An evaporation waveguide-based offshore millimeter wave over-the-horizon positioning and navigation method

Abstract

The application discloses a kind of evaporative waveguide-based offshore millimeter wave over-the-horizon positioning and navigation method.First, establish evaporative waveguide ray model, according to waveguide characteristics, select the best transmitting antenna height and transmitting power;Then initialize reference node, according to the position coordinates of reference node, establish a preliminary three-dimensional positioning network coordinate system;Measure the distance between the newly added unknown node to be measured and the reference node;Finally, the accurate coordinates of the target node are calculated by using the obtained distance combined with the trilateration algorithm.Compared with the prior art, the present application makes full use of the characteristics of evaporative waveguide, and through scientific design of system parameters such as antenna height and transmission power, realizes the efficiency and accuracy of over-the-horizon positioning and navigation.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of sea surface radio positioning, and particularly relates to a beyond-visual-range sea millimeter wave beyond-visual-range positioning and navigation method based on an evaporation duct. BACKGROUND

[0002] In the marine environment, due to the complex characteristics of wireless signal propagation, the traditional positioning and navigation technology faces many challenges. The evaporation duct phenomenon formed in the evaporation layer of the sea surface makes the electromagnetic wave propagate farther along the sea surface under certain conditions. At the same time, the electromagnetic signal outside the waveguide layer has small external energy and transmits hidden signals. This waveguide effect is particularly effective for high-frequency electromagnetic waves, such as millimeter wave signals, which can achieve long-distance propagation in the evaporation duct and have great application potential. However, the existing sea positioning system usually relies on satellite positioning technology or low-frequency radio positioning technology. When the satellite positioning is disturbed by weather, sea waves and multipath effect and even fails to cover, it is difficult to meet the demand for high-precision positioning.

[0003] Under this background, the millimeter wave positioning technology based on the evaporation duct becomes a novel and potential alternative positioning technology. The millimeter wave frequency band has the characteristics of large bandwidth and strong anti-interference, and combined with the trapping effect of the evaporation duct, the signal propagation capability on the sea surface can be effectively enhanced. At the same time, the pseudo-random code ranging technology is an accurate distance measurement method, which can be applied to the high-frequency band to realize high-precision distance measurement between nodes. By combining the pseudo-random code ranging technology and the three-edge positioning method, the sea positioning accuracy can be further improved. However, the existence of the evaporation duct changes the electromagnetic wave propagation, and it is necessary to analyze this special case and design appropriate system parameters to realize higher-precision beyond-visual-range positioning and navigation.

[0004] The application is a millimeter wave positioning method based on the evaporation duct environment. By utilizing the trapping effect of the waveguide on the electromagnetic wave and the pseudo-random code ranging technology, the reliability and accuracy of sea positioning can be significantly improved, which is particularly suitable for the high-precision beyond-visual-range positioning demand in the complex marine environment. SUMMARY

[0005] In order to cope with the complex environmental characteristics of the sea, when the commonly used satellite navigation cannot cover or even fail, the application provides a sea millimeter wave positioning and navigation method based on the evaporation duct, which can realize beyond-visual-range positioning. In the ray tracing model commonly used in evaporation duct research, the best system setting is obtained according to the waveguide characteristics, and on this basis, the pseudo-random ranging technology, three-edge measurement positioning and other methods are used to complete the positioning of the unknown node on the sea. The refraction effect of the evaporation duct and the ranging positioning error are fully analyzed and compensated to realize higher-precision millimeter wave positioning and navigation. The technical scheme of the application 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 according to the position coordinates of the reference node.

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

[0009] Step (4), three-edge positioning and node position calculation: use the distance obtained in step (3) to calculate the accurate coordinates of the target node by combining the three-edge positioning algorithm.

[0010] Step (5), construct and maintain the marine communication network.

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

[0012] Using the parabolic equation (PE) model, the path loss under different propagation distances is calculated in combination with the characteristics of the evaporation waveguide. According to the path loss value, the appropriate transmitting power is selected.

[0013] The specific steps are as follows:

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

[0015] Obtain the meteorological characteristics in the current marine environment, obtain the evaporation waveguide refractive index profile in the current environment, establish an evaporation waveguide ray model, and simulate the path of electromagnetic wave propagation under the effect of evaporation waveguide.

[0016] The atmospheric refraction index n gradually decreases with the increase of height. Based on the atmospheric refraction index n, the refractive index N is calculated:

[0017]

[0018] Where p is the atmospheric pressure, unit hPa, e is the water vapor pressure, unit hPa, T is the atmospheric temperature, unit 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 electromagnetic waves will bend towards the earth, and at this time the atmosphere is positively refractive, that is, the evaporation waveguide is formed.

