Time slot displacement calculation method based on momentum intersection relaxation constraint

Abstract

The invention provides a time slot displacement calculation method based on momentum intersection relaxation constraint, and the method comprises the steps: S1, selecting motion position points of a positioned carrier in two continuous time slots, and recording the motion position points as a first position point ST1 and a second position point ST2; s2, aiming at a target time slot position point STk of the positioned carrier, constructing a gradient description model based on motion continuity of the first position point ST1 and the second position point ST2, and estimating a virtual common point STk '; s3, based on a sphere intersection principle, converting a non-concurrent positioning problem of the positioned carrier into a concurrent solution problem; and S4, constructing an optimization problem of a relaxation constraint model, realizing quantitative calculation of time slot displacement, accurately estimating a virtual common point by selecting motion position points of continuous time slots to extract motion features, eliminating the problem of no solution or conjugate solution of a positioning equation caused by motion of a positioned carrier, reducing positioning errors, and meanwhile, by introducing the relaxation constraint model, realizing quantitative calculation of time slot displacement. Calculation redundancy caused by a complex filtering algorithm can be avoided, and calculation complexity is reduced.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of underwater acoustic positioning, and particularly relates to a time slot displacement calculation method based on momentum intersection relaxation constraint. BACKGROUND

[0002] In the scene of long-distance and large-depth underwater operation, due to the significant retardation of the water medium to the propagation of sound waves, the sound signal needs to experience a long propagation time from emission to reception, and during this period, the underwater moving carrier to be positioned is not in a static state, but continuously moves within the time slot of sound signal propagation, resulting in that the spatial position of the carrier when receiving the sound signals emitted by different beacons is dynamically changing, and the actual station position at the receiving time is significantly different.

[0003] This non-copoint condition caused by the space-time misalignment directly affects the construction and solution of the positioning equation: in the traditional positioning model, it is usually assumed that the carrier is at the same spatial point when receiving the signals of each beacon, and the actual position deviation will break this premise, resulting in no solution of the positioning equation set due to the mismatch of the constraint conditions; even if it can be solved in some scenarios, it is easy to produce a conjugate solution with extremely low precision (i.e. a pseudo-solution symmetrical to the true position), which seriously deviates from the actual position of the carrier.

[0004] For this problem, the existing technical solutions have obvious limitations: for the carrier with slow moving speed, the conventional method is to directly ignore the displacement within the time slot and approximate the receiving positions at different times as the same point, which can reduce the calculation difficulty, but will introduce a positioning error that cannot be ignored, especially in the scene of long-distance propagation, the cumulative error can reach several meters or even dozens of meters, which cannot meet the demand of high-precision operation; another solution is to dynamically estimate the displacement by using state estimation algorithms such as Kalman filtering, which can correct the deviation to a certain extent, but this kind of algorithm needs to continuously update the state equation and observation equation, which consumes a lot of computing resources, and with the increase of the number of carriers in the underwater operation cluster, the calculation complexity will increase exponentially, which is difficult to adapt to the real-time solution requirement of cluster collaborative operation, and seriously restricts the efficiency and response speed of the underwater operation system. SUMMARY

[0005] In view of this, the present application proposes a time slot displacement calculation method based on momentum intersection relaxation constraint, which introduces a virtual copoint to convert the non-copoint problem caused by target displacement into a copoint, thereby reducing the degrees of freedom for the solution of the positioning equation.

[0006] The technical solution of the present application is implemented as follows: A time slot displacement calculation method based on momentum intersection relaxation constraint, comprising the following steps: Step S1: Select the moving position points of the positioned carrier in two consecutive time slots, which are respectively recorded as the first position point ST1 and the second position point ST2; Step S2: Target time slot position point ST of the located carrier k , construct a gradient description model based on the motion continuity of the first position point ST1 and the second position point ST2, and estimate the virtual common point ST k '; Step S3: Based on the sphere intersection principle, the non-co-point positioning problem of the positioned carriers is converted into a co-point solving problem; Step S4: construct an optimization problem of a relaxed constraint model to achieve quantitative calculation of time slot displacement.

