Target position estimation method based on distributed RIS transmit array

Abstract

The present invention relates to a target position estimation method based on a distributed RIS transmit array, comprising: using a distributed RIS as a transmit array, wherein the distributed RIS comprises two RIS array surfaces, a target source and a receiving radio frequency chain are respectively provided on two sides of the RIS transmit array, the receiving radio frequency chain is connected to a receiving antenna, and the target source transmits a pilot signal to a space; transmitting the pilot signal to the receiving radio frequency chain by means of the RIS transmit array to obtain a receiving signal; processing the receiving signal to solve for an azimuth angle β and a pitch angle α of the target source relative to the two RIS array surfaces; and on the basis of the azimuth angle β and the pitch angle α, making two rays that respectively pass through the centers of the two RIS array surfaces, and solving for a median value of the shortest distance between the two rays, wherein the position of the median value is the position of the target source. The present invention can improve the positioning accuracy, and increase the operation speed of solving for a target position.

Description

Target position estimation method based on distributed RIS transmission array TECHNICAL FIELD

[0001] The present application belongs to the technical field of wireless communication, and particularly relates to a target position estimation method based on a distributed RIS transmission array. BACKGROUND

[0002] Wireless positioning and sensing are becoming increasingly important in the fifth generation (5G) wireless communication system. Position awareness is crucial to the success of numerous services, including the Internet of Things, integrated sensing technology, and autonomous vehicles. At the same time, high-precision positioning technology is also the basis and support for many applications, such as emergency rescue, autonomous driving, and healthcare. The most common way to obtain a position is through the Global Navigation Satellite System (GNSS), but when a certain number of satellites do not have a clear line of sight, such as in underground tunnels and inside buildings, satellite signals can be disturbed and may not be available.

[0003] Since the Reconfigurable Intelligent Surface (RIS) allows us to control the propagation environment to some extent, it is natural to explore its utility in positioning. Many researchers have explored the application of RIS in positioning, and the results show that as long as the RIS phase curve is properly designed, RIS can improve the positioning performance. Among them, using it as a transmission array is a promising scenario for RIS, where each RIS element can individually change the phase of the signal passing through it, and phase reconfigurability is the most important function of the transmission RIS. Signals can be transmitted through transmission RIS to form directional beams, and by deploying these transmission RIS to replace the walls of buildings, wireless signals from outdoors can be accurately focused on indoor users, which can assist in the perception of the position of indoor users from outdoors and communication. This is a promising way and application scenario to enhance communication and reduce electromagnetic pollution, and is also a promising development direction for integrated sensing technology. However, in the current prior art, the use of a single RIS transmission array for target position estimation technology has low positioning accuracy and long position solution time in simulation. SUMMARY

[0004] To solve the above technical problems, improve the accuracy of target position estimation, and reduce the position solution time in simulation, the present application proposes a target position estimation method based on a distributed RIS transmission array, which comprises:

[0005] S1: a distributed RIS is used as a transmissive array, the distributed RIS includes two RIS array surfaces, a target source and a receiving radio frequency chain are arranged on the two sides of the RIS transmissive array respectively, the receiving radio frequency chain is connected with a receiving antenna, and the target source emits a pilot signal to space;

[0006] S2: the pilot signal is transmitted to the receiving radio frequency chain through the RIS transmissive array to obtain a receiving signal;

[0007] S3: the receiving signal is processed to solve an azimuth angle β and a pitch angle α of the target source relative to the two RIS array surfaces respectively;

[0008] S4: two rays respectively passing through the centers of the two RIS array surfaces are drawn according to the azimuth angle β and the pitch angle α, and a median of the shortest distance between the two rays is solved, and the position of the median is the position of the target source.

[0009] Further, in S1, a distributed RIS transmissive array assisted positioning system is constructed, the system includes: two RIS array surfaces are arranged side by side as a transmissive array, each RIS array surface is connected with a receiving antenna RF, and the receiving antenna RF and a target source are located on the two sides of the RIS transmissive array respectively; each RIS array surface has M array elements, and the position of the i th array element is specifically represented as:

[0010] In the formula, q i represents the position of the i th array element, i represents the serial number of the array element, M represents the number of array elements of each RIS transmissive array, represents a real number set with a dimension of 3, [x i ,y i ,z i ] represents coordinates, r i represents the distance between the i th array element in the RIS transmissive array and the center of the transmissive array, the azimuth angle ψ i represents the included angle between the line connecting the i th array element and the origin and the positive direction of the x axis, represents transposition;

[0011] The position vector p of the target source is specifically: p=-λdc g (α g ,β g ) / 2π (g=1, 2),

[0012] Wherein, p represents the position vector of the target source, λ represents the wavelength of the signal, d represents the Euclidean distance from the target source to the midpoint of the RIS transmissive array, c g (α g ,β g ) represents the wave vector of the pilot signal reaching the g th RIS transmissive array, α gβ represents the elevation angle formed by the pilot signal and the g-th RIS transmission array. g This represents the azimuth angle formed by the pilot signal and the g-th RIS transmission array.

