Sea surface buoy positioning method and device based on zeroing neural dynamics to resist periodic noise

Abstract

This invention discloses a method and device for positioning a sea surface buoy based on zeroing neural dynamics to combat periodic noise. The method relates to the field of sea surface buoy positioning. The method comprises the following steps: establishing a position coordinate equation for the sea surface buoy; constructing a corresponding time-varying linear equation system based on the position coordinate equation for the sea surface buoy; and constructing an improved ZND model. The improved ZND model is used to solve the time-varying linear equation system to obtain the coordinate information of the sea surface buoy. The invention constructs an improved ZND model (i.e., the TPZND model) to address buoy positioning in noisy environments. Simulation results show that, compared with traditional ZND models and integral enhanced ZND (IEZND), the TPZND model exhibits superior convergence accuracy and speed under conditions of additive periodic noise simulating ocean motion. This invention provides enhanced noise resistance for sea surface buoy positioning.

Description

Technical Field

[0001] The present invention relates to the field of sea surface buoy positioning, and in particular to a sea surface buoy positioning method and device based on zeroing neural dynamics and anti-periodic noise. Background Art

[0002] Real-time location information for surface buoys is typically provided by GPS. However, given the inherent limitations of GPS technology, such as multipath effects and poor satellite geometry, it is difficult to accurately locate buoys in rainy or foggy ocean environments, which reduces positioning accuracy. In such situations, angle-of-arrival (AOA) positioning technology combined with wireless sensor networks can be used as an auxiliary method to improve the positioning accuracy of surface buoys.

[0003] However, the position of buoys on the sea surface is variable. In this case, the position of the signal source changes over time, which introduces additional complexity and transforms the problem into a time-varying positioning problem. Although AOA-based positioning methods are effective in many static and dynamic scenarios, they are susceptible to severe impacts from noise, dynamic environmental factors, and node mobility. For example, the complex movement of the sea water constantly introduces noise to the buoy, causing it to sway and change the direction of the antenna, ultimately affecting positioning accuracy. Summary of the Invention

[0004] In response to the above-mentioned deficiencies in the prior art, the present invention provides a sea surface buoy positioning method and device based on zeroing neurodynamics and anti-periodic noise, which solves the problem that the existing AOA-based positioning method is easily affected by the noise caused by sea water movement, resulting in affected positioning accuracy.

[0005] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is:

[0006] A method for positioning a sea surface buoy based on zeroing neural dynamics and anti-periodic noise is provided, which includes the following steps:

[0007] Establish the position coordinate equation of the sea surface buoy;

[0008] Based on the position coordinate equation of the sea surface buoy, the corresponding time-varying linear equations are constructed;

[0009] An improved ZND model is constructed and the time-varying linear equations are solved by the improved ZND model to obtain the coordinate information of the sea surface buoy.

[0010] Furthermore, the position coordinate equation of the sea surface buoy is expressed as:

[0011] ;

[0012] in represents the arrival angle between the sea surface buoy and the mth receiver at time t; Represents the coordinate information of the sea surface buoy at time t; is the coordinate information of the mth receiver.

[0013] Furthermore, the expression of the time-varying linear equations is:

[0014] ;

[0015] in , is a matrix of known coefficients containing the physical measurement properties of the communication signal between the surface buoy and the receiver; , is the unknown coordinate information of the sea surface buoy at time t; , is a known vector.

[0016] Furthermore, the improved ZND model includes a model corresponding to single-cycle noise and a model corresponding to multi-cycle noise.

[0017] Furthermore, the expression of the model corresponding to single-cycle noise is:

[0018] ;

[0019] in is the error function at time t; for The first derivative of ; , p is a constant; exp represents an exponential function with the natural constant e as the base; represents the two-norm; otherwise represents other situations; is a constant with a fixed value; is the noise compensation term, is an auxiliary dynamic variable used to compensate for periodic noise; and A second-order filter is formed to attenuate single-cycle noise; for The first derivative of ; for The first derivative of ; represents the single-cycle noise, A is the amplitude of the single-cycle noise, is the phase of the single-cycle noise; π is the circumference of the circle; f is the frequency of the single-cycle noise; is a real number greater than or equal to 1.

