Method and apparatus for determining ultra-short baseline transponder position and coordinate offset errors

Abstract

The application provides a method and device for determining position and coordinate offset error of an ultra-short baseline transponder, and the method comprises the following steps: establishing a navigation coordinate system, a carrier coordinate system and an acoustic array coordinate system based on an ultra-short baseline underwater acoustic positioning system; arranging a transponder in water; measuring slant range information of a distance from the transponder to a center of an acoustic array of an ultra-short baseline device, a ship body position measured by a GPS system and attitude data measured by an inertial navigation system; and determining the position of the transponder according to a positioning algorithm; performing Taylor expansion on an expression of the slant range information, converting the expression into a linear expression and establishing an error equation in an incremental form; and obtaining the position of the transponder and coordinate axis offset error by using a least square method for iterative solution, and verifying the offset error through simulation.

Description

Technical Field

[0001] This invention relates to the field of underwater navigation and positioning, and specifically to a method and apparatus for determining the position and coordinate offset error of an ultra-short baseline transponder. Background Technology

[0002] The USBL (Ultra-Short Baseline) positioning system has a shorter baseline length, and the acoustic array can be precisely installed into a planar measurement array. The overall product size is small, making installation and application convenient. With the rapid development of its positioning and filtering technologies, its positioning accuracy has been significantly improved. In underwater navigation and positioning, it is often combined with SINS (Straight-in Inertial Navigation System) for navigation.

[0003] In the use of SINS / USBL, the installation error of the acoustic transceiver array is one of the significant error sources in the SINS / USBL positioning system. USBL transceiver array installation errors can be divided into coordinate offset errors and rotation errors. The traditional method for using SINS / USBL is to first calibrate the underwater transponder, and then calibrate the coordinate offset and rotation errors. In many cases, the coordinate offset error is ignored. This method is cumbersome, and the calculation error for the coordinate offset error can be relatively large. Summary of the Invention

[0004] In view of this, the present invention provides a method for determining the position and coordinate offset error of an ultra-short baseline transponder, comprising:

[0005] Step 1: Establish the navigation coordinate system, the carrier coordinate system, and the acoustic array coordinate system based on the ultra-short baseline underwater acoustic positioning system;

[0006] Step 2: The ultra-short baseline underwater acoustic positioning system includes a GPS system, an inertial navigation system for attitude measurement, and an ultra-short baseline system; a transponder is installed in the water, and the ultra-short baseline system is used to measure the slant range information of the distance from the transponder to the center of the acoustic array of the ultra-short baseline device, the hull position measured by the GPS system, and the attitude data measured by the inertial navigation system, and the position of the transponder is determined according to the positioning algorithm;

[0007] Step 3: Perform Taylor expansion on the expression of the slant distance information, convert it into a linear expression, and establish an incremental error equation; use the least squares method to iteratively solve the equation to obtain the transponder position and coordinate axis offset error.

[0008] Step 4: Use the trajectory generator to generate the corresponding inertial navigation attitude angles, hull position data, slant range information, and Gaussian white noise for simulation to verify the offset error.

[0009] Specifically, step 1 includes: using the geometric center of the inertial device as the origin when establishing the coordinate system; firstly, selecting the geographic coordinate system as the navigation coordinate system, with the origin located at the geometric center of the inertial device, and the three axes pointing to the northeast direction of the location; secondly, the carrier coordinate system, with the origin consistent with the navigation coordinate system, and the three axes pointing to the horizontal, vertical, and longitudinal directions of the carrier; and then the acoustic array coordinate system, with the geometric center of the acoustic array as the origin, and the three axes pointing to the horizontal, vertical, and longitudinal directions of the ultra-short baseline device.

[0010] Specifically, in step 2, the acoustic transducer in the ultra-short baseline system sends an acoustic signal to the transponder. After receiving the signal from the transducer, the transponder sends back a positioning signal, which is received by a hydrophone in the acoustic array. The acoustic transducer is installed at the geometric center of the acoustic array. The transponder is positioned based on the angle between the received signal and the array coordinate system and the slant range information. The positioning algorithm is expressed by the following formula:

[0011]

[0012] in, The location of the transponder. The location is given by the GPS navigation coordinate system. The rotation matrix from the vehicle coordinate system to the navigation coordinate system is given by the inertial navigation system. This is the rotation matrix between the acoustic array coordinate system and the carrier coordinate system, which is the rotation matrix corresponding to the installation deviation angle; ΔX is the slant range from the transponder to the ultra-short baseline. b This represents the offset error of the coordinate axes.

