A method and apparatus for error identification in a multi-beacon long baseline positioning system

Abstract

This invention provides a method and apparatus for identifying errors in a multi-beacon long baseline positioning system. The method includes the following steps: acquiring an initial long baseline underwater positioning model; establishing a multi-beacon underwater positioning model based on the long baseline underwater positioning model and the geometric relationship between the underwater target center and the beacons; obtaining a system error identification model based on the multi-beacon underwater positioning model; calculating the time delay residual using the system error identification model and the underwater target positioning process; constructing an optimal test statistic D for the system error identification model by analyzing the time delay residual; obtaining a selection criterion for the system error identification model based on the optimal test statistic D; and selecting the optimal system error identification model based on the selection criterion. The system error identification model and optimal model selection criterion proposed in this invention can provide theoretical and technical support for high-precision measurement and navigation positioning of underwater targets.

Description

Technical Field

[0001] This invention relates to the field of underwater target positioning technology, and in particular to a method and apparatus for error identification in a multi-beacon long baseline positioning system. Background Technology

[0002] Unlike satellites and other space targets, which can be observed at distances in the hundreds of kilometers, long-baseline underwater positioning systems have shorter measurement distances. If the inconsistency between the location of multiple beacons and the center of the target is not taken into account, this system error can cause a large positioning error.

[0003] The applicant has identified at least the following problems in the existing technology: how to improve the positioning accuracy of long-baseline underwater targets. Summary of the Invention

[0004] The technical problem solved by the embodiments of the present invention is how to improve the positioning accuracy of long-baseline underwater targets.

[0005] To achieve the above objectives, in one aspect, embodiments of the present invention provide a method for error identification in a multi-beacon long baseline positioning system, comprising the following steps:

[0006] Obtain the initial long-baseline underwater positioning model;

[0007] Based on the aforementioned long-baseline underwater positioning model and the geometric relationship between the underwater target center and the beacon, a multi-beacon underwater positioning model is established.

[0008] A system error identification model is obtained based on the multi-beacon underwater positioning model;

[0009] The time delay residual is calculated by using the system error identification model and combining it with the underwater target positioning process.

[0010] By analyzing the time delay residual, the optimal test statistic D of the system error identification model is constructed, and the selection criterion of the system error identification model is obtained based on the optimal test statistic D.

[0011] The optimal system error identification model is selected based on the selection criteria.

[0012] On the other hand, embodiments of the present invention provide an error identification device for a multi-beacon long baseline positioning system, comprising:

[0013] Acquisition unit, used to acquire the initial long baseline underwater positioning model;

[0014] The construction unit is used to establish a multi-beacon underwater positioning model based on the long baseline underwater positioning model and the geometric relationship between the underwater target center and the beacon;

[0015] The identification unit is used to obtain the system error identification model based on the multi-beacon underwater positioning model;

[0016] The calculation unit is used to calculate the time delay residual by using the system error identification model and combining it with the underwater target positioning process;

[0017] The analysis unit is used to construct the optimal test statistic D of the system error identification model by analyzing the time delay residual, and to obtain the selection criteria of the system error identification model based on the optimal test statistic D.

[0018] The selection unit is used to select the optimal system error identification model according to the selection criteria.

[0019] The above technical solution has the following beneficial effects: Since the systematic errors in the measurement data are unknown in actual practice, this application constructs the optimal test statistic of the model by analyzing the time delay residual, and gives the optimal selection criterion for the systematic error identification model, so as to realize the effective estimation of underwater target position parameters and the reasonable identification of systematic error parameters.

[0020] This application analyzes time delay residuals to construct the optimal test statistic D for the model and provides the optimal selection criterion for the systematic error identification model. Numerical simulation scenarios are designed to verify this criterion. Different systematic errors of measurement elements are added to the measurement data in each simulation scenario. The target position parameters are solved using various solution models proposed in this application, and the corresponding statistic D is calculated. Simulation results show that the model achieves the highest target position solution accuracy when the statistic D is minimized. Therefore, the systematic error identification model and optimal model selection criterion proposed in this application can provide theoretical and technical support for high-precision measurement and navigation positioning of underwater targets. Attached Figure Description

[0021] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0022] Figure 1 This is a flowchart of an error identification method for a multi-beacon long baseline positioning system provided in an embodiment of the present invention;

[0023] Figure 2 This is a schematic diagram of the structure of an error identification device for a multi-beacon long baseline positioning system provided in an embodiment of the present invention;

[0024] Figure 3 This is a schematic diagram of the rectangular coordinate system of the long baseline positioning system provided in the embodiment of the present invention;

[0025] Figure 4This is a diagram of the multi-beacon positioning system provided in an embodiment of the present invention;

[0026] Figure 5 This is a target trajectory diagram of the first embodiment provided in this invention;

[0027] Figure 6 This is a target trajectory diagram of the second embodiment provided in this invention;

[0028] Figure 7 This is a diagram showing the rotation angle variation provided in an embodiment of the present invention. Detailed Implementation

[0029] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0030] The technical solution of this invention is as follows: This application constructs a multi-beacon system error identification model to improve underwater positioning accuracy. For structural system errors with inconsistent locations, a positioning model under a multi-beacon system is constructed; for measurement element system errors existing during the measurement process, a corresponding system error identification model is constructed based on the multi-beacon system positioning model. Since the types of system errors present in the measurement data are unknown during actual positioning, and an inappropriate system error identification model can also affect positioning accuracy, this application constructs the optimal test statistic D for the model by analyzing the time delay residual, and provides the optimal selection criterion for the system error identification model. Numerical simulation scenarios are designed to verify this criterion. Different measurement element system errors are added to the measurement data in each simulation scenario, and the target position parameters are solved using various solution models of this application, and the corresponding statistic D is calculated. Simulation results show that when the model's statistic D is minimized, the target position solution accuracy of the model is the highest. This verifies the effectiveness of the optimal model selection criterion.