[0020] Furthermore, the expression of the model corresponding to multi-periodic noise is:

[0021] ;

[0022] in is the error function at time t; for The first derivative of ; , p is a constant; exp represents an exponential function with the natural constant e as the base; represents the two-norm; otherwise represents other situations; is a constant with a fixed value; is the compensation term for the noise of the nth cycle, is the auxiliary dynamic variable used to compensate for the noise of the nth cycle; and A second-order filter is formed to attenuate the n-th cycle noise; and They are and The first derivative of ; is the frequency of the nth period noise; k is the total number of periods of multi-period noise; is multi-cycle noise, , is the amplitude of the noise in the nth cycle, is the phase of the n-th cycle noise; represents the nth cycle noise.

[0023] Furthermore, the specific method of solving the time-varying linear equations by the improved ZND model to obtain the coordinate information of the sea surface buoy is as follows:

[0024] Define the error function as E(t) = P(t)x(t)-q(t);

[0025] Substituting E(t) into the model corresponding to single-cycle noise and expanding it, we obtain the following neural dynamics model:

[0026] ;

[0027] Solving the above neural dynamics model, we can get the coordinate information of the sea surface buoy at time t .

[0028] A device for a sea surface buoy positioning method based on zeroing neural dynamics and anti-periodic noise is provided, comprising:

[0029] Sea surface buoy coordinate position equation construction module, used to establish the position coordinate equation of the sea surface buoy;

[0030] A time-varying linear equations construction module, used to construct a corresponding time-varying linear equations system based on the position coordinate equation of the sea surface buoy;

[0031] TPZND model construction module, used to construct the improved ZND model, that is, to obtain the TPZND model;

[0032] The sea surface buoy coordinate information solving module is used to solve the time-varying linear equations through the TPZND model to obtain the coordinate information of the sea surface buoy.

[0033] An electronic device is provided, comprising a memory and a processor, wherein a computer program is stored in the memory, and when the processor executes the computer program, a sea surface buoy positioning method based on zeroing neural dynamics and anti-periodic noise is implemented.

[0034] A computer-readable storage medium is provided, which stores a computer program. When the computer program is executed by a processor, a sea surface buoy positioning method based on zeroing neural dynamics to resist periodic noise is implemented.

[0035] The beneficial effects of the present invention are:

[0036] 1. The present invention constructs an improved ZND model (i.e., TPZND model) to solve the buoy positioning problem in a noisy environment. Simulation results show that compared with the traditional ZND model and the integral enhanced ZND (IEZND), the TPZND model has superior convergence accuracy and convergence speed under the conditions of additive periodic noise simulating ocean motion. The present invention has higher noise resistance for sea surface buoy positioning.

[0037] 2. The present invention introduces a noise compensation term ( ) to process periodic noise, so as to calibrate according to the noise frequency to reduce its impact on model convergence. By selecting an appropriate frequency f and weighting coefficient, the present invention can effectively offset the periodic interference at that frequency. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 Schematic diagram of the process of this method;

[0039] Figure 2 The convergence of the TPZND model of this method under different initial conditions;

[0040] Figure 3 Comparison diagram of the theoretical and calculated solutions of the TPZND model based on this method;

[0041] Figure 4 Comparison of performance calculated for different models in the absence of noise;

[0042] Figure 5 Comparison of performance calculated for different models in the case of single-cycle noise;

[0043] Figure 6The performance comparison of different models is calculated in the case of single-cycle noise and is displayed logarithmically on the Y axis;

[0044] Figure 7 The performance comparison of different models is calculated in the case of single-cycle noise and is displayed logarithmically on the Y axis;

[0045] Figure 8 To compare the performance of different models when multiple periodic noises are superimposed;

[0046] Figure 9 The performance comparison of different models is performed under the condition of superposition of multiple periodic noises and is displayed on the logarithmic Y axis;

[0047] Figure 10 Comparison between the calculated path obtained by the TPZND model and the target path in the case of single-cycle noise;