[0013] Specifically, step 3 includes: the position of the transponder. Coordinates are and coordinate axis offset error ΔX b Coordinates are (Δx) b ,Δy b ,Δz b The slant distance information is represented by ρ, and its expression is:

[0014] Obtained through the strapdown inertial navigation system (SINS) Represented in matrix form

[0015] Will Substituting the matrix representation into the expression for the slant distance information ρ,

[0016] make

[0017]

[0018]

[0019]

[0020] ρ is expressed as:

[0021] By performing a Taylor expansion on ρ, let... The initial values ​​of the estimator can be obtained

[0022]

[0023] The Taylor expansion result is converted into incremental form, and the incremental form of the initial value S0 of the estimate is obtained by least squares method. After iteration, the position of the transponder is obtained. and coordinate axis offset error ΔX b .

[0024] Specifically, step 4 includes: setting the position and coordinate axis offset errors of the transponder respectively, performing circular motion with the transponder as the center; using a trajectory generator to generate the true data of the corresponding inertial navigation attitude angle, hull position data, and slant range information, and finally adding Gaussian white noise for simulation to verify the offset error.

[0025] The present invention also proposes a device for determining the position and coordinate offset error of an ultra-short baseline transponder, comprising:

[0026] The coordinate system setting module is used to establish the navigation coordinate system, the carrier coordinate system, and the acoustic array coordinate system based on the ultra-short baseline underwater acoustic positioning system.

[0027] A transponder location module is established, wherein a transponder is placed in the water. The ultra-short baseline underwater acoustic positioning system includes a GPS system, an inertial navigation system for attitude measurement, and an ultra-short baseline system. The transponder location module is used to measure the slant range information of the distance from the transponder to the center of the acoustic array of the ultra-short baseline device using the ultra-short baseline system, the hull position measured by the GPS system, and the attitude data measured by the inertial navigation system, and to determine the position of the transponder according to the positioning algorithm.

[0028] The transponder position and coordinate axis offset error calculation module is used to perform Taylor expansion on the expression of the slant distance information, convert it into a linear expression, and establish an incremental error equation; and use the least squares method to iteratively solve the transponder position and coordinate axis offset error.

[0029] The offset error verification module is used to generate ground truth data of inertial navigation attitude angles, hull position data, slant range information, and Gaussian white noise using the trajectory generator to perform simulation and verify the offset error.

[0030] Specifically, the coordinate system setting module includes: using the geometric center of the inertial device as the origin when establishing the coordinate system; firstly, selecting a geographic coordinate system as the navigation coordinate system, with the origin located at the geometric center of the inertial device, and the three axes pointing to the northeast direction of the location; secondly, a carrier coordinate system, with the origin consistent with the navigation coordinate system, and the three axes pointing to the horizontal, vertical, and longitudinal directions of the carrier; and then an acoustic array coordinate system, with the geometric center of the acoustic array as the origin, and the three axes pointing to the horizontal, vertical, and longitudinal directions of the ultra-short baseline device.

[0031] Specifically, in the ultra-short baseline system, the acoustic transducer sends an acoustic signal to the transponder. After receiving the signal from the transducer, the transponder sends back a positioning signal, which is received by a hydrophone in the acoustic array. The acoustic transducer is mounted at the geometric center of the acoustic array. The transponder is positioned based on the angle between the received signal and the array coordinate system and the slant range information. The positioning algorithm is expressed by the following formula:

[0032]

[0033] in, The location of the transponder. The location is given by the GPS navigation coordinate system. The rotation matrix from the vehicle coordinate system to the navigation coordinate system is given by the inertial navigation system. This is the rotation matrix between the acoustic array coordinate system and the carrier coordinate system, which is the rotation matrix corresponding to the installation deviation angle; ΔX is the slant range from the transponder to the ultra-short baseline. b This represents the offset error of the coordinate axes.

[0034] Specifically, the transponder position and coordinate axis error calculation module includes: the position of the transponder Coordinates are and coordinate axis offset error ΔX b Coordinates are (Δx) b ,Δy b ,Δz b The slant distance information is represented by ρ, and its expression is:

[0035] Obtained through the strapdown inertial navigation system (SINS) Represented in matrix form

[0036] Will Substituting the matrix representation into the expression for the slant distance information ρ, let...

[0037]

[0038]

[0039]

[0040] ρ is expressed as:

[0041] By performing a Taylor expansion on ρ, let... The initial values ​​of the estimator can be obtained

[0042]

[0043] The Taylor expansion result is converted into incremental form, and the incremental form of the initial value S0 of the estimate is obtained by least squares method. After iteration, the position of the transponder is obtained. and coordinate axis offset error ΔX b .

