A time slot displacement calculation method based on momentum intersection relaxation constraint

Abstract

The application provides a time slot displacement calculation method based on momentum intersection relaxation constraint, steps S1, selecting the motion position points of a positioned carrier in two continuous time slots, and marking the first position point as ST1 and the second position point as ST2; step S2, for the 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 '; step S3, based on the sphere intersection principle, converting the non-common point positioning problem of the positioned carrier into a common point solving problem; step S4, constructing an optimization problem of a relaxation constraint model, realizing the quantitative calculation of the time slot displacement, extracting the motion characteristics by selecting the motion position points of the continuous time slots to accurately estimate the virtual common point, eliminating the positioning equation no solution or conjugate solution problem caused by the motion of the positioned carrier, reducing the positioning error, and meanwhile, by introducing the relaxation constraint model, the calculation redundancy caused by the complex filtering algorithm can be avoided, and the 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 a long-distance and deep underwater operation scene, 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 transmission 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 the sound signal propagation, resulting in that the spatial position of the carrier receiving the sound signals transmitted by different beacons is dynamically changed, 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 receives the signals of each beacon at the same spatial point, 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 in some scenarios, a conjugate solution with extremely low precision (i.e. a pseudo-solution symmetric to the true position) can be solved, which seriously deviates from the actual position of the carrier.

[0004] For this problem, the existing technical solutions have obvious limitations: for a 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. Although this simplification can reduce the calculation difficulty, it will introduce a positioning error that cannot be ignored, especially in long-distance propagation scenarios, the cumulative error can reach several meters or even dozens of meters, which cannot meet the high-precision operation requirements; 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 as the number of carriers in the underwater operation cluster increases, the calculation complexity will increase exponentially, which is difficult to adapt to the real-time solution requirements 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 solving the positioning equation.

[0006] The technical solution of the present application is implemented as follows:

[0007] A time slot displacement calculation method based on momentum intersection relaxation constraint, comprising the following steps:

[0008] Step S1, selecting motion position points of the positioned carrier in two continuous time slots, denoted as a first position point ST1 and a second position point ST2 respectively;

[0009] Step S2, constructing a gradient description model based on the motion continuity of the first position point ST1 and the second position point ST2 for a target time slot position point ST k of the positioned carrier, and estimating a virtual common point ST k ';

[0010] Step S3, converting the non-common point positioning problem of the positioned carrier into a common point solving problem based on the sphere intersection principle;

[0011] Step S4, constructing an optimization problem of a relaxation constraint model to realize the quantitative calculation of the time slot displacement.

[0012] Preferably, the positioned carrier comprises an autonomous underwater vehicle.

[0013] Preferably, the step S1 extracts motion features of the positioned carrier in adjacent time slots through the first position point ST1 and the second position point ST2 when selecting the first position point ST1 and the second position point ST2, and the motion features comprise displacement vectors, motion velocities and directions.

[0014] Preferably, the step S2 comprises the following steps:

[0015] 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;

[0016] Step S22, constructing a gradient description of the adjacent time slot position point ST k+1 for the target time slot position point ST k ;

[0017] Step S23, estimating the virtual common point ST k ' based on the gradient description .

[0018] Preferably, the momentum parameter Q in the step S21 is the product of the mass and the instantaneous velocity of the positioned carrier, and the initial value thereof is estimated based on the motion features of the first position point ST1 and the second position point ST2.

[0019] Preferably, the expression of the gradient description of the adjacent time slot position point ST k+1 is as follows:

[0020] ;

[0021] wherein is a momentum coefficient, learning rate of the gradient for increment distance, , are momentum parameters of the positioned carrier at target time slot position point ST k and adjacent time slot position point ST k+1 , is a gradient description of target time slot position point ST k , is a partial derivative of ST k with respect to , is a time slot momentum of adjacent time slot position point ST k+1 .

[0022] Preferably, the specific step of step S23 is: extracting the gradient description of target time slot position point ST k based on the expression of gradient description , virtual co-point ST k '= ST k + .

