Maritime millimeter wave beyond visual range positioning and navigation method based on evaporation waveguide

Abstract

The invention discloses a marine millimeter wave beyond visual range positioning and navigation method based on an evaporation waveguide. Firstly, an evaporation waveguide ray model is established, and the optimal transmitting antenna height and transmitting power are selected according to waveguide characteristics; then initializing a reference node, and establishing a preliminary three-dimensional positioning network coordinate system according to the position coordinates of the reference node; measuring the distance between the newly added unknown node to be measured and the reference node; and finally, calculating an accurate coordinate of the target node by utilizing the obtained distance and combining with a trilateral positioning algorithm. Compared with the prior art, the method has the advantages that the characteristics of the evaporation waveguide are fully utilized, and system parameters such as antenna height and transmitting power are scientifically designed, so that the high efficiency and accuracy of beyond-visual-range positioning and navigation are realized.

Description

Technical Field

[0001] The invention belongs to the technical field of sea surface radio positioning, and in particular relates to a beyond-horizon marine millimeter wave beyond-horizon positioning and navigation method based on an evaporation waveguide. Background Art

[0002] In the marine environment, due to the complex propagation characteristics of wireless signals, traditional positioning and navigation technologies face multiple challenges. The evaporation waveguide phenomenon formed in the evaporation layer on the ocean surface allows electromagnetic waves to propagate farther along the sea surface under certain conditions. At the same time, the electromagnetic signal spillover energy outside the waveguide layer is small, and the signal is transmitted covertly. This waveguide effect is particularly effective for high-frequency electromagnetic waves. For example, signals in the millimeter wave band can be propagated over long distances in the evaporation waveguide, and have great application potential. However, existing marine positioning systems usually rely on satellite positioning technology or low-frequency radio wave positioning technology. When they are interfered by weather, waves and multipath effects, and when satellite positioning cannot be covered or even fails, it is difficult to meet the needs of high-precision positioning.

[0003] In this context, millimeter wave positioning technology based on evaporation waveguides has become a novel and potential alternative positioning technology. The millimeter wave frequency band has the characteristics of large bandwidth and strong anti-interference. Combined with the capture effect of evaporation waveguides, it can effectively enhance the signal propagation capability on the sea surface. At the same time, pseudo-random code ranging technology is an accurate distance measurement method that can be applied to high-frequency bands to achieve high-precision distance measurement between nodes. By combining pseudo-random code ranging technology and three-sided positioning methods, the accuracy of maritime positioning can be further improved. However, the existence of evaporation waveguides changes the propagation of electromagnetic waves. It is necessary to analyze this special situation and design appropriate system parameters to achieve higher-precision beyond-line-of-sight positioning and navigation.

[0004] The present invention is a millimeter wave positioning method based on the evaporative waveguide environment. By utilizing the waveguide's capture effect on electromagnetic waves and pseudo-random code ranging technology, it can significantly improve the reliability and accuracy of offshore positioning, and is particularly suitable for beyond-line-of-sight high-precision positioning needs in complex marine environments. Summary of the invention

[0005] In order to cope with the complex environmental characteristics at sea, when the commonly used satellite navigation cannot cover or even fails, the present invention provides a method for millimeter wave positioning and navigation at sea based on evaporative waveguides, which can achieve beyond-line-of-sight positioning. In the ray tracing model commonly used in evaporative waveguide research, the optimal system settings are obtained according to the waveguide characteristics. On this basis, pseudo-random ranging technology, trilateral measurement positioning and other methods are used to complete the positioning of unknown nodes at sea, and the refraction effect of the evaporative waveguide and the ranging positioning error are fully analyzed and compensated to achieve higher-precision millimeter wave positioning and navigation. The technical solution of the present invention includes the following steps:

[0006] Step (1), system setting: establish an evaporation waveguide ray model and select the optimal transmitting antenna height and transmitting power according to the waveguide characteristics.

[0007] Step (2), initialize the reference node, and establish a preliminary three-dimensional positioning network coordinate system based on the position coordinates of the reference node.

[0008] Step (3), measuring the distance between the newly added unknown node to be measured and the reference node.

[0009] Step (4), three-sided positioning and node position calculation: Use the distance obtained in step (3) and the three-sided positioning algorithm to calculate the precise coordinates of the target node.

[0010] Step (5): Build and maintain the maritime communication network.

[0011] Furthermore, step (1) first establishes an evaporation waveguide ray model by acquiring environmental parameters of the evaporation waveguide. The environmental parameters of the evaporation waveguide include atmospheric refractive index, temperature, humidity and air pressure. The evaporation waveguide ray model calculates the propagation trajectory of the electromagnetic wave by correcting the refractive index. According to the evaporation waveguide ray model, an antenna height with small time delay and less energy dissipation is selected.

[0012] The parabolic equation (PE) model is used in combination with the characteristics of the evaporation waveguide to calculate the path loss at different propagation distances. The appropriate transmission power is selected based on the path loss value.

[0013] The specific steps are as follows:

[0014] (1.1) Establish the evaporation waveguide ray model:

[0015] The meteorological characteristics of the current marine environment are obtained, the refractive index profile of the evaporation duct in the current environment is obtained, the evaporation duct ray model is established, and the path of electromagnetic wave propagation under the evaporation duct effect is simulated.

[0016] The atmospheric refractive index n decreases gradually with the increase of altitude. The refractive index N is calculated based on the atmospheric refractive index n:

[0017]

[0018] Where p is atmospheric pressure in hPa, e is water vapor pressure in hPa, and T is atmospheric temperature in K. The refractive index gradient formula after derivation of the above refractive index is:

[0019]

[0020] h is the height above the ground. When dN / dh<0, the propagation trajectory of the electromagnetic wave will bend toward the earth, and the atmosphere at this time is positively refracted, forming an evaporation duct.

[0021] Define the atmospheric correction refractive index M:

[0022]

[0023] Among them, r e is the radius of the earth, which is 6370km; h is the height above the ground, in meters. Then we have:

[0024] M=N+0.157·h

[0025] The vertical refractive index of the evaporation duct (i.e., the atmosphere-corrected refractive index) M is calculated under neutral conditions using the following formula:

[0026]

[0027] Where M0 is the surface modified refractive index, δ is the evaporation duct height, and Z0 is the sea surface roughness.

[0028] The ray paths obey Snell's law, which is:

[0029] (r e +h1)n1coSθ1=(r e +h2)n2cosθ2

[0030] where θ1 and θ2 are the elevation angles of the ray at heights h1 and h2 from the Earth’s surface, n1 and n2 are the atmospheric refractive indices at the corresponding heights, and r e is the radius of the Earth (r e =6370km), the atmospheric correction refractive index M used can be expressed as:

[0031]

[0032] At this point, Snell's law can be described as:

[0033] M1cosθ1=M2cosθ2

[0034] where M1 and M2 are the atmospheric corrected refractive indices at altitudes h1 and h2.