[0013] Furthermore, in S2, after the pilot signal transmitted by the target source is transmitted through the channel, the output signal of the receiving antenna is represented as:

[0014] In the formula, W=[ω1,ω2,...,ω T ], ω t =Ω t g ant , t=1,2,...,T, G(α)=[g0(α)...g M-1 (α)], h(β)=e jβ ,

[0015] Where y′ represents the output signal of the receiving antenna, E s The signal average power is represented by γ, and the intermediate variable is represented by γ = ζ(p)e jθ ζ(p) represents the wireless channel amplitude vector between the RIS array and the target source, e represents the natural logarithm, j represents the imaginary number, and θ represents the signal phase. λ represents the wavelength of the signal, d represents the Euclidean distance from the target source to the midpoint of the RIS transmission array, and θ represents the wavelength of the signal. offset Represents the global phase offset; ω t W represents the product of the array element phase and the channel gain at time t, and W represents the product of ω. t The set consists of, where T represents the number of time points. α represents the transpose; G(α) represents the pitch angle formed by the signal and each array; β represents the azimuth angle formed by the signal and each array; n represents the noise vector.

[0016] Furthermore, the expression for the intermediate variable G(α) is specifically: G(α)=[g0(α)…g M-1 (α)], where the i-th element g with respect to α i The expression for (α) is:

[0017] In the formula, g i (α) represents the i-th element of the intermediate variable G(α) expression with respect to α, where i represents the element index, M represents the number of elements in the RIS array, and J n (·) represents the nth order Bessel function, where n = 2, j represents the imaginary number, α represents the elevation angle formed by the signal and each array, λ represents the signal wavelength, and ψ i Let r represent the coordinates of the i-th element. irepresents the distance of the ith array element from the array center.

[0018] Further, the S3 specifically comprises:

[0019] In the optimization function for solving the pitch angle a, the grid search is performed in the value range of the pitch angle a from 0° to 90° to obtain an estimated value of the pitch angle a, and the optimization function of the pitch angle a is expressed as:

[0020] wherein,

[0021] In the formula, represents the estimated value of the pitch angle, y' represents the output signal of the receiving antenna after the channel transmission, and ||·|| represents the calculation of the Euclidean distance, represents the estimated value of the variable a represented by a, G * represents the conjugate of G(a), W * represents the conjugate of W.

[0022] The estimated pitch angle a is substituted into the output signal of the receiving antenna to obtain an optimization function for solving the azimuth angle β, and the grid search is performed in the value range of β from 0° to 360° to obtain an estimated value of the azimuth angle β, and the optimization function of the azimuth angle β is expressed as:

[0023] wherein, represents the estimated value of the azimuth angle, represents the estimated value of the intermediate variable γ about the azimuth angle β, and γ = ζe jθ .

[0024] Further, the S4 specifically comprises:

[0025] According to the azimuth angle β and the pitch angle a of the target source relative to the first and second RIS array surfaces respectively, a first ray and a second ray l2 passing through the center point of the RIS array surface and corresponding to the azimuth angle β and the pitch angle a of the target source are obtained;

[0026] A vector perpendicular to the first ray and also perpendicular to the second ray l2 is obtained, the second ray l2 is translated along the vector to form a plane a, and the intersection t1 of the first ray l1 and the plane a is obtained;

[0027] The second ray l2 is translated along the vector perpendicular to the first ray and also perpendicular to the second ray to form a plane b, and the intersection t2 of the second ray l2 and the plane a is obtained;

[0028] The intersection t1 of the first ray l1 and the plane a and the intersection t2 of the second ray l2 and the plane a are connected together, and the center position of the two intersection connecting line segments is the target source position coordinate.

[0029] The present application has the beneficial effects that the present application constructs a distributed RIS array model assisted positioning system, proposes to use a geometric positioning algorithm of an out-of-plane straight line to perform position estimation, improves positioning accuracy compared with a single RIS array model, and reduces simulation solving time. BRIEF DESCRIPTION OF DRAWINGS

[0030] Fig. 1 is a step flowchart of an embodiment of the present application;

[0031] Fig. 2 is a schematic diagram of a distributed RIS transmission array assisted positioning system model in an embodiment of the present application;

[0032] Fig. 3 is a schematic diagram of definition and division of near-field and far-field regions;

[0033] Fig. 4 is a schematic diagram of the shortest distance principle of an out-of-plane straight line in the present application;

[0034] Fig. 5 is a performance comparison diagram of the method of the present application and a single RIS assisted positioning system in simulation verification of the present application. DETAILED DESCRIPTION

[0035] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0036] The embodiments of the present application provide a target position estimation method based on a distributed RIS as a transmission array, referring to Fig. 1, the method comprises:

[0037] S1: the distributed RIS is used as a transmission array, the distributed RIS includes two RIS array planes, a target source and a receiving radio frequency chain are respectively arranged on the two sides of the RIS transmission array, the receiving radio frequency chain is connected to a receiving antenna, and the target source transmits a pilot signal to space;

[0038] S2: the pilot signal is transmitted to the receiving radio frequency chain through the RIS transmission array to obtain a received signal;

[0039] S3: the received signal is processed to solve a bearing angle β and a pitch angle a of the target source relative to the two RIS array planes;

[0040] S4: two rays respectively passing through the centers of the two RIS array planes are drawn according to the bearing angle β and the pitch angle a, and a median of the shortest distance between the two rays is solved, and the position of the median is the position of the target source.

[0041] Fig. 2 is a schematic diagram of a distributed RIS transmission array assisted positioning system model constructed according to an embodiment of the present application.