[0023] Preferably, the specific step of step S3 is:

[0024] For virtual co-point ST k ' and adjacent time slot position point ST k+1 , respectively, a distance constraint with a transmitting beacon is established:

[0025] ;

[0026] wherein is the i-th virtual co-point, is the j-th adjacent time slot position point, , is the i, j-th transmitting beacon, , are a theoretical ranging value and a ranging error of virtual co-point ST k ' to the i-th transmitting beacon , are a theoretical ranging value and a ranging error of adjacent time slot position point ST k+1 to the j-th transmitting beacon .

[0027] Preferably, the optimization problem of step S4 is:

[0028] ;

[0029] wherein is a motion state function of the positioned carrier, the first term Error between the ith virtual common point and the jth emitting beacon , denotes the target time slot position point ST k deviation from the previous calculation result, is the relaxation coefficient.

[0030] Compared with the prior art, the beneficial effects of the present application are:

[0031] 1. Positioning accuracy is significantly improved: by selecting the motion position points of consecutive time slots to extract motion features, combining momentum parameters to construct a gradient description model, and accurately estimating the virtual common point, the non-common point problem is converted into a common point solution, which fundamentally eliminates the problem of no solution or conjugate solution of the positioning equation caused by the motion of the positioned carrier. Compared with the traditional method of ignoring displacement or relying on Kalman filtering, the positioning error is reduced by more than 30%;

[0032] 2. The calculation efficiency is greatly optimized: the relaxation constraint model is introduced, and the relaxation coefficient flexible balance positioning accuracy and historical result consistency, avoiding the calculation redundancy brought by complex filtering algorithm, reducing the calculation complexity, which can meet the real-time solution demand of underwater operation cluster, especially suitable for multi-carrier cooperative operation scene.

[0033] 3. Stronger dynamic adaptability: the gradient description model is constructed based on the continuity of the carrier motion, 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-high-speed underwater equipment.

[0034] 4. Outstanding engineering application value: the distance constraint based on the emitting 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 significantly improves the anti-interference ability and application reliability of deep sea positioning system in complex environment, and provides key technical support for deep sea resource exploration, underwater rescue and other scenes. BRIEF DESCRIPTION OF DRAWINGS

[0035] 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 also be obtained by those skilled in the art without creative labor.

[0036] Fig. 1 is a flowchart of a time slot displacement calculation method based on momentum intersection relaxation constraint of the present application;

[0037] Fig. 2 A schematic diagram of non-common point reception by a positioned carrier within a sound propagation time slot;

[0038] Fig. 3 This is a schematic diagram of virtual concurrent gradient optimization and time slot displacement correction under momentum constraints. Detailed Implementation

[0039] To better understand the technical content of this invention, a specific embodiment is provided below, and the invention will be further described in conjunction with the accompanying drawings.

[0040] See Figs. 1 to 3 The present invention provides a method for calculating time slot displacement based on momentum convergence relaxation constraints, comprising the following steps:

[0041] Step S1: Select the motion position points of the positioning carrier, including autonomous underwater vehicles, in two consecutive time slots, and denot them as the first position point ST1 and the second position point ST2, respectively. Extract the motion characteristics of the positioning carrier in adjacent time slots through the first position point ST1 and the second position point ST2. The motion characteristics include displacement vector, motion velocity and direction.

[0042] The target vehicle includes autonomous underwater vehicles (AUVs), etc. When it moves underwater, the starting time is t0, the corresponding starting point is ST0, and it passes through... Afterwards, the vehicle reaches the first position point ST1 and the second position point ST2. The first position point ST1 and the second position point ST2 are the positions where the positioned vehicle receives the acoustic wave signals emitted by the transmitting beacons SL1 and SL2, respectively, and the times of reception are respectively... as well as The positioning vehicle then continues to move underwater until it reaches the target time slot location ST. k The time when the acoustic signal transmitted by the transmitting beacon is received is However, due to the obstruction effect of the water medium on the propagation of sound waves, the positioning carrier is not stationary during the process from the transmission of the sound signal by the beacon to the reception of the sound signal by the positioning carrier. Instead, it will continue to move. After determining the first position point ST1 and the second position point ST2, the running characteristics of the first position point ST1 and the second position point ST2 can be extracted respectively, which can be used for the calculation of the initial parameters of the subsequent gradient description model.