[0035] The ray model used is related to the distance, and dM / dh is defined at this time i，j is the modified refractive index gradient at horizontal profile i and vertical height layer j, expressed as:

[0036] dM / dh i，j =(M a -M b ) / (H a -H b )×10 -3

[0037] The M value changes with the distance and height. a , M b is the modified refractive index value at a point on the ray propagation path, H a , H b Indicates that a , M b The corresponding height values, in the change of step units, are defined as follows:

[0038] M a =M i，j +K(M i+1，j -M i，j )

[0039] M b =M i，j+1 +K(M i+1，j+1 -M i，j+1 )

[0040] H a =H i，j +K(H i+1，j -H i，j )

[0041] H b =H i，j+1 +K(H i+1，j+1 -H i，j+1 )

[0042] Among them, H i，j is the height value at the vertical height layer j in the horizontal section i, M i，j is the height value H i，j When the refractive index is corrected, K is a function of the curvature at distance r, defined as:

[0043] K=(r m -r i ) / (r i+1 -r i )

[0044] Among them, r m Yes i and r i+1 The subscript i corresponds to the horizontal section, and j corresponds to the vertical section.

[0045] When the step distance r′-r and the elevation angle α are known, and α is not equal to 0, the elevation angle α′ at height h′ can be directly calculated. At this time:

[0046]

[0047] α′=α+(r′-r)(dM / dh i，j )

[0048] Given the vertical distribution of the modified refractive index M of the atmosphere, the ray with any starting elevation angle can be tracked according to the above formula.

[0049] (1.2) Setting the antenna height: Using the established evaporation waveguide ray model, calculate the propagation path and multipath delay characteristics of the ray at different transmitting antenna heights, which specifically includes the following steps:

[0050] Based on the constructed evaporation waveguide ray model, the propagation path of electromagnetic waves under the waveguide effect is simulated.

[0051] Calculate multipath propagation characteristics: Under different transmitting antenna heights, analyze the number of ray paths after the electromagnetic wave enters the waveguide layer, as well as the propagation delay of each path. Since the transmitting source must be in the waveguide layer for the electromagnetic wave to be captured, when setting the antenna height, select different transmitting antenna heights every Δh meters within the waveguide height range.

[0052] Evaluate multipath delay: The delay differences of multiple ray paths are combined to calculate the multipath delay difference.

[0053] By analyzing the ray propagation characteristics corresponding to multiple groups of antenna heights, the optimal antenna height H is found so that the number of received ray paths is large and the multipath delay difference is small. The specific rules for selecting the optimal antenna height are as follows:

[0054] First, consider the number of paths: for each antenna height, record the number of ray paths it corresponds to. Prioritize the antenna height H1 with the largest number of paths to ensure that the received signal energy is stronger and the reliability of the communication link is higher.

[0055] Secondly, multipath delay is considered: among the antenna height H1 with the largest number of paths, if its multipath delay difference is greater than the set threshold compared with other antenna heights, the antenna height with the second largest number of received rays is further selected, and so on. A comprehensive evaluation is performed on each candidate height to obtain the optimal antenna height.

[0056] (1.3) Setting the transmit power: The parabolic equation (PE) model is used to calculate the path loss and thus determine the transmit power.

[0057] According to the height, strength and ocean environment parameters of the evaporation waveguide, the PE model is used to calculate the path loss PL at the maximum communication distance D within the positioning range. After obtaining the path loss value PL, according to the link budget formula designed for the communication system, combined with the sensitivity P of the receiver r , Transmitting antenna gain G t and the receiving antenna gain G r , calculate the required transmission power P of the node t :

[0058] P t=PL+P r -G t -G r

[0059] The above formula is used to set the antenna transmission power with high efficiency and energy saving.

[0060] Furthermore, in step (2), the position coordinates of any four known nodes in the marine environment are obtained and marked as reference nodes A, B, C, and D. The precise positions of these nodes are known and fixed, and serve as reference points for the positioning of subsequent unknown nodes. Based on the position coordinates of these four reference nodes, a preliminary three-dimensional positioning network coordinate system is established.

[0061] Furthermore, the distance measurement algorithm in step (3) uses a two-way distance measurement method to calculate the distance between the unknown node and the reference node using the round-trip flight time (TOF) between the reference node and the unknown node, and finally calculates the position of the unknown node using a three-sided positioning algorithm. The specific steps are as follows:

[0062] (3.1) Ranging signal generation: First, a rubidium clock generates a reference signal of time and frequency provided to the entire system (evaporative waveguide communication system). Second, the pseudo-random sequence code generated by the clock provided by this reference is BPSK modulated and pulse formed to generate a ranging signal. The pseudo-random sequence code selects the m sequence.

[0063] The m-sequence generation process:

[0064] Determine the feedback polynomial: Choose a primitive feedback polynomial of the form:

[0065] f(x)=1+c1x+c2x 2 +…c i x i +…+c n-1 x n-1 +x n

[0066] Where n represents n register units, c i ∈{0,1} represents the coefficient of the feedback polynomial.

[0067] Initialize the linear feedback shift register (LFSR): Build a LFSR with n register cells, each register stores a binary value (0 or 1), and the initial state (seed) is the initial value in the register, which requires at least one non-zero bit (the seed cannot be all zeros).

[0068] Feedback logic: In each clock cycle, all values ​​in the register are shifted to the right, and the new input bit (feedback bit) is generated by the content of the specified register through an XOR operation. Assume that the register state is [a1, a2, …, an ], then the feedback position is:

[0069]

[0070] in, Indicates the exclusive OR operation. i are the coefficients of the feedback polynomial. In each shift operation, the rightmost register value is the output bit at the current moment.

[0071] Generate an m-sequence: In each clock cycle, perform a shift, calculate a new feedback bit, and record the current output bit. Repeat the operation until the register state returns to the initial state (seed). At this time, all the output bits obtained are the m-sequence.

[0072] Definition: An m-sequence with a period of p is denoted by:

[0073] a1,a2,a3,…,a p (p=2 n-1 )

[0074] After shifting this m sequence j times, the sequence becomes:

[0075] a j+1 ,a j+2 ,a j+3 ,…,a j+p

[0076] The corresponding terms of the above two sequences are multiplied and then added, and the resulting sum is used to measure the correlation between an m sequence and its j-time shift sequence, and it is called the m sequence a1, a2, a3, ..., a p The autocorrelation function of . It is denoted as:

[0077]

[0078] When binary digits 0 and 1 are used to represent the possible values ​​of code elements, the above formula can be expressed as

[0079]

[0080] In the formula, A and D are the number of identical and different corresponding elements of the m sequence and its j-shifted sequence in one period, respectively. Therefore, the above formula can be further rewritten as:

[0081]

[0082] From the shift-add characteristic, we can see that It is still an element in the m-sequence, so the numerator in the formula is equal to the difference between the number of 0s and the number of 1s in one cycle of the m-sequence. In addition, from the equilibrium of the m-sequence, it can be seen that the number of 0s is one less than the number of 1s in one cycle, so AD = -1 (when j is a non-zero integer) or p (when j is zero). Therefore, we get:

[0083]

[0084] The autocorrelation function of the m sequence has only two values, namely 1 and -1 / p.