[0007] Preferably, the positioned carrier includes an autonomous underwater vehicle.

[0008] Preferably, the step S1 selects a first position point ST1 and a second position point ST2, and extracts motion features of the positioned carrier in adjacent time slots through the first position point ST1 and the second position point ST2, wherein the motion features include a displacement vector, a motion speed and a direction.

[0009] Preferably, the specific steps of step S2 are: Step S21, estimating a momentum parameter Q for characterizing the inertia of the positioned carrier based on the first position point ST1 and the second position point ST2; Step S22: For the target time slot position ST k , construct the adjacent time slot position point ST k+1 Gradient description ; Step S23: Based on gradient description Estimated virtual common point ST k '.

[0010] Preferably, the momentum parameter Q in step S21 is the product of the mass of the positioned carrier and the instantaneous velocity, and its initial value is estimated based on the motion characteristics of the first position point ST1 and the second position point ST2.

[0011] Preferably, the adjacent time slot position point ST k+1 Gradient description The expression is: ; in is the momentum coefficient, is the learning rate of the incremental distance to gradient, 、 They are the located carrier at the target time slot position ST k and adjacent time slot position point ST k+1a gradient description of the target time slot position point ST a gradient description of the target time slot position point ST k a gradient description of the target time slot position point ST a gradient description of the target time slot position point ST k a gradient description of the target time slot position point ST a gradient description of the target time slot position point ST a gradient description of the target time slot position point ST k+1 a gradient description of the target time slot position point ST

[0012] Preferably, the specific step of step S23 is: extracting a gradient description of the target time slot position point ST a gradient description of the target time slot position point ST k a gradient description of the target time slot position point ST a gradient description of the target time slot position point ST k a gradient description of the target time slot position point ST k a gradient description of the target time slot position point ST .

[0013] Preferably, the specific step of step S3 is: a gradient description of the target time slot position point ST k a gradient description of the target time slot position point ST k+1 a gradient description of the target time slot position point ST ; wherein is the ith virtual common point, is the jth adjacent time slot position point, , is the ith, jth transmitting beacon, , is a theoretical ranging value of the virtual common point ST k to the ith transmitting beacon and a ranging error, is a theoretical ranging value of the adjacent time slot position point ST k+1 to the jth transmitting beacon and a ranging error.

[0014] Preferably, the optimization problem of step S4 is: ; wherein is a motion state function of the positioned carrier, the first term is an error between the ith virtual common point and the jth transmitting beacon , represents a deviation of the target time slot position point ST k from the previous calculation result, is a relaxation coefficient.

[0015] Compared with the prior art, the present application has the following beneficial effects: 1. Positioning accuracy is significantly improved: By selecting the motion position points of continuous time slots to extract motion features, a gradient description model is constructed by combining momentum parameters to accurately estimate the virtual common point, and the non-common point problem is converted into common point solving, which fundamentally eliminates the problem of no solution or conjugate solution of positioning equation caused by the motion of the positioned carrier. Compared with the traditional method of ignoring displacement or relying on Kalman filter, the positioning error is reduced by more than 30%; 2. The calculation efficiency is greatly optimized: the relaxation constraint model is introduced, and the relaxation coefficient The flexibility of the balance positioning accuracy is consistent with the historical results, which avoids the calculation redundancy brought by the complex filtering algorithm, reduces the calculation complexity, and can meet the real-time solving demand of underwater operation cluster, especially suitable for multi-carrier cooperative operation scene.

[0016] 3. Stronger dynamic adaptability: The gradient description model is constructed based on the continuity of the carrier motion, and the momentum parameter and the gradient update step can be dynamically adapted according to the actual motion speed, and the relaxation coefficient is adjusted with the carrier speed threshold, which can stably cope with the variable speed and variable direction motion of the carrier in the complex dynamic environment underwater, and the application range covers low-speed to medium-speed underwater equipment.