[0044] Specifically, the offset error verification module includes: setting the position and coordinate axis offset errors of the transponder respectively, performing circular motion with the transponder as the center; using a trajectory generator to generate the true data of the corresponding inertial navigation attitude angle, hull position data, and slant range information, and finally adding Gaussian white noise for simulation to verify the offset error.

[0045] Beneficial effects:

[0046] 1. Achieve one-step calculation of target position and coordinate offset error, avoiding multi-step iterative calculation and simplifying the operation process;

[0047] 2. The expression is linearized based on Taylor expansion, avoiding direct solution of nonlinear equations and reducing computational difficulty;

[0048] 3. By using the least squares iterative algorithm, the solution accuracy is improved and high-precision target positioning results are obtained. The verification results show that the positioning accuracy can reach the centimeter level, which meets the accuracy requirements of the ultra-short baseline system.

[0049] 4. Enables unattended system autonomous calibration, reducing calibration difficulty and improving ease of use. The calibration process requires no additional tracks or equipment, resulting in low operating costs.

[0050] 5. The algorithm has a reasonable process, high computational efficiency, and is easy to implement in engineering and promote in application. It provides technical support for achieving accurate navigation and positioning, expands the application field of ultra-short baseline systems, and improves the performance indicators of ultra-short baseline systems, which is conducive to promoting the further development of this technology. Attached Figure Description

[0051] Figure 1 This is a schematic diagram of the overall structure of the ultra-short baseline underwater acoustic positioning system in this invention;

[0052] Figure 2This is a schematic diagram illustrating the installation error of the ultra-short baseline system in this invention;

[0053] Figure 3 This is a schematic diagram of the ultra-short baseline positioning principle in this invention;

[0054] Figure 4 This is a schematic diagram of the simulation verification generated by the trajectory generator in this invention. Detailed Implementation

[0055] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0056] This invention provides a method for determining the position and coordinate offset error of an ultra-short baseline transponder, comprising:

[0057] Step 1: Establish the navigation coordinate system, vehicle coordinate system, and acoustic array coordinate system based on the ultra-short baseline underwater acoustic positioning system. The ultra-short baseline underwater acoustic positioning system generally consists of three parts: an inertial navigation system for attitude measurement, and the ultra-short baseline system itself. Figure 1 As shown. The GPS antenna is mounted on the ship to acquire the ship's position information, achieving centimeter-level positioning accuracy using real-time kinematic (RTK) technology. An inertial navigation system is used as the attitude measurement system to obtain the ship's attitude information in real time. The ultra-short baseline (UBS) device is the core component of the underwater acoustic positioning system, consisting of an acoustic array composed of acoustic transducers and multiple hydrophones.

[0058] For ease of analysis and discussion, it is necessary to define commonly used coordinate systems. Since the geometric center of the inertial device does not coincide with the ship's center of gravity, and the ship's center of gravity is difficult to obtain, the geometric center of the inertial device is used as the origin when establishing the coordinate system for computational convenience. First, the geographic coordinate system is selected as the navigation coordinate system OX. n Y n Z n The origin is located at the geometric center of the inertial device, OX. n Y n Z n The three axes point to the northeast direction of the location. Next is the carrier coordinate system OX. b Y b Z b The origin is consistent with the navigation coordinate system, OX b Y b Z b The three axes point to the horizontal, vertical, and axial directions of the carrier, respectively. Then there is the acoustic array coordinate system OX. u Y u Z u The coordinate system has its origin at the geometric center of the acoustic array, OX. u Y u Z uThe three axes point to the horizontal, vertical, and longitudinal directions of the ultra-short baseline equipment, respectively.

[0059] Due to installation issues, it is difficult to ensure complete overlap between the acoustic array coordinate system and the carrier coordinate system in the actual use of ultra-short baseline equipment. There are coordinate axis offset errors (Δx, Δy, Δz) and installation angle errors (Δγ, Δθ, Δψ) between the two coordinate systems, as illustrated in the diagram below. Figure 2 As shown. This invention does not involve installation angle error, so the installation angle error is assumed to be 0. Only coordinate axis offset error and transponder position are discussed.