[0085] (3.2) Determine the initial beam alignment of the signal transmitting node and the receiving node: Add an unknown node E to the communication network as the node to be located. The unknown node E acts as the transmitter to send signals, and the known reference node A acts as the receiver to The linear beam search is performed in the angle range of 0° to 180° with a step size of , and the received signal is matched filtered, and the maximum receiving peak value under different beam reception conditions is recorded, which is recorded as P i =[p1,…,p i ,…,p l ] T According to the maximum peak value received under different beams at the receiving end, find the optimal beam, that is, design p i The beam corresponding to the maximum value is used as the beam at the receiving end.

[0086] (3.3) The unknown node E transmits a ranging signal to the reference node A: The unknown node E transmits a ranging signal with a pseudo-random code to the reference node A, starts timing and records the transmission timestamp T1.

[0087] (3.4) Reference node A receives the signal and demodulates it: After receiving the ranging signal from the unknown node E, reference node A demodulates the signal and extracts the target signal. Reference node A uses the capture and tracking technology of pseudo-codes to synchronize the signal, and performs a cross-correlation operation with the local pseudo-random code to calculate the correlation value of the pseudo-random code. When the correlation value is the maximum, the receiving time T2 at that moment is recorded as the time of signal arrival.

[0088] (3.5) Reference node A replies with the ranging signal: After receiving the signal, reference node A regenerates an identical signal based on the received signal as a reply. Reference node A transmits the ranging signal with the pseudo-random code again, returns it to the unknown node E, and records the transmission timestamp T3. At the same time, the reference node adds its own precise location coordinate information when transmitting the ranging signal, so that the unknown node knows the location of the reference node.

[0089] (3.6) Unknown node E receives the return signal and demodulates it: After receiving the return signal from reference node A, unknown node E demodulates the modulated wave signal and extracts the target signal. Unknown node E uses pseudo code capture and tracking technology again to correlate the return signal. When the correlation value is the maximum, the receiving time T4 is recorded as the time of signal arrival.

[0090] (3.7) Calculate the flight time and distance between nodes: The signal flight time Δt is calculated by the following formula:

[0091]

[0092] Then, according to the propagation speed c of the electromagnetic wave, the propagation distance between node A and node E is calculated:

[0093] d1=Δt×c

[0094] Where c is the propagation speed of electromagnetic waves.

[0095] (3.8) Use the method of steps (3.3) to (3.7) to measure the distances d2, d3, and d4 between the unknown node E and the reference nodes B, C, and D.

[0096] Furthermore, in step (4), the distance between the target node E and the reference nodes A, B, C, and D is used as the radius of the sphere, and four spheres are drawn with the reference nodes as the center. The intersection of the four spheres is calculated as the position of the target node E by the least squares method.

[0097] Furthermore, the specific method of step (5) is as follows:

[0098] The obtained location information of the target node E is added to the communication network as a new reference node. New unknown nodes are gradually added to the network in the farther ocean area, and steps (2) to (4) are repeated to achieve mutual positioning between the newly added nodes, and a high-precision offshore positioning communication network containing multiple nodes is constructed. In view of the dynamically changing evaporation waveguide effect, the ranging and positioning path of each node is monitored and updated in real time to improve the positioning stability of the entire network.

[0099] The beneficial effects of the present invention are as follows:

[0100] Compared with the prior art, the present invention makes full use of the characteristics of the evaporation waveguide, and realizes the efficiency and accuracy of beyond-line-of-sight positioning and navigation by scientifically designing system parameters such as antenna height and transmission power. The evaporation waveguide can constrain electromagnetic waves to propagate within a specific height range, greatly extend the signal transmission distance, break through the limitations of traditional positioning and navigation technology within the line-of-sight range, and reduce the leakage of signal energy outside the waveguide layer, thereby enhancing the transmission anti-interference ability. The present invention establishes an evaporation waveguide ray model, combines parameters such as atmospheric refractive index distribution and waveguide height, optimizes the antenna height to improve the signal propagation quality and the number of paths, and reduces the multipath delay difference, thereby improving the reliability of the system. In addition, the parabolic equation model is used to accurately calculate the path loss in the evaporation waveguide environment, and the transmission power is scientifically set to achieve high efficiency and energy saving while ensuring the coverage range. These improvements effectively overcome the limitations of traditional technologies in multipath effect interference and satellite positioning failure in complex marine environments, making it possible for millimeter-wave band signals to achieve beyond-line-of-sight propagation and high-precision positioning in evaporation waveguides. By combining pseudo-random code ranging and three-lateral positioning technology, the present invention can not only meet the beyond-line-of-sight positioning needs in complex marine environments, but also flexibly adjust system parameters according to waveguide characteristics, further improving the reliability and applicability of positioning. BRIEF DESCRIPTION OF THE DRAWINGS

[0101] Figure 1 Diagram of the geometry of refraction rays layered for a spherical surface.

[0102] Figure 2 This is a simulation diagram of the evaporation waveguide ray model.

[0103] Figure 3 This is the path loss simulation diagram of the evaporation waveguide PE model.

[0104] Figure 4 Initialize the positioning network for the evaporation waveguide.

[0105] Figure 5 is the multipath delay at different antenna heights.

[0106] Figure 6 This is the path loss simulation result of the PE model at 25km. DETAILED DESCRIPTION

[0107] The specific implementation method of the present invention is further described below in conjunction with the accompanying drawings.

[0108] A method for over-the-horizon positioning and navigation of millimeter waves at sea based on an evaporative waveguide comprises the following steps:

[0109] Step (1), system setting: establish an evaporation waveguide model and select the optimal transmitting antenna height and transmitting power according to the waveguide characteristics.

[0110] In the evaporation waveguide communication system, properly setting the antenna height and transmission power is a key step to ensure communication quality and system energy efficiency. The evaporation waveguide is a special atmospheric phenomenon, and its unique electromagnetic wave propagation characteristics determine the need to adjust the system parameters in a targeted manner, and traditional models are not applicable to such environments.

[0111] The evaporation waveguide is a special waveguide environment formed by the changes in the temperature, humidity and air pressure distribution of the atmosphere above the ocean surface. It can confine the electromagnetic waves to propagate within a certain height range, thereby significantly extending the propagation distance. The system first establishes an evaporation waveguide ray model by acquiring the environmental parameters of the evaporation waveguide. This model provides a theoretical basis for subsequent antenna layout and power setting, and is an important foundation for system design. The environmental parameters of the evaporation waveguide include the atmospheric refractive index, temperature, humidity and air pressure. The evaporation waveguide ray model calculates the propagation trajectory of the electromagnetic wave by correcting the refractive index.