[0017] 4. The engineering application value is outstanding: The distance constraint based on the launch beacon and the virtual common point correction mechanism can be directly integrated into the existing underwater acoustic positioning system (such as long baseline, ultra-short baseline system), without additional hardware modification, which can significantly improve the anti-interference ability and application reliability of deep sea positioning system in complex environment, and provide key technical support for deep sea resource exploration, underwater rescue and other scenes. BRIEF DESCRIPTION OF DRAWINGS

[0018] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following will briefly introduce the drawings needed to be used in the embodiment description. Obviously, the drawings in the following description are only the preferred embodiments of the present application, and other drawings can be obtained by those skilled in the art without creating labor intensity.

[0019] Fig. 1 The flow chart of a time slot displacement calculation method based on momentum intersection relaxation constraint of the present application; Fig. 2 The schematic diagram of non-common point receiving of the positioned carrier in acoustic propagation time slot; Fig. 3 The schematic diagram of virtual common point gradient optimization and time slot displacement correction under momentum constraint. DETAILED DESCRIPTION

[0020] In order to better understand the technical content of the present application, a specific embodiment is provided below, and the present application is further described in combination with the drawings.

[0021] Referring toFigs. 1 to 3 The application provides a time slot displacement calculation method based on momentum intersection relaxation constraint, comprising the following steps: Step S1, selecting the motion position points of a positioned carrier including an autonomous underwater vehicle in two continuous time slots, respectively denoted as a first position point ST1 and a second position point ST2, extracting the motion characteristics of the positioned carrier in adjacent time slots through the first position point ST1 and the second position point ST2, wherein the motion characteristics include a displacement vector, a motion speed and a direction; The positioned carrier includes an autonomous underwater vehicle (AUV) and the like, which moves underwater, and the starting time is t0, and the starting point is ST0, respectively reaches the first position point ST1 and the second position point ST2, and the first position point ST1 and the second position point ST2 are positions at which the positioned carrier receives acoustic wave signals transmitted by transmitting beacons SL1 and SL2, respectively, and the receiving time is t1 and t2, respectively. And then the positioned carrier continuously moves underwater and moves to a target time slot position point ST k , and the time at which the positioned carrier receives the acoustic wave signals transmitted by the transmitting beacon is t3. However, due to the retardation of the water medium to acoustic wave propagation, the positioned carrier continuously moves in the process from the time when the transmitting beacon transmits the acoustic signals to the time when the positioned carrier receives the acoustic signals, and after the first position point ST1 and the second position point ST2 are determined, the running characteristics of the first position point ST1 and the second position point ST2 can be extracted, which can be used for initial parameter calculation of a subsequent gradient description model.

[0022] Step S2, for a target time slot position point ST k of the positioned carrier, constructing a gradient description model based on the motion continuity of the first position point ST1 and the second position point ST2, and estimating a virtual common point ST k ', and the specific steps are as follows: Step S21, estimating a momentum parameter Q for representing the motion inertia of the positioned carrier based on the first position point ST1 and the second position point ST2, wherein the momentum parameter Q is the product of the mass and the instantaneous speed of the positioned carrier, and the initial value is estimated based on the motion characteristics of the first position point ST1 and the second position point ST2; Step S22, for the target time slot position point ST k , constructing a gradient description k+1 of a nearby time slot position point ST k+1 , and the expression of the gradient description of the nearby time slot position point ST k+1 is as follows: ​​​is the momentum coefficient, which is used to adjust the weight of the influence of momentum on the gradient. is the learning rate of the incremental distance to the gradient, which is used to control the step size of the gradient update. The carrier is located at the target time slot position ST k The momentum parameters are calculated based on the motion characteristics of historical positions including ST1 and ST2. The target time slot position ST k The gradient description of For ST k about The partial derivative of , characterizes the rate of change of position with gradient, is the adjacent time slot position point ST k+1 The time slot momentum.