[0048] Figure 11 This is the residual graph of AOA positioning solved by TPZND model in the case of single-cycle noise;

[0049] Figure 12 2D error diagram of AOA positioning solved by TPZND model in the case of single-cycle noise;

[0050] Figure 13 Comparison between the calculated path obtained by the IEZND model and the target path in the case of single-cycle noise;

[0051] Figure 14 This is the residual graph of AOA positioning solved by IEZND model in the case of single-cycle noise;

[0052] Figure 15 2D error diagram of AOA positioning solved by IEZND model in the case of single-cycle noise;

[0053] Figure 16 Comparison between the calculated path obtained by the TPZND model and the target path when multiple single-cycle noises are superimposed;

[0054] Figure 17 This is the residual graph of AOA positioning solved by TPZND model when multiple single-cycle noises are superimposed;

[0055] Figure 18 2D error diagram of AOA positioning solved by TPZND model under the condition of multiple single-cycle noise superposition;

[0056] Figure 19 Comparison between the calculated path obtained by the IEZND model and the target path when multiple single-cycle noises are superimposed;

[0057] Figure 20 This is the residual graph of AOA positioning solved by IEZND model when multiple single-cycle noises are superimposed;

[0058] Figure 21 Figure 2 shows the 2D error diagram of AOA positioning solved using the IEZND model when multiple single-cycle noises are superimposed. DETAILED DESCRIPTION

[0059] The specific embodiments of the present invention are described below to facilitate understanding of the present invention by those skilled in the art. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations utilizing the concepts of the present invention are protected.

[0060] like Figure 1 As shown, the sea surface buoy positioning method based on zeroing neural dynamics to resist periodic noise includes the following steps:

[0061] S1. Establish the position coordinate equation of the sea surface buoy;

[0062] S2. Constructing a corresponding time-varying linear equation system based on the position coordinate equation of the sea surface buoy;

[0063] S3. Construct an improved ZND model, solve the time-varying linear equations using the improved ZND model, and obtain the coordinate information of the sea surface buoy. In this embodiment, the improved ZND model is defined as a TPZND model.

[0064] In this embodiment, the AOA algorithm calculates the position of an unknown node (surface buoy) by measuring the angle at which the communication signal reaches the receiver (i.e., the anchor node). Consider a two-dimensional mobile scenario where the position of the unknown node changes over time and m anchor nodes are randomly distributed and fixed.

[0065] First, define the coordinates of m anchor nodes and unknown nodes as:

[0066] ;

[0067] Where m is the number of receivers, x m and y m Represent the coordinates of the mth receiver on the x-axis and y-axis respectively, represents a real number matrix with 2 rows and m columns. x(t) and y(t) represent the coordinates of the sea surface buoy as the signal source on the x-axis and y-axis at time t respectively. The coordinates will change with time. Represents a real matrix with 2 rows and 1 column.

[0068] Using the definition of trigonometric functions based on the angle between the receiver and the target:

[0069] ;

[0070] in, represents the arrival angle of the communication signal between the unknown node and the i-th anchor node, and is the distance between the target and the receiver, defined as:

[0071] ;

[0072] According to the trigonometric function relationship, we can get:

[0073] ;

[0074] Rewrite the above equation as a linear equation:

[0075] ;

[0076] Then, the above equation can be rewritten as:

[0077] ;

[0078] Finally, the AOA-based sea surface buoy positioning problem is expressed in a two-dimensional mobile scenario as follows:

[0079] ;

[0080] Therefore, the AOA-based sea surface buoy positioning problem can be uniformly expressed as follows:

[0081] ;

[0082] Obviously, this is a time-varying dynamic linear matrix equation. is a matrix of known coefficients that contains the physical measured properties of the communication signal. is a known vector, Is the unknown vector, where q = 2, containing the coordinates of the unknown nodes that need to be solved. Therefore, the next task is to solve this equation.

[0083] First, construct the error function, in represents the error function of the aforementioned time-varying linear equations.