[0112] The height of the antenna directly affects the angle and propagation path of the electromagnetic wave entering the waveguide layer, thus determining the transmission quality of the signal. In the evaporative waveguide environment, the energy of electromagnetic wave propagation is concentrated in the waveguide layer, but this propagation does not follow the traditional free space spherical expansion law, so the choice of antenna position is particularly important. According to the evaporative waveguide ray model, the antenna height is selected when the time delay is small and the energy spillover is less.

[0113] In addition, since the evaporation waveguide channel environment is more complex than the ordinary wireless communication channel, the traditional propagation loss calculation models (such as free space model, diffraction model and scattering model) cannot accurately reflect the path loss in the evaporation waveguide environment. The parabolic equation (PE) model is used in combination with the characteristics of the evaporation waveguide to calculate the path loss under different propagation distances, and the appropriate transmission power is selected according to the path loss value. Reasonable transmission power can not only ensure the strength of the signal reaching the receiving end, but also achieve high efficiency and energy saving.

[0114] The specific steps are as follows:

[0115] (1.1) Establish an evaporation duct ray model: The evaporation duct ray model is a theoretical model used to describe the propagation characteristics of electromagnetic waves in an evaporation duct environment. The model is based on the principles of geometric optics and treats electromagnetic waves as rays. It assumes that in an evaporation duct environment, the rays propagate along the path determined by the change in refractive index. Through precise measurement or theoretical calculation of the vertical distribution of atmospheric refractive index, combined with the basic equations of ray propagation (such as Snell's law, etc.), the ray propagation trajectory, propagation distance, and changes in signal intensity can be determined, providing important theoretical support for applications such as maritime communications and radar detection. Obtain the meteorological characteristics of the current marine environment, obtain the evaporation duct refractive index profile in the current environment, establish an evaporation duct ray model, and simulate the path of electromagnetic wave propagation under the evaporation duct effect.

[0116] The formation of evaporation ducts is mainly caused by the uneven distribution of the atmospheric refractive index. In the actual atmospheric environment, parameters such as atmospheric composition, pressure, temperature and humidity change with altitude. This change causes the atmospheric refractive index n to gradually decrease with increasing altitude. The refractive index n of the lower troposphere is approximately between 1.000250 and 1.000400, which is close to 1. The refractive index N is calculated based on the atmospheric refractive index n:

[0117]

[0118] Where p is atmospheric pressure in hPa, e is water vapor pressure in hPa, and T is atmospheric temperature in K. The refractive index gradient formula after derivation of the above refractive index is:

[0119]

[0120] h is the height above the ground. When dN / dh<0, the propagation trajectory of the electromagnetic wave will bend toward the earth, and the atmosphere at this time is positively refracted, forming an evaporation duct.

[0121] Define the atmospheric correction refractive index M:

[0122]

[0123] Among them, r e is the radius of the earth, which is 6370km; h is the height above the ground, in meters. Then we have:

[0124] M=N+0.157·h

[0125] The vertical refractive index of the evaporation duct (i.e., the atmosphere-corrected refractive index) M is calculated under neutral conditions using the following formula:

[0126]

[0127] Where M0 is the surface modified refractive index, δ is the evaporation waveguide height, and Z0 is the sea surface roughness, which is usually 1.5×10 -4 .

[0128] The atmospheric environment height space is evenly distributed in layers. The refractive index n in each layer changes linearly with the height. The layer height is much smaller than the radius of the earth. Then the ray path obeys Snell's law, that is:

[0129] (r e +h1)n1coSθ1=(r e +h2)n2cosθ2

[0130] where θ1 and θ2 are the elevation angles of the ray at heights h1 and h2 from the Earth’s surface, n1 and n2 are the atmospheric refractive indices at the corresponding heights, and r e is the radius of the Earth (r e =6370km), the atmospheric correction refractive index M used can be expressed as:

[0131]

[0132] At this point, Snell's law can be described as:

[0133] M1cosθ1=M2Cosθ2

[0134] where M1 and M2 are the atmospheric corrected refractive indices at altitudes h1 and h2.

[0135] The ray model used in the present invention is related to the distance, such as Figure 1 As shown, dM / dh is defined at this time i，j is the modified refractive index gradient at horizontal profile i and vertical height layer j, expressed as:

[0136] dM / dh i，j =(M a -M b ) / (H a -H b )×10 -3

[0137] The M value changes with the distance and height. a , M b is the modified refractive index value at a point on the ray propagation path, H a , H b Indicates that a , M b The corresponding height values, in the change of step units, are defined as follows:

[0138] M a =M i，j +K(M i+1,j -M i，j )

[0139] M b =M i，j+1 +K(M i+1，j+1 -M i，j+1 )

[0140] H a =H i，j +K(H i+1，j -H i，j )

[0141] H b=H i，j+1 +K(H i+1，j+1 -H i，j+1 )

[0142] Among them, H i，j is the height value at the vertical height layer j in the horizontal section i, M i，j is the height value H i，j When the refractive index is corrected, K is a function of the curvature at distance r, defined as:

[0143] K=(r m -r i ) / (r i+1 -r i )

[0144] Among them, r m Yes i and r i+1 The subscript i corresponds to the horizontal section, and j corresponds to the vertical section.

[0145] When the step distance r′-r and the elevation angle α are known, and α is not equal to 0, the elevation angle α′ at height h′ can be directly calculated. At this time:

[0146]

[0147] α′=α+(r′-r)(dM / dh i，j )

[0148] Given the vertical distribution of the modified refractive index M value of the atmosphere, the ray with any starting elevation angle can be tracked according to the above formula, such as Figure 2 shown.

[0149] (1.2) Setting the antenna height: Using the established evaporation waveguide ray model, calculate the propagation path and multipath delay characteristics of the ray at different transmitting antenna heights. Specifically, the following steps are included:

[0150] Based on the constructed evaporation waveguide ray model, the propagation path of electromagnetic waves under the waveguide effect is simulated.

[0151] Calculate multipath propagation characteristics: Under different transmitting antenna heights, analyze the number of ray paths after the electromagnetic wave enters the waveguide layer, as well as the propagation delay of each path. Since the transmitting source must be in the waveguide layer for the electromagnetic wave to be captured, when setting the antenna height, select different transmitting antenna heights at intervals of Δh meters (2 meters or 3 meters in the embodiment) within the waveguide height range.

[0152] Evaluate multipath delay: The delay differences of multiple ray paths are combined to calculate the multipath delay difference.

[0153] When the waveguide conditions are fixed, different antenna heights will result in differences in the number of ray paths and multipath delay at the receiving end. By analyzing the ray propagation characteristics corresponding to multiple groups of antenna heights, an optimal antenna height H can be found so that the number of received ray paths is large and the multipath delay difference is small. The specific rules for selecting the optimal antenna height are as follows:

[0154] First, consider the number of paths: for each antenna height, record the number of ray paths it corresponds to. Prioritize the antenna height H1 with the largest number of paths to ensure that the received signal energy is stronger and the reliability of the communication link is higher.