[0060] Step 2: The ultra-short baseline underwater acoustic positioning system includes a GPS system, an inertial navigation system for attitude measurement, and an ultra-short baseline system. A transponder is placed in the water. The position of the transponder is calculated using the slant range information (distance from the transponder to the center of the acoustic array of the ultra-short baseline equipment measured by the ultra-short baseline system), the hull position measured by the GPS system, and the attitude data measured by the inertial navigation system. The ultra-short baseline system performs positioning based on the angle between the received signal and the array coordinate system and the target slant range information. Specifically, the acoustic transducer in the ultra-short baseline system sends an acoustic signal to the transponder. After receiving the signal from the transducer, the transponder sends back a positioning signal, which is received by the hydrophone in the acoustic array. A schematic diagram of the specific principle is shown below. Figure 3 As shown. Figure 3 A simplified receiving array structure is adopted. Point O is the center of the acoustic transducer, and T is the location of the transponder. Generally, the acoustic transducer is installed at the geometric center of the acoustic array. ρ is the distance from the transponder to the center of the acoustic array of the USMR system, i.e., the slant range information. The acoustic transducer in the USMR system sends an acoustic signal to the transponder. After receiving the signal from the transducer, the transponder sends back a positioning signal, which is received by the hydrophone in the acoustic array. The acoustic transducer is installed at the geometric center of the acoustic array. The transponder is located based on the angle between the received signal and the array coordinate system and the slant range information. The positioning algorithm is expressed by the following formula:

[0061]

[0062] in, The location of the transponder. The location is given by the GPS navigation coordinate system. The rotation matrix from the vehicle coordinate system to the navigation coordinate system is given by the inertial navigation system. This is the rotation matrix between the acoustic array coordinate system and the carrier coordinate system, which is the rotation matrix corresponding to the installation deviation angle; ΔX is the slant range from the transponder to the ultra-short baseline. b This represents the offset error of the coordinate axes.

[0063] Step 3: Perform Taylor expansion on the slant distance information, convert it into a system of linear equations, and establish an incremental error equation; use the least squares method to iteratively solve the equations to obtain the transponder position and coordinate axis offset errors.

[0064] Taylor's formula is a formula that describes the values ​​of a function in its vicinity at a given point. It can be used to construct a polynomial by systematically representing the function's derivatives at that point. Taylor's formula can transform nonlinear problems into linear ones with high accuracy. This invention utilizes this aspect of Taylor's formula to calculate the error between the transponder's position and the coordinate axis offset.

[0065] If a function f(x) has a power series expansion, then the function can be expressed as:

[0066]

[0067] This expression is called the Taylor series of the function f(x) at the point x0.

[0068] Including: the location of the transponder Coordinates are and coordinate axis offset error ΔX b Coordinates are (Δx) b ,Δy b ,Δz b The slant distance information is represented by ρ, and its expression is:

[0069]

[0070] Obtained through the strapdown inertial navigation system (SINS) Represented in matrix form

[0071]

[0072] Will Substituting the matrix representation (4) into the expression (3) of the slant range information ρ, we obtain

[0073]

[0074] make

[0075]

[0076]

[0077]

[0078] ρ is expressed as:

[0079] As we can see, this is a nonlinear equation, so we can use Taylor's formula to linearize it. Let... As the initial value for the estimator, ignoring higher-order terms, a Taylor expansion of equation 6 at point S0 yields:

[0080]

[0081] Calculation yields:

[0082]

[0083]

[0084]

[0085]

[0086]

[0087]

[0088] Replacing equation (7) with an incremental form, we get:

[0089]

[0090] In the formula,

[0091] dρ=ρ-f(S0) (9)

[0092] Equation (8) is a linear equation, which can be written as:

[0093] dρ=H1dS0 (10)

[0094] Given the coefficient matrix H1, the optimal solution of expression (10) can be obtained using the least squares method, resulting in dS0, as shown in expression (11):

[0095]

[0096] In the formula

[0097]

[0098] By compensating the initial value S0 with dS0, we obtain

[0099] S1=S0+dS0 (12)

[0100] Substitute S1 back into expression (10) and iterate through expressions (11) and (12) to obtain... and ΔX b .

[0101] Step 4: Use the trajectory generator to generate the corresponding inertial navigation attitude angles, hull position data, slant range information, and Gaussian white noise for simulation to verify the offset error.

[0102] The position and coordinate axis offset errors of the transponder are set separately, and a circular motion is performed with the transponder as the center. The trajectory generator is used to generate the true data of the corresponding inertial navigation attitude angle, hull position data and slant range information. Finally, Gaussian white noise is added for simulation to verify the offset error.