[0021] The atmospheric correction refractive index M is defined as:

[0022]

[0023] where r e is the earth radius, taken as 6370 km; and 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 atmospheric correction refractive index) M under neutral conditions is calculated using the following equation:

[0026]

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

[0028] The ray path obeys Snell's law, i.e.:

[0029] (r e +h1)n1cosθ1= (r e +h2)n2cosθ2

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

[0031]

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

[0033] M1cosθ1= M2cosθ2

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

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

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

[0037] M is a function of distance and height, M a , M b is the modified refractive index value at a point on the ray path, H a , H b represents the height value corresponding to M a , M b , in step units, the above values 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] where H i，j is the height value at horizontal profile i, vertical height layer j, M i，j is the value of the modified refractive index at height H i，j , and K is a function of the curvature of the distance r, defined as:

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

[0044] where r m is the midpoint of r i and r i+1 , and the subscript i corresponds to the horizontal profile and j corresponds to the vertical profile.

[0045] When the step distance r' - r is known, and the elevation angle α value is 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] After the vertical distribution of the modified refractive index M value of the atmosphere is given, the rays of any initial elevation angle can be tracked according to the above formula.

[0049] (1.2) Set the antenna height: through the established evaporation duct ray model, the propagation path and multipath delay characteristics of the rays under different transmitting antenna heights are calculated, which specifically includes the following steps:

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

[0051] Calculate the multipath propagation characteristics: under different transmitting antenna heights, analyze the number of ray paths after the electromagnetic wave enters the waveguide layer, and the propagation delay of each path. Since the transmitting source must be in the waveguide layer, the electromagnetic wave can be captured, and when setting the antenna height, different transmitting antenna heights are selected every interval of Δh meters within the waveguide height range.

[0052] Evaluate the multipath delay: the multipath delay difference is calculated by integrating the time delay differences of multiple ray paths.

[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 corresponding to it. Preferentially select the antenna height H1 with the most paths to ensure stronger received signal energy and higher communication link reliability.

[0055] Secondly consider the multipath delay: in the antenna height H1 with the most paths, if its multipath delay difference is greater than a set threshold compared to other antenna heights, then further select the antenna height with the second most received ray paths, and so on. The optimal antenna height is obtained by comprehensively evaluating each candidate height.

[0056] (1.3) Set the transmitting power: the parabolic equation (PE) model is used to calculate the path loss, thereby determining the transmitting power.

[0057] According to the height, intensity of the evaporation duct and the ocean environment parameters, the PE model is used to calculate the path loss PL under the maximum communication distance D in the positioning range. After obtaining the path loss value PL, according to the link budget formula designed by the communication system, combined with the sensitivity of the receiver P r , the transmitting antenna gain G t and the receiving antenna gain G r , the required transmitting power P t of the node is calculated:

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

[0059] By the above formula, the efficient and energy-saving antenna transmission power is set.

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

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

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

[0063] m sequence generation process:

[0064] Determine the feedback polynomial: select a primitive feedback polynomial, which has 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, and c i ∈{0,1} represents the coefficients of the feedback polynomial.

[0067] Initialize the linear feedback shift register (LFSR): construct an LFSR containing n register units, each register storing a binary value (0 or 1), and the initial state (seed) is the initial value in the register, requiring 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 a new input bit (feedback bit) is generated by the contents of the specified register through an XOR operation. Assuming the register state is [a1, a2, …, an], the feedback bit is generated by the XOR operation of a1 and a2, and the new state of the register is [a2, a3, …, an, a1].n If the feedback bit is 0, then the feedback bit is:

[0069]

[0070] where, denotes the XOR operation. i is the coefficient of the feedback polynomial. The value of the rightmost register is the output bit at the current time after each shift operation.

[0071] Generating an m-sequence: in each clock cycle, a shift is performed, a new feedback bit is calculated, and the current output bit is recorded. The operation is repeated until the register state returns to the initial state (seed), at which point all the output bits obtained are the m-sequence.

[0072] Definition: an m-sequence with a period of p is denoted as:

[0073] a1, a2, a3, …, a p (p = 2 n-1 )

[0074] After j shifts of the m-sequence, the sequence becomes:

[0075] a j+1 , a j+2 , a j+3 , …, a j+p

[0076] The product of the corresponding terms of the above two sequences is added to obtain a sum, which is used to measure the correlation between an m-sequence and its j-shifted sequence, and is called the autocorrelation function of the m-sequence a1, a2, a3, …, a p . Denoted as:

[0077]

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

[0079]

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

[0081]

[0082] From the shift-addition property, it can be seen that, Still an element in the m-sequence, so the numerator in the equation is equal to the difference between the number of 0s and 1s in one period of the m-sequence. In addition, it is known from the balance of the m-sequence that there is one more 1 than 0 in one period, so A-D = -1 (for j a non-zero integer) or p (for j zero). Thus, we have:

[0083]

[0084] The autocorrelation function of the m-sequence has only two values, 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, which is the node to be positioned. Send a signal from the unknown node E as the transmitting end, and the known reference node A as the receiving end to perform a linear beam search with a step size of 0° to 180°. After matching filtering the received signal, record the maximum received peak value under different beam reception, denoted as P i = [p1, …, p i , …, p l ] T . According to the maximum peak value received by the receiving end under different beams, find the optimal beam, i.e., design the beam corresponding to the maximum value in p i as the beam of 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 and demodulates the signal: After receiving the ranging signal from the unknown node E, the reference node A demodulates the signal and extracts the target signal. The reference node A uses the pseudo-code acquisition and tracking technology to synchronize the signal and performs cross-correlation operation with the local pseudo-random code to calculate the correlation value of the pseudo-random code. At the maximum correlation value, record the time T2 of the moment as the time of signal arrival.