[0155] Secondly, multipath delay is considered: among the antenna height H1 with the largest number of paths, if its multipath delay difference is greater than the set threshold compared with other antenna heights, the antenna height with the second largest number of received rays is further selected, and so on. A comprehensive evaluation is performed on each candidate height to obtain the optimal antenna height.

[0156] (1.3) Setting the transmission power: In the present invention, in order to achieve the goal of energy saving and high efficiency under the premise of ensuring the positioning coverage, reasonably setting the antenna transmission power Pt is one of the most important steps. The present invention adopts the parabolic equation (PE) model commonly used in evaporation waveguide research to calculate the path loss, so as to scientifically determine the transmission power. Another commonly used model in evaporation waveguide research is the PE model. The PE model is an approximate algorithm for calculating the propagation of electromagnetic wave energy. It is the result of a parabolic approximation of the Helmholtz wave equation. It simulates the forward propagation of radio waves and can more conveniently calculate the transmission loss at long distances, such as Figure 3 As shown, the green curve is the free space path loss and the blue curve is the evaporation waveguide path loss.

[0157] According to the height, strength and ocean environment parameters of the evaporation duct, the PE model is used to calculate the path loss PL at the maximum communication distance D within the positioning range. The PE model is solved by numerical methods and can accurately calculate the path loss during electromagnetic wave propagation in the evaporation duct environment. After obtaining the path loss value PL, according to the link budget formula designed for the communication system, combined with the sensitivity P of the receiver r , Transmitting antenna gain G t and the receiving antenna gain G r , calculate the required transmission power P of the node t :

[0158] P t =PL+P r -G t -G r

[0159] The above formula is used to set the antenna transmission power with high efficiency and energy saving.

[0160] Step (2), initialization of reference nodes: obtain the position coordinates of any four known nodes in the marine environment, marked as reference nodes A, B, C, and D. The precise positions of these nodes are known and fixed, and serve as reference points for the positioning of subsequent unknown nodes. Based on the position coordinates of these four reference nodes, a preliminary three-dimensional positioning network coordinate system is established.

[0161] Step (3), newly added distance measurement between unknown node to be measured and reference node: the distance measurement algorithm uses two-way distance measurement method, and uses the round-trip flight time (TOF) between the reference node and the unknown node to calculate the distance between the unknown node and the reference node, and finally calculates the position of the unknown node through the three-sided positioning algorithm. This method requires the node to have the ability to send and receive signals at the same time. In the measurement, it is necessary to receive and send signals. By calculating the time interval between sending and receiving messages, the distance between nodes can be measured.

[0162] (3.1) Ranging signal generation: First, a rubidium clock generates a reference signal of time and frequency provided to the entire system (evaporation waveguide communication system). Secondly, the pseudo-random sequence code generated by the clock provided by this reference is BPSK modulated and pulse-shaped to generate a ranging signal. The pseudo-random sequence code selects the m-sequence, which has a sharp autocorrelation, high precision, anti-interference and good confidentiality. The m-sequence (maximum length sequence) is a pseudo-random binary sequence, and its generation principle is based on a linear feedback shift register (LFSR). The LFSR consists of several register units and a feedback logic circuit.

[0163] The m-sequence generation process:

[0164] Determine the feedback polynomial: Choose a primitive feedback polynomial of the form:

[0165] f(x)=1+c1x+c2x 2 +…c i x i +…+c n-1 x n-1 +x n

[0166] Where n represents n register units, c i ∈{0,1} represents the coefficient of the feedback polynomial, which determines which registers participate in the feedback.

[0167] Initialize the linear feedback shift register (LFSR): Build a LFSR with n register cells, each register stores a binary value (0 or 1), and the initial state (seed) is the initial value in the register, which requires at least one non-zero bit (the seed cannot be all zeros).

[0168] Feedback logic: In each clock cycle, all values ​​in the register are shifted to the right, and the new input bit (feedback bit) is generated by the content of the specified register through an XOR operation. Assume that the register state is [a1, a2, …, a n ], then the feedback position is:

[0169]

[0170] in, Indicates the exclusive OR operation. i are the coefficients of the feedback polynomial. In each shift operation, the rightmost register value is the output bit at the current moment.

[0171] Generate an m-sequence: In each clock cycle, perform a shift, calculate a new feedback bit, and record the current output bit. Repeat the operation until the register state returns to the initial state (seed). At this time, all the output bits obtained are the m-sequence.

[0172] The m-sequence has a very sharp autocorrelation characteristic. The pseudo-random code ranging technology used in ranging uses this characteristic to calculate the signal propagation delay. In the m-sequence, +1 is often used to represent 0 and -1 is used to represent 1. Definition: The m-sequence with a period of p is denoted as:

[0173] a1,a2,a3,…,a p (p=2 n-1 )

[0174] After shifting this m sequence j times, the sequence becomes:

[0175] a j+1 ,a j+2 ,a j+3 ,…,a j+p

[0176] The corresponding terms of the above two sequences are multiplied and then added, and the resulting sum is used to measure the correlation between an m sequence and its j-time shift sequence, and it is called the m sequence a1, a2, a3, ..., a p The autocorrelation function of . It is denoted as:

[0177]

[0178] When binary digits 0 and 1 are used to represent the possible values ​​of code elements, the above formula can be expressed as

[0179]

[0180] In the formula, A and D are the number of identical and different corresponding elements of the m sequence and its j-shifted sequence in one period, respectively. Therefore, the above formula can be further rewritten as:

[0181]

[0182] From the shift-add characteristic, we can see that It is still an element in the m-sequence, so the numerator in the formula is equal to the difference between the number of 0s and the number of 1s in one cycle of the m-sequence. In addition, from the equilibrium of the m-sequence, it can be seen that the number of 0s is one less than the number of 1s in one cycle, so AD = -1 (when j is a non-zero integer) or p (when j is zero). Therefore, we get:

[0183]

[0184] The autocorrelation function of the m sequence has only two values, namely 1 and -1 / p.

[0185] (3.2) Determine the initial beam alignment of the signal transmitting node and the receiving node: Add an unknown node E to the communication network as the node to be located. The unknown node E acts as the transmitter to send signals, and the known reference node A acts as the receiver to The linear beam search is performed in the angle range of 0° to 180° with a step size of , and the received signal is matched filtered, and the maximum receiving peak value under different beam reception conditions is recorded, which is recorded as P i =[p1,…,p i ,…,p l ] T According to the maximum peak value received under different beams at the receiving end, find the optimal beam, that is, design p i The beam corresponding to the maximum value is used as the beam at the receiving end.

[0186] (3.3) The unknown node E transmits a ranging signal to the reference node A: The unknown node E transmits a ranging signal with a pseudo-random code to the reference node A, starts timing and records the transmission timestamp T1.