[0042] In S1, a distributed RIS transmission array assisted positioning system is constructed. Referring to Fig. 2, the system includes: two RIS array surfaces arranged side by side as transmission arrays, each RIS array surface is connected with a receiving antenna RF, and the receiving antenna RF and the target source p (the target source is a single target source) are located on the two sides of the RIS transmission array respectively. The target source p transmits a signal, the signal is transmitted to the receiving antenna RF through the RIS transmission array to obtain a received signal. The RIS is a plane composed of sub-wavelength metamaterials, which can control the wireless propagation channel by applying the required transformation to the input signal through the software control of each metamaterial. The target source p is also often regarded as a user in a communication system.

[0043] In Fig. 2, p represents the target source, and its position is represented as p = [x, y, z] T , where x, y, and z represent coordinates, x, z > 0. O1 and O2 represent the center positions of the first and second RIS transmission arrays respectively. The Euclidean distances of the target source to the midpoint positions of the first and second RIS transmission arrays are d1 and d2 respectively, and Each RIS transmission array has a receiving antenna (Radio Frequency, RF) below it, which is λ (λ is the signal wavelength) away from the RIS reflection array surface. The output signals of the first receiving antenna RF1 and the second receiving antenna RF2 are y t1 and y t2 respectively.

[0044] Each RIS array surface has M elements, and each element has a size of A = a x a (usually the area of each element is set to λ 2 / 4). The position of the i-th element is set as where i = 1, 2,..., M, M is a positive integer representing the total number of elements, and r i represents the distance of each element from the center of the array. The azimuth angle ψ i is the angle between the line connecting the element and the origin and the positive direction of the x-axis. The azimuth angle and the elevation angle of the target source relative to array 1 are β11 and α1, and the azimuth angle and the elevation angle relative to array 2 are β2 and α2, β j ∈ [0, 2π], α j ∈ [0, π / 2], where j = 1, 2. The azimuth angle β is defined as the angle between the projection of the line connecting the target source and the center of the array on the xoy plane and the positive direction of the x-axis, and the elevation angle α is defined as the angle between the line connecting the target source and the center of the array and the positive direction of the z-axis. α and β can be called as angle of arrival (AoAs).

[0045] Thus, the wave vector c g (α g ,β g ) of the signal reaching each RIS array can be written as

[0046] wherein c g (α g ,β g ) represents the wave vector of the signal reaching each RIS array, λ represents the signal wavelength, d represents the Euclidean distance from the target source to the midpoint of the RIS transmission array, α represents the elevation angle of the signal with each array, and β represents the azimuth angle of the signal with each array.

[0047] After transformation, the position vector of the target source can be represented by the wave vector as:

[0048] p=-λdc g (α g ,β g ) / 2π(g=1,2), wherein p represents the position vector of the target source.

[0049] In the distributed RIS transmission array assisted positioning system constructed by the embodiment of the application, the two receiving antennas connected by the two RIS transmission arrays do not affect each other by default.

[0050] In S2, the target source signal is modeled, specifically:

[0051] Assuming that the signal model is a narrowband signal, the pilot signal S t transmitted by the signal source at time t is transmitted to the receiver connected to the single antenna through the lens on the RIS, and has E s represents the average power of the signal, and T represents the number of times. There are M elements on each RIS array, and at time t, the phase of the element can be written as Ω t =diag(u t,0 ,...,u t,M-1 ), wherein the absolute value of the phase of the i-th element at time t is equal to 1, i.e.: |u t,i |=1,

[0052] At time t, the baseband signal y t output by the receiving antenna is specifically represented as:

[0053] wherein

[0054] b(p)=∑[b(p)] i ,

[0055] where e is the natural logarithm, j is the imaginary unit, θ is the signal phase, θ offset represents the global phase offset, in practice, a certain phase offset will be caused by the lack of phase synchronization between the transmitter and receiver and other effects; g ant represents the fixed known channel gain between the RIS array and the receiving antenna, represents the Mx1-dimensional complex number set; Ω t represents the RIS array element phase at time t, ζ(p) represents the wireless channel amplitude vector between the RIS array and the target source at time t, ζ(p) ≥ 0 M , 0 M represents the MxM-dimensional zero matrix; b(p) represents the phase vector of the channel, [b(p)] i represents the phase vector of the i-th element channel, ‖·‖ represents the calculation of the Euclidean distance, p represents the target source position, q i represents the i-th element position in the RIS array; S t represents the pilot signal transmitted by the target signal source, n t represents the noise at time t, which is an additive white Gaussian noise with mean 0 and variance N0 / 2 (assuming independent and identically distributed), N0 represents the power spectral density of the noise.

[0056] b(p) = ∑ [b(p)] i represents the phase vector of the channel, which is obtained by summing the phase vectors of the channels of each element in the RIS array.

[0057] In order to further simplify formula (2), a new variable is introduced, which can be set as the signal vector The element phase and channel gain product at time t is represented as ω t = Ω t g ant The set composed of ω t is represented as W, represents the MxT-dimensional complex number set, W = [ω1, ω2, …, ω T ], t = 1, 2, …, T, T represents the number of time, and the noise vector The received signal vector

[0058] Combined with the baseband signal output by the receiving antenna, formula (2) is simplified as:

[0059] where, W = [ω1, ω2, …, ω T ], ω t = Ω t g ant, t = 1, 2,..., T b(p) = ∑ [b(p)] i ,

[0060] where y represents the received antenna output signal, e is a natural logarithm, j is an imaginary number, θ offset represents a global phase offset, λ represents the wavelength of the signal, d represents the Euclidean distance from the target source to the midpoint of the RIS transmission array; ω t represents the product of the element phase and the channel gain at time t, W represents a set composed of ω t , T represents the number of time points; ζ(p) represents the wireless channel amplitude vector between the RIS array surface and the target source, ζ(p) ≥ 0 M ; b(p) represents the phase vector of the channel, diag(s) represents a diagonal matrix operation, represents dot product, and for simplicity, let E s represents the average power of the signal.

