Low earth orbit satellite navigation fusion method and system assisted by reconfigurable intelligent surface

Abstract

The application provides a reconfigurable intelligent surface assisted low-orbit satellite navigation and communication fusion method and system, including the following steps: step S1: joint design of communication and navigation double indexes for phase shift of the RIS array; step S2: user side pseudo-range positioning according to received navigation data to obtain three-dimensional position coordinates of the user; step S3: after solving the three-dimensional position coordinate information of the user, the three-dimensional position coordinate information is sent to the satellite by using an antenna; step S4: the line-of-sight channel between the satellite and the user is reconstructed by using the three-dimensional position coordinates of the user and the three-dimensional position coordinates of the satellite as an estimated channel of the real channel, and a downlink beamforming vector is designed at the satellite side according to the estimated channel; and step S5: a communication link is established between the satellite and the user to provide communication services for the user. The application provides a solution for the problem of difficult satellite communication channel feedback.

Description

Technical Field

[0001] This invention relates to the field of deep space exploration relay communication, specifically to a reconfigurable intelligent surface-assisted low-Earth orbit satellite communication and navigation fusion method and system. Background Technology

[0002] In recent decades, global satellite systems have experienced rapid development. With advancements in launch technology, launchable satellites have become increasingly larger and more complex, with communication and navigation being two crucial functions. In recent years, the demand for multimedia services such as music, video, and television has grown rapidly. Related research shows that mobile data demand has increased more than tenfold in the past decade, with the proportion of video services increasing annually. The amount of information is experiencing explosive growth, undoubtedly posing a severe challenge to the transmission capacity of existing mobile communication networks. Due to limited frequency and power resources, inter-system interference, and hardware limitations, terrestrial mobile communication systems alone can hardly meet the rapidly growing communication demands. Therefore, the solution of using low-Earth orbit (LEO) satellite networks to provide communication services to terrestrial users has received widespread attention from academia and industry. Satellites have advantages such as wide coverage and high bandwidth, which can effectively complement terrestrial systems. For example, in recent years, international companies such as OneWeb, Telasat, and SpaceX have been building or preparing to build LEO satellite networks, while China is also building LEO satellite systems such as Hongyan.

[0003] Global Navigation Satellite Systems (GNSS) play a vital role in people's daily lives, providing users with precise location, speed, and time information. GNSS includes global, regional, and augmentation systems, such as the US GPS, Russia's GLONASS, Europe's Galileo, and China's BeiDou Navigation Satellite System, as well as related augmentation systems, such as the US WAAS (Wide Area Augmentation System), Europe's EGNOS (European Geostationary Navigation Overlay System), and Japan's MSAS (Multi-Function Transport Satellite Augmentation System). It also encompasses other satellite navigation systems under construction or planned for the future. GNSS provides global coverage, low cost, and high-precision spatiotemporal services, and has been widely adopted globally since its inception. However, traditional GNSS systems are mainly distributed in medium and high orbits. Navigation signals attenuate significantly after transmission distances of tens of thousands of kilometers, resulting in weak signal strength and problems such as weak coverage in urban areas, susceptibility to building obstruction, and an insufficient number of visible satellites. In this context, reconfigurable intelligent surfaces (RIS) deployed within urban areas can reflect satellite signals, increasing the number of visible satellites. Simultaneously, the low Earth orbit commonly used by communication satellites offers advantages such as weak signal attenuation, low latency, and low cost, providing possibilities for improvements in navigation satellites. Navigation systems and satellite systems can leverage each other's strengths, functionally integrating to enhance overall performance.

[0004] It is understood that previous research on communication and navigation fusion has mainly focused on base stations in terrestrial communication systems, with less research on satellite-based communication and navigation fusion, and primarily involving single-satellite systems. Therefore, this invention proposes a reconfigurable intelligent surface-assisted low-Earth orbit satellite communication and navigation fusion scheme under a multi-satellite system.

[0005] Patent document CN115941413A discloses a method for generating and receiving high-power communication-guided fusion navigation signals. First, it performs serial-to-parallel conversion of communication information and baseband spread spectrum of navigation information. Then, it performs baseband modulation mapping and power allocation on the communication and navigation information. Guard interval symbols are generated, IFFT transformation is performed, and serial-to-parallel conversion and cyclic prefix addition are added to complete OFDM waveform modulation of the communication-guided signal. After passing through a transmission channel, the signal is broadcast via a transmission antenna. A receiving antenna receives the communication-guided fusion navigation signal, which is then converted into a digital sampled signal through a receiving channel. The digital sampled signal is read and used for navigation signal detection. It is correlated with the receiver's coarse synchronization local reference signal to achieve coarse synchronization, obtaining the coarse synchronization delay estimate and coarse synchronization Doppler estimate of the navigation signal. Finally, the navigation signal is demodulated to generate a receiver's fine synchronization local reference signal, which is then finely synchronized with the digital sampled signal to obtain the fine synchronization delay estimate and fine synchronization Doppler estimate of the navigation signal. However, this invention does not take advantage of the fact that the direct path power between the satellite and the ground user is much greater than the scattered path power in the satellite-ground scenario, reconstruct the channel based on the three-dimensional position information of the user and the satellite, perform channel estimation for downlink communication, and design beamforming based on this. Summary of the Invention

[0006] To address the shortcomings of existing technologies, the purpose of this invention is to provide a reconfigurable intelligent surface-assisted low-Earth orbit satellite communication and navigation fusion method and system.

[0007] A reconfigurable smart surface-assisted low-Earth orbit satellite communication and navigation fusion method provided by the present invention includes:

[0008] Step S1: Design the phase shift of the RIS array by combining communication and navigation parameters.

[0009] Step S2: Perform pseudorange positioning on the user side based on the received navigation data to obtain the user's three-dimensional position coordinates;

[0010] Step S3: After calculating the user's own three-dimensional position coordinates, the three-dimensional position coordinates are transmitted to the satellite using an antenna;

[0011] Step S4: Using the user's three-dimensional position coordinates and the satellite's three-dimensional position coordinates, reconstruct the line-of-sight channel between the satellite and the user, which serves as the estimated channel for the real channel. Based on the estimated channel, design the downlink beamforming vector on the satellite side.