[0023] Step S23: Based on gradient description Estimated virtual common point ST k ', from the gradient description The expression to extract the target time slot position point ST k Gradient description , virtual common point ST k '=ST k + .

[0024] By constructing a gradient description model, the target time slot position point ST is converted to the target time slot position point ST by using the motion continuity of the previous position points ST1 and ST2. k With the nearby point ST k+1 Association, estimate the virtual common point ST k ', effectively solving the problem of position mismatch between time slots caused by carrier motion, laying the foundation for the subsequent transformation of non-collateral positioning into collateral solution, and improving the solvability and accuracy of the positioning equation.

[0025] Step S3: Based on the sphere intersection principle, the non-co-point positioning problem of the positioned carrier is transformed into a co-point solving problem. The specific steps are as follows: For the virtual common point ST k ' and adjacent time slot position point ST k+1 Establish distance constraints from the transmitting beacon respectively: ; in is the i-th virtual common point, is the jth adjacent time slot position point, 、 are the i-th and j-th transmitting beacons, 、 They are virtual common points ST k 'To the i-th transmitting beacon theoretical ranging value and ranging error of the i-th virtual common point, respectively, are adjacent time slot position points ST k+1 to the j-th emitting beacon theoretical ranging value and ranging error of the i-th virtual common point.

[0026] Since the position of the virtual common point is the ideal target position, the non-common point positioning problem of the positioned carrier is converted into a common point solving problem by selecting the sphere intersection principle. The distance constraint based on the sphere intersection principle effectively utilizes the basic principle of acoustic positioning, making the positioning process more consistent with the actual physical scene. Not only does it solve the problem of no solution or conjugate solution caused by non-common point conditions in traditional positioning, but it also provides a feasible framework for subsequent accurate positioning calculation, greatly improving the reliability and accuracy of positioning, and ensuring that the positioning result truly reflects the actual position of the positioned carrier.

[0027] Step S4, construct the optimization problem of the relaxed constraint model to realize the quantitative calculation of the time slot displacement, and the optimization problem of the relaxed constraint model is: ; wherein is the motion state function of the positioned carrier, the first term is the error between the i-th virtual common point and the j-th emitting beacon , representing the positioning accuracy deviation, denotes the deviation of the target time slot position point ST k from the previous calculation result, is the relaxation coefficient, used to balance the weights of the two errors and realize flexible adjustment of the constraint strength.

[0028] subject to the joint constraints of the gradient and the acoustic ranging parameters, the constraint condition is converted into a flexible form, and the optimization problem of the relaxed constraint model is constructed. By balancing the sum of squares of the errors of the target time slot position point and the virtual common point position, as well as the sum of squares of the deviation of the target time slot position point from the previous calculation result, the quantitative calculation of the time slot displacement is realized, wherein the relaxation coefficient can flexibly adjust the constraint strength according to the motion state of the positioned carrier, enhancing the adaptability of the algorithm to different motion scenarios. While ensuring the positioning accuracy, it effectively avoids the result from fluctuating greatly due to single measurement error or sudden interference, improving the stability and robustness of the displacement quantitative calculation, and providing a strong guarantee for continuous and reliable positioning in complex underwater environments.

[0029] The present application can overcome the influence of the positioning carrier time slot movement error, weaken the influence of the space error dispersion in the time slot interval, analyze the spatial gradient change of the positioning carrier movement in the sound signal propagation time slot, combine the ranging factor, introduce the relaxation rule and the constraint condition optimization sphere intersection calculation process, flexibly adjust the constraint strength, reduce the negative influence of the time slot factor, introduce the virtual common point method to correct the target virtual position, eliminate the non-common point problem caused by the positioning carrier movement, thereby significantly improve the accuracy and rapidity of the system positioning calculation, further improve the positioning precision and the system real-time calculation ability, provide an efficient calculation framework for the deep sea positioning system, and significantly improve the application ability in the complex underwater environment.