[0084] Then introduce the original ZND model: , is the error function For the first-order derivative of time t, γ is an adjustable convergence coefficient that remains fixed throughout the entire convergence process. In theory, the larger the value of γ, the faster the convergence speed.

[0085] The present invention first changes the fixed convergence coefficient into the time-varying convergence coefficient s(t) of the adaptive error and names it AEPCF.

[0086] ;

[0087] ;

[0088] Among them, p is a constant term, exp(p*k) represents e to the power of p*t, and exp(p*k) represents e to the power of p*t k Power, || ||2 represents the second norm of the error function, t k = t|| ||2≤0.01, which means that when || ||2Conditions met|| ||2≤0.01 then t k Fixed to a constant value that does not change over time, s(t) is also fixed to a constant value. Incorporating a constraint on the error norm alleviates the disadvantage of the coefficient continuing to increase even after convergence has been achieved, thereby preventing unnecessary waste of computational resources.

[0089] To address the unique challenges that the ocean environment presents to AOA-based positioning, we begin with a brief analysis of ocean waves. The motion of ocean water is complex; to simplify the problem, the dynamic height of the sea surface is It can be expressed as:

[0090] ;

[0091] in, represents the wave amplitude, Indicates frequency, For phase.

[0092] If we set x = 0 to observe the change in the water surface at the origin (corresponding to the location of the sea surface buoy), we get:

[0093] ;

[0094] The actual ocean waves are composed of various frequency components N f Therefore, the ocean waves can be expressed as the sum of all frequency components given in:

[0095] ;

[0096] in , g is the gravitational constant, is the wave amplitude of the i-th frequency component; is the wave angular frequency of the i-th frequency component, is the wave phase of the i-th frequency component;

[0097] By setting x = 0 and , the formula is simplified to:

[0098] ;

[0099] Therefore, additive periodic noise is defined as:

[0100] ;

[0101] The superposition of multiple periodic noises is defined as:

[0102] ;

[0103] in .

[0104] The influence of seawater motion on positioning is complex. To simplify the analysis, in this embodiment, sea waves are regarded as additional environmental noise and integrated into the modified ZND model for calculation:

[0105] ;

[0106] This embodiment introduces noise compensation To deal with periodic noise; we assume that the frequency f is known, and the amplitude A and phase Unknown. Noise compensation term It can be calibrated according to the noise frequency f to reduce its impact on model convergence. Therefore, the formula is modified as follows:

[0107] ;

[0108] Before defining the noise compensation term, the rate of change of the periodic noise must be analyzed. The second-order derivative of the periodic noise with respect to time t yields:

[0109] .

[0110] Based on the above formula, we constructed an improved ZND model design to combat single-cycle noise, that is, the model corresponding to single-cycle noise:

[0111] ;

[0112] The term introduces an additional feedback path, forming a second-order dynamic system, which helps to mitigate potential noise and periodic disturbances. and The second-order resonant feedback term in the model can adapt to periodic noise with frequency f. Specifically: and The coupling produces a second-order filter that can attenuate periodic noise. By selecting an appropriate frequency f and weighting coefficient, the system can effectively cancel out periodic interference at that frequency. is an auxiliary dynamic variable used to compensate for periodic noise, essentially The second-order dynamic adjustment term, whose evolution is controlled by the noise frequency f, is designed based on the inverse modeling of the second-order dynamic characteristics of the noise.

[0113] The simulation results show that when Convergence is improved when the linear coefficients of match the second derivative form of the periodic noise. To optimize the model. The design parameters satisfy , which is a real number. Usually, The value of is determined by two conditions: for low-frequency periodic noise, ; For high frequency periodic noise, .

[0114] The model for multi-cycle noise extends the model for single-cycle noise by combining the linear superposition of multiple additive single-cycle noises and their respective single-cycle compensation terms. The model for multi-cycle noise is expressed as follows:

[0115] ;

[0116] Similarly, by applying the derivation process similar to the model corresponding to single-cycle noise, we can derive the improved ZND model, which is able to suppress multi-cycle noise (the superposition of multiple single-cycle noise):

[0117] ;

[0118] The error function is defined as E(t) = P(t)x(t)-q(t). Substituting E(t) into the above equations and expanding them, we get the neural dynamics model: , used to solve AOA-based wireless network positioning in the presence of single-cycle noise. Multi-cycle noise is similar to single-cycle noise and will not be described here.

