A method for calibrating the position of seabed acoustic beacons using Kalman filtering

Abstract

The present invention discloses a method for calibrating the position of a submarine acoustic beacon using a Kalman filter method, which belongs to the technical field of position calibration and is used for calibrating the position of a submarine acoustic beacon, including establishing a position motion equation, calculating the distance between the submarine acoustic beacon and a sea surface buoy, predicting the position and variance, substituting the predicted value into the calculation formula of the distance between the submarine acoustic beacon and the sea surface buoy, predicting the distance, and finally correcting the predicted distance value. The present invention fuses the submarine acoustic beacon motion information with the ranging information by modeling the motion characteristics of the submarine acoustic beacon; when the ranging point is relatively close to the submarine acoustic beacon and the water depth is relatively deep, a good calibration accuracy can still be obtained; in the ranging and positioning of the working mother ship around the beacon, a high positioning accuracy can be obtained without sailing a full circle.

Description

Technical Field

[0001] The invention discloses a method for calibrating a seabed acoustic beacon position by adopting a Kalman filtering method, and belongs to the technical field of position calibration. Background Art

[0002] The hydroacoustic positioning method has been widely used in marine scientific research and underwater engineering development activities. Its basic principle is similar to that of satellite positioning. Multiple hydroacoustic beacons (generally at least 3-4) are deployed on the seabed to construct a positioning array. When the vehicle enters the array range, the position of the vehicle is calculated by measuring the distance to the hydroacoustic beacon. In hydroacoustic positioning, the position of the acoustic beacon is used as the reference for positioning calculation, and its accuracy is particularly critical to positioning accuracy. In practical applications, since acoustic beacons are often deployed on the deeper seabed, their positions are quite different from their positions on the sea surface, so calibration is required. The commonly used calibration method is that the mother ship sails around the beacon (approximate) position on the water surface, and measures the distance to the seabed acoustic beacon based on its own position (obtained by satellite positioning) on ​​the track. After obtaining the distance information at more than 3 track points, the hydroacoustic positioning method can be used to calculate the position of the seabed acoustic beacon. From the analysis of the ranging and positioning solution formula, it can be seen that only when the ranging base points are distributed around the seabed acoustic beacon (rather than on one side) can more accurate calibration information be obtained. Therefore, in practice, it is generally required that the mother ship travel more than half a circle before the position of the seabed acoustic beacon can be determined more accurately.

[0003] In response to the problems of the prior art, the buoy is tied to the submarine acoustic beacon by a cable, which can float on the water surface or be pulled underwater. The buoy is equipped with a satellite positioning antenna and receiver, and a hydroacoustic communication transducer. The satellite positioning information is obtained through the buoy, and the position information is sent to the submerged buoy through the hydroacoustic communication transducer to complete the position calibration. This method avoids the mother ship from sailing around the beacon for a long time, and has certain application advantages. However, when the water depth in the sea area is deep, the cable is long, and under the action of the ocean current, the buoy part deviates far from the position of the submarine acoustic beacon, resulting in a large position error. At the same time, under the action of the ocean current, the buoy generally floats on the submarine acoustic beacon, but cannot float around it. The configuration is poor, and the calculation of the submerged buoy position by multiple ranging methods will also result in large errors. Summary of the invention

[0004] The object of the present invention is to provide a method for calibrating the position of a seabed acoustic beacon using a Kalman filter method, so as to solve the problem of poor accuracy in the calibration of the position of a seabed acoustic beacon in the prior art.

[0005] The method for calibrating the position of a seabed acoustic beacon using the Kalman filter method includes:

[0006] The position motion equation is established to calculate the distance between the submarine acoustic beacon and the sea surface buoy, and the position and variance at time k+1 are predicted. The predicted value of the position at time k+1 is substituted into the calculation formula of the distance between the submarine acoustic beacon and the sea surface buoy, the distance is predicted, and finally the predicted distance value is corrected.

[0007] Establishing the position motion equation includes assuming that the horizontal position of the seabed acoustic beacon at time k is ( ), the position motion equation is established as:

[0008] ;

[0009] In the formula, is Gaussian white noise. Gaussian white noise means that each time the distance is measured, the position of the buoy changes randomly under the interference, with a mean of 0 and a variance of , the variance matrix is .