[0187] (3.4) Reference node A receives the signal and demodulates it: After receiving the ranging signal from the unknown node E, reference node A demodulates the signal and extracts the target signal. Reference node A uses the capture and tracking technology of pseudo-codes to synchronize the signal, and performs a cross-correlation operation with the local pseudo-random code to calculate the correlation value of the pseudo-random code. When the correlation value is the maximum, the receiving time T2 at that moment is recorded as the time of signal arrival.

[0188] (3.5) Reference node A replies to the ranging signal: After receiving the signal, reference node A regenerates an identical signal based on the received signal as a reply. Reference node A transmits the ranging signal with the pseudo-random code again, returns it to the unknown node E, and records the transmission timestamp T3. At the same time, the reference node adds its own precise location coordinate information when transmitting the ranging signal, so that the unknown node knows the location of the reference node.

[0189] (3.6) The unknown node E receives the return signal and demodulates it: After receiving the return signal from the reference node A, the unknown node E demodulates the modulated signal and extracts the target signal. The unknown node E uses the pseudo code capture and tracking technology again to perform correlation processing on the return signal. When the maximum correlation value is reached, the receiving time T4 is recorded as the time of signal arrival.

[0190] (3.7) Calculate the flight time and the distance between nodes: Calculate the signal flight time Δt by the following formula:

[0191]

[0192] Then, according to the propagation speed c of the electromagnetic wave, the propagation distance between node A and node E is calculated:

[0193] d1=Δt×c

[0194] Where c is the propagation speed of electromagnetic waves.

[0195] (3.8) Use the method of steps (3.3) to (3.7) to measure the distances d2, d3, and d4 between the unknown node E and the reference nodes B, C, and D.

[0196] Step (4), three-sided positioning and node position calculation: Utilize the path length obtained in step (3) and combine it with the three-sided positioning algorithm to calculate the precise coordinates of the target node E.

[0197] Specific operations include:

[0198] In the case of beyond-horizon positioning, the distance between nodes is very far, and the distance data obtained by ranging is the length of the arc along the earth's surface. In 3D trilateral positioning, a circle is constructed with a straight line as the radius to solve the target position. In order to reduce the positioning error, the measured arc distance value d is first i Converted into straight line distance value l i , that is, the chord length corresponding to the arc length of a circle with a radius equal to the radius of the earth R. According to the arc length formula, the central angle can be obtained:

[0199]

[0200] The chord length is:

[0201]

[0202] The distance between the target node E and the reference nodes A, B, C, and D is used as the radius of the sphere, and four spheres are drawn with the reference node as the sphere center. The intersection of the four spheres is calculated as the position of the target node E by the least squares method.

[0203] In three-dimensional space, there are N reference points with known positions, usually N ≥ 4, and an origin reference point (0,0,0) is added as a constraint to ensure that the calculated coordinate position is on the earth's spherical surface. The goal is to determine the position of the target point based on the positions of these known points and their distances from the target point. The coordinates of the known reference point (x i ,y i ,z i ) and their straight-line distance to the target point l i , i=1,2,3,…,N+1.

[0204] According to the three-dimensional Euclidean distance formula:

[0205]

[0206] Expanding the square gives the distance equation:

[0207]

[0208] Differentiate the distance equation to eliminate the nonlinear term and get:

[0209]

[0210] This equation takes the form:

[0211] Ax+By+Cz=D

[0212] in:

[0213]

[0214] Finally, the linear equation is formed:

[0215]

[0216] Use the least squares method to solve the target point position:

[0217] P=(A T A) -1 A T D

[0218] in:

[0219]

[0220] The estimated coordinates of the node to be located can be obtained: (x, y, z).

[0221] Step (5), build and maintain the maritime communication network: add the obtained location information of the target node E to the communication network as a new reference node. Gradually add new unknown nodes to the farther ocean area in the network, repeat steps (2) to (4) to achieve mutual positioning between the newly added nodes, and build a high-precision offshore positioning communication network containing multiple nodes. In view of the dynamically changing evaporation waveguide effect, monitor and update the ranging and positioning path of each node in real time to improve the positioning stability of the entire network.

[0222] Example

[0223] In order to verify the applicability and accuracy of the present invention, a MATLAB simulation method is used to simulate the offshore positioning scene in the East China Sea region of my country. The following are the specific implementation steps:

[0224] 1. Initialization of the positioning network

[0225] In the simulation environment, points A, B, C, and D in the East China Sea area are selected as initial reference points, and point E is the unknown node that needs to be located. Figure 4 The geographical location of each node is expressed in longitude and latitude:

[0226] Point A (121.645382°E, 28.706788°N)

[0227] Point B (121.571993°E, 28.688081°N)

[0228] Point C (121.635634°E, 28.515178°N)

[0229] Point D (121.564619°E, 28.623316°N)

[0230] Point E (121.800000°E, 28.600000°N)

[0231] 2. System parameter setting

[0232] Set the evaporation waveguide height to 15 meters. When other parameters remain unchanged, only change the transmitting antenna height. The antenna height is set to 1m, 3m, 5m, 7m, and 10m respectively. Calculate the multipath delay at different antenna heights through the ray model, such as Figure 5 As shown, considering the results of a large number of received rays and a small multipath delay, the transmitting antenna height is selected to be 3m.

[0233] The positioning range of this simulation is 25km, and the path loss PL calculated by the PE model is about 135dB. Figure 6 As shown, the receiver sensitivity P r is -100dB, transmitting antenna gain G t and the receiving antenna gain G r The transmission power P required by the node is calculated as 3dBi. t :

[0234] P t =PL+P r -G t +G r =35dBm Set the simulation channel to Ricean channel, set the Ricean K-factor of the evaporation waveguide Ricean channel to 8, the relative multipath delay to [0ns 4ns 10ns], the relative amplitude to [0dB-3dB-5dB], and the pseudo-random code element width to 40M.

[0235] 3. Distance measurement

[0236] The distance between nodes is measured using a two-way ranging technology based on pseudo-random codes. Points A, B, C, and D are used as known reference points. The arc distance between point E and each reference point is calculated by calculating the cross-correlation function, and the straight-line distance is calculated using the arc length formula. This straight-line distance is used as the distance data for the final positioning algorithm.

[0237] 4. Positioning Algorithm

[0238] Based on the measured straight-line distances between point E and reference points A, B, C, and D, the specific position of point E is determined using the three-sided positioning algorithm.

[0239] 5. Simulation results and analysis

[0240] Through simulation verification, in the evaporation waveguide environment, the pseudo-random code two-way ranging and three-sided positioning algorithm can achieve accurate positioning of point E, and the longitude and latitude position of point E (121.799995°E, 28.599997°N) is obtained by simulation, and the positioning error is within a reasonable range. The simulation results show that the method of the present invention is suitable for complex electromagnetic environments at sea and has good positioning performance.