[0012] Step S5: Select a satellite and establish a communication link with the user to provide communication services to the user.

[0013] Preferably, in step S1:

[0014] The RIS array is used by both communication and navigation systems. The phase shift of the RIS array is designed with both communication and navigation parameters in mind.

[0015] When designing the phase shift of the RIS array for both communication and navigation purposes, the first step is to ensure that the navigation gain provided by the RIS exceeds a preset threshold so that the ground receiver can receive the signal. On this basis, the communication gain is maximized.

[0016] Preferably, in step S1:

[0017] The phase shift of the RIS array is used to jointly design navigation and communication metrics, with the transmitted navigation signal being x. N The navigation signals received by ground users via RIS reflection are represented as

[0018]

[0019] Among them, h RU h is the navigation channel vector between the RIS and the user. sR Let Θ be the navigation channel vector between the satellite and the RIS, where Θ = diag([θ1, θ2, ..., θ...). M ]) is the phase shift matrix of the RIS array, which is a diagonal matrix, p sN n represents the satellite's navigation signal transmission power. N Additive white Gaussian noise during navigation;

[0020] The communication signal transmitted by the satellite launched by RIS is x. C The communication signal received by the ground user via RIS reflection is represented as:

[0021]

[0022] Among them, H RU H is the communication channel matrix between the RIS and the user. sR p is the communication channel matrix between the satellite and the RIS. sC w is the satellite's communication signal transmission power. sR The downlink beamforming vector for the satellite, v is the receive vector on the user side, and n C Additive white Gaussian noise during communication;

[0023] Obtain the navigation channel gain G reflected by RIS N (θ) and communication channel gain G C (θ,w sR v):

[0024]

[0025] G C (0, w) sR ,v)=|v H HRU ΘH sR W sR | 2 .

[0026] Where θ is the phase shift vector of the RIS array;

[0027] The channel states of the satellite, RIS, and user links are known. Based on these known channel states, the RIS array, being a phase-shift design, requires a joint design that considers both communication and navigation metrics, balancing navigation channel gain and communication channel gain. This leads to the following optimization problem.

[0028]

[0029] stC1:||w sR || 2 =1,

[0030] C2:||v|| 2 =1,

[0031]

[0032] C4:G N (0)≥G N，th .

[0033] The optimization objective of the optimization problem is to maximize the gain of the communication channel while satisfying constraints. Constraints C1 and C2 are modulus constraints on the communication beamforming vectors at the transmitter and receiver, constraint C3 indicates that only the phase shift of each reflection element in the RIS array is adjustable, and constraint C4 indicates that the navigation channel gain reflected through the RIS array must be higher than a preset threshold. c Let G be the achievable spectral efficiency for the user, ζ be the large-scale fading between the satellite and the user, and G be the achievable spectral efficiency for the user. c For the communication channel gain, G N For navigation channel gain, σ 2 For noise power, θ i For each element of the RIS array vector θ, the optimization problem is calculated using the maximum ratio transfer criterion. The optimal beamforming vector in the problem is obtained by removing constraints C1 and C2. Transform it into the following form:

[0034]

[0035]

[0036] C2:G N (0)≥G N，th .

[0037] Using the log-barrier method, the optimization problem is... The constraint C2 is placed into the logarithmic function and added to the objective function. This relaxes and transforms the original problem, resulting in the following optimization problem.

[0038]

[0039]

[0040] Introducing variable k to balance the order of magnitude and weights of the two terms in the objective function, the optimization problem... The solution is obtained by transforming the solution onto the Riemannian manifold represented by C1 and using the Riemann conjugate gradient method.

[0041] Preferably, in step S2:

[0042] Ground users receive navigation signals from four or more satellites and perform pseudorange positioning on the user side based on the received navigation data to obtain the user's three-dimensional position coordinates.

[0043] Satellite navigation signals originate from the direct path from the satellite to the user, or from the reflected path from the satellite to the RIS to the user;

[0044] The observation equation for positioning using the pseudorange method is:

[0045]

[0046] in, r represents the pseudorange between satellite s and the ground receiver. (s) δt represents the actual distance between satellite s and the ground receiver. u and δt (s) It refers to the receiver clock bias and the satellite clock bias, T (s) It is the neutral atmospheric tropospheric propagation delay, I (s) It is ionospheric propagation delay. Representing unmodeled ranging errors: including receiver noise, multipath effects; satellite clock bias information broadcast to users via satellite navigation signals, known to the receiver; neutral atmospheric tropospheric propagation delay T. (s) and ionospheric propagation delay I (s) Based on the mathematical model, an estimation is performed, given the receiver information; the error-corrected pseudorange measurement value is expressed as...

[0047]

[0048] The observation equation after error correction is expressed as follows:

[0049]

[0050] There are two satellite connection methods. The first is a direct connection between the satellite and the user's LoS (LoS). The second is a connection where the satellite is not visible to the user's line of sight and its signal is reflected through a RIS (Radio Router Array). The distance expression is as follows:

[0051]

[0052] In the above formula, x (s) y (s) , z (s) The three-dimensional coordinates of satellite s are x and y respectively. R y R , z R These are the three-dimensional coordinates of RIS, r sR Let x, y, z be the distance between the obscured satellite and the RIS array, and let x, y, z be the user's three-dimensional position coordinates to be determined. Measurement errors in formula (9) are omitted. The system of nonlinear algebraic equations for calculating the user's location is obtained as follows:

[0053]

[0054] in, The pseudorange of the satellite path reflected by RIS. The distance from the satellite reflected by the RIS to the RIS;