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

[0089] (3.6) Unknown node E receives the backhaul signal and demodulates: After receiving the backhaul signal from the reference node A, the unknown node E demodulates the modulated wave signal to extract the target signal. The unknown node E uses the pseudo code capture and tracking technology again, and carries out correlation processing on the backhaul signal. At the maximum correlation value, the receiving time T4 is recorded as the time of signal arrival.

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

[0091]

[0092] Then according to the propagation speed c of 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 wave.

[0095] (3.8) The distances d2, d3, d4 between the unknown node E and the reference nodes B, C, D are measured by the method of steps (3.3)-(3.7).

[0096] Further, in step (4), the distances between the target node E and the reference nodes A, B, C, D are taken as the radii of the balls, and four balls are drawn with the reference nodes as the centers. The intersection of the four balls is calculated as the position of the target node E by the least square method.

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

[0098] The obtained position 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 further ocean area, and steps (2)-(4) are repeated to realize the mutual positioning between the new nodes, and a high-precision offshore positioning communication network containing multiple nodes is constructed. For the dynamic change of the evaporation duct effect, the ranging and positioning path of each node is monitored and updated in real time to improve the positioning stability of the whole network.

[0099] The present application has the following advantages:

[0100] Compared with the prior art, the application makes full use of the characteristics of the evaporation waveguide, realizes the efficiency and accuracy of over-the-horizon positioning and navigation by scientifically designing system parameters such as antenna height and transmission power. The evaporation waveguide can confine the electromagnetic wave in a specific height range for propagation, greatly extend the signal transmission distance, break through the limitation of traditional positioning and navigation technology in the line-of-sight range, and reduce the leakage of signal energy outside the waveguide layer, thereby enhancing the transmission anti-interference ability. The application establishes an evaporation waveguide ray model, combines the atmospheric refractive index distribution and waveguide height parameters, optimizes the antenna height to improve the propagation quality and path quantity of the signal, reduces the multipath time delay difference, and thus improves the reliability of the system. In addition, the path loss in the evaporation waveguide environment is accurately calculated by using the parabolic equation model, and the transmission power is scientifically set to ensure the coverage range while realizing efficient energy saving. These improvements effectively overcome the limitations of traditional technology in complex marine environment multipath effect interference and satellite positioning failure, making it possible for millimeter wave signals to realize over-the-horizon propagation and high-precision positioning in the evaporation waveguide. By combining pseudo-random code ranging and three-dimensional positioning technology, the application can not only meet the over-the-horizon positioning needs in complex marine environment, but also flexibly adjust the system parameters according to the waveguide characteristics, further improving the reliability and applicability of positioning. BRIEF DESCRIPTION OF DRAWINGS

[0101] Figure 1 The figure is a layered refractive ray geometry diagram.

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

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

[0104] Figure 4 The figure is an evaporation waveguide initialization positioning network.

[0105] Figure 5 The figure is a multipath time delay under different antenna heights.

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

[0107] The specific implementation method of the application will be further described below in combination with the drawings.

[0108] A sea millimeter wave over-the-horizon positioning and navigation method based on evaporation waveguide includes the following steps:

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

[0110] In the evaporation duct communication system, the reasonable setting of the height of the antenna and the transmitting power is the key step to ensure the communication quality and the system energy efficiency. The evaporation duct is a special atmospheric phenomenon, and its unique electromagnetic wave propagation characteristics determine the need for targeted adjustment of system parameters, while the traditional model is not applicable to such environment.

[0111] The evaporation duct is a special waveguide environment formed by the change of temperature, humidity and air pressure distribution of the atmospheric layer above the sea surface, which can confine the electromagnetic wave within a certain height range and significantly extend the propagation distance. The system first establishes an evaporation duct ray model by obtaining the environmental parameters of the evaporation duct, which provides a theoretical basis for the subsequent antenna layout and power setting and is an important basis for system design. The environmental parameters of the evaporation duct include atmospheric refractive index, temperature, humidity and air pressure, and the evaporation duct ray model calculates the propagation trajectory of electromagnetic waves by modifying the refractive index.