[0061] A channel model is constructed, and the output signal after the channel is obtained.

[0062] In the present application, the near-field condition in the Fresnel region greater than the Fresnel distance is mainly considered, and the electromagnetic near-field effect in the Fraunhofer distance is ignored, and the specific area division is as shown in FIG. 3. FIG. 3 is a schematic diagram for defining and dividing the far-field and near-field regions. The division distances and calculation methods of different regions are given in FIG. 3, which are used to illustrate the application range of the channel in the present application. In the present application, the near-field condition in the Fresnel region greater than the Fresnel distance is mainly considered.

[0063] The constructed channel considers the amplitude and phase changes of the received signal on the RIS elements, which is close to the real positioning scene. The amplitude depends on the position of the RIS element relative to the target source (equivalent to the user), and the phase depends on the distance to each RIS element. The element phase needs to consider the wavefront curvature. The phase vector [b(p)] i of the i-th element channel is as follows:

[0064] wherein:

[0065] wherein, ||p-q i || represents the Euclidean distance from the target source to the i-th element of the RIS transmission array, ||·|| represents the calculation of the Euclidean distance, q iFor the position of the i-th element in the RIS transmission array, when calculating the coordinates of each RIS array relative to the target source position respectively, the center of the currently calculated RIS array is taken as the coordinate center to establish a coordinate system, that is, the Euclidean distance from the target source to the midpoint position of the current RIS transmission array is represented as (As shown in FIG. 2, the center of the RIS transmission array is the coordinate origin in the system model); r i represents the distance of the i-th element from the center of the RIS transmission array; α represents the elevation angle of the signal and the RIS transmission array, and β represents the azimuth angle of the signal and the RIS transmission array.

[0066] It can be obviously seen that when d >> ||q i ||, , formula (5) can be written as: ||p-q i ||-d=-r i sinɑcos(β-ψ i ) (6)

[0067] In formula (6), ||·|| represents the calculation of the Euclidean distance, α represents the elevation angle of the signal and the RIS transmission array, and β represents the azimuth angle of the signal and the RIS transmission array; ψ i is the included angle formed by the i-th element and the midpoint of the array and the positive direction of the x-axis. It is observed from formula (6) that the final result is irrelevant to the distance from the target source to the RIS array plane.

[0068] The amplitude vector of the channel model is as follows:

[0069] wherein

[0070] represents the amplitude vector of the channel model, x, y, and z represent the coordinates of the receiving antenna position. x i , y i represents the coordinates of the i-th element, and a represents the element size, a = λ / 2.

[0071] In order to ensure the consistency between the far field and the near field, f(α, β) = 1-sin 2 (α)sin 2 (β) can be allowed.

[0072] Therefore, after the transmitted pilot signal passes through the channel, the output signal of the receiving antenna is written as:

[0073] wherein Wα[ω1,ω2,...,ω T ], ω t =Ω tg ant , t = 1, 2,..., T,

[0074] where y' represents the received antenna output signal after channel transmission, E s represents the signal average power, ζ(p) represents the wireless channel amplitude vector between the RIS array and the target source; ω t represents the product of the array element phase and channel gain at time t, W represents a set composed of ω t , T represents the number of time, b(p) represents the phase vector of the channel, , and n represents the noise vector.

[0075] Fisher information analysis is performed below, and the RIS array phase is designed.

[0076] The intermediate variable y can be set when the received antenna output signal y' does not consider the noise part where the unknown parameter can be set as

[0077] The Fisher information matrix (FIM) can be written as:

[0078] In the above formula, μ is the received antenna output signal without considering the noise part; η is the unknown parameter;

[0079] The partial derivative can be written as has:

[0080] where p represents the target source position coordinates; d represents the Euclidean distance from the target source to the midpoint position of the two RIS transmission arrays; is the phase vector of the channel; an intermediate variable e i is introduced i = (q i -p) / ||q i -p||, where q i represents the RIS array element position, ||·|| represents the Euclidean distance, and a set composed of e i is represented as: Q = [e0, e1,..., e M-1 ].

[0081] F(η) represents the Fisher information matrix of all unknown information, and the equivalent FIM information matrix F(p) about the user position needs to be obtained, and its expression is:

[0082] where [F(η)] 1,1 represents the element of the first row and the first column in the F(η) matrix, and [F(η)] 3:5,3:5represents the elements of the 3rd to 5th rows and the 3rd to 5th columns in the F(η) matrix; [F(η)] 3:5,1:2 represents the elements of the 3rd to 5th rows and the 1st to 2nd columns in the F(η) matrix; represents the elements of the 1st to 2nd rows and the 1st to 2nd columns in the F(η) matrix; [F(η)] 1:2,3:5 represents the elements of the 1st to 2nd rows and the 3rd to 5th columns; N0 represents the power spectral density of noise, * represents taking the conjugate, and the phase and channel gain product is ω t = Ω t g ant , then W = [ω1, ω2,..., ω T ]; is the phase vector of the channel; b H (p) represents the conjugate transpose of the phase vector of the array surface, and ζ(p) represents the wireless channel amplitude vector between the RIS array surface and the target source.