[0055] The system of equations, p = [x, y, z, δt], is solved using Newton's iteration method and the least squares method. u ], p k =[x k y k , z k ,δt u，k ] T Let l represent the user position and clock error in the k-th iteration, and denote the left side of each equation in the system of equations (11) as l. (s) In each iteration, l (s) (p) in p k-1 The first-order Taylor expansion at a given point approximates it, simplifying the system of equations into matrix equations:

[0056] G·Δp=b, (15)

[0057] Where, Δp=[xx k-1 yy k-1 ,zz k-1 ,δt u -δt u，k-1 ] T =[Δx, Δy, Δz, Δδt] u ] T

[0058]

[0059] Let δt be the distance from satellite s to the ground receiver in the (k-1)th iteration. u,k-1 r represents the user clock skewness during the (k-1)th iteration. (N) The distance between satellite N and the ground receiver. The pseudorange between satellite N and the ground receiver;

[0060] Where N≥4, using the least squares method, the matrix equation (15) yields the following LS solution:

[0061] Δp=(G T G) -1 G T b, (17)

[0062] Update the value of variable p k =p k-1 +Δp, and continue to execute the next iteration until convergence.

[0063] Preferably, the relationship between positioning error, clock error, and ranging error is obtained:

[0064]

[0065] Where, ε x , ε y , ε z These represent the errors in the user's three-dimensional coordinates x, y, and z, respectively. ε represents the error caused by the user's clock skew. ρ For pseudorange measurement errors between satellite users;

[0066] Derive the covariance matrix of positioning error and clock error:

[0067]

[0068] Where H = (G T G) -1 It is a 4×4 symmetric matrix. It is the variance of the user's equivalent ranging error. The above formula shows that the variance of the ranging error is transformed into the variance of the positioning and clock errors after being amplified by matrix H.

[0069] The accuracy factor is used to represent the amplification effect of the error, and it depends on the geometric distribution of the satellite. The value of the accuracy factor is obtained from matrix H:

[0070] Geometric precision factor:

[0071]

[0072] Among them, h 11 h is the first diagonal element of matrix H, located in the first row and first column. 22 h is the second diagonal element of matrix H. 33 h is the third diagonal element of matrix H. 44 Let tr(H) be the fourth diagonal element of matrix H, and let tr(H) be the trace of matrix H, which is the sum of the diagonal elements.

[0073] Position accuracy factor:

[0074]

[0075] Clock precision factor:

[0076]

[0077] The positioning error is calculated using an accuracy factor; the three-dimensional position error is as follows:

[0078]

[0079] Where, σ P σ is the standard deviation of the three-dimensional position error. x σ is the standard deviation of the user's x-coordinate error. y σ is the standard deviation of the user's y-coordinate error. z The standard deviation of the user's z-coordinate error;

[0080] Using an additional visible satellite provided by RIS in conjunction with existing visible satellites for positioning, and employing pseudorange positioning to complete the positioning, the user obtains their own three-dimensional position coordinates and transmits these coordinates to the visible satellite via an antenna.

[0081] Preferably, in step S2:

[0082] After calculating their own three-dimensional position coordinates, users use an antenna to send this information to a visible satellite.

[0083] After receiving the three-dimensional position coordinates information from the user, the satellite shares this information with other satellites via inter-satellite links.

[0084] Preferably, in step S3:

[0085] After receiving information from the user, the satellite uses the user's three-dimensional position coordinates and its own three-dimensional position coordinates to reconstruct the line-of-sight channel between the satellite and the user. This channel serves as an estimated channel for the actual channel between the two. Based on the estimated channel, the satellite designs the downlink beamforming vector.

[0086] Using the user's 3D location information and its own 3D location information, the satellite calculates the channel parameters between the two, including large-scale attenuation ξ, large-scale phase shift φ, and the azimuth angle on the satellite side. Angle of elevation Azimuth angle on the user side Angle of elevation Using this information, the Loss of Space (LoS) channel between the satellite and the user can be reconstructed:

[0087]

[0088] Among them, a R a T These are the array response vectors of the receiver and transmitter, respectively; singular value decomposition is performed on the reconstructed LosS channel:

[0089] H LoS =U∑V, (25)

[0090] U and V are both unitary matrices and conjugate symmetric matrices.

[0091] Optimal beamforming variable w on the satellite side s And the optimal beamforming variable v on the user side s Represented as:

[0092]

[0093]

[0094] Where V(:,1) represents the first column of matrix V, and for each satellite, the achievable spectral efficiency when providing services to users is expressed as:

[0095]

[0096] Among them, H s p is the equivalent channel from satellite s to the user. max σ is the maximum communication transmission power of the satellite. n This represents the noise standard deviation.

[0097] Preferably, in step S4:

[0098] From multiple available satellites, one satellite is selected to establish a communication link with the user and provide communication services to the user;

[0099] Satellite selection is based on the spectral efficiency of ground users.

[0100] Choose the satellite with the highest achievable spectral efficiency for communication:

[0101] A reconfigurable smart surface-assisted low-Earth orbit satellite communication and navigation fusion system provided by the present invention includes:

[0102] Module M1: Joint design of communication and navigation parameters for phase shifting of RIS arrays;

[0103] Module M2: Performs pseudorange positioning on the user side based on the received navigation data to obtain the user's three-dimensional position coordinates;

[0104] Module M3: After calculating the user's own three-dimensional position coordinates, it uses an antenna to send the three-dimensional position coordinates to the satellite;

[0105] Module M4: Using the user's three-dimensional position coordinates and the satellite's three-dimensional position coordinates, the line-of-sight channel between the satellite and the user is reconstructed as an estimated channel of the real channel. Based on the estimated channel, the downlink beamforming vector is designed on the satellite side.

[0106] Module M5: Selects satellites and users to establish communication links and provide communication services to users.

[0107] Compared with the prior art, the present invention has the following beneficial effects:

[0108] 1. The purpose of this invention is to provide a reconfigurable intelligent surface-assisted low-orbit satellite communication and navigation fusion scheme. The navigation system introduces a RIS array to provide additional visible satellites to improve the user's positioning accuracy. At the same time, the communication system can use positioning information to estimate downlink communication channels, simplify the process, reduce communication establishment latency, and improve user experience.