[0030] The above merely describes the preferred embodiments of the present application and is not intended to limit the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A time slot displacement calculation method based on momentum intersection relaxation constraint, characterized in that: The following steps are involved: Step S1: Select the moving position points of the positioned carrier in two consecutive time slots, which are respectively recorded as the first position point ST1 and the second position point ST2; Step S2: Target time slot position point ST of the located carrier k , construct a gradient description model based on the motion continuity of the first position point ST1 and the second position point ST2, and estimate the virtual common point ST k '; Step S3: Based on the sphere intersection principle, the non-co-point positioning problem of the positioned carriers is converted into a co-point solving problem; Step S4: construct an optimization problem of a relaxed constraint model to achieve quantitative calculation of time slot displacement.

2. The time slot displacement calculation method based on momentum convergence relaxation constraint according to claim 1, characterized in that: The positioned carrier includes an autonomous underwater vehicle.

3. The time slot displacement calculation method based on momentum convergence relaxation constraint according to claim 1, characterized in that: In step S1, a first position point ST1 and a second position point ST2 are selected, and motion features of the positioned carrier in adjacent time slots are extracted through the first position point ST1 and the second position point ST2. The motion features include a displacement vector, a motion speed, and a direction.

4. The time slot displacement calculation method based on momentum convergence relaxation constraint according to claim 3 is characterized in that: The specific steps of step S2 are: Step S21, estimating a momentum parameter Q for characterizing the inertia of the positioned carrier based on the first position point ST1 and the second position point ST2; Step S22: For the target time slot position ST k , construct the adjacent time slot position point ST k+1 Gradient description ; Step S23: Based on gradient description Estimated virtual common point ST k '.

5. The time slot displacement calculation method based on momentum convergence relaxation constraint according to claim 4 is characterized in that: The momentum parameter Q in step S21 is the product of the mass of the positioned carrier and the instantaneous velocity, and its initial value is estimated based on the motion characteristics of the first position point ST1 and the second position point ST2.

6. The time slot displacement calculation method based on momentum intersection relaxation constraint according to claim 4 is characterized in that: The adjacent time slot position point ST k+1 Gradient description The expression is: ； in is the momentum coefficient, is the learning rate of the incremental distance to gradient, 、 They are the located carrier at the target time slot position ST k and adjacent time slot position point ST k+1 The momentum parameter, The target time slot position ST k The gradient description of For ST k about The partial derivative of is the adjacent time slot position point ST k+1 The time slot momentum.

7. The time slot displacement calculation method based on momentum convergence relaxation constraint according to claim 5, characterized in that: The specific steps of step S23 are: based on the gradient description The expression to extract the target time slot position point ST k Gradient description , virtual common point ST k '=ST k + .

8. The time slot displacement calculation method based on momentum convergence relaxation constraint according to claim 1 is characterized in that: The specific steps of step S3 are: For the virtual common point ST k ' and adjacent time slot position point ST k+1 Establish distance constraints from the transmitting beacon respectively: ； in is the ith virtual common point, is the jth adjacent time slot position point, 、 are the i-th and j-th transmitting beacons, 、 They are virtual common points ST k 'To the i-th transmitting beacon The theoretical distance measurement value and distance measurement error, They are adjacent time slot position points ST k+1 To the jth transmitting beacon The theoretical distance measurement value and distance measurement error.

9. The time slot displacement calculation method based on momentum convergence relaxation constraint according to claim 1, characterized in that: The optimization problem of step S4 is: ； in is the motion state function of the positioned carrier, the first term is the i-th virtual common point With the jth transmitting beacon The error between Indicates the target time slot position point ST k The deviation from the previous calculation result, is the relaxation coefficient.

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