[0112] The height of the antenna directly affects the angle and propagation path of the electromagnetic wave entering the waveguide layer, thereby determining the transmission quality of the signal. In the evaporation duct 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 selection of antenna position is particularly important. According to the evaporation duct ray model, the antenna height is selected when the time delay is small and the energy overflow is less.

[0113] In addition, due to the more complex evaporation duct channel environment than ordinary wireless communication channel, the traditional propagation loss calculation model (such as free space model, diffraction model and scattering model) cannot accurately reflect the path loss in the evaporation duct environment. Using the parabolic equation (PE) model, combined with the characteristics of the evaporation duct, the path loss at different propagation distances is calculated, and according to the path loss value, the appropriate transmitting power is selected. Reasonable transmitting power not only ensures the strength of the signal reaching the receiving end, but also realizes 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 the evaporation duct environment. Based on the principles of geometric optics, the model treats electromagnetic waves as rays, and it assumes that the rays propagate along the path determined by the change of refractive index in the evaporation duct environment. Through accurate 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 the change of signal strength can be determined, which provides important theoretical support for applications such as maritime communication and radar detection. Obtain the meteorological characteristics of the current maritime environment, get the evaporation duct refractive index profile in the current environment, establish the evaporation duct ray model, and simulate the propagation path of electromagnetic waves under the effect of evaporation duct.

[0116] Evaporation duct is mainly caused by the uneven distribution of atmospheric refractive index. In the actual atmospheric environment, atmospheric composition, pressure, temperature and humidity parameters change with the height, which makes the atmospheric refractive index n gradually decreases with the increase of height. The refractive index n of the lower troposphere is about 1.000250 to 1.000400, close to 1. The refractive index N is calculated based on the atmospheric refractive index n:

[0117]

[0118] Where p is the atmospheric pressure, unit hPa, e is the water vapor pressure, unit hPa, T is the atmospheric temperature, unit 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 electromagnetic wave will bend to the earth, and the atmosphere at this time is positive refraction, that is, evaporation duct is formed.

[0121] The atmospheric correction refractive index M is defined as:

[0122]

[0123] Where, r e is the radius of the earth, 6370 km; h is the height above the ground, unit m. Then:

[0124] M = N + 0.157·h

[0125] The vertical refractive index of evaporation duct (i.e. atmospheric correction refractive index) M under neutral conditions is calculated by the following formula:

[0126]

[0127] In the formula, M0 is the surface correction refractive index, δ is the evaporation duct height, Z0 is the sea surface roughness, usually 1.5 × 10 -4 .

[0128] The atmospheric environment height space is uniformly stratified, the refractive index n in each layer changes linearly with the height, and the layer height is much smaller than the radius of the earth, so the ray path obeys Snell's law, that is:

[0129] (r e +h1)n1cosθ1 = (r e +h2)n2cosθ2

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

[0131]

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

[0133] M1cosθ1 = M2Cosθ2

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

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

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

[0137] The value of M changes with distance and height, M a , M b is the modified refractive index value at a certain point on the ray propagation path, H a , H b indicates the height value corresponding to M a , M b , in the step unit change, the above values 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] where H i，j is the height value at horizontal profile i, vertical height layer j, M i，j is the value of the modified refractive index when the height value H i，j , and K is a function of the curvature with respect to r distance, defined as:

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

[0144] where r m is the midpoint of r i and r i+1 , and the subscript i corresponds to the horizontal profile, while j corresponds to the vertical profile.

[0145] When the step distance r' - r is known, and the elevation angle a value is known, and a is not equal to 0, the elevation angle a' at the height h' can be directly calculated, at this time:

[0146]

[0147] a' = a + (r' - r)(dM / dh i，j )

[0148] After the vertical distribution of the modified refractive index M value of the atmospheric layer is given, the rays of any initial elevation angle can be tracked according to the above formula, as shown in Figure 2 .

[0149] (1.2) Set the antenna height: through the established evaporation duct ray model, the propagation path and multipath delay characteristics of the rays under different transmitting antenna heights are calculated, including the following steps:

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

[0151] Calculate the multipath propagation characteristics: under different transmitting antenna heights, analyze the ray path number after the electromagnetic wave enters the waveguide layer, and the propagation delay of each path. Since the transmitting source must be in the waveguide layer, electromagnetic waves can be captured, and when setting the antenna height, different transmitting antenna heights are selected every Δh meters (2 meters or 3 meters are selected in the embodiment) in the waveguide height range.

[0152] Evaluate the multipath delay: integrate the time delay differences of multiple ray paths to calculate the multipath delay difference.

[0153] Under the condition of fixed waveguide, different antenna heights will cause differences in the number of ray paths and multipath time 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, which makes the number of received ray paths more and the multipath time delay difference smaller. 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 corresponding number of ray paths. Preferentially select the antenna height H1 with the most paths to ensure stronger received signal energy and higher communication link reliability.