[0109] 2. Compared with low-overhead channel estimation schemes, the present invention has better performance in terms of spectral efficiency. Compared with high-overhead channel estimation schemes, the communication-navigation fusion-based scheme proposed in this invention greatly simplifies the satellite downlink communication process at the cost of slight loss in spectral efficiency, and reduces user communication latency caused by channel estimation by 50%, providing a solution to the problem of difficult satellite communication channel feedback. Attached Figure Description

[0110] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0111] Figure 1 This is a schematic diagram of a reconfigurable smart surface-assisted low-Earth orbit satellite system according to an embodiment of the present invention;

[0112] Figure 2 This is a flowchart of the reconfigurable smart surface-assisted low-Earth orbit satellite communication and navigation fusion scheme according to an embodiment of the present invention;

[0113] Figure 3The topological distribution of satellites is shown in three different maps, corresponding to excellent, medium, and poor, respectively.

[0114] Figure 4 This diagram illustrates the positioning accuracy under three different satellite distributions when the standard deviation of the ranging error is 1 meter.

[0115] Figure 5 This diagram illustrates the positioning accuracy under three different satellite distributions when the standard deviation of the ranging error is 3 meters.

[0116] Figure 6 This diagram illustrates the impact of introducing an additional satellite reflected by the RIS array on the user's positioning accuracy, when the user already has four visible satellites.

[0117] Figure 7 This diagram illustrates a comparison of the communication performance of the channel reconstruction scheme via communication-navigation fusion described in this embodiment of the invention with other channel estimation schemes. Detailed Implementation

[0118] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the scope of protection of the present invention.

[0119] Example 1:

[0120] This invention provides a reconfigurable smart surface-assisted low-Earth orbit satellite communication and navigation fusion scheme. Introducing a reconfigurable smart surface into the navigation system can provide additional visible satellites to improve positioning accuracy, such as... Figure 6 As shown; simultaneously, positioning information can be used to assist satellites in channel estimation for downlink communication. This method can achieve excellent downlink communication performance, as demonstrated in simulations. Figure 7 As shown, this method also greatly simplifies the satellite downlink communication process. When a user has a communication request, this scheme simplifies the process of the satellite transmitting downlink pilot for channel estimation and the process of the user feeding back channel information, thereby reducing the user communication delay caused by channel estimation by 50%.

[0121] like Figures 1-7 As shown, this invention provides a reconfigurable intelligent surface-assisted low-Earth orbit (LEO) satellite communication and navigation fusion scheme, which integrates communication and navigation functional modules on a LEO satellite and utilizes user location information obtained from the navigation system to assist the satellite in estimating downlink communication channels. For example... Figure 1As shown, each low-Earth orbit satellite is equipped with hardware for both navigation and communication systems. These two systems operate on different frequency bands and do not interfere with each other. The satellite can simultaneously provide navigation and communication services to ground users. Inter-satellite links are established between the satellites for information transmission. Ground users can simultaneously receive and process signals from both systems, and they also have the capability to transmit small amounts of data back to the satellites. RIS (Radio Routers for Low Earth Orbit) are placed on high-rise buildings in urban areas to reflect satellite signals and improve satellite coverage.

[0122] The first step is to enable the RIS array to be used by both communication and navigation systems simultaneously. Considering the possibility of the RIS participating in subsequent communication, the phase shift of the RIS array is designed with both communication and navigation parameters in mind.

[0123] The second step involves the ground user receiving navigation signals from four or more satellites. Based on the received navigation data, pseudorange positioning is performed on the user's side to obtain the user's three-dimensional position coordinates.

[0124] The third step involves the user calculating their own three-dimensional position coordinates and then using an antenna to transmit this information to a visible satellite.

[0125] The fourth step involves the satellite, after receiving information from the user, reconstructing the line-of-sight (LoS) channel between the satellite and the user using the user's three-dimensional position coordinates and its own three-dimensional position coordinates. This reconstructed channel serves as an estimated channel for the actual channel between the two. Based on this estimated channel, downlink beamforming vectors are designed on the satellite side.

[0126] The fifth step involves selecting one of the multiple available satellites to establish a communication link with the user and provide communication services.

[0127] The first step in designing the phase shift of the RIS array for both communication and navigation is to ensure that the navigation gain provided by the RIS exceeds a certain threshold so that the ground receiver can receive the signal normally. On this basis, the communication gain should be maximized as much as possible.

[0128] The satellite navigation signal in the second step may come from the satellite-user direct path or from the satellite-RIS-user reflective path.

[0129] In the third step, after receiving the three-dimensional position coordinates information sent by the user, the satellite can share this information with other satellites through inter-satellite links.

[0130] In the fourth step, based on the three-dimensional position coordinates of the satellite and the user, the large-scale attenuation and phase shift between the satellite and the user are first calculated using distance. Then, the azimuth and elevation angles of the antenna on the satellite side and the angle information on the user side are calculated, and the Loss Channel is reconstructed.

[0131] The satellite selection in step five is based on the spectral efficiency (SE) of the ground users.

[0132] This invention provides a reconfigurable intelligent surface-assisted low-Earth orbit satellite communication and navigation fusion scheme. This scheme utilizes the characteristic that the direct path power between the satellite and the ground user is much greater than the scattered path power in the satellite-ground scenario. Based on the three-dimensional position information of the user and the satellite, the channel is reconstructed, the channel estimation for downlink communication is performed, and beamforming design is carried out based on this.