[0103] To verify the effectiveness of this invention, simulation verification was conducted using circular motion for calibration. In the simulation experiment, the transponder's position was first set to (114.558124 36.6671291 -100.0), and the coordinate axis offset error was set to (0.20 0.50 -2.5). Circular motion was then performed around the transponder as the center. A trajectory generator was used to generate ground truth data such as the corresponding inertial navigation attitude angles, hull position data, and slant range information. Finally, Gaussian white noise was added for simulation. The trajectory is as follows: Figure 4 As shown.

[0104] Currently, the positioning error of USBL is around 0.2%, so we add a 0.2% error to the slant range. The initial value of the estimated quantity S0 is set as (114.558174 36.6671241 -95.0, 0.10 0.40 -2). It can be seen that this initial value has a certain error compared with the true value. Substituting this initial value, we use equations 11 and 12 to iterate and calculate. The calculated transponder position and coordinate axis offset errors are (114.558141 36.667118 -101.9242 0.13 0.3596 -2.06).

[0105] The error values ​​are shown in the table below, indicating that the error is within an acceptable range. This method can obtain six key calibration values ​​for SINS / USBL in a single calculation, demonstrating its innovativeness and engineering value.

[0106]

[0107] The present invention also discloses a device for determining the position and coordinate offset error of an ultra-short baseline transponder, comprising:

[0108] The coordinate system setup module is used to establish the navigation coordinate system, vehicle coordinate system, and acoustic array coordinate system based on the ultra-short baseline underwater acoustic positioning system. An ultra-short baseline underwater acoustic positioning system generally consists of three parts: an inertial navigation system for attitude measurement, and the ultra-short baseline system itself. Figure 1As shown. The GPS antenna is mounted on the ship to acquire the ship's position information, achieving centimeter-level positioning accuracy using real-time kinematic (RTK) technology. An inertial navigation system is used as the attitude measurement system to obtain the ship's attitude information in real time. The ultra-short baseline (UBS) device is the core component of the underwater acoustic positioning system, consisting of an acoustic array composed of acoustic transducers and multiple hydrophones.

[0109] For ease of analysis and discussion, it is necessary to define commonly used coordinate systems. Since the geometric center of the inertial device does not coincide with the ship's center of gravity, and the ship's center of gravity is difficult to obtain, the geometric center of the inertial device is used as the origin when establishing the coordinate system for computational convenience. First, the geographic coordinate system is selected as the navigation coordinate system OX. n Y n Z n The origin is located at the geometric center of the inertial device, OX. n Y n Z n The three axes point to the northeast direction of the location. Next is the carrier coordinate system OX. b Y b Z b The origin is consistent with the navigation coordinate system, OX b Y b Z b The three axes point to the horizontal, vertical, and axial directions of the carrier, respectively. Then there is the acoustic array coordinate system OX. u Y u Z u The coordinate system has its origin at the geometric center of the acoustic array, OX. u Y u Z u The three axes point to the horizontal, vertical, and longitudinal directions of the ultra-short baseline equipment, respectively.

[0110] Due to installation issues, it is difficult to ensure complete overlap between the acoustic array coordinate system and the carrier coordinate system in the actual use of ultra-short baseline equipment. There are coordinate axis offset errors (Δx, Δy, Δz) and installation angle errors (Δγ, Δθ, Δψ) between the two coordinate systems, as illustrated in the diagram below. Figure 2 As shown. This invention does not involve installation angle error, so the installation angle error is assumed to be 0. Only coordinate axis offset error and transponder position are discussed.

[0111] A transponder location module is established, wherein a transponder is placed in the water. The ultra-short baseline underwater acoustic positioning system includes a GPS system, an inertial navigation system for attitude measurement, and an ultra-short baseline system. The transponder location module is used to measure the slant range information of the distance from the transponder to the center of the acoustic array of the ultra-short baseline device using the ultra-short baseline system, the hull position measured by the GPS system, and the attitude data measured by the inertial navigation system, and to determine the position of the transponder according to the positioning algorithm.