[0031] This invention provides a method for error identification in a multi-beacon long baseline positioning system, such as... Figure 1 As shown, it includes the following steps:

[0032] S101: Obtain the initial long baseline underwater positioning model;

[0033] Establish a rectangular coordinate system as follows Figure 3As shown, with a point within the measurement range of the long baseline system as the origin O(0,0,0), the ox, oy, and oz axes are perpendicular to each other, pointing due east, due north, and sky respectively, forming a right-handed coordinate system. The long baseline positioning system is deployed as shown below, with a beacon installed on the target. The long baseline system is strictly time-aligned with the beacon. During underwater positioning, beacon X emits an acoustic signal at a known time, and the long baseline system receives the acoustic signal, thus obtaining the acoustic signal's trajectory from beacon X to station X. i The one-way propagation delay t for i = 1, ..., n i The slope distance R from the target to the station can be calculated using formula (1). i .

[0034] R i =ct i (1)

[0035] Where c is the speed of sound underwater.

[0036] The location of surface stations can be obtained using the Global Navigation Satellite System (GNSS), while the location of seabed stations can be obtained through calibration before the experiment. The location is determined based on the target object X = [x, y, z]. T With station X i =[x i ,y i ,z i ] T The geometric relationship between (i = 1, ..., n) is given by the following system of equations:

[0037]

[0038] Combining formulas (1) and (2), the underwater positioning model for a long baseline system is as follows:

[0039]

[0040] Model (3) can be solved using the Gauss-Newton iteration method, and the coordinates of the underwater target can then be obtained.

[0041] The Jacobian matrix of model (3) is:

[0042]

[0043] in i represents the i-th measuring station.

[0044] S102: Based on the aforementioned long-baseline underwater positioning model and the geometric relationship between the underwater target center and the beacon, establish a multi-beacon underwater positioning model;

[0045] like Figure 4As shown, K beacons (the target is approximately cylindrical) are installed at equal intervals outside the target, with the target center at the same depth as the beacons. The long baseline system is strictly time-aligned with the beacons. During underwater positioning, beacon X... j The acoustic signal is transmitted from beacon X to a long baseline system, and the acoustic signal is received by the long baseline system. j To station X i The one-way propagation delay t for i = 1, ..., n ij The beacon X can be calculated using formula (1). j To station X i Slope distance R ij .

[0046] R ij =ct ij (5)

[0047] Due to factors such as the target's own obstruction and the limited angle of the beacon's emitted acoustic signal, the long baseline system outputs the arrival time of the acoustic signal of only one beacon at a time during positioning, and then calculates the time delay of the acoustic signal propagation in the water.

[0048] like Figure 4 As shown, according to beacon X j =[x j ,y j ,z j ] T With station X i =[x i ,y i ,z i ] T The geometric relationships can be used to construct the following system of equations:

[0049]

[0050] Assuming the target center X points towards beacon X at an angle θ with the eastward direction, and since the beacons are equidistantly installed outside the target, the target center X and beacon X... j The relationship can be represented as:

[0051]

[0052] Combining formulas (6) and (7), the underwater positioning model for a long baseline system under a multi-beacon architecture is as follows:

[0053]

[0054] Using the Gauss-Newton iterative solvable model (8), its Jacobian matrix is:

[0055]

[0056] in J j Let j be the station number corresponding to the j-th beacon.

[0057] S103: The system error identification model is obtained based on the multi-beacon underwater positioning model;

[0058] S104: Calculate the time delay residual by using the system error identification model and combining it with the underwater target positioning process;

[0059] S105: By analyzing the time delay residual, construct the optimal test statistic D for the system error identification model, and obtain the selection criterion for the system error identification model based on the optimal test statistic D.

[0060] S106: Select the optimal system error identification model according to the selection criteria.

[0061] The system error identification models include: sound speed error identification model, time delay error identification model, and sound speed and time delay error identification model.

[0062] The underwater positioning model for a multi-beacon system is as follows:

[0063]

[0064] Where X is the target to be measured, X = [x, y, z] T ;X j Let X be the position of beacon j, j = 1,...,K; i Let i be the position of station i, where i = 1, ..., n;

[0065] t ij For acoustic signals from beacon X j To station X i The one-way propagation delay is in seconds (s); c is the underwater speed of sound in meters per second (m / s); θ is the rotation angle in degrees (degrees); r is the target radius in meters (m); and j is the station number corresponding to the j-th beacon.