[0133] The reconfigurable smart surface-assisted low-Earth orbit satellite communication and navigation fusion scheme described in the embodiments of the present invention will be described in detail below with reference to the accompanying drawings and specific implementation details. Firstly, to ensure the normal operation of the RIS array, the phase shift of the RIS array needs to be jointly designed for navigation and communication parameters. Assume the transmitted navigation signal is x. N The navigation signal received by ground users via RIS reflection can be represented as

[0134]

[0135] Among them, h RU h is the navigation channel vector between the RIS and the user. sR Let Θ be the navigation channel vector between the satellite and the RIS, where Θ = diag([θ1, θ2, ..., θ...). M ]) is the phase shift matrix of the RIS array, which is a diagonal matrix, p sN n represents the satellite's navigation signal transmission power. N This is additive white Gaussian noise during navigation. Assume the communication signal transmitted by the satellite launched by RIS is x. C Then the communication signal received by the ground user via RIS reflection can be represented as

[0136]

[0137] Among them, H RU H is the communication channel matrix between the RIS and the user. sR p is the communication channel matrix between the satellite and the RIS. sC w is the satellite's communication signal transmission power. sR The downlink beamforming vector for the satellite, v is the receive vector on the user side, and n C This is additive white Gaussian noise during the communication process. From this, we can obtain the navigation channel gain G reflected by the RIS. N (θ) and communication channel gain G C (θ,w sR v):

[0138]

[0139] G C (θ,w sR ,v)=|v H H RU ΘH sR w sR | 2 .

[0140] Where θ is the phase shift vector of the RIS array.

[0141] It is worth noting that for RIS-assisted systems, much work has already conducted in-depth research on related channel estimation methods. Therefore, we assume that the channel state of the satellite-RIS-user link is perfectly known. Based on the known channel state, the RIS array phase-shift design needs to be jointly designed considering both communication and navigation metrics, i.e., balancing the gains of the two. Therefore, the following optimization problem can be constructed.

[0142]

[0143] StC1:||w sR || 2 =1,

[0144] C2:||v|| 2 =1,

[0145]

[0146] C4:G N (θ)≥G N，th .

[0147] The optimization objective of the problem is to maximize the gain of the communication channel while satisfying four constraints. Constraints C1 and C2 are mode constraints on the communication beamforming vectors at the transmitter and receiver. Constraint C3 states that only the phase shift of each reflection element in the RIS array is adjustable. Constraint C4 states that the gain of the navigation channel reflected through the RIS array must be higher than a threshold to ensure that the ground user receiver can correctly receive the navigation signal. c Let G be the achievable spectral efficiency for the user, ζ be the large-scale fading between the satellite and the user, and G be the achievable spectral efficiency for the user. c For the communication channel gain, G N For navigation channel gain, σ 2 For noise power, θ i Let θ be each element of the RIS array vector. Using the MRT (Maximum Ratio Transmission) criterion, we can calculate the optimization problem. The optimal beamforming vector in the original optimization problem is obtained by removing constraints C1 and C2. It can be transformed into the following form:

[0148]

[0149]

[0150] C2:G N (θ)≥G N，th .

[0151] Two constraints remain in this optimization problem. We employ the log-barrier method to simplify the optimization problem. The constraint C2 is incorporated into the logarithmic function and added to the objective function. This relaxes the original problem and undergoes some transformations, ultimately yielding the following optimization problem.

[0152]

[0153]

[0154] The purpose of introducing the variable k is to balance the orders of magnitude of the two terms in the objective function and to control their weights. Although C1 is a non-convex constraint, it is a typical Riemannian manifold. Therefore, the optimization problem... It can be transformed to the Riemannian manifold represented by C1 and solved using the Riemannian Conjugate Gradient (RCG) method.

[0155] After completing the phase-shift design of the RIS array, users can receive additional satellite navigation signals not only from the LoS satellites but also through reflections from the RIS array, thereby achieving positioning or improving positioning accuracy. The observation equation for positioning using the pseudorange method is:

[0156]

[0157] in, r represents the pseudorange between satellite s and the ground receiver. (s) δt represents the actual distance between satellite s and the ground receiver. u and δt (s) It refers to the receiver clock bias and the satellite clock bias, T (s) It is the propagation delay in the neutral atmosphere (troposphere), I (s) It is ionospheric propagation delay. This represents the unmodeled ranging error, including receiver noise, multipath effects, and other minor influencing factors. Satellite clock bias information is broadcast to users via satellite navigation signals and is therefore known to the receiver. Neutral atmospheric (tropospheric) propagation delay T. (s) and ionospheric propagation delay I (s) The measurement can be estimated based on a mathematical model, and can be considered known to the receiver. Therefore, we can express the error-corrected pseudorange measurement as follows:

[0158]

[0159] The error-corrected observation equation can be expressed as:

[0160]

[0161] In this work, there are two satellite connection methods: the first is a direct connection between the satellite and the user's LoS (LoS); the second is a connection where the satellite is not visible to the user's line of sight and requires signal reflection via a RIS (Reflection Signal Array). The distance expressions for the two cases are slightly different and can be expressed as follows:

[0162]

[0163] In the above formula, x (s) y (s) , z (s) The three-dimensional coordinates of satellite s are x and y respectively. R y R , z R These are the three-dimensional coordinates of RIS, r sR Let be the distance from satellite s to RIS. (x, y, z) are the user's three-dimensional position coordinates to be determined. Measurement error in formula (9) is omitted. We can obtain a system of nonlinear algebraic equations for calculating the user's location:

[0164]

[0165] in, The pseudorange of the satellite path reflected by RIS. The distance from the satellite reflected by the RIS to the RIS.

[0166] We use Newton's iteration method and the least squares method (LS) to solve the above system of equations. Assume p = [x, y, z, δt] u ], p k =[x k y k , z k ,δt u，k ] TLet l represent the user position and clock error in the k-th iteration. (s) This represents the left-hand side of the equality sign for each equation in the system of equations (11). In each iteration, we use l (s) (p) in p k-1 We can approximate it using the first-order Taylor expansion at the given location, expressed as:

[0167]

[0168] in, Let δt be the distance from satellite s to the ground receiver in the (k-1)th iteration. u,k-1 This represents the user clock offset during the (k-1)th iteration.