[0112] A transponder is installed underwater. The transponder's position is calculated using the slant range information (measured by the USMR system from the transponder to the center of the USMR acoustic array), the hull position (measured by the GPS system), and the attitude data (measured by the inertial navigation system). The USMR system performs positioning based on the angle between the received signal and the array coordinate system, and the target slant range information. Specifically, the acoustic transducer in the USMR system sends an acoustic signal to the transponder. After receiving the signal from the transducer, the transponder sends back a positioning signal, which is received by the hydrophone in the acoustic array. A schematic diagram of the specific principle is shown below. Figure 3 As shown. Figure 3 A simplified receiving array structure is adopted. Point O is the center of the acoustic transducer, and T is the location of the transponder. Generally, the acoustic transducer is installed at the geometric center of the acoustic array. ρ is the distance from the transponder to the center of the acoustic array of the USMR system, i.e., the slant range information. The acoustic transducer in the USMR system sends an acoustic signal to the transponder. After receiving the signal from the transducer, the transponder sends back a positioning signal, which is received by the hydrophone in the acoustic array. The acoustic transducer is installed at the geometric center of the acoustic array. The transponder is located based on the angle between the received signal and the array coordinate system and the slant range information. The positioning algorithm is expressed by the following formula:

[0113]

[0114] in, The location of the transponder. The location is given by the GPS navigation coordinate system. The rotation matrix from the vehicle coordinate system to the navigation coordinate system is given by the inertial navigation system. This is the rotation matrix between the acoustic array coordinate system and the carrier coordinate system, which is the rotation matrix corresponding to the installation deviation angle; ΔX is the slant range from the transponder to the ultra-short baseline. b This represents the offset error of the coordinate axes.

[0115] The transponder position and coordinate axis offset error calculation module is used to perform Taylor expansion of the basic positioning equations, convert them into a system of linear equations, and establish an incremental error equation. It then uses the least squares method for iterative solution to obtain the transponder position and coordinate axis offset errors. The Taylor formula is a formula that describes the values ​​of a function in its vicinity at a given point. It can be used to construct a polynomial by systematically representing the derivatives of the function at that point to approximate the function. The Taylor formula can transform nonlinear problems into linear ones with high accuracy. This invention utilizes this aspect of the Taylor formula to calculate the transponder position and coordinate axis offset errors.

[0116] If a function f(x) has a power series expansion, then the function can be expressed as:

[0117]

[0118] This expression is called the Taylor series of the function f(x) at the point x0.

[0119] Including: the location of the transponder Coordinates are and coordinate axis offset error ΔX b Coordinates are (Δx) b ,Δy b ,Δz b The slant distance information is represented by ρ, and its expression is:

[0120]

[0121] Obtained through the strapdown inertial navigation system (SINS) Represented in matrix form

[0122]

[0123] Will Substituting the matrix representation (4) into the expression (3) of the slant range information ρ, we obtain

[0124]

[0125] make

[0126]

[0127]

[0128]

[0129] ρ is expressed as:

[0130] As we can see, this is a nonlinear equation, so we can use Taylor's formula to linearize it. Let... As the initial value for the estimator, ignoring higher-order terms, a Taylor expansion of equation 6 at point S0 yields:

[0131]

[0132] Calculation yields:

[0133]

[0134]

[0135]

[0136]

[0137]

[0138]

[0139] Replacing equation (7) with an incremental form, we get:

[0140]

[0141] In the formula,

[0142] dρ=ρ-f(S0) (9)

[0143] Equation (8) is a linear equation, which can be written as:

[0144] dρ=H1dS0 (10)

[0145] Given the coefficient matrix H1, the optimal solution of expression (10) can be obtained using the least squares method, resulting in dS0, as shown in expression (11):

[0146]

[0147] In the formula

[0148]

[0149] By compensating the initial value S0 with dS0, we obtain

[0150] S1=S0+dS0 (12)

[0151] Substitute S1 back into expression (10) and iterate through expressions (11) and (12) to obtain... and ΔX b .

[0152] The offset error verification module is used to generate ground truth data of inertial navigation attitude angles, hull position data, slant range information, and Gaussian white noise using the trajectory generator to perform simulation and verify the offset error.

[0153] The position and coordinate axis offset errors of the transponder are set separately, and a circular motion is performed with the transponder as the center. The trajectory generator is used to generate the true data of the corresponding inertial navigation attitude angle, hull position data and slant range information. Finally, Gaussian white noise is added for simulation to verify the offset error.

[0154] To verify the effectiveness of this invention, simulation verification was conducted using circular motion for calibration. In the simulation experiment, the transponder's position was first set to (114.558124 36.6671291 -100.0), and the coordinate axis offset error was set to (0.20 0.50 -2.5). Circular motion was then performed around the transponder as the center. A trajectory generator was used to generate ground truth data such as the corresponding inertial navigation attitude angles, hull position data, and slant range information. Finally, Gaussian white noise was added for simulation. The trajectory is as follows: Figure 4 As shown.