[0066] The sound velocity error identification model is as follows:

[0067]

[0068] Where ν is the measured value of the speed of sound, and t ij For acoustic signals from beacon X j To station X i The one-way propagation delay is expressed in seconds (s); Δc is the sound speed error; and X is the target object, where X = [x, y, z]. T θ is the rotation angle in degrees; r is the target radius in meters; j is the station number corresponding to the j-th beacon, j = 1,...,K; X iLet i be the position of station i, where i = 1, ..., n;

[0069] The time delay error identification model is specifically as follows:

[0070]

[0071] Where, τ ij Δt represents the time delay measurement; Δc represents the time delay system error; c represents the underwater sound speed in m / s; X represents the target object, X = [x, y, z]. T θ is the rotation angle in degrees; r is the target radius in meters; j is the station number corresponding to the j-th beacon, j = 1,...,K; X i Let i be the position of station i, where i = 1, ..., n;

[0072] The sound speed and time delay error identification model is specifically as follows:

[0073]

[0074] Where ν is the measured value of the speed of sound, τ ij Δt is the measured time delay value; Δc is the time delay systematic error; c is the underwater sound speed error in m / s; X is the target to be measured, X = [x, y, z] T θ is the rotation angle in degrees; r is the target radius in meters; j is the station number corresponding to the j-th beacon, j = 1,...,K; X i Let i be the position of station i, where i = 1, ..., n.

[0075] By comparing the magnitudes of the optimal test statistic D, the model with the smallest optimal test statistic D is the optimal system error identification model; the optimal test statistic D is:

[0076] D = RSS + (2N - n)σ 2 ;

[0077] Where is the RSS residual sum of squares; n is the number of measures, N is the number of unknowns, and σ is the standard deviation of the time delay random error.

[0078] The present invention also provides an error identification device for a multi-beacon long baseline positioning system, such as... Figure 2 As shown, it includes:

[0079] Acquisition unit 21 is used to acquire the initial long baseline underwater positioning model;

[0080] Construction unit 22 is used to establish a multi-beacon underwater positioning model based on the long baseline underwater positioning model and the geometric relationship between the underwater target center and the beacon;

[0081] Identification unit 23 is used to obtain the system error identification model based on the multi-beacon underwater positioning model;

[0082] The calculation unit 24 is used to calculate the time delay residual by using the system error identification model and combining it with the underwater target positioning process;

[0083] Analysis unit 25 is used to construct the optimal test statistic D of the system error identification model by analyzing the time delay residual, and to obtain the selection criteria of the system error identification model based on the optimal test statistic D.

[0084] Selection unit 26 is used to select the optimal system error identification model according to the selection criteria.

[0085] The system error identification model includes: sound speed error identification model, time delay error identification model, and sound speed and time delay error identification model.

[0086] The multi-beacon underwater positioning model is as follows:

[0087]

[0088] Where X is the target to be measured, X = [x, y, z] T ;X j Let X be the position of beacon j, j = 1,...,K; i Let i be the position of station i, where i = 1, ..., n;

[0089] t ij For acoustic signals from beacon X j To station X i The one-way propagation delay is in seconds (s); c is the underwater speed of sound in meters per second (m / s); θ is the rotation angle in degrees (degrees); r is the target radius in meters (m); and j is the station number corresponding to the j-th beacon.

[0090] The sound speed error identification model is specifically as follows:

[0091]

[0092] Where ν is the measured value of the speed of sound, and t ij For acoustic signals from beacon X j To station X i The one-way propagation delay is expressed in seconds (s); Δc is the sound speed error; and X is the target object, where X = [x, y, z]. T θ is the rotation angle in degrees; r is the target radius in meters; j is the station number corresponding to the j-th beacon, j = 1,...,K; X i Let i be the position of station i, where i = 1, ..., n;

[0093] The time delay error identification model is specifically as follows:

[0094]

[0095] Where, τ ij Δt represents the time delay measurement; Δc represents the time delay system error; c represents the underwater sound speed in m / s; X represents the target object, X = [x, y, z]. T θ is the rotation angle in degrees; r is the target radius in meters; j is the station number corresponding to the j-th beacon, j = 1,...,K; X i Let i be the position of station i, where i = 1, ..., n;

[0096] The sound speed and time delay error identification model is specifically as follows:

[0097]

[0098] Where ν is the measured value of the speed of sound, τ ij Δt is the measured time delay value; Δc is the time delay systematic error; c is the underwater sound speed error in m / s; X is the target to be measured, X = [x, y, z] T θ is the rotation angle in degrees; r is the target radius in meters; j is the station number corresponding to the j-th beacon, j = 1,...,K; X i Let i be the position of station i, where i = 1, ..., n.

[0099] The optimal system error identification model is determined by comparing the magnitudes of the optimal test statistic D; the model with the smallest optimal test statistic D is the one that minimizes the error. The optimal test statistic D is:

[0100] D = RSS + (2N - n)σ 2 ;

[0101] Where is the RSS residual sum of squares; n is the number of measures, N is the number of unknowns, and σ is the standard deviation of the time delay random error.

[0102] Since the systematic errors present in the measurement data are unknown in practice, this application constructs the optimal test statistic for the model by analyzing the time delay residuals and provides the optimal selection criteria for the systematic error identification model, thereby achieving effective estimation of underwater target position parameters and reasonable identification of systematic error parameters.