[0169] Let Δp = [xx] k-1 yy k-1 ,zz k-1 ,δt u ,δt u，k-1 ] T =[Δx, Δy, Δz, Δδt] u ] T The above formula can be simplified to

[0170]

[0171] Therefore, each equation in the system of equations (11) can be rewritten as

[0172]

[0173] Therefore, the original system of equations can be simplified into matrix equations:

[0174] G·Δp=b, (15)

[0175] in

[0176]

[0177] Where, r (N) The distance between satellite N and the ground receiver. This is the pseudorange between satellite N and the ground receiver.

[0178] Where N≥4. Using the least squares method, the matrix equation (15) can be solved using the following LS solution:

[0179] Δp=(G T G) -1 G T b, (17)

[0180] Then update the value of variable p. k =pk-1 +Δp, and continue to execute the next iteration until convergence.

[0181] Pseudorange positioning relies on pseudorange measurement, and pseudorange measurement error is unavoidable. We will now analyze the impact of measurement error on positioning error and clock error. Through mathematical derivation, the relationship between positioning error, clock error, and ranging error can be obtained:

[0182]

[0183] Where, ε x , ε y , ε z These represent the errors in the user's three-dimensional coordinates x, y, and z, respectively. ε represents the error caused by the user's clock skew. ρ This refers to the pseudorange measurement error between satellite users.

[0184] Based on this, we can derive the covariance matrix of the positioning error and the clock error:

[0185]

[0186] Where H = (G T G) -1 It is a 4×4 symmetric matrix. This is the variance of the User Equivalent Ranging Error (UERE). The above formula shows that the variance of the ranging error, after being amplified by matrix H, is transformed into the variances of the positioning and clock errors. Therefore, it can be known that the positioning error and clock error depend on the following two factors:

[0187] Distance measurement error: the variance of the distance measurement error The larger the value, the greater the variance of the positioning error and clock error.

[0188] Satellite geometric distribution: Matrices G and H depend only on the number of visible satellites and their geometric distribution relative to the user.

[0189] We use the Dilution of Precision (DOP) to represent the amplification effect of errors, which depends entirely on the satellite's geometric distribution. The value of DOP can be obtained from matrix H. Commonly used precision factors are listed below:

[0190] Geometric Precision Factor (GDOP):

[0191]

[0192] Among them, h 11 Let h be the first diagonal element of matrix H (the element located in the first row and first column). 22h is the second diagonal element of matrix H. 33 h is the third diagonal element of matrix H. 44 Let tr(H) be the fourth diagonal element of matrix H, and let tr(H) be the trace of matrix H (the sum of the diagonal elements).

[0193] Position Precision Factor (PDOP):

[0194]

[0195] Clock Precision Factor (TDOP):

[0196]

[0197] Positioning error can therefore be calculated using an accuracy factor, such as three-dimensional position error:

[0198]

[0199] Where, σ P σ is the standard deviation of the three-dimensional position error. x σ is the standard deviation of the user's x-coordinate error. y σ is the standard deviation of the user's y-coordinate error. z This represents the standard deviation of the user's z-coordinate error.

[0200] If a user has three visible satellites, they can use an additional visible satellite launched by RIS to work in conjunction with the existing three visible satellites for positioning. Figure 3 The document presents three different satellite distributions. All three distribution maps are top-down views of Earth from space. The satellite positions in the maps are projections of the satellites' actual positions onto the Earth's spherical unfolding. The longer the line connecting the satellite and the user, the farther the distance between the satellite and the user. Figure 3 The three satellite distribution topologies shown each have their advantages and disadvantages. The more dispersed the satellite distribution, the smaller the positioning accuracy factor tends to be, and the better the positioning effect. For the three distributions, we simulated the positioning accuracy under different ranging errors, such as... Figure 4 , 5 As shown, each scenario underwent 100 independent positioning calculations, and the dashed line in the figure represents the average positioning error of the 100 positioning calculations. It can be seen that, under the same satellite distribution, the smaller the variance of the ranging error of the ground user's receiver, the higher the user's average positioning accuracy. Under the condition of equal ranging error variance, a satellite distribution with a smaller accuracy factor (better) can provide users with higher positioning accuracy compared to a satellite distribution with a larger (worse) accuracy factor.

[0201] When a user has four visible satellites but their distribution is less than ideal, the additional visible satellites provided by RIS can improve the user's positioning accuracy. We present the improvement in user positioning accuracy achieved by introducing RIS under two different satellite distributions, such as... Figure 5 As shown in the image, an additional satellite can significantly improve the previously unsatisfactory satellite distribution, greatly reducing user positioning errors and improving positioning accuracy.

[0202] After completing the positioning using the pseudorange positioning method described above, the user can obtain their own three-dimensional position coordinates and transmit these coordinates to a visible satellite via an antenna. Using the user's three-dimensional position information and their own, the satellite can calculate the channel parameters between them, including large-scale attenuation ξ, large-scale phase shift φ, and the azimuth angle on the satellite side. Angle of elevation Azimuth angle on the user side Angle of elevation This information can be used to reconstruct the Loss of Space (LoS) channel between the satellite and the user:

[0203]

[0204] Where a R a T These are the array response vectors for the receiver and transmitter, respectively. Then, Singular Value Decomposition (SVD) is performed on the reconstructed LosS channel, i.e.:

[0205] H LoS =U∑V, (25)

[0206] Where U and V are both unitary matrices (conjugate symmetric matrices).

[0207] Therefore, the optimal beamforming variable w on the satellite side s And the optimal beamforming variable v on the user side s It can be represented as:

[0208]

[0209]

[0210] Where V(:,1) represents the first column of matrix V. For each satellite, the achievable spectral efficiency when providing services to users can be expressed as:

[0211]

[0212] Among them, H s p is the equivalent channel from satellite s to the user. max σ is the maximum communication transmission power of the satellite.n This represents the noise standard deviation.

[0213] Finally, the satellite with the highest achievable spectral efficiency was selected for communication.