[0241] The above contents are further detailed descriptions of the present invention in combination with specific / preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, they can also make several substitutions or modifications to these described embodiments without departing from the concept of the present invention, and these substitutions or modifications should be regarded as belonging to the protection scope of the present invention.

[0242] Parts of the present invention that are not described in detail belong to the well-known technologies of those skilled in the art.

Claims

1. A method for marine millimeter wave over-the-horizon positioning and navigation based on evaporative waveguide, characterized in that: The following steps are involved: Step (1) System setup: Establish an evaporation waveguide ray model and select the optimal transmitting antenna height and transmitting power according to the waveguide characteristics; Step (2) initializing the reference node and establishing a preliminary three-dimensional positioning network coordinate system according to the position coordinates of the reference node; Step (3) measuring the distance between the newly added unknown node to be measured and the reference node; Step (4) three-sided positioning and node position calculation: using the distance obtained in step (3) and the three-sided positioning algorithm to calculate the precise coordinates of the target node; Step (5) Build and maintain the maritime communication network.

2. The method for marine millimeter wave over-the-horizon positioning and navigation based on evaporative waveguide according to claim 1 is characterized in that: Step (1) firstly establishes an evaporation waveguide ray model by acquiring environmental parameters of the evaporation waveguide; the environmental parameters of the evaporation waveguide include atmospheric refractive index, temperature, humidity and air pressure, and the evaporation waveguide ray model calculates the propagation trajectory of the electromagnetic wave by correcting the refractive index; and selects an antenna height with small time delay and less energy spillover according to the evaporation waveguide ray model; The parabolic equation PE model is used in combination with the evaporation waveguide characteristics to calculate the path loss at different propagation distances. The appropriate transmission power is selected based on the path loss value.

3. The method for marine millimeter wave over-the-horizon positioning and navigation based on evaporative waveguide according to claim 2 is characterized in that: The evaporation waveguide ray model is established as follows: Obtain the meteorological characteristics of the current marine environment, obtain the refractive index profile of the evaporation duct in the current environment, establish an evaporation duct ray model, and simulate the path of electromagnetic wave propagation under the evaporation duct effect; The atmospheric refractive index n gradually decreases with increasing altitude; the refractive index N is calculated based on the atmospheric refractive index n: Where p is atmospheric pressure in hPa, e is water vapor pressure in hPa, and T is atmospheric temperature in K. The refractive index gradient formula after derivation of the above refractive index is: h is the height above the ground; when dN / dh<0, the propagation trajectory of the electromagnetic wave will bend toward the earth, and the atmosphere at this time is positively refracted, that is, an evaporation waveguide is formed; Define the atmospheric correction refractive index M: Among them, r e is the radius of the earth, which is 6370 km; h is the height above the ground, in meters; then: M=M+0.157·h The vertical refractive index of the evaporation duct, i.e., the atmospheric corrected refractive index M, is calculated under neutral conditions using the following formula: Where M0 is the surface corrected refractive index, δ is the evaporation duct height, and Z0 is the sea surface roughness; The ray paths obey Snell's law, which is: (r e +h1)n1cosθ1=(r e +h2)n2cosθ2 Where θ1 and θ2 are the elevation angles of the ray at heights h1 and h2 from the earth's surface, n1 and n2 are the atmospheric refractive indices at the corresponding heights, and r e is the radius of the earth, and the atmospheric correction refractive index M can be expressed as: At this point, Snell's law can be described as: M1cosθ1=M2cosθ2 where M1 and M2 are the atmospheric corrected refractive indices at altitudes h1 and h2; The ray model used is related to the distance, and dM / dh is defined at this time i,j is the modified refractive index gradient at horizontal profile i and vertical height layer j, expressed as: dM / dh i,j =(M a -M b ) / (H a -H b )×10 -3 The M value changes with the distance and height. a , M b is the modified refractive index value at a point on the ray propagation path, H a , H b Indicates that a , M b The corresponding height values, in the change of step units, are defined as follows: M a =M i,j +K(M i+1,j -M i,j ) M b =M i,j+1 +K(M i+1,j+1 -M i,j+1 ) H a =H i,j +K(H i+1,j -H i,j ) H b =H i,j+1 +K(H i+1,j+1 -H i,j+1 ) Among them, H i,j is the height value at the vertical height layer j in the horizontal section i, M i,j is the height value H i,j When the refractive index is corrected, K is a function of the curvature at distance r, defined as: K＝(r m -r i ) / (r i+1 -r i ) Among them, r m Yes i and r i+1 The subscript i corresponds to the horizontal section, and j corresponds to the vertical section; When the step distance r'-r and the elevation angle α are known, and α is not equal to 0, the elevation angle α' at height h' can be directly calculated. At this time: α'=α+(r'-r)(dM / dh i,j ) Given the vertical distribution of the modified refractive index M of the atmosphere, the ray with any starting elevation angle can be tracked according to the above formula.

4. The method for marine millimeter wave over-the-horizon positioning and navigation based on evaporative waveguide according to claim 3 is characterized in that: Setting the antenna height includes the following steps: Based on the constructed evaporation waveguide ray model, the propagation path of electromagnetic waves under the waveguide effect is simulated; Calculate multipath propagation characteristics: Under different transmitting antenna heights, analyze the number of ray paths after the electromagnetic wave enters the waveguide layer, as well as the propagation delay of each path; because the transmitting source must be in the waveguide layer for the electromagnetic wave to be captured, when setting the antenna height, select different transmitting antenna heights at intervals of Δh meters within the waveguide height range; Evaluate multipath delay: Combine the delay differences of multiple ray paths and calculate the multipath delay difference; By analyzing the ray propagation characteristics corresponding to multiple groups of antenna heights, the optimal antenna height H is found so that the number of received ray paths is large and the multipath delay difference is small; the specific rules for selecting the optimal antenna height are as follows: First, consider the number of paths: for each antenna height, record the number of ray paths it corresponds to; give priority to the antenna height H1 with the largest number of paths to ensure that the received signal energy is stronger and the reliability of the communication link is higher; Secondly, multipath delay is considered: among the antenna height H1 with the largest number of paths, if its multipath delay difference is greater than the set threshold compared with other antenna heights, the antenna height with the second largest number of received rays is further selected, and so on. A comprehensive evaluation is performed on each candidate height to obtain the optimal antenna height.

5. The method for marine millimeter wave over-the-horizon positioning and navigation based on evaporative waveguide according to claim 3 is characterized in that: The specific method for setting the transmit power is as follows: According to the height, strength and ocean environment parameters of the evaporation waveguide, the PE model is used to calculate the path loss PL at the maximum communication distance D within the positioning range; after obtaining the path loss value PL, according to the link budget formula designed for the communication system, combined with the sensitivity P of the receiver r , Transmitting antenna gain G r and the receiving antenna gain G r , calculate the required transmission power P of the node t : P t =PL+P r -G t -G r The above formula is used to set the antenna transmission power with high efficiency and energy saving.