[0010] Calculating the distance between the submarine acoustic beacon and the sea surface buoy includes: assuming the position of the sea surface buoy at time k is ( ), the distance between the seafloor acoustic beacon and the sea surface buoy at time k for:

[0011] ;

[0012] In the formula, is the depth of the seafloor acoustic beacon, is the ranging error.

[0013] The prediction of the position at time k+1 includes: assuming that the estimated position of the seafloor acoustic beacon at time k is ( ), the variance estimate is , predict the position at time k+1:

[0014] ;

[0015] In the formula, and is the predicted value of the position at time k+1.

[0016] Predicting the variance at time k+1 includes predicting the variance at time k+1:

[0017] ;

[0018] In the formula, is the predicted value of the variance at time k+1.

[0019] Predicting the distance includes measuring the distance between the sea surface buoy and the seabed acoustic beacon. Assume that the buoy position at time k+1 obtained from the satellite positioning information is ( , ), substitute the predicted value of the k+1 time position into Calculation formula to predict the position at time k+1:

[0020] ;

[0021] In the formula, is the estimated distance between the bottom acoustic beacon and the surface buoy at time k+1.

[0022] Correction of the distance includes: assuming that the actual distance measured at time k+1 is , correct the distance prediction value:

[0023] = ;

[0024] In the formula, is the gain matrix at time k+1;

[0025] The variance estimate at time k+1 is:

[0026] ;

[0027] in, is the second-order identity matrix;

[0028] The gain matrix at time k+1 is:

[0029] ;

[0030] In the formula, is the Jacobian matrix of the distance measurement equation at time k+1.

[0031] The Jacobian matrix is:

[0032] .

[0033] Compared with the prior art, the present invention has the following beneficial effects: the present invention overcomes the disadvantage of poor buoy position configuration when calibrating the position of the seabed acoustic beacon, and fuses its motion information with the ranging information by modeling the motion characteristics of the seabed acoustic beacon; when the ranging point is horizontally close to the seabed acoustic beacon and the water depth is relatively deep, good calibration accuracy can still be achieved; in the ranging and positioning of the working mother ship around the beacon, a high positioning accuracy can be obtained without sailing a full circle. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is a simulation diagram of the seabed acoustic beacon position calibration;

[0035] Figure 2 It is the curve diagram of the position error variation of the seabed acoustic beacon;

[0036] Figure 3 This is a simulation diagram of the calculation of the position of the seabed acoustic beacon using the recursive least squares method;

[0037] Figure 4 It is the curve diagram of the calculation error of the seabed acoustic beacon position;

[0038] Figure 5 This is the curve of the error in calculating the position of the seabed acoustic beacon after 120 ranging times;

[0039] Figure 6 This is a simulation diagram of the calculation of the position of the seabed acoustic beacon under the circumnavigation and ranging of the working mother ship;

[0040] Figure 7 It is the curve diagram of the calculation error of the seabed acoustic beacon position;

[0041] Figure 8 This is the curve of the error in calculating the position of the seabed acoustic beacon after 150 ranging times; DETAILED DESCRIPTION

[0042] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention is described clearly and completely below. Obviously, the described embodiments are part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0043] The method for calibrating the position of a seabed acoustic beacon using the Kalman filter method includes:

[0044] The position motion equation is established to calculate the distance between the submarine acoustic beacon and the sea surface buoy, and the position and variance at time k+1 are predicted. The predicted value of the position at time k+1 is substituted into the calculation formula of the distance between the submarine acoustic beacon and the sea surface buoy, the distance is predicted, and finally the predicted distance value is corrected.

[0045] Establishing the position motion equation includes assuming that the horizontal position of the seabed acoustic beacon at time k is ( ), the position motion equation is established as:

[0046] ;

[0047] In the formula, is Gaussian white noise. Gaussian white noise means that each time the distance is measured, the position of the buoy changes randomly under the interference, with a mean of 0 and a variance of , the variance matrix is .

[0048] Calculating the distance between the submarine acoustic beacon and the sea surface buoy includes: assuming the position of the sea surface buoy at time k is ( ), the distance between the seafloor acoustic beacon and the sea surface buoy at time k for:

[0049] ;

[0050] In the formula, is the depth of the seafloor acoustic beacon, is the ranging error.

[0051] The prediction of the position at time k+1 includes: assuming that the estimated position of the seafloor acoustic beacon at time k is ( ), the variance estimate is , predict the position at time k+1:

[0052] ;

[0053] In the formula, and is the predicted value of the position at time k+1.