[0214] Figure 7 The communication performance of the channel reconstruction scheme using the communication-navigation fusion method described in this invention was compared with other channel estimation schemes. As shown in the figures, compared to the fixed array antenna scheme and the low-overhead analog codebook scheme, the scheme presented in this invention has a certain performance gain; compared to the ideal situation where the channel state is perfectly known, the communication performance difference of this scheme is very small; compared to the relatively high-overhead digital codebook scheme, this scheme greatly simplifies the satellite downlink communication process at the cost of slight communication performance loss. When a user makes a communication request, this scheme simplifies the process of the satellite transmitting downlink pilots for channel estimation and the process of the user feeding back channel information, reducing the user communication delay caused by channel estimation by 50%. Furthermore, this study found that when the distance between the navigation signal transmitter and receiver is sufficiently large (such as in satellite navigation scenarios), the channel reconstructed using the scheme presented in this invention is minimally affected by the user's positioning accuracy, and the differences in reconstructed channels under different positioning error conditions have virtually no impact on the subsequent communication process.

[0215] Those skilled in the art will understand that, in addition to implementing the system, apparatus, and their modules provided by this invention in purely computer-readable program code, the same program can be implemented in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system, apparatus, and their modules provided by this invention can be considered a hardware component, and the modules included therein for implementing various programs can also be considered structures within the hardware component; alternatively, modules for implementing various functions can be considered both software programs implementing the method and structures within the hardware component.

[0216] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A reconfigurable intelligent surface-assisted low-Earth orbit satellite communication and navigation fusion method, characterized in that, include: Step S1: Design the phase shift of the RIS array by combining communication and navigation parameters. Step S2: Perform pseudorange positioning on the user side based on the received navigation data to obtain the user's three-dimensional position coordinates; Step S3: After calculating the user's own three-dimensional position coordinates, the three-dimensional position coordinates are transmitted to the satellite using an antenna; Step S4: Using the user's three-dimensional position coordinates and the satellite's three-dimensional position coordinates, reconstruct the line-of-sight channel between the satellite and the user, which serves as the estimated channel for the real channel. Based on the estimated channel, design the downlink beamforming vector on the satellite side. Step S5: Select a satellite and establish a communication link with the user to provide communication services to the user; In step S1: The RIS array is used by both communication and navigation systems. The phase shift of the RIS array is designed with both communication and navigation parameters in mind. When designing the phase shift of the RIS array for both communication and navigation purposes, the first step is to ensure that the navigation gain provided by the RIS exceeds a preset threshold so that the ground receiver can receive the signal. On this basis, the communication gain is maximized.

2. The reconfigurable intelligent surface-assisted low-Earth orbit satellite communication and navigation fusion method according to claim 1, characterized in that, In step S1: The phase shift of the RIS array is used to jointly design navigation and communication metrics, and the transmitted navigation signal is... The navigation signals received by ground users via RIS reflection are represented as in, This is the navigation channel vector between the RIS and the user. This is the navigation channel vector between the satellite and the RIS. The phase shift matrix of the RIS array is a diagonal matrix. The satellite's navigation signal transmission power. Additive white Gaussian noise during navigation; The communication signals transmitted by the satellite reflected by RIS are The communication signal received by the ground user via RIS reflection is represented as: in, This is the communication channel matrix between the RIS and the user. The communication channel matrix between the satellite and the RIS. This refers to the satellite's communication signal transmission power. Assigning downlink beamforming vectors to the satellite, This is the receive vector on the user side. Additive white Gaussian noise during communication; Obtain the navigation channel gain via RIS reflection. and communication channel gain : in, This is the phase shift vector of the RIS array; The channel states of the satellite, RIS, and user links are known. Based on these known channel states, the phase shift design of the RIS array needs to consider both communication and navigation metrics in a joint design, balancing the navigation channel gain and the communication channel gain. This leads to the following optimization problem. : N represents the number of satellites; The optimization objective of the optimization problem is to maximize the gain of the communication channel while satisfying constraints, where the constraints are... and restrictions It is a mode constraint on the communication beamforming vectors at both the transmitting and receiving ends. This means that only the phase shift of each reflection unit in the RIS array is adjustable, limiting... This means that the navigation channel gain reflected by the RIS array must be higher than a preset threshold. For the user's achievable spectral efficiency, For large-scale fading between satellites and users, For communication channel gain, For navigation channel gain, For noise power, RIS array vector For each element; using the maximum ratio transfer criterion, calculate the optimization problem. The optimal beamforming vector in the model has had its limitations removed. and restrictions Optimization problem Transform it into the following form: Using the log-barrier method, the optimization problem is... Limitations By incorporating the logarithmic function and adding it to the objective function, the original problem is relaxed and transformed, resulting in the following optimization problem. : Introducing variables Balancing the orders of magnitude and weights of the two terms in the objective function to solve the optimization problem. Switch to The solution is obtained using the Riemann conjugate gradient method on the Riemann manifold represented by the given information.

3. The reconfigurable intelligent surface-assisted low-Earth orbit satellite communication and navigation fusion method according to claim 1, characterized in that, In step S2: Ground users receive navigation signals from four or more satellites and perform pseudorange positioning on the user side based on the received navigation data to obtain the user's three-dimensional position coordinates. Satellite navigation signals originate from the direct path from the satellite to the user, or from the reflected path from the satellite to the RIS to the user; The observation equation for positioning using the pseudorange method is: in, Indicates satellite s The pseudorange between the ground receiver and the ground receiver Indicates satellite s The actual distance between the receiver and the ground receiver. and It refers to receiver clock bias and satellite clock bias. It is a neutral atmospheric tropospheric propagation delay. It is ionospheric propagation delay. Representing unmodeled ranging errors: including receiver noise, multipath effects; satellite clock bias information broadcast to users via satellite navigation signals, which is known to the receiver; and neutral atmospheric tropospheric propagation delay. and ionospheric propagation delay Based on the mathematical model, and given the receiver information, the error-corrected pseudorange measurement is expressed as follows: This represents the pseudorange measurement value after error correction; The observation equation after error correction is expressed as follows: There are two satellite connection methods. The first is a direct connection between the satellite and the user's LoS (LoS). The second is a connection where the satellite is not visible to the user's line of sight and its signal is reflected through a RIS (Radio Router Array). The distance expression is as follows: In the above formula, , , Let be the three-dimensional coordinates of satellite s. , , These are the three-dimensional coordinates of RIS. The distance between the obscured satellite and the RIS array is given by x, y, z, which are the user's three-dimensional position coordinates to be determined. The measurement error in formula (9) is omitted. This yields a system of nonlinear algebraic equations for calculating the user's location: in, The pseudorange of the satellite path reflected by RIS. The distance from the satellite reflected by the RIS to the RIS; The system of equations was solved using Newton's iteration method and the least squares method. , Let the user position and clock error be represented in the k-th iteration, and let the left side of each equation in the system of equations (11) be expressed as... In each iteration, using exist The first-order Taylor expansion at a given point approximates it, simplifying the system of equations into matrix equations: in, , Let be the distance from satellite s to the ground receiver in the (k-1)th iteration. The user clock skew during the (k-1)th iteration; The distance between satellite N and the ground receiver. The pseudorange between satellite N and the ground receiver; in Using the least squares method, the matrix equation (15) yields the following LS solution: Update the value of the variable And continue to execute the next iteration until convergence.