[0103] This application analyzes time delay residuals to construct the optimal test statistic D for the model and provides the optimal selection criterion for the systematic error identification model. Numerical simulation scenarios are designed to verify this criterion. Different systematic errors of measurement elements are added to the measurement data in each simulation scenario. The target position parameters are solved using various solution models proposed in this application, and the corresponding statistic D is calculated. Simulation results show that the model achieves the highest target position solution accuracy when the statistic D is minimized. Therefore, the systematic error identification model and optimal model selection criterion proposed in this application can provide theoretical and technical support for high-precision measurement and navigation positioning of underwater targets.

[0104] Example 1:

[0105] This invention provides a method for identifying errors in a multi-beacon long baseline positioning system. First, it constructs a multi-beacon underwater positioning model to address structural system errors caused by inconsistencies in location. Furthermore, in long baseline system positioning, measurement data may contain measurement element system errors such as site system errors, sound velocity system errors, and time delay system errors. While site system errors can be corrected during underwater station calibration, this application primarily considers sound velocity system errors and time delay system errors. Assuming that the underwater sound velocity is constant at all locations at the same time and that all measurement element system errors are constant, this application constructs corresponding system error identification models based on the multi-beacon underwater positioning model for situations where only sound velocity errors, time delay errors, or both sound velocity and time delay errors exist simultaneously.

[0106] Multi-beacon underwater positioning model:

[0107] like Figure 3 As shown, K beacons (the target is approximately cylindrical) are installed at equal intervals outside the target, with the target center at the same depth as the beacons. The long baseline system is strictly time-aligned with the beacons. During underwater positioning, beacon X... j The acoustic signal is transmitted from beacon X to a long baseline system, and the acoustic signal is received by the long baseline system. j To station X i The one-way propagation delay t for i = 1, ..., n ij The beacon X can be calculated using formula (1). j To station X i Slope distance R ij .

[0108] R ij =ct ij (10)

[0109] Due to factors such as the target's own obstruction and the limited angle of the beacon's emitted acoustic signal, the long baseline system outputs the arrival time of the acoustic signal of only one beacon at a time during positioning, and then calculates the time delay of the acoustic signal propagation in the water.

[0110] like Figure 3 As shown, according to beacon X j =[x j ,y j ,z j ] T With station X i =[x i ,y i ,z i ] T The geometric relationships can be used to construct the following system of equations:

[0111]

[0112] Assuming the target center X points towards beacon X at an angle θ with the eastward direction, and since the beacons are equidistantly installed outside the target, the target center X and beacon X... j The relationship can be represented as:

[0113]

[0114] Combining formulas (6) and (7), the underwater positioning model for a long baseline system under a multi-beacon architecture is as follows:

[0115]

[0116] Using the Gauss-Newton iterative solvable model (8), its Jacobian matrix is:

[0117]

[0118] in J j Let j be the station number corresponding to the j-th beacon.

[0119] Sound speed error identification model:

[0120] Sound velocity error is a major factor affecting the underwater target localization accuracy of acoustic systems. Assume that during a long baseline system measurement, the measured sound velocity is ν and the measured time delay is t. ij Let the sound speed error be Δc. Ignoring time delay error, according to formula (5), the ranging error ΔR caused by the sound speed error is... ij for:

[0121] ΔR ij =t ij Δc (15)

[0122] According to formula (15), when the sound speed error remains constant, the larger the time delay measurement value, the larger the ranging error.

[0123] Let the slope distance measurement value be R ij The actual value is According to beacon X j With station X i The geometric relationship can be obtained as follows:

[0124]

[0125] According to formulas (5) and (7), the sound velocity error identification model can be written as:

[0126]

[0127] Its Jacobi matrix is:

[0128]

[0129] Where t ij For acoustic signals from beacon X j To station X i The one-way propagation delay.

[0130] Delay error identification model:

[0131] Time delay error is another major factor affecting the positioning accuracy of long baseline systems. Assume the time delay measurement value in the measurement is τ. ij The time delay system error is Δt, and there is no sound speed error. The ranging error caused by the time delay error is ΔR. According to formula (5), the ranging error ΔR is:

[0132] ΔR=cΔt (19)

[0133] Based on the center X of the target to be measured and the measuring station X i The geometric relationship can be obtained as follows:

[0134]

[0135] The time delay error identification model is as follows:

[0136]

[0137] Its Jacobi matrix is:

[0138]

[0139] Sound speed and time delay error identification model:

[0140] Assume the time delay measurement value is τ ij The measured speed of sound is ν. If both a time delay error Δt and a speed of sound error Δc exist in the measurement data, the combined ranging error caused by these errors is ΔR. ij According to formula (5), we can obtain:

[0141]

[0142] in c is the true value of the slant range, and t is the true value of the speed of sound. ij This is the truth value for the time delay.

[0143] According to formula (23), the ranging error ΔR ij for:

[0144]

[0145] Where ν is the measured underwater sound velocity, and τ ij This is the time delay measurement value.

[0146] Slope distance measurement value R ij It can be represented as:

[0147]

[0148] Therefore, the identification model for time delay error and sound speed error is as follows:

[0149]

[0150] Its Jacobi matrix is:

[0151]

[0152] Similar to the solution process of model (8), models (17), (21), and (26) can all be solved using the Gauss-Newton method. In the underwater target localization process, we usually do not know which measurement system errors exist during the localization process. Since selecting an inappropriate system error identification model increases the complexity of the model and reduces the localization accuracy of underwater targets, choosing a suitable system error identification model is a key issue in improving the localization accuracy of underwater targets.