[0054] Predicting the variance at time k+1 includes predicting the variance at time k+1:

[0055] ;

[0056] In the formula, is the predicted value of the variance at time k+1.

[0057] Predicting the distance includes measuring the distance between the sea surface buoy and the seabed acoustic beacon. Assume that the buoy position at time k+1 obtained from the satellite positioning information is ( , ), substitute the predicted value of the k+1 time position into Calculation formula to predict the position at time k+1:

[0058] ;

[0059] In the formula, is the estimated distance between the bottom acoustic beacon and the surface buoy at time k+1.

[0060] Correction of the distance includes: assuming that the actual distance measured at time k+1 is , correct the distance prediction value:

[0061] = ;

[0062] In the formula, is the gain matrix at time k+1;

[0063] The variance estimate at time k+1 is:

[0064] ;

[0065] in, is the second-order identity matrix;

[0066] The gain matrix at time k+1 is:

[0067] ;

[0068] In the formula, is the Jacobian matrix of the distance measurement equation at time k+1.

[0069] The Jacobian matrix is:

[0070] .

[0071] The present invention provides a method for calibrating the position of a submarine acoustic beacon using a Kalman filter method for a hydroacoustic positioning beacon with a "surface buoy-submarine acoustic beacon" structure. By establishing a model of random changes in the position of the submarine acoustic beacon and using multiple ranging information from the surface buoy, the Kalman filter is used to estimate the position of the submarine buoy. Simulation and experiments show that this method can obtain relatively accurate submarine acoustic beacon position information and has advantages in application.

[0072] At present, the acoustic beacons used in hydroacoustic positioning (long baseline) are usually deployed by a working mother ship. After the beacon falls to the bottom, the working mother ship sails around the deployment point on the sea surface. During the voyage, the working mother ship uses the acoustic beacon to transmit a question and answer signal, and obtains the distance information by calculating the response signal delay of the seabed acoustic beacon. In this way, the accurate position of multiple points on the track is obtained through satellite positioning, and then these points are used as a reference to obtain the distance information from the seabed acoustic beacon, and then the position of the seabed acoustic beacon can be calculated by the hydroacoustic positioning method.

[0073] Since the calibration navigation area is small, a rectangular coordinate system can be established. Assume that 4 points are taken on the track, and their positions are ( , , ), .in is the altitude, which can be considered equal to zero for the working mother ship. The three-dimensional position coordinates of the seabed acoustic beacon are ( ),in is its depth. The distance of the seabed acoustic beacon measured at each point is , then the distance measurement equation can be established.

[0074] ;

[0075] There are many ways to solve this system of equations. Here is a linearization method. First, define the expression:

[0076] , , ;

[0077] It can also be defined Then define , , Three parameters:

[0078] ;

[0079] ;

[0080] ;

[0081] Then, by subtracting the equations in the system of equations one by one, a linear equation can be established:

[0082] ;

[0083] in:

[0084] , , ;

[0085] The solution to a general system of linear equations is calculated using the following formula:

[0086] ;

[0087] The problem with this method is that when the working mother ship sails for a short time, the track points are distributed on a shorter track, and the ranging equation is highly correlated, which makes the probability of matrix A being singular greater. When there is an error in the measurement, a large positioning error will occur. Therefore, when using the working mother ship to calibrate the position, it takes a long time to sail and circle at least half a circle, usually 3 / 4 to 1 circle in practice.

[0088] A hydroacoustic positioning beacon with a "surface buoy-seabed acoustic beacon" structure, wherein the seabed acoustic beacon part is a hydroacoustic positioning transducer, which is anchored to the seabed. The buoy part includes a satellite positioning module, a hydroacoustic signal transducer and a computing control board, and the buoy part is tied to the seabed acoustic beacon by a cable. The buoy can be pulled down by the cable to sink into the sea or released to float to the surface.

[0089] This type of acoustic beacon has the characteristics of high degree of automation and position recalibration function. After deployment, the transponder transducer is anchored to the seabed, and the buoy part is released and floats to the surface to receive satellite positioning signals.

[0090] There are two methods for calibrating the position of the submarine acoustic beacon. One is to assume that the horizontal position of the buoy is consistent with the submarine acoustic beacon, and the positioning signal of the buoy can be used directly as the position of the submarine acoustic beacon. The second is to consider that the buoy cable is long and the buoy is offset under the action of the ocean current. For a depth of thousands of meters on the seabed, its position offset may reach hundreds of meters, and its position information can no longer be used as the position of the submerged buoy. Since the buoy floats on the sea surface, its position is not fixed, so it can be calculated using multi-point ranging information. At this time, the method is similar to the working mother ship's circumnavigation ranging positioning.