[0043] Step S2: Target time slot location point ST of the positioned carrier. k A gradient description model is constructed based on the motion continuity of the first position point ST1 and the second position point ST2, and the virtual co-point ST is estimated. k The specific steps are as follows:

[0044] Step S21, estimating a momentum parameter Q for characterizing the motion inertia of the positioned carrier based on the first position point ST1 and the second position point ST2, the momentum parameter Q being the product of the mass and the instantaneous velocity of the positioned carrier, and the initial value thereof being estimated based on the motion characteristics of the first position point ST1 and the second position point ST2;

[0045] Step S22, constructing a gradient description of the adjacent time slot position point ST k k+1 The expression of the gradient description of the adjacent time slot position point ST k+1 is as follows:

[0046] ;

[0047] wherein is a momentum coefficient for adjusting the influence weight of the momentum on the gradient, is a learning rate of the incremental distance on the gradient for controlling the step length of the gradient update, is the momentum parameter of the positioned carrier at the target time slot position point ST k , which is calculated based on the motion characteristics of the historical position points including ST1 and ST2, is the gradient description of the target time slot position point ST k , is the partial derivative of ST k with respect to , which characterizes the rate of change of the position with respect to the gradient, is the time slot momentum of the adjacent time slot position point ST k+1 .

[0048] Step S23, estimating a virtual common point ST k ' based on the gradient description , extracting the gradient description of the target time slot position point ST k from the expression of the gradient description , and the virtual common point ST k ' = ST k + .

[0049] By constructing the gradient description model, the motion continuity of the previous position points ST1 and ST2 is utilized to associate the target time slot position point ST k with the adjacent point ST k+1 , estimate the virtual common point ST k ', effectively solve the problem of non-coincidence of the positions between time slots caused by the motion of the carrier, lay a foundation for converting the non-common point positioning into common point solving in the subsequent, and improve the solvability and accuracy of the positioning equation. ​​​

[0050] Step S3, based on the principle of sphere intersection, the non-coplanar positioning problem of the positioned carrier is converted into a coplanar solution problem, and the specific steps are as follows:

[0051] For virtual copoint ST k ' and adjacent time slot position point ST k+1 , respectively, the distance constraints of the transmitting beacons are established:

[0052] ;

[0053] Wherein is the i-th virtual copoint, is the j-th adjacent time slot position point, , is the i-th and j-th transmitting beacon, , is the theoretical ranging value and ranging error of the virtual copoint ST k ' to the i-th transmitting beacon , respectively, is the theoretical ranging value and ranging error of the adjacent time slot position point ST k+1 to the j-th transmitting beacon .

[0054] Since the position of the virtual copoint is the ideal target position, the principle of sphere intersection is selected to convert the non-coplanar positioning problem of the positioned carrier into a coplanar solution problem, and the distance constraints of the transmitting beacons are established based on the principle of sphere intersection, which effectively utilizes the basic principle of acoustic positioning, makes the positioning process more consistent with the actual physical scene, not only solves the problem of no solution or conjugate solution caused by non-coplanar conditions in traditional positioning, but also provides a feasible framework for subsequent accurate positioning calculation, greatly improves the reliability and accuracy of positioning, and ensures that the positioning result can truly reflect the actual position of the positioned carrier.

[0055] 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:

[0056] ;

[0057] Wherein is the motion state function of the positioned carrier, the first term is the error between the i-th virtual copoint and the j-th transmitting beacon , representing the positioning accuracy deviation, represents the deviation of the target time slot position point ST k from the previous calculation result, is the relaxation coefficient, used to balance the weight of the two errors and realize the flexible adjustment of the constraint strength.

[0058] Constrained by the gradient and the acoustic ranging parameters, the constraint condition is converted into a flexible form, and the optimization problem of the relaxation constraint model is constructed. By balancing the error sum of squares of the target time slot position point and the virtual common point position, and the deviation sum of squares of the target time slot position point and the last 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, enhance the adaptability of the algorithm to different motion scenes, effectively avoid the result from fluctuating greatly due to single measurement error or sudden interference, improve the stability and robustness of the displacement quantitative calculation, and provide a strong guarantee for the continuous and reliable positioning in the complex underwater environment.

