim 1 based on the equivalent ranging model of power series, which is characterized in that described In step (1) in the case where no Sound speed profile data, MF method is executed, by demarcating transponder location, actual measurement is carried out and adopts Sample and time delay sample is calculated and oblique distance sample includes:

It obtains calibrated benchmark transponder location or transponder location is demarcated using Long baselines scaling method, be denoted as p_s(x_s,y_s, H), (x_s,y_s) it is transponder GPS coordinate, H is transponder depth；

Surveying vessel detours above transponder, records its GPS location p while measuring time delay_k(x_k,y_k,0)；

Oblique distance r is obtained according to GPS location and transponder calibration position_k=| | p_k-p_s||。

4. the sound ray modification method according to claim 1 based on the equivalent ranging model of power series, which is characterized in that described Step (2) includes:

In PF method, N number of initial glancing angle is chosen in (0,90 °), calculates N number of horizontal distance sample R_kWith time delay sample t_k(k=1,2,3 ..., N), and then obtain N number of oblique distance sample

In MF method, time delay sample t is randomly selected from the sample of actual measurement sampling_kWith N number of oblique distance sample r_k。

5. the sound ray modification method according to claim 4 based on the equivalent ranging model of power series, which is characterized in that described According to θ in PF method₀=arcsin (- 0.0093k²+ 0.2135k-0.1934) choose N number of initial glancing angle.

6. the sound ray modification method according to claim 1 based on the equivalent ranging model of power series, which is characterized in that described Step (3) includes:

It is learnt according to equivalent gradient tracing, time delay t and horizontal distance R and initial glancing angle θ₀Existence function relationship t=f (θ₀), R=g (θ₀), obtain the functional relation of oblique distance r and time delay t:H is transponder depth；

The continuous function is indicated with the form of power series, enables h (t)=a₀+a₁t+a₂t²+a₃t³+…+a_ntⁿ, then equivalent velocity of sound table It is shown asWherein n indicates the order of power series；

Enable A_n=[a₀ a₁ … a_n]^T, h_N=[r₁ r₂ … r_N]^T,Then there is h_N=T_{N× n}A_n, coefficient matrices A_nIt is calculated by least square method:

7. the sound ray modification method according to claim 6 based on the equivalent ranging model of power series, which is characterized in that described The order n value range 2~4 of power series.

8. the sound ray modification method according to claim 6 based on the equivalent velocity of sound ranging model of power series, which is characterized in that The step (4) includes: for maximum horizontal effective distance R_maxInterior any time delay t_j, obtain corresponding oblique distance correction result r_j: