Error correction method for multi-sensor network system under the background of synaesthesia integration

Abstract

The present invention relates to a multi-sensor network system error correction method under the background of synaesthesia integration, comprising: determining the type of system error existing in the base station network under the background of synaesthesia integration; determining the observation model of the base station in the global coordinate system; determining the state transition model of the cooperative moving target according to the position vector and velocity vector of the cooperative moving target in the global coordinate system, and determining the position of the cooperative stationary target; combining the observation model of the base station, the state transition model of the cooperative moving target and the position of the cooperative stationary target, and determining the target function of the base station system error correction according to the position matching error of the cooperative target in the global coordinate system; solving the target function using a coordinate cyclic descent algorithm based on an alternating direction multiplier method, and obtaining the optimal estimate of each base station system error parameter. The method improves the estimation accuracy of the system error and obtains good system tracking performance.

Description

Technical Field

[0001] The present invention belongs to the technical field of sensor system error correction, and in particular relates to a multi-sensor network system error correction method under the background of synaesthesia integration. Background Art

[0002] Communication and perception integration is one of the research hotspots of potential key technologies of 6G networks. The integrated system of communication not only has wireless communication functions, but also has the ability to perceive the state of targets in the coverage area, and complete functions such as positioning, tracking, imaging, and identification. By fusing the information received by multiple base stations, higher positioning accuracy and more stable detection performance can be obtained. However, in practical applications, a series of uncontrollable external factors such as the directional error of the array antenna, the signal processing delay system error, and hardware limitations will cause each base station to have different degrees of system errors, which seriously affects the information fusion performance of the base station network and reduces the positioning accuracy. Therefore, system error correction technology plays an important role in improving the system performance of the base station network.

[0003] At present, a series of studies have been conducted on the error correction technology of multi-sensor network systems. For example, Fortunati et al. proposed a linear least squares estimation algorithm, which established a linear least squares model for the data measured by each sensor and calculated its least squares solution as the system error estimate. Zhou et al. proposed a maximum likelihood estimation algorithm, which established a joint likelihood function model of system error and target state and solved it using a two-step iterative optimization method. Okello et al. proposed using the Kalman filter algorithm to estimate the system error and target state. The above-mentioned system error correction algorithms all deal with the nonlinear part of the system error correction problem through linear approximation or large computational complexity, which will bring about problems such as model mismatch or limitation of computational complexity, resulting in unsatisfactory estimation performance.

[0004] However, in practical applications, multi-sensor networks often work in an asynchronous manner, and most of the existing multi-sensor network system error correction technologies are studied for synchronous working modes. In addition, due to the nonlinear transformation between the coordinate systems of each sensor, the error correction problem of multi-sensor network systems is often highly nonlinear, and the design of effective nonlinear optimization algorithms is also a research direction that needs to be solved urgently. Summary of the invention

[0005] In order to solve the above problems existing in the prior art, the present invention provides a multi-sensor network system error correction method under the background of synaesthesia integration. The technical problem to be solved by the present invention is achieved through the following technical solutions:

[0006] The embodiment of the present invention provides a multi-sensor network system error correction method under the background of synaesthesia integration, comprising the steps of:

[0007] Step 1, determining the types of system errors existing in the base station network under the background of synaesthesia integration, wherein the base station network includes a plurality of base stations, the base station network is located in a global coordinate system, each base station is located in a respective local coordinate system, and the plurality of base stations observe the cooperative target in the global coordinate system in their respective spherical coordinate systems;

[0008] Step 2, determining the observation model of the base station in the global coordinate system according to the position relationship between the position of the cooperation target in the local coordinate system of each base station and the global coordinate system, and combining the transformation relationship between the global coordinate system and the spherical coordinate system;

[0009] Step 3, determining a state transition model of the cooperative moving target according to the position vector and velocity vector of the cooperative moving target in the global coordinate system, and determining the position of the cooperative stationary target;

[0010] Step 4, combining the observation model of the base station, the state transition model of the cooperative moving target and the position of the cooperative stationary target, and determining the objective function of the base station system error correction according to the position matching error of the cooperative target in the global coordinate system;

[0011] Step 5: Solve the objective function using a coordinate cyclic descent algorithm based on an alternating direction multiplier method to obtain an optimal estimate of the system error parameters of each base station.

[0012] In one embodiment of the present invention, the types of system errors include measurement errors and coordinate axis rotation errors, wherein the measurement errors include distance system errors, azimuth system errors and pitch angle system errors, and the coordinate axis rotation errors include roll rotation angle system errors, tilt rotation angle system errors and yaw rotation angle system errors.

[0013] In one embodiment of the present invention, step 2 comprises:

[0014] The relationship between the position of the cooperation target in the local coordinate system of each base station and the position in the global coordinate system is:

[0015] ξ k '=R T (Θ m,sk +ΔΘ sk )(ξ k -p sk )

[0016] Among them, ξ k '=[x' k ,y' k ,z' k ] T represents the position of the target at time k in the local coordinate system of the base station, Θm,sk =(α m,sk ,β m,sk ,γ m,sk ) represents the measured rotation angles of the base station’s coordinate system around the x, y, and z axes at time k, ΔΘ sk represents the base station's coordinate axis rotation angle system error, ξ k =[x k ,y k ,z k ] T represents the position of the target at time k in the global Cartesian coordinate system, represents the position of the base station working at time k, and R represents the rotation matrix, which is used to transform the local coordinate system of the base station into the Cartesian global coordinate system, satisfying R -1 (θ)=R T The properties of (Θ),

[0017] R(Θ) is defined as:

[0018]

[0019] Among them, (α, β, γ) represents the rotation angle, R x , R y , R z Represents the rotation matrix around the x, y, and z axes;

[0020] The transformation relationship between the global coordinate system and the spherical coordinate system is:

[0021]

[0022] Among them, z t,k represents the actual measurement vector of the base station, ρ t,k Represents the actual measurement parameter of distance, φ t,k Represents the actual measurement parameter of azimuth, η t,k represents the actual measurement parameter of the pitch angle, c represents the propagation speed of electromagnetic waves, t t,k Indicates the real delay of electromagnetic wave propagation;

[0023] Combining the position relationship and the transformation relationship, the observation model of the base station at time k in the global coordinate system is expressed as:

[0024]

[0025] Where h(·) represents the measurement function of the base station about the target at time k, Δz sk =[Δρ sk ,Δφ sk ,Δη sk ] T Indicates base station s kThe additive measurement system error, n k ∈R 3 is a zero-mean Gaussian error, whose probability distribution follows and are the measurement noise variances at range, azimuth and elevation, respectively, m,k represents the distance measurement vector of the base station in the presence of errors, φ m,k represents the azimuth angle measurement vector of the base station in the presence of errors, η m,k represents the elevation angle measurement vector of the base station in the presence of errors, c represents the electromagnetic wave propagation speed, t m,k Represents the measured value of electromagnetic wave propagation delay in the presence of errors.

[0026] In one embodiment of the present invention, step 3 comprises:

[0027] In the global coordinate system, assuming that the cooperative motion target obeys the linear uniform motion model, the discrete state vector of the cooperative motion target is defined according to the position vector and velocity vector of the cooperative motion target in the global coordinate system:

[0028]

[0029] Among them, ξ k =[x k ,y k ,z k ] T and V k =[v x,k ,v y,k ,v z,k ] T They represent the position vector and velocity vector of the cooperative moving target at time k respectively;

[0030] Determine the state transition model of the cooperative motion target according to the discrete state vector of the cooperative motion target:

[0031] s k+1 =Fs k +ω k

[0032] Where F is the state transfer matrix, T represents the base station observation time interval, represents the Kronecker operator, I3 represents the 3×3 dimensional identity matrix, ω k represents the motion noise of the target at time k;

[0033] The covariance matrix of the motion process noise is:

[0034]

[0035] Where q represents the intensity of process noise;

[0036] The positions of the cooperative stationary targets are: in, represents the position of the first cooperative stationary target, Indicates the position of the second cooperative stationary target.

[0037] In one embodiment of the present invention, step 4 comprises:

[0038] According to the observation model of the base station and the unbiasedness of the unbiased coordinate conversion function, it is calculated that:

[0039] E[ξ k -R(Θ m,sk +ΔΘ sk )h -1 (z m,k +Δz sk )-p sk ]=0

[0040] Among them, E represents the expectation, ξ k represents the position of the target in the global coordinate system at time k, R represents the rotation matrix, Θ m,sk Represents the measured value of the axis rotation angle, ΔΘ sk Represents the axis rotation error, h -1 represents the unbiased coordinate transformation function, z m,k Indicates the measured data, Δz sk Indicates the measurement error, p sk represents the location of the base station working at time k;

[0041] The cooperative target position is obtained by nonlinear transformation based on the observation model of the base station and the system error:

[0042] ξ k =R(θ m,sk +ΔΘ sk )h -1 (z m,k +Δz sk )+p sk +ε k

[0043] Where R represents the rotation matrix, Θ m,sk Represents the measured value of the axis rotation angle, ΔΘ sk represents the axis rotation error, h -1 represents the unbiased coordinate transformation function, z m,k Indicates the measured data, Δz sk Indicates the measurement error, p sk represents the location of the base station working at time k, εk represents the unmodeled zero-mean error;

[0044] Based on the position of the cooperative target and in combination with the position matching error of the cooperative target in the global coordinate system, an objective function of base station system error correction is established:

[0045]

[0046] Where k = 1, 2...K represents the discrete observation time, ξ k represents the position of the target in the global coordinate system at time k, R represents the rotation matrix, R represents the rotation matrix, Θ m,sk Represents the measured value of the axis rotation angle, ΔΘ sk represents the axis rotation error, h -1 represents the unbiased coordinate transformation function, z m,k Indicates the measured data, Δz sk Indicates the measurement error, p sk represents the location of the base station working at time k, Φ n Represents the system error parameter.

[0047] In one embodiment of the present invention, step 5 comprises:

[0048] The objective function is decomposed into several sub-problems to be solved by block variables, wherein the block variables include the distance system error Δρ=[Δρ1, Δρ2...Δρ N ] T 、Pitch angle system error Δη=[Δη1,Δη2...Δη N ] T , roll angle system error Δα=[Δα1,Δα2...Δα N ] T 、Tilt angle system error Δβ=[Δβ1,Δβ2...Δβ N ] T and yaw angle system error Δγ=[Δγ1,Δγ2...Δγ N ] T ;

[0049] The objective function is decomposed and solved by using a coordinate cyclic descent algorithm. During the solving process, the subproblems of solving the plurality of block variables are divided into subproblems about distance system error and subproblems about angle system error. The subproblems about distance system error and subproblems about angle system error are alternately updated and solved iteratively to obtain the optimal estimate of the system error parameter of each base station, wherein:

[0050] The subproblem about the distance system error is equivalent to an unconstrained linear least squares optimization problem, and the unconstrained linear least squares optimization problem is directly solved analytically to obtain an analytical solution to the subproblem about the distance system error;

[0051] The subproblem about the angle system error is equivalent to a quadratic constrained quadratic programming problem, and the alternating direction multiplier method is used to solve the quadratic constrained quadratic programming problem to obtain the optimal solution to the subproblem about the angle system error.

[0052] In one embodiment of the present invention, the objective function is solved using a coordinate cyclic descent algorithm, comprising the steps of:

[0053] 1) For each block variable Δρ 0 ,Δη 0 ,Δα 0 ,Δβ 0 ,Δγ 0 Initialize, give the iteration stop condition, and set the current number of iterations to 1;

[0054] 2) Fixed Δη 0 ,Δα 0 ,Δβ 0 ,Δγ 0 , Δρ 0 Substitute it into the objective function as an independent variable and solve it to obtain Then, Substitute into the objective function and fix Δα 0 ,Δβ 0 ,Δγ 0 , Δη 0 As an independent variable, we solve it to get And so on, until we get End this iteration;

[0055] The five block variables of the tth iteration are expressed as:

[0056]

[0057]

[0058]

[0059]

[0060]

[0061] Where f represents the objective function, Δρ, Δη, Δα, Δβ, and Δγ represent five system error variables;

[0062] 3) Determine whether the current iteration result meets the iteration stop condition. If so, terminate the iteration and output the Δρ obtained by the current iteration number. * ,Δη * ,Δα * ,Δβ * ,Δγ * As the optimal system error vector Φ * ; Otherwise, increase the number of iterations by 1 and repeat step 2).

[0063] In one embodiment of the present invention, the subproblem about the distance system error is equivalent to an unconstrained linear least squares optimization problem, and the unconstrained linear least squares optimization problem is directly solved analytically to obtain an analytical solution to the subproblem about the distance system error, including:

[0064] When (Δη, Δα, Δβ, Δγ) is fixed, the subproblem about the distance system error Δρ can be equivalently expressed as an unconstrained linear least squares optimization problem, and the unconstrained linear least squares optimization problem is expressed in matrix form:

[0065]

[0066] Among them, the coefficient matrix represents a full rank matrix, the constant vector K represents the number of observations, and N represents the number of base stations;

[0067] Directly solve the unconstrained linear least squares optimization problem and obtain the analytical expression for the distance system error subproblem: Δρ * =-(G T G) -1 G T c.

[0068] In one embodiment of the present invention, the angle system error subproblem is equivalent to a quadratic constrained quadratic programming problem, and the alternating direction multiplier method is used to solve the quadratic constrained quadratic programming problem to obtain the optimal solution to the angle system error subproblem, including:

[0069] The angle system error subproblem is equivalent to a quadratic constrained quadratic programming problem:

[0070]

[0071] Where C is defined as Coefficient matrix H∈R 3K*2N represents a full rank matrix, c∈R 3K is a constant vector, c represents a constant matrix, K represents the number of observations, and N represents the number of base stations;

[0072] The quadratic constrained quadratic programming problem is solved using the alternating direction multiplier method.

[0073] In one embodiment of the present invention, solving the quadratic constrained quadratic programming problem using an alternating direction multiplier method includes:

[0074] 1) Initialize x 0 ,z 0 ,λ 0 , set ρ>0, where ρ is a predefined positive parameter to ensure that the augmented Lagrangian function is a convex function;

[0075] 2) Given the iteration stop condition and the maximum number of iterations, let the current number of iterations be 1;

[0076] 3) An auxiliary variable z=x is introduced to reformulate the quadratic constrained quadratic programming problem. The augmented Lagrangian function of the reformulated quadratic constrained quadratic programming problem is:

[0077]

[0078] Among them, ρ>0 is the penalty parameter, λ∈R 2N is the Lagrange multiplier of the equality constraint x=z, g(z) represents the indicator function,

[0079] 4) Solve the variables in parallel by iterative calculation. The kth iteration is:

[0080] 4.1) The problem is an unconstrained strongly convex quadratic problem, and the solution is:

[0081]

[0082] Among them, x k+1 represents the optimization variable, L ρ represents the Lagrangian function, z k represents the optimization variable, λ k represents the Lagrange multiplier, H represents the coefficient matrix, ρ represents the penalty parameter, I represents the identity matrix, and c represents the constant matrix;

[0083] 4.2) The problem is a projection problem, and the solution is:

[0084]

[0085] Among them, z k+1 represents the optimization variable, L ρ represents the Lagrangian function, x k+1 represents the optimization variable, λ krepresents the Lagrange multiplier, ρ represents the penalty parameter, y represents the intermediate variable, and I2 represents the 2*2 identity matrix;

[0086] 4.3) The update of Lagrange multiplier is: k+1 =λ k +ρ(x k+1 -z k+1 );

[0087] 5) Determine whether the original residual and the dual residual meet the iteration stop condition. If so, terminate the iteration and output the x obtained in the current iteration. * as the optimal variable solution for this subproblem; otherwise, the number of iterations is increased by 1 and step 4 is repeated).

[0088] Compared with the prior art, the present invention has the following beneficial effects:

[0089] The present invention is based on the integration of communication and perception, studies the system error correction technology of three-dimensional asynchronous multi-sensor networks, establishes the objective function of base station system error correction according to the position matching error of the cooperative target in the global coordinate system, uses the coordinate cyclic descent algorithm based on the alternating direction multiplier method to solve the objective function, and obtains the optimal estimate of the system error of each base station, effectively solves the system error correction problem before coordinated perception and data fusion of multi-base station networks, improves the estimation accuracy of system errors, and obtains good system tracking performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0090] Figure 1 A schematic flow chart of a multi-sensor network system error correction method in the context of synaesthesia integration provided by an embodiment of the present invention;

[0091] Figure 2 A schematic flow chart of another multi-sensor network system error correction method in the context of synaesthesia integration provided by an embodiment of the present invention;

[0092] Figure 3 A schematic diagram of the spatial deployment of various base stations and cooperative target locations in the context of synaesthesia integration provided by an embodiment of the present invention;

[0093] Figure 4 A schematic diagram of a system error type provided by an embodiment of the present invention;

[0094] Figure 5a-5e A comparison chart of estimation performance results of the augmented Kalman filter estimation algorithm provided by an embodiment of the present invention and the multi-sensor network system error correction method under the background of synaesthesia integration;

[0095] Figure 6A comparison diagram of tracking performance results of a base station network before and after correcting system errors in a multi-sensor network system error correction method under the background of synaesthesia integration provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0096] The present invention is further described in detail below with reference to specific embodiments, but the embodiments of the present invention are not limited thereto.

[0097] Embodiment 1

[0098] The design principle of the multi-sensor network system error correction method under the background of interaesthesia integration in this embodiment is: since the base station sensor system error changes very slowly over time, the sensor system error is treated as an unknown constant contained in the measurement data for a relatively long period of time. Therefore, the multi-sensor network system error correction problem is studied as a parameter estimation problem. The system error correction scheme is based on the observation data of the base station on the cooperative target, with the objective function of minimizing the sum of squares of the errors between the true state of the target and the target state observed by the sensor, and establishes a unified asynchronous base station network system error estimation model. The constructed model is a non-convex optimization problem. Then a mathematical optimization algorithm is designed to solve the non-convex optimization problem and estimate the system error.

[0099] See also Figure 1 and Figure 2 , Figure 1 A flowchart of a multi-sensor network system error correction method in the context of synaesthesia integration provided by an embodiment of the present invention is provided. Figure 2 A schematic flow chart of another multi-sensor network system error correction method in the context of synaesthesia integration provided by an embodiment of the present invention.

[0100] The multi-sensor network system error correction method of this embodiment includes the following steps:

[0101] S1. Determine the types of system errors existing in the base station network under the background of synaesthesia integration, wherein the base station network includes a plurality of base stations, the base station network is located in a global coordinate system, each base station is located in a respective local coordinate system, and the plurality of base stations observe a cooperative target in the global coordinate system in respective spherical coordinate systems.

[0102] See also Figure 3 , Figure 3 A schematic diagram of the spatial deployment of various base stations and cooperative target locations in a synaesthesia integration background provided by an embodiment of the present invention, wherein: Figure 3 The whole shown is a base station network.

[0103] The task of the base station network is to obtain observation data by observing cooperative targets, and then estimate the system error using the system error correction method. Assume that the base station network contains N base station nodes, N is a positive integer greater than 1, and in this embodiment, N is 4. The base station network is located in a global coordinate system, and each base station is located in its own local coordinate system. The several base stations observe the cooperative targets in the global coordinate system in their own spherical coordinate systems. Among them, the global coordinate system refers to the coordinate system established based on the global base station network, which can also be called the global Cartesian coordinate system. In the global coordinate system, each base station has its own coordinates; the local coordinate system refers to the rectangular coordinate system established with each base station itself as the origin; the spherical coordinate system refers to the coordinate system formed by the base station using its own base station as the origin for ranging side angles when performing observations.

[0104] Multiple base station location coordinates In order to ensure the spatial observation diversity of the base station observation data, it is assumed that there is one cooperative moving target and two cooperative stationary targets in the coverage area of ​​the base station network. The entire synaesthesia network perceives the target information in the coverage area in an asynchronous manner. The entire base station network obtains the target position information in an asynchronous working manner. It is assumed that there is only one base station observing the target at each moment, and the corresponding communication base station is labeled s. k Indicates that the observation time interval of each base station is T, T = 2s. In order to simplify the mathematical notation, the observation time of different base stations during the entire working time is mapped to a unified time axis, and the discrete observation time is represented as k = 1, 2...K, and each base station is set to observe 10 times.

[0105] Specifically, the types of system errors include measurement errors and coordinate axis rotation errors. Measurement errors include distance system errors, azimuth system errors, and pitch angle system errors. Coordinate axis rotation errors refer to the rotational alignment errors between the base station's own coordinate system and the global coordinate system, mainly including the base station's rotation angle errors corresponding to roll, tilt, and yaw, namely, roll rotation angle system errors, tilt rotation angle system errors, and yaw rotation angle system errors. Since the base station system error changes slowly over time, over a relatively long period of time, the system error is regarded as an unknown constant contained in the measurement data. In this embodiment, it is assumed that the system error is an additive error. Define ΔΘ=[Δα,Δβ,Δγ] T represents the rotation angle error, Δz=[Δρ,Δφ,Δη] T Represents the measurement error, such as Figure 4 As shown, Figure 4 A schematic diagram of a system error type provided for an embodiment of the present invention, wherein the dotted line represents actual data, the solid line represents measured data, and the difference between the two represents the error.

[0106] S2. Determine the observation model of the base station in the global coordinate system based on the position relationship between the position of the cooperation target in the local coordinate system of each base station and the global coordinate system, and in combination with the transformation relationship between the global coordinate system and the spherical coordinate system.

[0107] Specifically, the relationship between the position of the cooperation target in the local coordinate system of each base station and the position in the global coordinate system is:

[0108] ξ k =R(θ sk,t )ξ k '+p sk (1)

[0109] Among them, ξ k '=[x' k ,y' k ,z' k ] T represents the position of the target at time k in the local coordinate system of the base station, Θ sk,t =(α sk,t ,β sk,t ,γ sk,t ) represents the true angle of rotation of the base station coordinate system around the x, y, and z axes at time k, ξ k =[x k ,y k ,z k ] T represents the position of the target at time k in the global Cartesian coordinate system, represents the position of the base station working at time k, and R represents the rotation matrix, which is used to transform the local coordinate system of the base station into the Cartesian global coordinate system, satisfying R -1 (θ)=R T The properties of (θ).

[0110] R(Θ) is defined as:

[0111]

[0112] Among them, (α, β, γ) represents the rotation angle, R x , R y , R z A rotation matrix representing rotations around the x, y, and z axes.

[0113] But in practice sk,t =(α sk,t ,β sk,t ,γ sk,t ) cannot be measured accurately, only the error Θ can be measured m , that is, Θ t =Θ m+ΔΘ, then the above equation (1) can be restated as:

[0114] ξ k '=R T (Θ m,sk +ΔΘ sk )(ξ k -p sk ) (3)

[0115] Among them, ΔΘ sk represents the base station's coordinate axis rotation angle system error, Θ m,sk =(α m,sk ,β m,sk ,γ m,sk ) represents the measured values ​​of the rotation angles of the coordinate system of the base station working at time k around the x, y, and z axes respectively.

[0116] The transformation relationship between the global Cartesian coordinate system and the spherical coordinate system is:

[0117]

[0118] Among them, z t,k represents the actual measurement vector of the base station, ρ t,k Represents the actual measurement parameter of distance, φ t,k Represents the actual measurement parameter of azimuth, η t,k represents the actual measurement parameter of the pitch angle, c represents the propagation speed of electromagnetic waves, t t,k Indicates the real delay of electromagnetic wave propagation;

[0119] Combining the position relationship and the transformation relationship, that is, combining equations (3) and (4), the observation model of the base station at time k in the global coordinate system is expressed as:

[0120]

[0121] Where h(·) represents the measurement function of the base station about the target at time k, Δz sk =[Δρ sk ,Δφ sk ,Δη sk ] T Indicates base station s k The additive measurement system error, n k ∈R 3 is a zero-mean Gaussian error, whose probability distribution follows and are the measurement noise variances at range, azimuth and elevation, respectively, m,k represents the distance measurement vector of the base station in the presence of errors, φ m,k represents the azimuth angle measurement vector of the base station in the presence of errors, ηm,k represents the elevation angle measurement vector of the base station in the presence of errors, c represents the electromagnetic wave propagation speed, t m,k Represents the measured value of electromagnetic wave propagation delay in the presence of errors.

[0122] It is worth noting that from Figure 4 It can be seen from the system error diagram that the azimuth error Δφ and the yaw error Δγ are coupled and cannot be distinguished. They can be combined into a system error to avoid the Fisher information matrix singularity caused by ambiguity in the estimation problem. In this embodiment, the azimuth error Δφ is defined as Δφ=0, and only the yaw error Δγ is considered. Therefore, the goal of system error correction in the context of synaesthesia integration is to use the observation data of the base station Estimate the system error parameter Φ of each base station n =[Δρ n ,Δη n ,Δα n ,Δβ n ,Δγ n ] T ,n=1,2...N.

[0123] S3. Determine a state transition model of the cooperative moving target according to the position vector and velocity vector of the cooperative moving target in the global coordinate system, and determine the position of the cooperative stationary target.