[0155] Second, consider the multipath time delay: in the antenna height H1 with the most paths, if its multipath time delay difference is greater than a set threshold compared to other antenna heights, then further select the antenna height with the second most received rays, and so on. Comprehensive evaluation of each candidate height leads to the optimal antenna height.

[0156] (1.3) Set the transmit power: in the present application, in order to achieve the goal of energy saving and efficiency under the premise of ensuring positioning coverage, one of the most important steps is to reasonably set the antenna transmit power Pt. The present application uses the parabolic equation (PE) model commonly used in evaporation waveguide research to calculate the path loss, thereby scientifically determining the transmit power. The PE model commonly used in evaporation waveguide research is a kind of approximate algorithm for calculating the propagation of electromagnetic wave energy, which is a result of parabolic approximation of Helmholtz wave equation. It simulates the forward propagation of radio waves and can conveniently calculate the transmission loss at a long distance, as shown in Figure 3 , where the green curve is the free space path loss and the blue curve is the evaporation waveguide path loss.

[0157] According to the height, intensity and ocean environment parameters of the evaporation waveguide, the PE model is used to calculate the path loss PL under the maximum communication distance D in the positioning range. The PE model is solved by numerical method and can accurately calculate the path loss in the process of electromagnetic wave propagation in the evaporation waveguide environment. After obtaining the path loss value PL, according to the link budget formula designed by the communication system, combined with the sensitivity P r of the receiver, the transmit antenna gain G t and the receive antenna gain G r , the required transmit power P t of the node is calculated:

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

[0159] Through the above formula, the efficient and energy-saving antenna transmit power is set.

[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 which are known and fixed, serving as reference points for the positioning of subsequent unknown nodes. According to the position coordinates of the four reference nodes, a preliminary three-dimensional positioning network coordinate system is established.

[0161] Step (3), measurement of the distance between the newly added unknown node and the reference nodes: the ranging algorithm uses a two-way ranging method to calculate the distance between the unknown node and the reference nodes using the round-trip time of flight (TOF), and finally calculates the position of the unknown node through a trilateration algorithm. This method requires nodes to have both sending and receiving signal capabilities, both receiving and sending signals in the measurement, and calculating the time interval between sending and receiving messages to measure the distance between nodes.

[0162] (3.1), ranging signal generation: first, a reference signal of time and frequency is generated by a rubidium clock and provided to the entire system (evaporative waveguide communication system), and second, a pseudo-random sequence code generated by the clock is modulated by BPSK and pulse shaping to generate a ranging signal. The pseudo-random sequence code selects an m sequence, which has sharp autocorrelation, high precision, good anti-interference, and good secrecy. The m sequence (maximum length sequence) is a kind of pseudo-random binary sequence, and its generation principle is based on a linear feedback shift register (LFSR). The LFSR is composed of a plurality of register units and a feedback logic circuit.

[0163] m sequence generation process:

[0164] Determine the feedback polynomial: select a primitive feedback polynomial, which has 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 coefficients of the feedback polynomial, which determines which registers participate in feedback.

[0167] Initialize the linear feedback shift register (LFSR): construct an LFSR containing n register units, each register storing 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 right, and the new input bit (feedback bit) is generated by XORing the contents of the specified register. Assume the register state is [a1, a2, ..., a...]. n The feedback bit is:

[0169]

[0170] in, This represents the XOR operation. i These 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 m-sequence: In each clock cycle, perform a shift operation, calculate the new feedback bit, and record the current output bit. Repeat this operation until the register state returns to the initial state (seed). The resulting output bits are the m-sequence.

[0172] m-sequences possess very sharp autocorrelation properties, which are utilized in pseudo-random code ranging techniques to calculate signal propagation delay. In m-sequences, +1 is often used to represent 0, and -1 to represent 1. Definition: An m-sequence with period 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 two sequences above are multiplied and then added together. The sum is used to measure the correlation between an m-sequence and its j-th shifted sequence, and this sum is called the m-sequence a1, a2, a3, ..., a p The autocorrelation function of . Noted as:

[0177]

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

[0179]

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

[0181]

[0182] From the shift-addition property, Still an element in the m-sequence, so the numerator in the equation is equal to the difference between the number of 0s and 1s in one period of the m-sequence. In addition, from the balance of the m-sequence, the number of 0s is one less than the number of 1s in one period, so A-D = -1 (when j is a nonzero integer) or p (when j is zero). Thus we have:

[0183]

[0184] The autocorrelation function of the m-sequence has only two values, 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, which is the node to be positioned. Send a signal from the unknown node E as the transmitting end, and the known reference node A as the receiving end to Perform linear beam search on the angle range of 0° to 180° with a step size of 10°. After matching filtering the received signal, record the maximum received peak value under different beam receiving conditions, denoted as P i = [p1, …, p i , …, p l ] T According to the maximum peak value received by the receiving end under different beams, find the optimal beam, that is, design the beam corresponding to the maximum value in p i as the beam of 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 and demodulates the signal: After the reference node A receives the ranging signal from the unknown node E, it performs signal demodulation and extracts the target signal. The reference node A uses the pseudo-code acquisition and tracking technology to synchronize the signal and performs cross-correlation operation with the local pseudo-random code to calculate the correlation value of the pseudo-random code. At the maximum correlation value, record the receiving time T2 at that time as the time of signal arrival.