6. The method for marine millimeter wave over-the-horizon positioning and navigation based on evaporative waveguide according to claim 1 is characterized in that: In step (2), the position coordinates of any four known nodes in the offshore environment are obtained and marked as reference nodes A, B, C, and D. The precise positions of these nodes are known and fixed, and serve as reference points for the positioning of subsequent unknown nodes. Based on the position coordinates of these four reference nodes, a preliminary three-dimensional positioning network coordinate system is established.

7. The method for marine millimeter wave over-the-horizon positioning and navigation based on evaporative waveguide according to claim 1 or 6, characterized in that: The distance measurement algorithm in step (3) uses a two-way distance measurement method to calculate the distance between the unknown node and the reference node using the round-trip flight time TOF between the reference node and the unknown node, and finally calculates the position of the unknown node using a three-sided positioning algorithm.

8. The method for marine millimeter wave over-the-horizon positioning and navigation based on evaporative waveguide according to claim 7 is characterized in that: The specific steps are as follows: (3.1) Ranging signal generation: First, a rubidium clock generates a reference signal for the time and frequency of the entire system. Then, a pseudo-random sequence code is generated under the clock provided by this reference. After BPSK modulation and pulse shaping, a ranging signal is generated. The pseudo-random sequence code selects an m sequence; The m-sequence generation process: Determine the feedback polynomial: Choose a primitive feedback polynomial of the form: f(x)=1+c1x+c2x 2 +…c i x i +…+c n-1 x n-1 +x n Where n represents n register units, c i ∈{0,1} represents the coefficient of the feedback polynomial; Initialize the linear feedback shift register LFSR: construct a LFSR containing n register units, each register stores a binary value, and the initial state is the initial value in the register, requiring at least one non-zero bit; Feedback logic: In each clock cycle, all values ​​in the register are shifted right, and the new input bit is generated by the content of the specified register through an XOR operation; assuming the register state is [a 1, a 2, ...,a n ], then the feedback position is: in, Indicates XOR operation; c i are the coefficients of the feedback polynomial; for each shift operation, the rightmost register value is the output bit at the current moment; Generate m-sequence: In each clock cycle, perform a shift, calculate the new feedback bit, and record the current output bit. Repeat the operation until the register state returns to the initial state. At this time, all the output bits obtained are the m-sequence. Definition: An m-sequence with a period of p is denoted by: <h2 style=";text-align:left;direction:ltr">a1,a2,a3,…,a<h2 style=";text-align:left;direction:ltr"> p <h2 style=";text-align:left;direction:ltr"> (p=2<h2 style=";text-align:left;direction:ltr"> n-1 <h2 style=";text-align:left;direction:ltr"> ) After shifting this m sequence j times, the sequence becomes: a j+1 ,a j+2 ,a j+3 ,…,a j+p The corresponding terms of the above two sequences are multiplied and then added, and the resulting sum is used to measure the correlation between an m sequence and its j-time shift sequence, and it is called the m sequence a1, a2, a3, ..., a p The autocorrelation function of is: When binary digits 0 and 1 are used to represent the possible values ​​of code elements, the above formula can be expressed as In the formula, A and D are the number of identical and different corresponding elements of the m sequence and its j-shifted sequence in one period, respectively. Therefore, the above formula can be further rewritten as: From the shift-add characteristic, we can see that It is still an element in the m-sequence, so the numerator in the formula is equal to the difference between the number of 0s and the number of 1s in one cycle of the m-sequence; in addition, from the equilibrium of the m-sequence, it can be seen that the number of 0s is one less than the number of 1s in one cycle, so AD = -1 or p; therefore: The autocorrelation function of the m-sequence has only two values, 1 and -1 / p; (3.2) Determine the initial beam alignment of the signal transmitting node and the receiving node: Add an unknown node E to the communication network as the node to be located; the unknown node E acts as the transmitter to send signals, and the known reference node A acts as the receiver to The linear beam search is performed in the angle range of 0° to 180° with a step size of , and the received signal is matched filtered, and the maximum receiving peak value under different beam reception conditions is recorded, which is recorded as P i =[p1,…,p i ,…,p l ] T ; According to the maximum peak value received under different beams at the receiving end, find the optimal beam, that is, design p i The beam corresponding to the maximum value is used as the beam at the receiving end; (3.3) The unknown node E transmits a ranging signal to the reference node A: The unknown node E transmits a ranging signal with a pseudo-random code to the reference node A, starts timing and records the transmission timestamp T1; (3.4) Reference node A receives the signal and demodulates it: After receiving the ranging signal from the unknown node E, reference node A demodulates the signal and extracts the target signal. Reference node A uses the pseudo-code capture and tracking technology to synchronize the signal and calculates the correlation value of the pseudo-random code by performing a cross-correlation operation with the local pseudo-random code. When the correlation value is the maximum, the receiving time T2 is recorded as the signal arrival time. (3.5) Reference node A replies to the ranging signal: After receiving the signal, reference node A regenerates an identical signal based on the received signal as a reply. Reference node A transmits the ranging signal with a pseudo-random code again, returns it to the unknown node E, and records the transmission timestamp T3. At the same time, the reference node adds its own precise location coordinate information when transmitting the ranging signal, so that the unknown node knows the location of the reference node. (3.6) The unknown node E receives the return signal and demodulates it: After receiving the return signal from the reference node A, the unknown node E demodulates the modulated signal and extracts the target signal. The unknown node E uses the pseudo code capture and tracking technology again to perform correlation processing on the return signal. When the correlation value is the maximum, the receiving time T4 is recorded as the arrival time of the signal. (3.7) Calculate the flight time and distance between nodes: The signal flight time Δt is calculated by the following formula: Then, according to the propagation speed c of the electromagnetic wave, the propagation distance between node A and node E is calculated: d1=Δt×c Where c is the propagation speed of electromagnetic waves; (3.8) Use the method of steps (3.3) to (3.7) to measure the distances d2, d3, and d4 between the unknown node E and the reference nodes B, C, and D.

9. The method for marine millimeter wave over-the-horizon positioning and navigation based on evaporative waveguide according to claim 8, characterized in that: In step (4), the distance between the target node E and the reference nodes A, B, C, and D is used as the radius of the sphere, and four spheres are drawn with the reference node as the center; the intersection of the four spheres is calculated by the least squares method as the position of the target node E.

10. The method for marine millimeter wave over-the-horizon positioning and navigation based on evaporative waveguide according to claim 9, characterized in that: The specific method of step (5) is as follows: The obtained location information of the target node E is added to the communication network as a new reference node; new unknown nodes are gradually added to the network in farther ocean areas, and steps (2) to (4) are repeated to achieve mutual positioning between the newly added nodes, and a high-precision offshore positioning communication network containing multiple nodes is constructed; in view of the dynamically changing evaporation waveguide effect, the ranging and positioning path of each node is monitored and updated in real time to improve the positioning stability of the entire network.

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