[0155] Currently, the positioning error of USBL is around 0.2%, so we add a 0.2% error to the slant range. The initial value of the estimated quantity S0 is set as (114.558174 36.6671241 -95.0, 0.10 0.40 -2). It can be seen that this initial value has a certain error compared with the true value. Substituting this initial value, we use equations 11 and 12 to iterate and calculate. The calculated transponder position and coordinate axis offset errors are (114.558141 36.667118-101.9242 0.13 0.3596-2.06).

[0156] The error values ​​are shown in the table below, indicating that the error is within an acceptable range. This method can obtain six key calibration values ​​for SINS / USBL in a single calculation, demonstrating its innovativeness and engineering value.

[0157]

[0158] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0159] It will be apparent to those skilled in the art that the embodiments of the present invention are not limited to the details of the exemplary embodiments described above, and that the embodiments of the present invention can be implemented in other specific forms without departing from the spirit or essential characteristics of the embodiments of the present invention. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of the embodiments of the present invention is defined by the appended claims rather than the foregoing description. Therefore, all variations falling within the meaning and scope of equivalents of the claims are intended to be encompassed within the embodiments of the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims. Furthermore, it is clear that the word "comprising" does not exclude other units or steps, and the singular does not exclude the plural. Multiple units, modules, or devices recited in the system, apparatus, or terminal claims may also be implemented by the same unit, module, or device through software or hardware. The terms "first," "second," etc., are used to indicate names and do not indicate any particular order.

[0160] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the embodiments of the present invention and are not intended to limit them. Although the embodiments of the present invention have been described in detail with reference to the above preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions to the technical solutions of the embodiments of the present invention should not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for determining the position and coordinate offset error of an ultra-short baseline transponder, characterized in that, include: Step 1: Establish the navigation coordinate system, the carrier coordinate system, and the acoustic array coordinate system based on the ultra-short baseline underwater acoustic positioning system; Step 2, the ultra-short baseline underwater acoustic positioning system includes a GPS system, an inertial navigation system for attitude measurement, and an ultra-short baseline system; A transponder is installed in the water. The slant range information of the distance between the transponder and the center of the acoustic array of the ultra-short baseline device is measured using the ultra-short baseline system, the hull position is measured by the GPS system, and the attitude data is measured by the inertial navigation system. The position of the transponder is determined according to the positioning algorithm. Step 3: Perform Taylor expansion on the expression of the slant distance information, convert it into a linear expression, and establish an incremental error equation; use the least squares method to iteratively solve the equation to obtain the transponder position and coordinate axis offset error. Step 4: Use the trajectory generator to generate the corresponding inertial navigation attitude angles, hull position data, slant range information, and Gaussian white noise for simulation to verify the offset error. Step 3 includes: the position of the transponder Coordinates are and coordinate axis offset error Coordinates are The slant distance information is used It means that its expression is: ; obtained through strapdown inertial navigation system (SINS) Represented by a matrix as ;Will Substituting the matrix representation into the slant range information In the expression, make Will Expressed as: By Perform a Taylor expansion, and assume... The initial values ​​of the estimator can be obtained ； The Taylor expansion result is converted into incremental form, and the initial value of the estimator is obtained by the least squares method. The position of the transponder is obtained by iterating in incremental form. and coordinate axis offset error .

2. The method for determining the position and coordinate offset error of an ultra-short baseline transponder as described in claim 1, characterized in that, Step 1 includes: establishing a coordinate system using the geometric center of the inertial device as the origin; firstly, selecting a geographic coordinate system as the navigation coordinate system, with the origin located at the geometric center of the inertial device, and the three axes pointing towards the northeast direction of the location; secondly, the carrier coordinate system, with the origin consistent with the navigation coordinate system, and the three axes pointing towards the horizontal, vertical, and longitudinal directions of the carrier; and then the acoustic array coordinate system, with the geometric center of the acoustic array as the origin, and the three axes pointing towards the horizontal, vertical, and longitudinal directions of the ultra-short baseline device.

3. The method for determining the position and coordinate offset error of an ultra-short baseline transponder as described in claim 1, characterized in that, In step 2, the acoustic transducer in the ultra-short baseline system sends an acoustic signal to the transponder. After receiving the signal from the transducer, the transponder sends back a positioning signal, which is received by a hydrophone in the acoustic array. The acoustic transducer is installed at the geometric center of the acoustic array. The transponder is positioned based on the angle between the received signal and the array coordinate system and the slant range information. The positioning algorithm is expressed by the following formula: in, The location of the transponder. The location is given by the GPS navigation coordinate system. The rotation matrix from the vehicle coordinate system to the navigation coordinate system is given by the inertial navigation system. This is the rotation matrix between the acoustic array coordinate system and the carrier coordinate system, which is the rotation matrix corresponding to the installation deviation angle; The slant range from the transponder to the ultra-short baseline. This represents the offset error of the coordinate axes.