[0153] Optimal model selection criteria:

[0154] For processing long baseline measurement data, different system error identification models will have varying degrees of accuracy. Therefore, selecting a suitable system error identification model is crucial to effectively improve the positioning accuracy of long baseline systems. Assume that during underwater positioning, the true time delay of the long baseline system at a certain moment is t = [t1, t2, ..., t...]. n ] T Measurements were performed to obtain time delay data τ = [τ1, τ2, ..., τ]. n ] T Assume the measurement data model is as follows:

[0155]

[0156] Where e is the random error.

[0157] Suppose that the parameter to be estimated, β∈R, is a certain systematic error identification model. N×1 and design matrix H∈R n×N They are respectively:

[0158]

[0159] Assume b = [b1, b2, ..., b n ] T It is the error after t is represented by the combination of the parameter to be estimated β and the design matrix H.

[0160] t=Hβ+b (30)

[0161] Then formula (28) can be written as:

[0162] τ=Hβ+b+e (31)

[0163] Using the least squares method, according to formula (31), the estimate of β can be obtained as follows:

[0164]

[0165] therefore It is an estimate of t, and its estimation error is:

[0166]

[0167] make:

[0168] H X =H(H) T H) -1 H T (34)

[0169] Formula (33) can be written as:

[0170]

[0171] According to formula (30), we have:

[0172]

[0173] We can obtain:

[0174]

[0175] According to the formula for calculating the sum of squared residuals, we have:

[0176]

[0177] Combining formulas (37) and (38), we can obtain:

[0178]

[0179] Let the optimal test statistic D of the systematic error identification model be:

[0180] D = RSS + (2N - n)σ 2 (40)

[0181] If σ 2 When the statistic Q = nN is large, σ can be given by the sum of squared residuals of the time delay. 2 The estimation. Let the sum of squared residuals corresponding to the q systematic error identification models be RSS1, RSS2, ..., RSS. q The corresponding statistics Q are Q1, Q2, ..., Q q Then σ 2 Estimate for

[0182]

[0183] Calculate using formula (41) Substituting into formula (40), the magnitude of the statistic D for each model can be calculated.

[0184] The key to accurately calculating the position of underwater targets using measurement data from long baseline systems is to select a suitable systematic error identification model that minimizes both the sum of squared residuals and the number of variables. When multiple systematic error identification models are available for positioning, it is only necessary to compare the magnitude of the statistic D; the model with the smallest statistic D is the optimal systematic error identification model.

[0185] Regarding the optimal selection criterion for the systematic error identification model as in formula (40), when the number of parameters in the model is the same, it is only necessary to calculate the sum of squared residuals of different models, and the model with the smallest sum of squared residuals is optimal; while when the number of parameters in the model is different, it is necessary to calculate the statistic D of different models, and the model with the smallest statistic D is optimal.

[0186] This optimal model selection criterion is effective for both linear and nonlinear models.

[0187] Numerical simulation

[0188] Simulation Design:

[0189] This application assumes that the underwater sound speed is constant at the same time and does not consider the influence of sound ray bending. The numerical simulation process is as follows.

[0190] Simulation Design: The underwater target is a cylinder with a radius r of 1m. Six beacons are fixed at equal intervals on the outer side of the target. It is assumed that the beacons remain at the same depth throughout the target's movement. Ten monitoring stations are deployed underwater, and one monitoring station is deployed on the surface. The beacons and monitoring stations are strictly synchronized.

[0191] The simulation included four scenarios, each with different errors added to the measurement data to verify the applicability of the optimal model selection criterion: no measurement element systematic error, systematic error added only to time delay measurement, systematic error added only to sound velocity measurement, and systematic error added to both time delay and sound velocity. It was assumed that the systematic error did not change with time or target location.

[0192] For the three simulation scenarios mentioned above, the models (3), (8), (17), (21) and (26) are used for calculation respectively.

[0193] 1. Set the true measurement value and initial iteration value: The target moves approximately vertically in the water, and the target coordinate sequence and rotation angle at time k (k = 1, ..., m) are respectively X k =[x k ,y k ,z k ] T and θ k ,like Figure 5 , Figure 6 and Figure 7 As shown in Table 1, the beacon numbers corresponding to the stations are determined based on the geometric relationship between the stations and the beacons.

[0194] Table 1 Correspondence between stations and beacons

[0195]

[0196] The true value of the underwater sound speed is set to c = 1500 m / s. According to formula (8), Figure 7 The true value t of the one-way time delay t of the acoustic signal propagating from the beacon to the corresponding station is calculated using Table 1. ij The initial coordinates of the target are X0 = [0, 0, -10m], the initial value of the rotation angle iteration is θ = 0°, the initial value of the time delay error iteration is Δt0 = 0s, and the initial value of the sound speed error iteration is Δc0 = 0m / s.

[0197] 2. Generate measurement data: Set the standard deviation of the station site random error to σ. X =0.05m, standard deviation σ of random time delay error t =50us. Based on the three simulation scenarios, system errors were added to the sound speed and time delay data respectively to obtain the sound speed measurement value ν and the time delay measurement value τ. The slant range measurement value R was calculated using formula (5). c .