[0083] In the present application, PEB is used to represent the positioning performance, and the PEB in meters is represented by the following formula for comparison with the positioning performance of other positioning models:

[0084] In the formula, PEB represents the positioning error boundary, [F -1 (η)] 3:5,3:5 represents the inverse of the elements of the 3rd to 5th rows and the 3rd to 5th columns in the F(η) matrix, and trace represents the trace, [F -1 (p)] represents the inverse.

[0085] The PEB can be related to the root mean square error (RMSE) of the unbiased estimator

[0086] In the formula, represents the estimated position of the target, ||·|| represents the calculation of the Euclidean distance, and p represents the actual position of the target set in the simulation; represents the expectation.

[0087] The performance of the target position estimation and the design of the RIS array phase have a great relationship, in order to eliminate the influence of the fixed known channel gain from the RIS array to the single receiving antenna, therefore, the design where the fixed phase Ω ant = diag(ω ant,0 ,..., ω ant,M-1 ), and has Each phase of each element of the RIS array at any time is set individually, and the phase of each element at time t is:​ where denotes uniform distribution from 0 to 2π.

[0088] The position estimation of the target source according to the above modeling is roughly divided into three steps: first, the maximum likelihood estimation is used to estimate the target for the respective pitch angle α of the two RIS arrays; second, the maximum likelihood estimation is used to obtain the azimuth angle β using the estimated pitch angle; a geometric relationship model is constructed; and a non-planar straight line geometric positioning method is used to solve the most possible position of the target, i.e. the estimated position of the target source.

[0089] S3 is specifically:

[0090] S301: Transform the output signal of the receiving antenna, and the transformed expression contains the separate expression form of the pitch angle α and the azimuth angle β, specifically:

[0091] The phase vector b(p) of the channel contains the information of the pitch angle α and the azimuth angle β, so the formula (8) is rewritten as:

[0092] where γ = ζ(p)e jθ , W = [ω1, ω2, …, ω T ], ω t = Ω t g ant , t = 1, 2, …, T, b(ɑ, β) = Σ[b(α, β)] i

[0093] In the formula, y' represents the output signal of the receiving antenna after channel transmission, E s represents the average power of the signal, γ represents an intermediate variable introduced for the purpose of simplifying formula (8); ω t represents the product of the element phase and the channel gain at time t, W represents a set composed of ω t , T represents the number of time; ɑ and β are the pitch angle and the azimuth angle of the signal and each array, respectively; n is a noise vector, and [b(ɑ, β)] i represents the phase vector of the i-th item in the channel.

[0094] The phase vector can be simplified by ignoring the amplitude change of the signal, and the i-th item of the phase vector of the channel can be written as:

[0095] In the formula, [b(α, β)] i represents the phase vector of the i-th item in the channel, α represents the pitch angle of the signal and each array, and β represents the azimuth angle of the signal and each array; λ is the wavelength of the signal; ψ i is the azimuth angle of the RIS element, and ri is the distance of the ith element from the array center.

[0096] The above equation can be re-written using the Bessel expansion formula as:

[0097] where J n (·) is the nth order Bessel function, n is usually taken as 2; a represents the elevation angle of the signal with respect to the array; b represents the azimuth angle of the signal with respect to the array; l is the wavelength of the signal; y i is the azimuth angle of the element; r i is the distance of each element from the array center O.

[0098] The case of |n| > N is neglected (as n increases, |J n (·)| tends to zero), so we have:

[0099] where |J n (·)| represents the nth order Bessel function; N represents a value beyond which it decays to zero; a represents the elevation angle of the signal with respect to the array; b represents the azimuth angle of the signal with respect to the array; l is the wavelength of the signal; y i is the azimuth angle of the element; r i is the distance of each element from the array center O.

[0100] A new variable is introduced to simplify equation (17), and the following variables are defined under n = -N,..., N: [h(β)] n = e jnβ (19)

[0101] where J n (·) represents the nth order Bessel function, n is usually taken as 2; a represents the elevation angle of the signal with respect to the array; b represents the azimuth angle of the signal with respect to the array; l is the wavelength of the signal; y i is the azimuth angle of the element; r i is the distance of each element from the array center O.

[0102] Therefore, the phase vector can be represented as:

[0103] Let G(a) = [g0(a)... g M-1 (a)], then we have:

[0104] where G(a) = [g0(a)... g M-1 (a)], and h(β) = e jβ .

[0105] Thus, the pitch angle a and the azimuth angle β are separated and expressed, and the formula (14) is rewritten as:

[0106] In the formula, y' represents the signal output by the receiving antenna after channel transmission.

[0107] S302: The optimization function of the pitch angle a is solved according to the formula (21), and the grid search is performed in the value range of 0° to 90° of the pitch angle a to obtain the estimated value of the pitch angle, specifically:

[0108] An intermediate variable v is introduced, When v is expressed by a, it is:

[0109] In the formula, represents the estimated expression of v expressed by a, G(a) = [g0(a)...g M-1 (α)], G * (α) represents the conjugate of G(a), W * represents the conjugate of W, and y' represents the signal output by the receiving antenna after channel transmission.