[0124] Specifically, in order to ensure the spatial diversity of the observation data, it is assumed that there is one cooperative moving target and two cooperative stationary targets in the coverage area, where the positions of the cooperative stationary targets are: represents the position of the first cooperative stationary target, Indicates the position of the second cooperative stationary target.

[0125] Furthermore, in the global coordinate system, assuming that the moving target obeys the linear uniform motion model, the discrete state vector of the cooperative moving target is defined according to the position vector and velocity vector of the cooperative moving target in the global coordinate system:

[0126]

[0127] Among them, ξ k =[x k ,y k ,z k ] T and V k =[v x,k ,v y,k ,v z,k ] T They represent the position vector and velocity vector of the cooperative moving target at time k respectively.

[0128] Determine the state transition model of the cooperative motion target according to the discrete state vector of the motion target:

[0129] s k+1 =Fs k +ω k (7)

[0130] Among them, F is the state transfer matrix, which is a block matrix. T represents the base station observation time interval, and in this embodiment, the value is T = 2s. represents the Kronecker operator, I3 represents the 3×3 dimensional identity matrix, ω k The noise of the target's motion process at time k is a Gaussian white noise with zero mean and covariance matrix, which is used to measure the uncertainty of the target state transition;

[0131] Motion process noise ω k The covariance matrix Q k for:

[0132]

[0133] Here, q represents the intensity of process noise.

[0134] S4. Determine the objective function of base station system error correction by combining the observation model of the base station, the state transition model of the cooperative moving target and the position of the cooperative stationary target, and according to the position matching error of the cooperative target in the global coordinate system.

[0135] Specifically, the goal of system error correction is to estimate the various system error parameters of the base station. Therefore, the multi-sensor network system error correction problem can be solved as a parameter estimation problem. Considering the Gaussian measurement noise n in the spherical coordinate system k In the coordinate conversion (spherical coordinates to Cartesian coordinates), there will be deviations. This embodiment uses an unbiased coordinate conversion function:

[0136]

[0137] Among them, ρ k represents the distance measurement, φ k represents the azimuth measurement value, η k represents the measured value of the pitch angle, λ φ and λ η represents an intermediate variable;

[0138] According to the observation model of the base station and the unbiasedness of the unbiased coordinate conversion function, it can be obtained that:

[0139] E[ξ k -R(Θ m,sk+ΔΘ sk )h -1 (z m,k +Δz sk )-p sk ]=0 (10)

[0140] Among them, E represents the expectation, ξ k represents the position of the target in the global coordinate system at time k, R represents the rotation matrix, Θ m,sk Represents the measured value of the axis rotation angle, ΔΘ sk represents the axis rotation error, h -1 represents the unbiased coordinate transformation function, z m,k Indicates the measured data, Δz sk Indicates the measurement error, p sk represents the location of the base station working at time k.

[0141] The measurement data z obtained by the observation model of the base station m,k and system error Φ sk The cooperative target position ξ is obtained through nonlinear transformation k :

[0142] ξ k =R(θ m,sk +ΔΘ sk )h -1 (z m,k +Δz sk )+p sk +ε k (11)

[0143] Where R represents the rotation matrix, Θ m,sk Represents the measured value of the axis rotation angle, ΔΘ sk represents the axis rotation error, h -1 represents the unbiased coordinate transformation function, z m,k Indicates the measured data, Δz sk Indicates the measurement error, p sk represents the location of the base station working at time k, ε k represents the unmodeled zero-mean error

[0144] Based on the cooperative target position (11), this embodiment proposes to minimize the position matching error of the cooperative target in the global coordinate system: minimize the sum of squares of the errors between the real position of the target and the target position observed by the base station, establish a nonlinear least squares formula for estimating the base station system error Φ, and obtain the objective function of the base station system error correction:

[0145]

[0146] Where k = 1, 2...K represents the discrete observation time, ξ k represents the position of the target in the global coordinate system at time k, R represents the rotation matrix, R represents the rotation matrix, Θ m,sk Represents the measured value of the axis rotation angle, ΔΘ sk represents the axis rotation error, h -1 represents the unbiased coordinate transformation function, z m,k Indicates the measured data, Δz sk Indicates the measurement error, p sk represents the location of the base station working at time k, Φ n Represents the system error parameter.

[0147] Since the constructed model contains the product of multiple trigonometric functions and is highly nonlinear, the established model is a typical non-convex optimization problem.

[0148] S5, using a coordinate cyclic descent algorithm based on an alternating direction multiplier method to solve the objective function and obtain an optimal estimate of the system error parameter of each base station. Specifically comprising the steps of:

[0149] S51, decomposing the objective function into several sub-problems for solving block variables.

[0150] Specifically, considering that the base station system error correction model, namely the objective function (12), is a difficult non-convex optimization problem, since there is nonlinear coordinate transformation in the objective function, the high nonlinearity will increase the estimation error. In order to solve this difficulty, a coordinate cyclic descent algorithm based on the alternating direction multiplier method is designed to solve the original non-convex optimization problem and estimate the system error of the sensor.