[0198] 3. Solution: Let the single-beacon system non-identification error be Model 1 (M1), the multi-beacon system non-identification error be Model 1 (M2), the multi-beacon system sound speed identification error be Model 2 (M3), the multi-beacon system time delay identification error be Model 3 (M4), and the multi-beacon system sound speed and time delay identification errors be Model 4 (M5). In each simulation scenario, based on the principles of Models 1-5, the target parameters are solved using Gauss-Newton iteration: First, set the accuracy ε. min and maximum number of iterations k max Then, the initial values ​​are substituted into the Jacobian matrix J to calculate the descent direction. This process is repeated until the termination condition is met, and finally the target coordinates are obtained. Twist angle The timing system error Δt and the sound velocity system error Δc are used to further calculate the position error. Rotation error Δθ and its statistic D.

[0199] 4. Iterative calculation: Using the Monte Carlo method, the calculation is repeated 100 times from process 0 to process 0, and the results of each calculation are recorded. The final results are statistically analyzed.

[0200] Simulation results:

[0201] Simulation Scenario 1: No systematic errors are included in the measurement data. The simulation results are shown below.

[0202] Table 2 shows the solution results for simulation scenario 1.

[0203]

[0204]

[0205] Simulation Scenario 2: Only a system error of -2 m / s is added to the sound velocity data. The simulation results are shown below.

[0206] Table 3 shows the solution results for simulation scenario 2.

[0207]

[0208] Simulation Scenario 3: Only a system error of -500us is added to the delay data. The simulation results are shown below.

[0209] Table 4 shows the solution results for simulation scenario 3.

[0210]

[0211] Simulation Scenario 4: A system error of -2 m / s was added to the sound speed data, and a system error of -500 μs was added to the time delay data. The simulation results are shown in Table 5.

[0212] Table 5 shows the solution results for simulation scenario 4.

[0213]

[0214]

[0215] Based on the simulation results of the three scenarios above, we can conclude that:

[0216] 1) Among the simulation results of the above four scenarios, the target position parameter solution accuracy of the single beacon system non-identification error model is the worst, and the statistic D of this model is also the largest among all models.

[0217] 2) When there is no measurement element system error, the multi-beacon system non-identification error model has the highest accuracy in solving the target position parameters and rotation angle, and the statistical quantity D of the model is also the smallest.

[0218] 3) When only one measurement error exists, the model that identifies the corresponding systematic error has the smallest solution error, with an average position solution error of approximately 0.16m. It also provides the most accurate estimation of the systematic error and has the smallest statistic D. If an inappropriate systematic error identification model is chosen, the position solution accuracy will decrease, and non-existent systematic errors will be calculated. Furthermore, the model's statistic D will increase. For example, if the measurement data only contains a sound velocity systematic error, but a time delay error identification model is chosen, the average position solution error will be 0.74m, and a time delay error will be calculated, even though this simulation scenario does not incorporate the time delay error. If a solution model that identifies both sound velocity and time delay errors is chosen, the target position solution error will be 0.17m, representing a 6.15% increase in positioning error compared to the sound velocity error identification model, and a time delay error will also be calculated.

[0219] 4) When both sound velocity error and time delay error exist in the measurement data, the model that identifies both sound velocity and time delay errors has the smallest solution error. The average position solution error is around 0.17m, the calculated sound velocity error deviates from the true sound velocity error by 0.48%, and the calculated time delay error deviates from the true time delay error by 0.90%. Simultaneously, the statistical quantity D is also the smallest. If a model that only identifies one systematic error is used, the two systematic errors present in the measurement will be calculated into one systematic error. In this case, the average deviation of the calculated position parameters from the true value is greater than 0.7m, the calculated systematic error deviates significantly from the true value, and the statistical quantity D of this model is also larger.

[0220] 5) The model's statistic D is positively correlated with the target position calculation error. The smaller the statistic D, the smaller the target position calculation error, reflecting a better fit between the systematic error identification model and the real model, and higher calculation accuracy.

[0221] In summary, the analysis of the results shows that when random errors are relatively small compared to systematic errors, if multiple systematic error identification models can be selected during the solution process, the optimal systematic error identification model can be selected by calculating the statistics D of each model and according to the optimal model selection criteria.

[0222] Systematic errors in traditional long-baseline underwater positioning, such as inconsistency errors, sound velocity system errors, and time delay system errors, can lead to a decrease in underwater target positioning accuracy. Therefore, this application constructs a multi-beacon system error identification model to improve underwater positioning accuracy. For structural systematic errors caused by inconsistency, a positioning model under a multi-beacon system is constructed. For measurement element systematic errors present during the measurement process, a corresponding systematic error identification model is constructed based on the multi-beacon system positioning model. Since we do not know which systematic errors exist in the measurement data during actual positioning, and an inappropriate systematic error identification model can also affect positioning accuracy, this application constructs the optimal test statistic D for the model by analyzing the time delay residual and provides the optimal selection criterion for the systematic error identification model. Finally, this application designs numerical simulation scenarios to verify this criterion. Different measurement element systematic errors are added to the measurement data in each simulation scenario. The target position parameters are solved using various solution models proposed in this application, and the corresponding statistic D is calculated. Simulation results show that when the model's statistic D is minimized, the target position solution accuracy is the highest, verifying the effectiveness of the optimal model selection criterion. Therefore, the systematic error identification model and optimal model selection criteria proposed in this application can provide theoretical and technical support for high-precision measurement and navigation positioning of underwater targets.