[0188] (3.5) Reference node A replies the ranging signal: After receiving the signal, reference node A generates a same signal as a reply based on the received signal, and transmits the ranging signal with pseudo-random code again to unknown node E, and records the transmission time stamp T3. Meanwhile, the reference node adds its accurate position coordinate information when transmitting the ranging signal, so that the unknown node knows the position of the reference node.

[0189] (3.6) Unknown node E receives the returned signal and demodulates: After receiving the returned signal from reference node A, unknown node E demodulates the modulated signal to extract the target signal. Unknown node E uses the pseudo-code capture and tracking technology again to correlate the returned signal. At the maximum correlation value, the receiving time T4 is recorded as the time of signal arrival.

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

[0191]

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

[0193] d1 = Δt x c

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

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

[0196] Step (4) Triangulation and node position calculation: Use the path lengths obtained in step (3) to calculate the accurate coordinates of target node E by triangulation algorithm.

[0197] The specific operation includes:

[0198] In the case of over-the-horizon, the distance between nodes is very far, and the distance data obtained by ranging is the arc length along the earth's surface, while in three-dimensional triangulation, the target position is solved by taking a circle with a straight line as the radius. In order to reduce the positioning error, the measured arc distance value d i is converted to the straight distance value l i , that is, the chord length corresponding to the arc length of the circle with the earth's radius R as the radius. According to the arc length formula, the central angle can be obtained:

[0199]

[0200] Then the chord length is:

[0201]

[0202] Draw four spheres with the distances of target node E to reference nodes A, B, C, D as the radius and the reference nodes as the center of the spheres. Calculate the intersection of the four spheres as the position of target node E by least square method.

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

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

[0205]

[0206] Expand the square to get the distance equation:

[0207]

[0208] Differencing the distance equation to eliminate the nonlinear term, we get:

[0209]

[0210] The equation is in the form:

[0211] Ax+By+Cz=D

[0212] Where:

[0213]

[0214] Finally, a linear equation is formed:

[0215]

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

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

[0218] Where:

[0219]

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

[0221] Step (5), constructing and maintaining the marine communication network: adding the obtained position information of the target node E to the communication network as a new reference node. New unknown nodes are gradually added to the communication network in the further marine area, and steps (2) to (4) are repeated to realize the mutual positioning between the new nodes, and a high-precision marine positioning communication network containing multiple nodes is constructed. In view of the dynamic change of the evaporation duct effect, the ranging and positioning path of each node is monitored and updated in real time to improve the positioning stability of the whole network.

[0222] Embodiments

[0223] In order to verify the applicability and precision of the present application, the matlab simulation method is used to simulate the marine positioning scene in the East China Sea area. 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 the initial reference points, and point E is the unknown node to be positioned, as shown in Figure 4 The geographical positions of the nodes are represented by longitude and latitude:

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

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

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

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

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

[0231] 2. System parameter setting

[0232] The evaporation duct height is set to 15 meters. Under the condition that other parameters remain unchanged, only the height of the transmitting antenna is changed, and the antenna height is set to 1 m, 3 m, 5 m, 7 m and 10 m. The multipath time delay under different antenna heights is calculated by the ray model, as shown in Figure 5 The results of more comprehensive received rays and smaller multipath time delay are selected, and the height of the transmitting antenna is 3 m.

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

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

[0235] 3. Ranging

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

[0237] 4. Positioning algorithm

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

[0239] 5. Simulation results and analysis

[0240] Through simulation verification, in the evaporation duct environment, the precise positioning of the E point can be realized by using the pseudo-random code two-way ranging and the three-side positioning algorithm, the latitude and longitude position (121.799995°E, 28.599997°N) of the E point is obtained through simulation, and the positioning error is within a reasonable range. The simulation results show that the method is suitable for a complex electromagnetic environment on the sea, and has good positioning performance.

[0241] The above content is a further detailed description of the present application in combination with specific / preferred embodiments, and the specific implementation of the present application cannot be limited to these descriptions. For ordinary skilled persons in the technical field to which the present application belongs, some substitutions or modifications can be made to the described embodiments without departing from the concept of the present application, and these substitutions or modifications should be regarded as belonging to the protection scope of the present application.

[0242] The part not described in detail in the present application belongs to the known technology of those skilled in the art.