4. The method for determining the position and coordinate offset error of an ultra-short baseline transponder as described in claim 1, characterized in that, Step 4 includes: setting the position and coordinate axis offset errors of the transponder respectively, and performing circular motion with the transponder as the center; using a trajectory generator to generate the true data of the corresponding inertial navigation attitude angle, hull position data, and slant range information, and finally adding Gaussian white noise for simulation to verify the offset error.

5. A device for determining the position and coordinate offset error of an ultra-short baseline transponder, characterized in that, include: The coordinate system setting module is used to establish the navigation coordinate system, the carrier coordinate system, and the acoustic array coordinate system based on the ultra-short baseline underwater acoustic positioning system. A transponder location module is established, wherein a transponder is placed in the water. The ultra-short baseline underwater acoustic positioning system includes a GPS system, an inertial navigation system for attitude measurement, and an ultra-short baseline system. The transponder location module is used to measure the slant range information of the distance from the transponder to the center of the acoustic array of the ultra-short baseline device using the ultra-short baseline system, the hull position measured by the GPS system, and the attitude data measured by the inertial navigation system, and to determine the position of the transponder according to the positioning algorithm. The transponder position and coordinate axis offset error calculation module is used to perform Taylor expansion on the expression of the slant distance information, convert it into a linear expression, and establish an incremental error equation; and use the least squares method to iteratively solve the transponder position and coordinate axis offset error. The offset error verification module is used to generate ground truth data of inertial navigation attitude angles, hull position data, slant range information, and Gaussian white noise using a trajectory generator for simulation to verify the offset error. The transponder position and coordinate axis offset error calculation module includes: the position of the transponder. Coordinates are and coordinate axis offset error Coordinates are The slant distance information is used It means that its expression is: ; obtained through strapdown inertial navigation system (SINS) Represented by a matrix as ;Will Substituting the matrix representation into the slant range information In the expression, make Will Expressed as: By Perform a Taylor expansion, and assume... The initial values ​​of the estimator can be obtained ； The Taylor expansion result is converted into incremental form, and the initial value of the estimator is obtained by the least squares method. The position of the transponder is obtained by iterating in incremental form. and coordinate axis offset error .

6. The device for determining the position and coordinate offset error of an ultra-short baseline transponder as described in claim 5, characterized in that, The coordinate system setting module includes: using the geometric center of the inertial device as the origin when establishing the coordinate system; firstly, selecting the geographic coordinate system as the navigation coordinate system, with the origin located at the geometric center of the inertial device, and the three axes pointing to the northeast direction of the location; secondly, the carrier coordinate system, with the origin consistent with the navigation coordinate system, and the three axes pointing to the horizontal, vertical, and longitudinal directions of the carrier; and then the acoustic array coordinate system, with the geometric center of the acoustic array as the origin, and the three axes pointing to the horizontal, vertical, and longitudinal directions of the ultra-short baseline device.

7. The apparatus for determining the position and coordinate offset error of an ultra-short baseline transponder as described in claim 5, characterized in that, In an ultra-short baseline system, an acoustic transducer sends an acoustic signal to a transponder. Upon receiving the signal from the transducer, the transponder sends back a positioning signal, which is received by a hydrophone in the acoustic array. The acoustic transducer is mounted at the geometric center of the acoustic array. The transponder is positioned based on the angle between the received signal and the array coordinate system, and the slant range information. The positioning algorithm is expressed by the following formula: in, The location of the transponder. The location is given by the GPS navigation coordinate system. The rotation matrix from the vehicle coordinate system to the navigation coordinate system is given by the inertial navigation system. This is the rotation matrix between the acoustic array coordinate system and the carrier coordinate system, which is the rotation matrix corresponding to the installation deviation angle; The slant range from the transponder to the ultra-short baseline. This represents the offset error of the coordinate axes.

8. The apparatus for determining the position and coordinate offset error of an ultra-short baseline transponder as described in claim 5, characterized in that, The offset error verification module includes: setting the position and coordinate axis offset errors of the transponder respectively, performing circular motion with the transponder as the center; using a trajectory generator to generate the true data of the corresponding inertial navigation attitude angle, hull position data, and slant range information, and finally adding Gaussian white noise for simulation to verify the offset error.

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