[0110] The optimization function of the pitch angle a is obtained according to the formula (22), and its specific expression is:

[0111] In the formula, represents the estimated value of the pitch angle, y' represents the signal output by the receiving antenna after channel transmission, and ‖·‖ represents the calculation of the Euclidean distance, represents the estimated value of v expressed by the variable a, where γ represents an intermediate variable for simplifying the formula, γ = ζe jθ .

[0112] According to the optimization function of the pitch angle a, i.e., the formula (23), the grid search is performed in the value range of 0° to 90° of the pitch angle a to obtain the estimated value of the pitch angle.

[0113] Thus, the pitch angles of the target source to the two RIS arrays can be calculated, which are represented as a1 and a2. Specifically, a1 represents the pitch angle of the target source to the first RIS array, and a2 represents the pitch angle of the target source to the second RIS array.

[0114] S303: The optimization function of the azimuth angle β is solved according to the formula (21), and the grid search is performed in the value range of 0° to 360° of β to obtain the estimated value of the azimuth angle, specifically:

[0115] The output signal y' of the receiving antenna is obtained by substituting a obtained in S302 into the formula (21).

[0116] Construct a maximum likelihood estimation model, let γ = ζ(p)e jθ Then, the maximum likelihood estimates of the channel gain and the target source location (i.e., the user location) are obtained, and their specific expressions are as follows:

[0117] In the formula, This represents the maximum likelihood estimate of the channel gain. This represents the maximum likelihood estimate of the target source (i.e., the user's location).

[0118] Based on the maximum likelihood estimate of the channel gain Find the maximum likelihood estimate of the target source location p. The calculation formula is as follows:

[0119] In the formula, W * y' represents the conjugate of W; y' represents the received antenna output signal after transmission through the channel; b H (p) denotes the conjugate transpose of b(p).

[0120] For the sake of simplicity, let

[0121] estimate Substituting the values ​​will yield an estimated value.

[0122] in, This represents the estimated location of the target source, and ||·|| represents the calculation of the Euclidean distance. Denotes the orthogonal projection operator on L. This represents the product of the channel phase gain matrix and the phase vector.

[0123] The maximum likelihood estimation model constructed above can be based on the maximum likelihood estimate of the target source location p. Obtain the maximum likelihood estimate of the azimuth angle β. use to replace b(p) in Obtain the maximum likelihood estimate of the azimuth angle β. Its expression is:

[0124] In the formula, This represents the maximum likelihood estimate of the azimuth angle β. Indicates to Please transpose the given text.

[0125] According to The expression can be solved Azimuth angle, get the optimization function of azimuth angle:

[0126] In the formula, Indicates the estimated value of the azimuth angle, y' indicates the output signal of the receiving antenna after the channel transmission, Indicates the estimated value of the variable γ about the azimuth angle β

[0127] According to the optimization function of the azimuth angle β, that is, formula (24), the grid search is performed on the value range of the azimuth angle β in 0° to 90°, and the estimated value of the azimuth angle β is obtained. Thus, the azimuth angles of the target source to the two RIS arrays can be calculated, which are respectively represented as: β1 and β2. Specifically, β1 represents the azimuth angle of the target source to the first RIS array plane, and β2 represents the azimuth angle of the target source to the second RIS array plane.

[0128] S4 is specifically:

[0129] Using the above steps, the azimuth angle and the elevation angle of the target source relative to the two RIS arrays can be obtained, and two rays passing through the centers (O1 or O2) of the RIS arrays can be made, and the two rays intersect at a point, which is the target position. However, in actual situations, errors will be generated in the measurement process and the calculation process, and the probability of the two generated rays intersecting at a point is 0. Therefore, a method of "shortest distance of skew lines taking the median value" is proposed to determine the target point position, and the algorithm schematic diagram is shown in FIG. 4.

[0130] FIG. 4 is a schematic diagram of the shortest distance principle of skew lines in the application. In FIG. 4, [x, y, z] represents a three-dimensional coordinate system, O1 represents the center of the first RIS array, O2 represents the center of the second RIS array, l1 represents a first ray passing through the center O1 of the first RIS array and corresponding to the azimuth angle β1 and the elevation angle α1 of the target source relative to the first RIS array, l2 represents a second ray passing through the center O2 of the second RIS array and corresponding to the azimuth angle β2 and the elevation angle α2 of the target source relative to the second RIS array, and the vector f represents a vector perpendicular to the first ray l1 and the second ray l2. The second ray l2 is translated along the vector f to form a plane a, and the intersection point of the first ray l1 and the plane a is also the nearest point t1 on the first ray l1 to the second ray l2. The first ray l1 is translated along the vector f to form a plane b, and the intersection point of the second ray l2 and the plane a is the nearest point t2 on the second ray l2 to the first ray l1. The midpoint position of the line segment t1 t2 is the position P of the target source.

[0131] According to S3, the target's pitch angles a1 and a2, azimuth angles b1 and b2 relative to the two RIS arrays have been calculated, and the coordinates of the two RIS array center points (O1 and O2) are known.

[0132] S401: According to the azimuth angle b and the pitch angle a of the target source relative to the first and second RIS array planes respectively, the first ray l1 and the second ray l2 passing through the center points of the RIS array planes and corresponding to the azimuth angle b and the pitch angle a of the target source are obtained respectively, which are specifically represented as:

[0133] In the formula,

[0134] In the formula, l1 represents the first ray passing through the center of the first RIS transmission array, l2 represents the second ray passing through the center of the second RIS transmission array, p1 represents the coordinates of the point through which the first straight line passes, p2 represents the coordinates of the point through which the second straight line passes, d represents the slope of the first straight line, t represents the second straight line, v1 represents the direction vector of the first ray, v2 represents the direction vector of the second ray, [x'1, y'1, z'1] represents the position coordinates of any point on the first ray, [x'2, y'2, z'2] represents the position coordinates of any point on the second ray, T represents transposition, a1 represents the pitch angle of the first straight line, b1 represents the azimuth angle of the first straight line, a2 represents the pitch angle of the second straight line, and b2 represents the azimuth angle of the second straight line.