Claims

1. A method for maritime millimeter wave over-the-horizon positioning and navigation based on evaporation ducts, characterized in that, The method comprises the following steps: Step (1) establishing an evaporation waveguide ray model, and selecting an optimal transmitting antenna height and transmitting power according to the waveguide characteristics; Step (2) initializing a reference node, and establishing a preliminary three-dimensional positioning network coordinate system according to the position coordinates of the reference node; Step (3) a ranging algorithm for measuring distance uses a two-way ranging method, and the distance between an unknown node and a reference node is calculated by using the round-trip time of flight (TOF) between the reference node and the unknown node; (3.1) a reference signal of time and frequency is generated by a rubidium clock and provided to the whole system, a pseudo-random sequence code is generated by a clock generated from the reference, the pseudo-random sequence code is selected as an m sequence, the ranging signal is generated after BPSK modulation and pulse shaping; (3.2) Add an unknown node E in the communication network, as a node to be positioned; send signals by unknown node E as the transmitting end, and known reference node A as the receiving end to Linear beam search is performed on the angle range of 0° to 180° with a step of 0°. After the received signals are matched filtered, the maximum receiving peak value under different beam receiving conditions is recorded, denoted as ; according to the maximum peak value received by the receiving end under different beams, the optimal beam is found, that is, the beam corresponding to the maximum value in the design is designed as the beam of the receiving end; (3.3) the unknown node E transmits the ranging signal with the pseudo-random code to the reference node A, starts timing and records the transmission time stamp T1; (3.4) the reference node A receives the ranging signal from the unknown node E, demodulates the signal and extracts the target signal; the reference node A performs signal synchronization by using the pseudo-code capture and tracking technology, and performs cross-correlation operation with the local pseudo-random code to calculate the correlation value of the pseudo-random code; at the maximum correlation value, the receiving time T2 is recorded as the time of arrival of the signal; (3.5) after completing signal reception, the reference node A generates a same signal based on the received signal as a reply, and transmits the ranging signal with the pseudo-random code to the unknown node E again, and records the transmission time stamp T3; the reference node adds its own accurate position coordinate information when transmitting the ranging signal, so that the unknown node knows the position of the reference node; (3.6) the unknown node E receives the return signal from the reference node A, demodulates the modulated wave 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; at the maximum correlation value, the receiving time T4 is recorded as the time of arrival of the signal; (3.7) The time of flight of the signal is calculated by the following equation The propagation distance between the nodes A and E is calculated according to the propagation speed c of electromagnetic waves: Where c is the propagation speed of electromagnetic waves; (3.8) the distances between the unknown node E and the reference nodes B, C and D are measured by using the method of steps (3.3)-(3.7) 、 、 ； Step (4) the accurate coordinates of the unknown node are calculated by using the distances obtained in step (3) and combining a three-edge positioning algorithm; Step (5) constructing and maintaining a marine communication network.

2. The method of claim 1, wherein, Step (1) first, an evaporation waveguide ray model is established 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 electromagnetic waves by correcting the refractive index; an antenna height with small time delay and less energy overflow is selected according to the evaporation waveguide ray model; The path loss under different propagation distances is calculated by using a parabolic equation (PE) model in combination with the evaporation waveguide characteristics, and the optimal transmitting power is selected according to the path loss value.

3. The method of claim 2, wherein the method further comprises: The evaporation waveguide ray model is established as follows: Obtaining the meteorological characteristics in the current marine environment, obtaining the evaporation waveguide refractive index profile in the current environment, establishing an evaporation waveguide ray model, and simulating the path of electromagnetic wave propagation under the effect of evaporation waveguide; The atmospheric refractive index n gradually decreases with the increase of height; the refractive index N is calculated based on the atmospheric refractive index n: Wherein p is atmospheric pressure, unit is hPa, e is water vapor pressure, unit is hPa, T is atmospheric temperature, unit is 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 path of the electromagnetic wave will bend towards the earth, and the atmosphere at this time is positive refraction, that is, evaporation waveguide is formed; The atmospheric modified refractive index M is defined as: wherein R is the earth radius, taken as 6370 km; h is the height above ground, in meters; then: The vertical refractive index of the evaporation waveguide, that is, the atmospheric modified refractive index M, is calculated under neutral conditions using the following formula: wherein is the surface correction refractive index, is the evaporation waveguide height, is the sea surface roughness; The ray path is subject to Snell's law, that is: where are the elevation angles of the rays from the heights of are the atmospheric refraction indices at the respective heights, is the earth radius, and the atmospheric correction refraction M used can be expressed as:​​​​ At this time, Snell's law can be described as: wherein and are highly and the atmospheric refractive index at the location of The adopted ray model is distance dependent, where the definition of the modified refractive index gradient at the horizontal profile i, vertical height layer j is given by: is the modified refractive index gradient at the horizontal profile i, vertical height layer j, expressed as: The M value changes with distance and altitude. It is the corrected refractive index value at a certain point along the propagation path of the ray. Indicates and The corresponding height values, with variations in step size, are defined as follows: wherein, is the height value at the horizontal profile i, vertical height layer j, is the height value is the value of the refractive index when the correction is applied, K is a function of the curvature with respect to r distance, defined as: wherein is and the midpoint of the horizontal section, the index i corresponding to the horizontal section, and j to the vertical section; When the step distance and the elevation value are known, and not equal to 0, the elevation in the height can be directly calculated as: After the vertical distribution of the modified refractive index M of the given atmosphere is given, the rays of any initial elevation angle can be tracked according to the above formula.