[0223] This application constructs a long baseline positioning system error identification model based on a multi-beacon architecture. To correct structural system errors caused by inconsistencies in location, this application establishes the slant range as a function related to the positions of two underwater points (underwater beacon and long baseline station), the target radius, and the rotation angle, thereby transforming the traditional positioning model into a multi-beacon positioning model. Furthermore, addressing potential measurement element system errors such as sound velocity errors or time delay errors during underwater target positioning, this application constructs three system error identification models based on the multi-beacon positioning model: a sound velocity error identification model, a time delay error identification model, and a sound velocity and time delay error identification model.

[0224] The optimal selection criterion for the systematic error identification model in this application is as follows: Since the systematic errors present in the measurement data are unknown in practice, this application constructs the optimal test statistic of the model by analyzing the time delay residuals and provides the optimal selection criterion for the systematic error identification model, thereby achieving effective estimation of underwater target position parameters and reasonable identification of systematic error parameters.

[0225] It should be understood that the specific order or hierarchy of steps in the disclosed process is an example of an exemplary method. Based on design preferences, it should be understood that the specific order or hierarchy of steps in the process may be rearranged without departing from the scope of this disclosure. The appended method claims provide elements of various steps in an exemplary order and are not intended to limit the scope to the specific order or hierarchy described.

[0226] In the above detailed description, various features are combined together in a single embodiment to simplify this disclosure. This approach to disclosure should not be construed as reflecting an intention that embodiments of the claimed subject matter require more features than are explicitly stated in each claim. Rather, as reflected in the appended claims, the invention is presented with fewer features than all of the features of the single disclosed embodiment. Therefore, the appended claims are hereby explicitly incorporated into the detailed description, wherein each claim stands alone as a preferred embodiment of the invention.

[0227] The disclosed embodiments have been described above to enable any person skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein can be applied to other embodiments without departing from the spirit and scope of this disclosure. Therefore, this disclosure is not limited to the embodiments given herein, but is consistent with the broadest scope of the principles and novel features disclosed herein.

[0228] The foregoing description includes examples of one or more embodiments. It is certainly impossible to describe all possible combinations of components or methods in order to describe the above embodiments, but those skilled in the art will recognize that further combinations and arrangements of the various embodiments are possible. Therefore, the embodiments described in this application are intended to cover all such changes, modifications, and variations that fall within the scope of the appended claims. Furthermore, the term "comprising" as used in the specification or claims is interpreted in a manner similar to the term "including," as interpreted when used as a conjunction in the claims. Additionally, the use of any term "or" in the specification of the claims is intended to mean "non-exclusive or."

[0229] Those skilled in the art will also understand that the various illustrative logical blocks, units, and steps listed in the embodiments of the present invention can be implemented by electronic hardware, computer software, or a combination of both. To clearly demonstrate the interchangeability of hardware and software, the functions of the various illustrative components, units, and steps described above have been generally described. Whether such functionality is implemented through hardware or software depends on the specific application and the overall system design requirements. Those skilled in the art can implement the described functions using various methods for each specific application, but such implementation should not be construed as exceeding the scope of protection of the embodiments of the present invention.

[0230] The various illustrative logic blocks or units described in the embodiments of this invention can be implemented or operate the described functions using a general-purpose processor, digital signal processor, application-specific integrated circuit (ASIC), field-programmable gate array or other programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof. The general-purpose processor can be a microprocessor; alternatively, it can be any conventional processor, controller, microcontroller, or state machine. The processor can also be implemented using a combination of computing devices, such as a digital signal processor and a microprocessor, multiple microprocessors, one or more microprocessors combined with a digital signal processor core, or any other similar configuration.

[0231] The steps of the methods or algorithms described in the embodiments of this invention can be directly embedded in hardware, a software module executed by a processor, or a combination of both. The software module can be stored in RAM, flash memory, ROM, EPROM, EEPROM, registers, hard disk, removable disk, CD-ROM, or any other form of storage medium in the art. Exemplarily, the storage medium can be connected to the processor so that the processor can read information from and write information to the storage medium. Optionally, the storage medium can also be integrated into the processor. The processor and storage medium can be housed in an ASIC, which can be housed in a user terminal. Optionally, the processor and storage medium can also be housed in different components of the user terminal.

[0232] In one or more exemplary designs, the functions described in the embodiments of the present invention can be implemented in hardware, software, firmware, or any combination of these three. If implemented in software, these functions can be stored on a computer-readable medium or transmitted on a computer-readable medium in the form of one or more instructions or code. Computer-readable media include computer storage media and communication media that facilitate the transfer of computer programs from one place to another. Storage media can be any available media that can be accessed by a general-purpose or special-purpose computer. For example, such computer-readable media can include, but is not limited to, RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to carry or store program code in the form of instructions or data structures and other forms that can be read by a general-purpose or special-purpose computer, or a general-purpose or special-purpose processor. Furthermore, any connection can be suitably defined as a computer-readable medium, for example, if the software is transmitted from a website, server or other remote resource via a coaxial cable, fiber optic cable, twisted pair, digital subscriber line (DSL) or wirelessly, such as infrared, wireless and microwave, it is also included in the defined computer-readable medium. The disks and discs mentioned include compressed disks, laser discs, optical discs, DVDs, floppy disks, and Blu-ray discs. Disks typically copy data magnetically, while disks typically copy data optically using lasers. Combinations of the above can also be contained in computer-readable media.