[0135] S402: The vector perpendicular to the first ray l1 and the second ray l2 at the same time is solved, and the calculation formula is specifically:

[0136] In the formula, f represents the vector perpendicular to the first ray l1 and the second ray l2 at the same time, v1 represents the direction vector of the first ray, and v2 represents the direction vector of the second ray.

[0137] S403: The second ray l2 is translated along the vector f to form a plane a, which contains the point p2 and is perpendicular to f2=v2xf, so the intersection of the first ray l1 and the plane a is also the nearest point t1 on the first ray l1 to the second ray l2, which is specifically represented as:

[0138] In the formula, p1 represents the coordinates of the point through which the first straight line l1 passes, p2 represents the coordinates of the point through which the second straight line l2 passes, f1 represents the vector of the plane perpendicular to the first straight line l1, and f2 represents the vector of the plane perpendicular to the second straight line l2.

[0139] S404: Translate the first ray l1 along the vector f to form a plane b containing the point p1 and perpendicular to f1=v1xf, then the intersection of the second ray l2 and the plane a is the point t2 on the second ray l2 closest to the first ray l1, which is specifically represented as:

[0140] S405: Connect the points t1 and t2 to form a line segment, and solve the midpoint position of the line segment, which is the target source position coordinate.

[0141] Simulation verification: The results are simulated using MATLAB software, and the simulation parameters are as follows:

[0142] In the distributed array model, the center positions of the two RIS arrays are respectively set as and A receiving antenna is placed behind each RIS array, at and The signal operating frequency is 28GHz, the signal source transmission power is set to 1mW, the noise power spectral density is set to-174dBm / Hz, and the receiving noise coefficient is 8dB. The bandwidth is set to 1MHz to enable positioning based on 0.2ms observation. The prior information of the user position is a Gaussian probability density function where Σ p =σ 2 I3. These prior information is used in the design of RIS phase, and is not involved in the positioning process and the calculation of PEB. The extended position estimation uses N=5. At the same time, in order to eliminate the influence of the number of array elements on the positioning performance, 50*50 array elements are arranged on a single RIS array during the position estimation process, and 35*35 array elements are arranged on each array surface in the distributed array model. In order to reduce the error caused by the randomness of a single simulation, the RMSE value of each position in the simulation is the average value after 200 times of Monte Carlo.

[0143] The simulation results are shown in Figure 5, which shows that the positioning performance of the distributed RIS transmission array positioning model designed by the application is generally better than that of the existing single RIS transmission array model, which shows that the model designed by the application and the positioning algorithm proposed are superior to the existing single array model. At the same time, the time consumed by the MATLAB software simulation is also superior to the time consumed by the single array model, and the specific time consumed by the distributed model simulation is about 1 / 4 of the time consumed by the single array model.

[0144] Those skilled in the art can understand that all or part of the steps in the various methods of the above embodiments can be completed by programs instructing related hardware, and the programs can be stored in a computer readable storage medium, which can include ROM, RAM, magnetic disk or optical disk, etc.

[0145] While embodiments of the application have been shown and described, it is to be understood that the application is not limited to the details of the embodiments described, since numerous changes, modifications, substitutions and variations can be made thereto without departing from the spirit and scope of the application as defined by the appended claims and their equivalents.

Claims

1. A method for target position estimation based on distributed RIS transmissive array, characterized in that, The method comprises the following steps: S1: a distributed RIS is used as a transmissive array, the distributed RIS comprises two RIS array surfaces, a target source and a receiving radio frequency chain are arranged on the two sides of the RIS transmissive array respectively, the receiving radio frequency chain is connected to a receiving antenna, and the target source emits a pilot signal to space; S2: the pilot signal is transmitted to the receiving radio frequency chain through the RIS transmissive array to obtain a receiving signal; S3: the receiving signal is processed to solve a bearing angle β and a pitch angle α of the target source relative to the two RIS array surfaces respectively; S4: two rays respectively passing through the centers of the two RIS array surfaces are drawn according to the bearing angle β and the pitch angle α, and a median value of the shortest distance between the two rays is solved, and the position of the median value is the position of the target source.

2. The target position estimation method based on distributed RIS transmissive array according to claim 1, characterized in that, In S1, a distributed RIS transmission array assisted positioning system is constructed, which includes: two RIS array surfaces arranged side by side as a transmission array, each RIS array surface is connected with a receiving antenna RF, the receiving antenna RF and the target source are located on the two sides of the RIS transmission array respectively, each RIS array surface has M array elements, and the position of the i th array element is specifically represented as: In the formula, q i represents the i-th array element position, i represents the array element sequence number, M represents the number of array elements of each RIS transmission array, represents a set of real numbers of dimension 3, [x i , y i , z i ] represents coordinates, r i represents the distance of the i-th element in the RIS transmission array from the center of the transmission array, the azimuth angle ψ i represents the angle between the line connecting the i-th element and the origin and the positive direction of the x-axis, denotes transposition; The position vector of the target source is specifically denoted as: p = -λdc g (α g ,β g ) / 2π(g = 1, 2), wherein p represents the position vector of the target source, λ represents the wavelength of the signal, d represents the Euclidean distance from the target source to the midpoint position of the RIS transmission array, c g (α g ,β g ) represents the wave vector of the pilot signal reaching the gth RIS transmission array, ɑ g represents the elevation angle formed by the pilot signal and the gth RIS transmission array, and β g represents the azimuth angle formed by the pilot signal and the gth RIS transmission array.