4. The reconfigurable intelligent surface-assisted low-Earth orbit satellite communication and navigation fusion method according to claim 2, characterized in that: The relationship between positioning error, clock error, and ranging error is obtained: in, , , User's three-dimensional coordinates x, y, z The error, For the user's clock skew error, For pseudorange measurement errors between satellite users; Derive the covariance matrix of positioning error and clock error: in It is Symmetric matrix It is the variance of the user's equivalent ranging error. The above formula shows that the variance of the ranging error is transformed into the variance of the positioning and clock errors after being amplified by matrix H. The accuracy factor is used to represent the amplification effect of the error, and it depends on the geometric distribution of the satellite. The value of the accuracy factor is obtained from matrix H: Geometric precision factor: in, Let H be the first diagonal element of matrix H, located in the first row and first column. The second diagonal element of matrix H The third diagonal element of matrix H The fourth diagonal element of matrix H Let H be the trace of matrix H, and the sum of its diagonal elements. Position accuracy factor: Clock precision factor: The positioning error is calculated using an accuracy factor; the three-dimensional position error is as follows: in, The standard deviation of the three-dimensional position error. The standard deviation of the user's x-coordinate error. The standard deviation of the user's y-coordinate error. The standard deviation of the user's z-coordinate error; The system utilizes an additional visible satellite provided by RIS reflection to work in conjunction with existing visible satellites for positioning. It then employs pseudorange positioning to complete the positioning process. The user obtains their own three-dimensional position coordinates and transmits these coordinates to the visible satellite via an antenna.

5. The reconfigurable intelligent surface-assisted low-Earth orbit satellite communication and navigation fusion method according to claim 1, characterized in that, In step S2: After calculating their own three-dimensional position coordinates, users use an antenna to send this information to a visible satellite. After receiving the three-dimensional position coordinates information from the user, the satellite shares this information with other satellites via inter-satellite links.

6. The reconfigurable intelligent surface-assisted low-Earth orbit satellite communication and navigation fusion method according to claim 1, characterized in that, In step S3: After receiving information from the user, the satellite uses the user's three-dimensional position coordinates and its own three-dimensional position coordinates to reconstruct the line-of-sight channel between the satellite and the user, which serves as an estimated channel for the actual channel between the two. Based on the estimated channel, the downlink beamforming vector is designed on the satellite side. Using the user's 3D location information and its own 3D location information, the satellite calculates the channel parameters between the two, including large-scale attenuation. Large-scale phase shift azimuth angle on the satellite side Angle of elevation Azimuth angle on the user side Angle of elevation Using this information, the Loss of Space (LoS) channel between the satellite and the user can be reconstructed: in, These are the array response vectors of the receiver and transmitter, respectively; singular value decomposition is performed on the reconstructed LosS channel: in, and All are unitary matrices and conjugate symmetric matrices; Optimal beamforming variables on the satellite side and the optimal beamforming variables on the user side Represented as: in Representing the first column of matrix V, the spectral efficiency achievable for each satellite when providing services to users is expressed as: in, For the equivalent channel from satellite s to the user, This is the satellite's maximum communication transmission power. This represents the noise standard deviation.

7. The reconfigurable intelligent surface-assisted low-Earth orbit satellite communication and navigation fusion method according to claim 1, characterized in that, In step S4: From multiple available satellites, one satellite is selected to establish a communication link with the user and provide communication services to the user; Satellite selection is based on the spectral efficiency of ground users. Choose the satellite with the highest achievable spectral efficiency for communication: ; s selected It is the satellite with the highest achievable spectral efficiency; 's' is the satellite designation; SEs represent the spectral efficiency achievable when providing services to users for each satellite.

8. A reconfigurable intelligent surface-assisted low-Earth orbit satellite communication and navigation fusion system, characterized in that, include: Module M1: Joint design of communication and navigation parameters for phase shifting of RIS arrays; Module M2: Performs pseudorange positioning on the user side based on the received navigation data to obtain the user's three-dimensional position coordinates; Module M3: After calculating the user's own three-dimensional position coordinates, it uses an antenna to send the three-dimensional position coordinates to the satellite; Module M4: Using the user's three-dimensional position coordinates and the satellite's three-dimensional position coordinates, the line-of-sight channel between the satellite and the user is reconstructed as an estimated channel of the real channel. Based on the estimated channel, the downlink beamforming vector is designed on the satellite side. Module M5: Selects satellites and users to establish communication links and provide communication services to users; In module M1: The RIS array is used by both communication and navigation systems. The phase shift of the RIS array is designed with both communication and navigation parameters in mind. When designing the phase shift of the RIS array for both communication and navigation purposes, the first step is to ensure that the navigation gain provided by the RIS exceeds a preset threshold so that the ground receiver can receive the signal. On this basis, the communication gain is maximized.

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