[0059] The present application can overcome the influence of the time slot motion error of the positioned carrier, weaken the influence of the space error dispersion in the time slot interval, analyze the spatial gradient change of the motion of the positioned carrier in the time slot when the sound signal propagates, combine the ranging factors, introduce the relaxation rule and the constraint condition to optimize the calculation process of the sphere intersection, flexibly adjust the constraint strength, reduce the negative influence of the time slot factors, introduce the virtual common point method to correct the target virtual position, eliminate the non-common point problem caused by the motion of the positioned carrier, and significantly improve the accuracy and rapidity of the system positioning calculation, further improve the positioning precision and the real-time calculation ability of the system, provide an efficient calculation framework for the deep sea positioning system, and significantly improve the application ability of the deep sea positioning system in the complex underwater environment.

[0060] The above only describes the preferred embodiments of the present application and does not 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 method for calculating time-slot displacement based on momentum convergence relaxation constraints, characterized in that, Includes the following steps: Step S1: Select the movement position points of the positioning carrier in two consecutive time slots, and denot them as the first position point ST1 and the second position point ST2, respectively; Step S2: Target time slot location point ST of the positioned carrier. k A gradient description model is constructed based on the motion continuity of the first position point ST1 and the second position point ST2, and the virtual co-point ST is estimated. k '; Step S3: Based on the principle of sphere intersection, the non-common point localization problem of the carrier to be located is transformed into a common point solution problem; Step S4: Construct an optimization problem for a relaxed constraint model to achieve quantitative calculation of time slot displacement; The specific steps of step S2 are as follows: Step S21: Estimate the momentum parameter Q, which characterizes the motion 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 location point ST k Construct the nearest time slot location point ST k+1 gradient description ; Step S23: Gradient-based description Estimate virtual concurrent points ST k '; The specific steps of step S3 are as follows: For virtual common point ST k 'and adjacent time slot location point ST k+1 Establish distance constraints for each beacon: ； in For the i-th virtual common point, Let j be the location of the nearest time slot. , For the i-th and j-th transmitting beacons, , They are virtual common points ST k 'To the i-th transmitting beacon The theoretical ranging value and ranging error, These are the adjacent time slot locations ST. k+1 up to the j-th transmitting beacon The theoretical distance measurement value and distance measurement error; The optimization problem in step S4 is: ； in Let be the motion state function of the positioned carrier, the first term For the i-th virtual common point With the j-th transmitting beacon The error between them Indicates the target time slot location point ST k The deviation from the previous calculation result, is the relaxation coefficient.

2. The time-slot displacement calculation method based on momentum convergence relaxation constraints according to claim 1, characterized in that, The carrier being located includes an autonomous underwater vehicle.

3. The time-slot displacement calculation method based on momentum convergence relaxation constraints according to claim 1, characterized in that, In step S1, a first position point ST1 and a second position point ST2 are selected. The 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 displacement vector, motion velocity and direction.

4. The time-slot displacement calculation method based on momentum convergence relaxation constraints according to claim 1, characterized in that, In step S21, the momentum parameter Q is the product of the mass and instantaneous velocity of the positioned carrier, and its initial value is estimated based on the motion characteristics of the first position point ST1 and the second position point ST2.

5. The time-slot displacement calculation method based on momentum convergence relaxation constraints according to claim 1, characterized in that, The nearest time slot location point ST k+1 gradient description The expression is: ； in The momentum coefficient, The learning rate for incremental distance with respect to the gradient is . , These are the locations of the positioned vehicle at the target time slot ST. k and adjacent time slot location point ST k+1 momentum parameters, For the target time slot location point ST k Gradient description, ST k about The partial derivatives, For the nearest time slot location point ST k+1 The time slot momentum.

6. The time-slot displacement calculation method based on momentum convergence relaxation constraints according to claim 4, characterized in that, The specific steps of step S23 are as follows: based on gradient description Extracting the target time slot location point ST from the expression k gradient description Virtual concurrent ST k '=ST k + .

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