3. The target position estimation method based on distributed RIS transmissive array according to claim 1, characterized in that, In S2, the pilot signal transmitted by the target source, after channel transmission, the output signal of the receiving antenna is represented as: In the formula, W = [ω1, ω2,..., ω T ], ω t = Ω t g ant , t = 1, 2,..., T, G(a) = [g0(a)... g M-1 (α)], h(β) = e jβ , where y' represents the received antenna output signal, E s represents the signal average power, γ represents an intermediate variable, γ = ζ(p)e jθ , ζ(p) represents the wireless channel amplitude vector between the RIS array and the target source, e represents the natural logarithm, j represents the imaginary number, and θ represents the signal phase, λ represents the wavelength of the signal, d represents the Euclidean distance from the target source to the midpoint position of the RIS transmission array, θ offset represents the global phase offset; ω t represents the product of the array element phase and the channel gain at time t, W represents a set composed of ω t , T represents the number of time points, denotes transposition; ɑ denotes a pitch angle of a signal and each array, G(ɑ) denotes an intermediate variable about the pitch angle ɑ, β denotes a bearing angle of the signal and each array; and n denotes a noise vector.

4. The target position estimation method based on a distributed RIS transmissive array according to claim 3, characterized in that The expression of the intermediate variable G(a) is specifically: G(a) = [g0(a)... gi(a)... gM(a)], wherein the expression of the element gi(a) with respect to the pitch angle a is: M-1 gi(a) = a2+ a + 1 i The expression of the element gi(a) with respect to the pitch angle a is: wherein g i (α) represents an element of the i-th term in the intermediate variable G(α) with respect to the pitch angle α, i represents the serial number of the array element, M represents the number of array elements of the RIS array surface, J n (·) represents the n-th order Bessel function, and n = 2, j represents an imaginary number, α represents the pitch angle of the signal and each array, λ represents the signal wavelength, ψ i represents the i-th array element coordinate, r i represents the distance of the i-th array element from the array center.

5. The target position estimation method based on distributed RIS transmissive array according to claim 3, characterized in that, The S3 specifically comprises: According to the expression of the output signal of the receiving antenna, an optimization function of the pitch angle a is obtained. In solving the optimization function of the pitch angle a, a grid search is performed on the value range of the pitch angle a from 0° to 90° to obtain an estimated value of the pitch angle a. The optimization function of the pitch angle a is expressed as: wherein where y' represents the received antenna output signal, denotes the estimated value of the pitch angle, ||·|| denotes the computation of the Euclidean distance, denotes an estimate value represented by a variable a, G * (a) denotes taking a conjugate of G(a), W * denotes taking a conjugate of W; The estimated pitch angle a is substituted into the transformed received antenna output signal expression to obtain an optimization function for solving the azimuth angle β, and a grid search is performed in the range of 0° to 360° to obtain the estimated value of the azimuth angle β. The optimization function for the azimuth angle β is expressed as: where y' represents the received antenna output signal, an estimate of the azimuth angle, denotes a maximum likelihood estimation value about the bearing angle β.

6. The target position estimation method based on distributed RIS transmissive array according to claim 5, characterized in that, The optimization function process for solving the bearing angle β comprises: Construct the maximum likelihood estimation model, let γ = ζ(p)e jθ The maximum likelihood estimation values of the channel gain and the target source position are obtained, and the expression is specifically as follows: In the formulae, a maximum likelihood estimate value of a channel gain, denotes a maximum likelihood estimation value of the position of the target source; Maximum likelihood estimate of channel gain solving for the maximum likelihood estimate of the target source position p The calculation formula is: where W * represents the conjugate of W, b H (p) represents the conjugate transpose of b(p), The maximum likelihood estimate for the azimuth angle β is solved from the maximum likelihood estimate for the target source position p with the formula In the formulae, denotes the maximum likelihood estimate value with respect to the azimuth angle β, indicates that the transposition is solved.

7. The target position estimation method based on distributed RIS transmissive array according to claim 1, characterized in that, The S4 is specifically: According to the bearing angle β and the pitch angle α of the target source relative to the first and second RIS array surfaces respectively, a first ray and a second ray l2 passing through the center points of the RIS array surfaces and corresponding to the bearing angle β and the pitch angle α of the target source are obtained; A vector perpendicular to the first ray and also perpendicular to the second ray l2 is obtained, the second ray l2 is translated along the vector to form a plane a, and an intersection t1 of the first ray l1 and the plane a is obtained; The second ray l2 is translated along the vector perpendicular to the first ray and also perpendicular to the second ray to form a plane b, and an intersection t2 of the second ray l2 and the plane a is obtained; The intersection t1 of the first ray l1 and the plane a and the intersection t2 of the second ray l2 and the plane a are connected together, and the center position of the two intersection connecting line segments is the position coordinate of the target source.

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