[0151] There are two reasons for dividing the system error optimization variables into multiple blocks of optimization variables according to the error type. On the one hand, different types of system error variables have different geometric effects on the measurement data. On the other hand, in mathematical optimization, the sub-problems corresponding to the alternating minimization of various types of variables can be solved globally and effectively, making the solution to the entire problem more effective.

[0152] For the convenience of using mathematical symbols, the system error variables of each base station are divided into five types of system error variables, and Δρ is defined as [Δρ1, Δρ2...Δρ N ] T , Δη=[Δη1,Δη2...Δη N ] T , Δα=[Δα1,Δα2...Δα N ] T , Δβ=[Δβ1,Δβ2...Δβ N ] T , Δγ=[Δγ1,Δγ2...ΔγN ] T They represent the system errors of distance, pitch angle, roll angle, tilt angle and yaw angle respectively. The objective function (12) is a function of these five types of error variables and can be expressed as: f(Δρ, Δη, Δα, Δβ, Δγ).

[0153] S52. Use the coordinate cyclic descent algorithm to solve the objective function decomposition. During the solution process, divide the sub-problems of solving the several block variables into sub-problems about distance system error and sub-problems about angle system error, and alternately update and iterate the sub-problems about distance system error and angle system error to obtain the optimal estimate of the system error parameters of each base station.

[0154] Specifically, the coordinate cyclic descent algorithm is used to solve the objective function (12), and the specific process is as follows:

[0155] 1) For each block variable Δρ 0 ,Δη 0 ,Δα 0 ,Δβ 0 ,Δγ 0 Initialize, give the iteration stop condition, and set the current number of iterations to 1;

[0156] 2) Fixed Δη 0 ,Δα 0 ,Δβ 0 ,Δγ 0 , Δρ 0 Substitute it into the objective function as an independent variable and solve it to obtain Then, Substitute into the objective function and fix Δα 0 ,Δβ 0 ,Δγ 0 , Δη 0 As an independent variable, we solve it to get And so on, until we get End this iteration;

[0157] The five block variables of the tth iteration are expressed as:

[0158]

[0159]

[0160]

[0161]

[0162]

[0163] Where f represents the objective function, Δρ, Δη, Δα, Δβ, and Δγ represent five system error variables;

[0164] 3) Determine whether the current iteration result meets the iteration stop condition. If so, terminate the iteration and output the Δρ obtained by the current iteration number. * ,Δη * ,Δα * ,Δβ * ,Δγ * As the optimal system error vector Φ * ; Otherwise, increase the number of iterations by 1 and repeat step 2).

[0165] Furthermore, for the above five sub-problems (13)-(17), they are divided into sub-problems about distance system error and sub-problems about angle system error, and the solution algorithms are determined separately. These two types of sub-problems are updated and solved alternately to obtain the optimal estimate of the system error parameters of each base station.

[0166] For solving subproblem (13), the subproblem about distance system error is equivalent to an unconstrained linear least squares optimization problem, and the unconstrained linear least squares optimization problem is directly solved analytically to obtain an analytical solution to the subproblem about distance system error.

[0167] Specifically, when (Δη, Δα, Δβ, Δγ) is fixed, the subproblem about the distance system error Δρ can be equivalently expressed as an unconstrained linear least squares optimization problem:

[0168]

[0169] in, v ρ,k =ξ k -p sk , Δρ sk represents the distance system error, R represents the rotation matrix, Θ sk Represents the rotation angle of the coordinate axis, ΔΘ sk represents the rotation error, λ φ and λ η represents the intermediate variable in the unbiased coordinate transformation function, φ k represents the azimuth measurement value, η k Represents the measured value of the pitch angle, Δη sk represents the pitch angle error, ρ k represents the distance measurement, ξ k represents the position vector of the cooperation target at time k, p sk Indicates the location of the base station.

[0170] Represent function (18) in matrix form:

[0171]

[0172] Among them, the coefficient matrix represents a full rank matrix, the constant vector K represents the number of observations, and N represents the number of base stations;

[0173] Directly solve the unconstrained linear least squares optimization problem analytically, set its gradient equal to 0, and obtain the analytical expression for the distance system error subproblem (19):

[0174] Δρ * =-(G T G) -1 G T c (20)

[0175] For solving subproblems (14)-(17), the subproblem about the angle system error is equivalent to a quadratic constrained quadratic programming problem, and the alternating direction multiplier method is used to solve the quadratic constrained quadratic programming problem to obtain the optimal solution to the subproblem about the angle system error.

[0176] Specifically, it can be found that the sub-problems about the four system error variables Δη, Δα, Δβ, and Δγ have the same expression form, so the solution algorithm is designed for one of the angle system errors. When Δρ is fixed, the sub-problem about the angle system error is a nonlinear non-convex problem. Directly minimizing the angle error variable will increase the amount of calculation and complexity. It should be noted that the nonlinearity of the angle system error is reflected in the objective function in the form of sine / cosine trigonometric functions. The non-convexity of the objective function can be converted into non-convex constraints through basic variable equivalence substitution, and the sub-problem about the angle system error will be reformulated as a quadratic constrained quadratic programming problem (QCQP).