[0119] This embodiment also provides an electronic device, which includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it implements a sea surface buoy positioning method based on zeroing neural dynamics to resist periodic noise.

[0120] This embodiment also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements a sea surface buoy positioning method based on zeroing neural dynamics to resist periodic noise.

[0121] In this embodiment, the TPZND model and other comparative models are used to solve the same linear equations to compare the convergence and robustness of the TPZND model.

[0122]

[0123] The specific definitions of P(t) and Q(t) are as follows:

[0124] ;

[0125] ;

[0126] First, in the absence of noise interference, such as Figure 2 As shown in Figure 3, the TPZND model can converge quickly under multiple different initial conditions, and the residual error is close to zero. Figure 3 It is clearly shown that within a short time, the four calculated components of x converge to the actual components for different initial states. Figure 4 and Figure 5 It shows that in the absence of noise, all models converge in a finite time. Among them, the convergence performance of the ZND model and the TPZND model is consistent, indicating that the noise compensation term in the TPZND model It is invalid in the absence of noise, making it equivalent to the ZND model in this case. The convergence accuracy of the IEZND model is relatively low. After applying AEPCF to the TPZND model, both the convergence time and accuracy are improved. k The value of is 0.3040 seconds, which is comparable to the time required for the model to reach steady-state convergence. This shows that s(t) becomes a constant in a short time, effectively saving computing resources.

[0127] like Figure 6 and Figure 7 As shown in Figure 2, the convergence results of different models vary significantly under the interference of single-cycle noise. The ZND and IEZND models exhibit residual error oscillations within a certain range throughout the solution process and do not converge to zero. In contrast, the TPZND model, whether using constant coefficients or the AEPCF, successfully eliminates the oscillations and converges to zero in a short time. Furthermore, the model with the AEPCF exhibits faster convergence.

[0128] like Figure 8 and Figure 9As shown in Figure 1, under the interference of multiple single-cycle noise superposition, neither the ZND model nor the IEZND model converges to zero in a finite time, while the TPZND model reaches steady-state convergence within 2 seconds. After applying AEPCF, the convergence time is reduced to less than 0.5 seconds. Compared with the single-cycle noise case, the convergence of the TPZND model curve does not remain a straight line after reaching steady state, but exhibits periodic oscillations. However, the convergence accuracy remains at 10 -2 This is sufficient for buoy AOA positioning.

[0129] Next, the TPZND and IEZND models were used to simulate AOA buoy positioning, verifying their convergence under the interference of single-cycle noise or multiple single-cycle noise superposition. By setting a specified actual target path, simulation experiments were conducted to observe how well the calculated path solved by the positioning method fits the target path.

[0130] like Figure 10 、 Figure 11 、 Figure 12 、 Figure 13 、 Figure 14 、 Figure 15 、 Figure 16 、 Figure 17 、 Figure 18 、 Figure 19 、 Figure 20 and Figure 21 As shown in the figure, under the interference of single-cycle noise, the results of the TPZND model successfully converge to the specified target trajectory after a brief oscillation. The results show that after 1 second, the error converges to a low value and gradually approaches zero over time. In contrast, the IEZND model exhibits considerable error in the solution of the specific target trajectory. Under the interference of multiple single-cycle noise, the TPZND model effectively solves the convergence problem in AOA positioning under the interference of multiple single-cycle noise superposition, while the results obtained from the IEZND model are relatively less ideal.

[0131] In summary, the present invention constructs an improved ZND model (i.e., TPZND model) to solve the buoy positioning problem in a noisy environment. Simulation results show that compared with the traditional ZND model and the integral enhanced ZND (IEZND), the TPZND model has superior convergence accuracy and convergence speed under the additive periodic noise conditions of simulating ocean motion. The present invention has higher noise resistance for sea surface buoy positioning.