[0091] These two methods do not require a mother ship to sail around the beacon, which greatly simplifies the deployment process when applied, and has a certain degree of concealment and convenience. At the same time, after a period of application, the submarine acoustic beacon may be offset due to the influence of the ocean current, affecting the positioning error. At this time, the buoy can be floated and calibrated again, avoiding the use of a mother ship to sail to this sea area. These advantages make this system have a wider application prospect.

[0092] However, when this system is calibrated, the buoy floats on the sea surface. Although its position changes, it is likely to deviate to one direction under the action of waves during the calibration period. In this way, when measuring distance, even if multiple points are selected for ranging, it is inevitable that the measurement positions are all on one side of the submarine acoustic beacon position, resulting in a poor configuration of positioning calculation. As a result, when there is a measurement error, the position calibration error becomes larger.

[0093] In the previous acoustic beacon position calculation method, the position of the submarine acoustic beacon is considered to be completely unknown, and the distance measurement information is used to calculate it. In practice, it can be considered that the position of the submarine acoustic beacon is not far from its deployment point, or that it is close to the sea surface position of the sea surface buoy. On the other hand, it can be considered that during the ranging process, the anchor position does not change, and the submarine acoustic beacon is constrained by the anchor rope (usually 1-2 meters long) and randomly swings near the anchor position under interference conditions. Integrating these two pieces of information into the ranging and positioning calculation process can greatly improve its positioning accuracy in the presence of ranging error interference.

[0094] After being deployed, the acoustic beacon is fixed to the seabed by an anchor, and the depth is known. Assuming that the submerged buoy part swings within 1 meter of the anchor position, its horizontal position can be considered as a random value. Gaussian white noise indicates that the position of the submerged buoy changes randomly under the interference every time the distance is measured. The position of the sea surface buoy is affected by the cable constraint and the action of the waves. Its position changes within a certain range. At each distance measurement, the position can be accurately given by satellite positioning. The estimation of the position and variance of the seabed acoustic beacon is completed. It can be seen that since the movement of the seabed acoustic beacon is modeled, when calculating the position using the ranging information, this information is used through the ranging equation and the Jacobian matrix, thereby realizing full use of the prior information, and the position of the seabed acoustic beacon can be calculated more efficiently under unfavorable conditions.

[0095] Assuming that the seabed depth of the acoustic beacon deployment area is 1000 meters, a rectangular coordinate system is established. In the coordinate system, the anchor position of the seabed acoustic beacon is (20, 20), the unit is meter (the same below), and the variance of its random position change is 1 meter. 2 Affected by the ocean current, the buoy is not located directly above the submarine acoustic beacon, but floats in an area in a certain direction. Assume that its floating range is within a circular arc ring centered at (-100, 100), with a horizontal distance range of plus or minus 10 meters from the buoy and an azimuth range of plus or minus 30 degrees. The ranging error is 0 meters in mean and 5 meters in variance. 2 The white noise of the seabed acoustic beacon position calibration simulation is as follows Figure 1 As shown in the figure, the error curve of the submarine acoustic beacon position is as follows: Figure 2 shown.

[0096] As a comparison, it is still assumed that the buoy floats within this range. The recursive least squares method is used to calculate the position of the submerged buoy using the ranging information at different points. The simulation of the calculation of the submarine acoustic beacon position under the recursive least squares method is as follows: Figure 3 As shown in the figure, the error curve of the calculation of the seabed acoustic beacon position is as follows: Figure 4 As shown in the figure, the error curve of the calculation of the position of the seabed acoustic beacon after 120 ranging times is as follows: Figure 5 As shown in the figure, for the currently commonly used method of measuring the distance and positioning by the working mother ship around the buoy, it is assumed that the working mother ship is circling on a circular track about 150 meters away from the buoy, continuously measuring the distance and positioning, and using the recursive least squares method to calculate the position of the submarine acoustic beacon under the circumferential measurement of the working mother ship, as shown in the figure. Figure 6 As shown in the figure, the error curve of the calculation of the seabed acoustic beacon position is as follows: Figure 7 As shown in the figure, the error curve of the calculation of the position of the seabed acoustic beacon after 150 ranging times is as follows: Figure 8 shown.