[0233] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is 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.

Claims

1. A method for error identification in a multi-beacon long baseline positioning system, characterized in that, Includes the following steps: Obtain the initial long-baseline underwater positioning model; Based on the aforementioned long-baseline underwater positioning model and the geometric relationship between the underwater target center and the beacon, a multi-beacon underwater positioning model is established. A system error identification model is obtained based on the multi-beacon underwater positioning model; The time delay residual is calculated by using the system error identification model and combining it with the underwater target positioning process. By analyzing the time delay residual, the optimal test statistic D of the system error identification model is constructed, and the selection criterion of the system error identification model is obtained based on the optimal test statistic D. Select the optimal system error identification model according to the selection criteria; The system error identification model includes: a sound speed error identification model, a time delay error identification model, and a sound speed and time delay error identification model. The multi-beacon underwater positioning model is as follows: ， in, For the target to be tested, ; beacon Location, ; For the station Location, ; For acoustic signals from beacons to the station The one-way propagation delay is measured in seconds (s). The speed of sound underwater is expressed in m / s. is the rotation angle, in degrees; r is the target radius, in meters. For the first The station number corresponding to each beacon; The sound speed error identification model is specifically as follows: in, This is a measurement of the speed of sound. For acoustic signals from beacons to the station The one-way propagation delay is measured in seconds (s). This is the error in sound speed; The time delay error identification model is specifically as follows: in, This is a time delay measurement value; This is a time delay system error; This is the error in sound speed; The speed of sound underwater is expressed in m / s. The sound speed and time delay error identification model is specifically as follows: in, This is a measurement of the speed of sound. This is a time delay measurement value; This is a time delay system error; This is the error in sound speed; The speed of sound underwater is expressed in m / s. This refers to the time delay system error.

2. The error identification method for a multi-beacon long baseline positioning system according to claim 1, characterized in that, By comparing the magnitudes of the optimal test statistic D, the model with the smallest optimal test statistic D is the optimal system error identification model; the optimal test statistic D is: ； Among them, The sum of squared residuals; n is the number of measures, N is the number of unknowns, and σ is the standard deviation of the time delay random error.

3. An error identification device for a multi-beacon long baseline positioning system, characterized in that, The method for error identification of a multi-beacon long baseline positioning system according to any one of claims 1-2 includes: Acquisition unit, used to acquire the initial long baseline underwater positioning model; The construction unit is used to establish a multi-beacon underwater positioning model based on the long baseline underwater positioning model and the geometric relationship between the underwater target center and the beacon; The identification unit is used to obtain the system error identification model based on the multi-beacon underwater positioning model; The calculation unit is used to calculate the time delay residual by using the system error identification model and combining it with the underwater target positioning process; The analysis unit is used to construct the optimal test statistic D of the system error identification model by analyzing the time delay residual, and to obtain the selection criteria of the system error identification model based on the optimal test statistic D. The selection unit is used to select the optimal system error identification model according to the selection criteria.

4. The error identification device for a multi-beacon long baseline positioning system according to claim 3, characterized in that, The system error identification model includes: sound speed error identification model, time delay error identification model, and sound speed and time delay error identification model.

5. The error identification device for a multi-beacon long baseline positioning system according to claim 3, characterized in that, The multi-beacon underwater positioning model is as follows: ， in, For the target to be tested, ; beacon Location, ; For the station Location, ; For acoustic signals from beacons to the station The one-way propagation delay is measured in seconds (s). The speed of sound underwater is expressed in m / s. is the rotation angle, in degrees; r is the target radius, in meters. For the first The station number corresponding to each beacon.

6. The error identification device for a multi-beacon long baseline positioning system according to claim 4, characterized in that, The sound speed error identification model is specifically as follows: in, This is a measurement of the speed of sound. For acoustic signals from beacons to the station The one-way propagation delay is measured in seconds (s). For sound speed error, For the target to be tested, ; is the rotation angle, in degrees; r is the target radius, in meters. For the first The station number corresponding to each beacon. ; For the station Location, ; The time delay error identification model is specifically as follows: in, This is a time delay measurement value; This is a time delay system error; This is the error in sound speed; The speed of sound underwater is expressed in m / s. For the target to be tested, ; is the rotation angle, in degrees; r is the target radius, in meters. For the first The station number corresponding to each beacon. ; For the station Location, ; The sound speed and time delay error identification model is specifically as follows: in, This is a measurement of the speed of sound. This is a time delay measurement value; This is a time delay system error; This is the error in sound speed; The speed of sound underwater is expressed in m / s. This is a time delay system error; For the target to be tested, ; is the rotation angle, in degrees; r is the target radius, in meters. For the first The station number corresponding to each beacon. ; For the station Location, .

7. The error identification device for a multi-beacon long baseline positioning system according to claim 3, characterized in that, By comparing the magnitudes of the optimal test statistic D, the model with the smallest optimal test statistic D is the optimal system error identification model; the optimal test statistic D is: ； Among them, The sum of squared residuals; n is the number of measures, N is the number of unknowns, and σ is the standard deviation of the time delay random error.

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