Claims

1. A sea surface buoy positioning method based on zeroing neural dynamics to resist periodic noise, characterized in that: The following steps are involved: Establish the position coordinate equation of the sea surface buoy; Based on the position coordinate equation of the sea surface buoy, the corresponding time-varying linear equations are constructed; An improved ZND model is constructed and the time-varying linear equations are solved by the improved ZND model to obtain the coordinate information of the sea surface buoy. The improved ZND model includes the model corresponding to single-cycle noise and the model corresponding to multi-cycle noise; The expression of the model corresponding to single-cycle noise is: ; in is the error function at time t; for The first derivative of ; , p is a constant; exp represents an exponential function with the natural constant e as the base; represents the two-norm; otherwise represents other situations; is a constant with a fixed value; is the noise compensation term, is an auxiliary dynamic variable used to compensate for periodic noise; and A second-order filter is formed to attenuate single-cycle noise; for The first derivative of ; for The first derivative of ; represents the single-cycle noise, A is the amplitude of the single-cycle noise, is the phase of the single-cycle noise; π is the circumference of the circle; f is the frequency of the single-cycle noise; is a real number greater than or equal to 1; The expression of the model corresponding to multi-period noise is: ; in is the error function at time t; for The first derivative of ; , p is a constant; exp represents an exponential function with the natural constant e as the base; represents the two-norm; otherwise represents other situations; is a constant with a fixed value; is the compensation term for the noise in the nth cycle, is the auxiliary dynamic variable used to compensate for the noise of the nth cycle; and A second-order filter is formed to attenuate the n-th cycle noise; and They are and The first derivative of ; is the frequency of the nth period noise; k is the total number of periods of multi-period noise; is multi-cycle noise, , is the amplitude of the noise in the nth cycle, is the phase of the n-th cycle noise; represents the nth cycle noise.

2. The sea surface buoy positioning method based on zeroing neural dynamics and anti-periodic noise according to claim 1 is characterized in that: The position coordinate equation of the sea surface buoy is expressed as: ; in represents the arrival angle between the sea surface buoy and the mth receiver at time t; Represents the coordinate information of the sea surface buoy at time t; is the coordinate information of the mth receiver.

3. The sea surface buoy positioning method based on zeroing neural dynamics and anti-periodic noise according to claim 2 is characterized in that: The expression of the time-varying linear equations is: ； in , is a matrix of known coefficients containing the physical measurement properties of the communication signal between the surface buoy and the receiver; , is the unknown coordinate information of the sea surface buoy at time t; , is a known vector.

4. The sea surface buoy positioning method based on zeroing neural dynamics and anti-periodic noise according to claim 3 is characterized in that: The specific method of solving the time-varying linear equations by the improved ZND model to obtain the coordinate information of the sea surface buoy is as follows: Define the error function as E(t) = P(t)x(t)-q(t); Substituting E(t) into the model corresponding to single-cycle noise and expanding it, we obtain the following neural dynamics model: ; Solving the above neural dynamics model, we can get the coordinate information of the sea surface buoy at time t .

5. A device based on the sea surface buoy positioning method based on zeroing neural dynamics and anti-periodic noise according to any one of claims 1 to 4, characterized in that: include: Sea surface buoy coordinate position equation construction module, used to establish the position coordinate equation of the sea surface buoy; A time-varying linear equations construction module, used to construct a corresponding time-varying linear equations system based on the position coordinate equation of the sea surface buoy; TPZND model construction module, used to construct the improved ZND model, that is, to obtain the TPZND model; The sea surface buoy coordinate information solving module is used to solve the time-varying linear equations through the TPZND model to obtain the coordinate information of the sea surface buoy.

6. An electronic device, characterized in that: The method comprises a memory and a processor, wherein a computer program is stored in the memory, and when the processor executes the computer program, the method according to any one of claims 1 to 4 is implemented.

7. A computer-readable storage medium, characterized in that A computer program is stored, and when the computer program is executed by a processor, the method according to any one of claims 1 to 4 is implemented.

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