4. The method of claim 3, wherein the method further comprises: Setting the antenna height specifically includes the following steps: Based on the constructed evaporation waveguide ray model, the propagation path of electromagnetic wave under the effect of waveguide is simulated; Calculate multipath propagation characteristics: analyze the number of ray paths after the electromagnetic wave enters the waveguide layer at different transmitting antenna heights, and the propagation delay of each path; since the transmitting source must be in the waveguide layer, the electromagnetic wave can be captured, and when setting the antenna height, different transmitting antenna heights are selected every interval m in the waveguide height range; Evaluate the multipath time delay: integrate the time delay differences of multiple ray paths to calculate the multipath time 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 time delay difference is small; the specific rules for selecting the optimal antenna height are as follows: First consider the path number: for each antenna height, record the corresponding number of ray paths; select the antenna height with the most paths H1; Secondly consider the multipath time delay: in the antenna height with the most paths H1, if the multipath time delay difference is greater than the set threshold compared with other antenna heights, select the antenna height with the second most received ray paths, and so on. Comprehensive evaluation is made on each candidate height to obtain the optimal antenna height.

5. The method of claim 3, wherein, The specific method of setting the transmission power is as follows: Based on the height and strength of the evaporating waveguide and marine environmental parameters, the path loss PL under the maximum communication distance D within the positioning range is calculated using the PE model. After obtaining the path loss value PL, the link budget formula for the communication system design is used, combined with the receiver sensitivity. Transmit antenna gain and receiving antenna gain The transmit power required by the computing node : Through the above formula, the antenna transmission power of high efficiency and energy saving is set.

6. The method of claim 1, wherein, In step (2), the position coordinates of any four known nodes in the marine environment are obtained, marked as reference nodes A, B, C, and D. The accurate positions of these nodes are known and fixed, serving as reference points for the positioning of subsequent unknown nodes. A preliminary three-dimensional positioning network coordinate system is established based on the position coordinates of the four reference nodes.

7. The method according to claim 1 or 6, wherein, M sequence generation process: Determine the feedback polynomial: select a primitive feedback polynomial, which has the form: wherein denotes one register unit, denotes a coefficient of the feedback polynomial; Initialize a linear feedback shift register (LFSR): construct an LFSR containing a number of register elements, each register storing a binary value, the initial state being the initial values in the registers, requiring at least one non-zero bit; Feedback logic: At each clock cycle, all values in the registers are shifted to the right, and a new input bit is generated by an XOR operation of the contents of the specified registers; assuming the register state is then the feedback bit is: Wherein, ⊕ represents XOR operation; is the coefficient of the feedback polynomial; the value of the rightmost register is the output bit at the current time after each shift operation; Generate m sequence: in each clock cycle, shift once, calculate the new feedback bit, and record the current output bit. The loop operation continues until the register state returns to the initial state. At this time, all the output bits obtained are the m sequence; Definition: Period is the m-sequence, denoted as: After j times shifting of the m sequence, the sequence becomes: The corresponding terms of the above two sequences are multiplied and then added, and the resulting sum is used to measure the degree of correlation between an m-sequence and its jth shifted sequence, and is referred to as the autocorrelation function of the m-sequence ; denoted as: When binary digits 0 and 1 are used to represent the possible values of the code elements, the above formula is expressed as: In the formula, A' and D' are the number of elements in the m sequence and its j times shifted sequence that are the same and different in a period, respectively. Therefore, the above formula is rewritten as: From the characteristic of shift-addition, Still is the element in m sequence, so the numerator in the formula is equal to the difference between the number of 0 and 1 in a period of m sequence; in addition, from the uniformity of m sequence, the number of 0 is less than the number of 1 by one in a period, so or ; thus we get: The autocorrelation function of the m sequence has only two values, 1 and -1 / p'.

8. The method of claim 7, wherein the method is a method of maritime millimeter wave over-the-horizon positioning and navigation based on an evaporation duct. In step (4), the distances between the unknown node E and the reference nodes A, B, C and D are taken as the radii of the spheres, and four spheres are drawn with the reference nodes as the centers; the intersection of the four spheres is calculated by the least square method as the position of the unknown node E.

9. The method of claim 8, wherein, The specific method in step (5) is as follows: The obtained position information of the unknown node E is added to the communication network as a new reference node; new unknown nodes are gradually added to the network in the further ocean area, and steps (2) to (4) are repeated to realize the mutual positioning between the new nodes, and a high-precision ocean positioning communication network containing multiple nodes is constructed; for the dynamic change of the evaporation duct 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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