[0097] Depend on Figure 1 It can be seen that although there is a large deviation between the estimated position of the submarine acoustic beacon and the actual position at the beginning, as the ranging progresses, the motion characteristic information of the random swing of the submerged buoy floating near the anchor position is integrated with the ranging information, and the Kalman filter is used to continuously reduce the position estimation error. After more than 30 ranging and positioning, the error can reach a level less than 10 meters. Figure 2 If the traditional multi-marker ranging geometric solution method is still used, since the buoy is always biased to the side of the seabed acoustic beacon, the configuration is poor for hydroacoustic positioning. Therefore, when using the first few ranging information for positioning, the error is very large, such as Figure 3 As the ranging progresses, the buoy positions are distributed more and more, and the range is expanded (equivalent to the increase of acoustic positioning beacons), and the positioning error is continuously reduced, but the convergence speed is still slow. After 120 ranging times, the positioning error reaches a level within 50 meters, as shown in Figure 4and Figure 5 As shown, it is difficult to improve further. For the method of using the mother ship to circumvent the distance measurement, since the buoy is tied to the seabed acoustic beacon by a cable, the horizontal position distance is not far, and when the depth is large, the horizontal position calculation error caused by the distance measurement error is amplified, and its positioning accuracy still cannot reach a small level, such as Figure 6 , Figure 7 and Figure 8 As shown in the figure. Although the method of circling one circle to measure the distance and locate is adopted, the position configuration of the hydroacoustic positioning beacon is continuously improved as the mother ship sails, so the positioning error is rapidly reduced, but it still only reaches about 40 meters after circling one circle, and it is difficult to reduce it further. In fact, in engineering applications, in order to obtain a higher position calculation accuracy, the radius of the mother ship's circling is required to exceed the water depth, generally Depth (Depth is the water depth) is better.

[0098] The Kalman filtering method using ranging information effectively utilizes the motion information of the buoy and the ranging information, so that the position of the seabed acoustic beacon can still be calibrated with high accuracy under unfavorable conditions.

[0099] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, a person skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some or all of the technical features may be replaced by equivalents, and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for calibrating the position of an underwater acoustic beacon using a Kalman filter method, characterized in that: include: Establish the position motion equation, calculate the distance between the submarine acoustic beacon and the sea surface buoy, and predict the position and variance at time k+1. Substitute the predicted value of the position at time k+1 into the calculation formula of the distance between the submarine acoustic beacon and the sea surface buoy, predict the distance, and finally correct the predicted distance value; Establishing the position motion equation includes assuming that the horizontal position of the seafloor acoustic beacon at time k is (x k ,y k ), the position motion equation is established as: In the formula, [ω xk ω yk ] T is Gaussian white noise. Gaussian white noise means that each time the distance is measured, the position of the buoy changes randomly under the interference, with a mean of 0 and a variance of σ k , the variance matrix is ​​Q k ; Calculating the distance between the submarine acoustic beacon and the sea surface buoy includes: assuming that the position of the sea surface buoy at time k is (x bk ,y bk ), the distance R between the seafloor acoustic beacon and the sea surface buoy at time k k for: Where h is the depth of the seafloor acoustic beacon, v k is the ranging error; The prediction of the position at time k+1 includes: assuming that the estimated position of the seafloor acoustic beacon at time k is The variance estimate is P k , predict the position at time k+1: In the formula, and is the predicted value of the position at time k+1; Predicting the variance at time k+1 includes predicting the variance at time k+1: In the formula, is the predicted value of the variance at time k+1; Predicting the distance includes measuring the distance between the sea surface buoy and the seabed acoustic beacon. Suppose the buoy position at time k+1 obtained from the satellite positioning information is (x bk+1 ,y bk+1 ), substitute the predicted value of the k+1 time position into R k Calculation formula to predict the position at time k+1: In the formula, is the estimated distance between the bottom acoustic beacon and the surface buoy at time k+1; Correction of the distance includes assuming that the actual distance measured at time k+1 is R k+1 , correct the distance prediction value: In the formula, K k+1 is the gain matrix at time k+1; The variance estimate at time k+1 is: Where I is the second-order identity matrix; The gain matrix at time k+1 is: In the formula, H k+1 is the Jacobian matrix of the distance measurement equation at time k+1; The Jacobian matrix is:

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