[0177] The specific solution process of sub-problems (14)-(17) is as follows:

[0178] The objective function (12) can be reformulated as:

[0179]

[0180] in, v η,k =ξ k -p sk , Δρ sk represents the distance system error, R represents the rotation matrix, Θ sk Represents the rotation angle of the coordinate axis, ΔΘ sk Table rotation error, λ φ and λ ηrepresents the intermediate variable in the unbiased coordinate transformation function, φ k represents the azimuth measurement value, η k Represents the measured value of the pitch angle, Δη sk represents the pitch angle error, ρ k represents the distance measurement, ξ k represents the position vector of the cooperation target at time k, p sk Indicates the location of the base station.

[0181] Define x=[cosΔη1, sinΔη1,…, cosΔη N ,sinΔη N ] T , through variable substitution, function (21) is expressed as a QCQP problem:

[0182]

[0183] Where C is defined as Coefficient matrix H∈R 3K*2N represents a full rank matrix, c∈R 3K is a constant vector, c represents a constant matrix, K represents the number of observations, and N represents the number of base stations.

[0184] Since the equality constraint in problem (22) is non-convex, the QCQP problem is a non-convex optimization problem. Therefore, the alternating direction multiplier method is used to solve problem (22).

[0185] Specifically, the non-convex equality constraint in problem (22) has the property of being “easy to project”. Let proj c (x) indicates that point x is The projection on the equality constraint C. proj c (x) has the following forms:

[0186]

[0187] Among them, D x is a diagonal matrix defined as: represents the Kronecker operation, and I2 represents the 2*2 identity matrix.

[0188] Based on the property of “easy projection”, an auxiliary variable x=z is introduced in problem (22), and problem (22) is reformulated as:

[0189]

[0190] Among them, g(z) is an indicator function,

[0191] In the alternating direction multiplier method, the augmented Lagrangian function is used to solve the problem. The augmented Lagrangian function of equation (24) is:

[0192]

[0193] Among them, ρ>0 is the penalty parameter, λ∈R 2N is the Lagrange multiplier of the equality constraint x=z, g(z) represents the indicator function,

[0194] Therefore, the specific steps of the alternating direction multiplier method to solve the sub-problem about the angle system error are:

[0195] 1) Initialize x 0 ,z 0 ,λ 0 , set ρ>0, where ρ is a predefined positive parameter to ensure that the augmented Lagrangian function is a convex function;

[0196] 2) Given the iteration stop condition and the maximum number of iterations, let the current number of iterations be 1;

[0197] 3) An auxiliary variable z=x is introduced to reformulate the quadratic constrained quadratic programming problem. The augmented Lagrangian function of the reformulated quadratic constrained quadratic programming problem can be found in formula (25).

[0198] 4) Solve the variables in parallel by iterative calculation. The kth iteration is:

[0199] 4.1) The problem is an unconstrained strongly convex quadratic problem, and the solution is:

[0200]

[0201] Among them, x k+1 represents the optimization variable, L ρ represents the Lagrangian function, z k represents the optimization variable, λ k represents the Lagrange multiplier, H represents the coefficient matrix, ρ represents the penalty parameter, I represents the identity matrix, and c represents the constant matrix;

[0202] 4.2) The problem is a projection problem, and the solution is:

[0203]

[0204] Among them,

[0205] z k+1 represents the optimization variable, L ρ represents the Lagrangian function, xk+1 represents the optimization variable, λ k represents the Lagrange multiplier, ρ represents the penalty parameter, y represents the intermediate variable, and I2 represents the 2*2 identity matrix;

[0206] 4.3) The update of Lagrange multiplier is: k+1 =λ k +ρ(x k+1 -z k+1 );

[0207] 5) Determine whether the original residual and the dual residual meet the iteration stop condition. If so, terminate the iteration and output the x obtained in the current iteration. * as the optimal variable solution for this subproblem; otherwise, the number of iterations is increased by 1 and step 4 is repeated).

[0208] The alternating direction multiplier method is used in turn to obtain the optimal solutions to the subproblems of the four system error variables Δη, Δα, Δβ, and Δγ, and substitute them into the coordinate cyclic descent algorithm in the above steps.

[0209] Furthermore, the above method is used to estimate the system error variables of each base station, and then the root mean square error RMSE of the estimated value is used as an evaluation indicator of the estimation performance of the system error correction algorithm to verify the effectiveness of the estimation algorithm.

[0210] Specifically, define is the system error parameter Φ n =[Δρ n ,Δη n ,Δα n ,Δβ n ,Δγ n ] T , n=1,2...N, calculate the root mean square error of each base station system error parameter: in, Represents the system error parameter estimated by the estimation algorithm, and θ represents the true system error parameter.

[0211] Finally, the estimated system error parameters are used to compensate the measurement data, and the fixed extended Kalman filter algorithm is used for target tracking. The improvement of the synaesthesia network tracking performance is compared before and after the system error correction.

[0212] This embodiment is based on the integration of communication and perception, and studies the system error correction technology of three-dimensional asynchronous multi-sensor network. According to the position matching error of the cooperative target in the global coordinate system, a nonlinear least squares model is established, and the optimal estimate of the system error of each base station is obtained by solving the optimization problem. Due to the high nonlinearity in the constructed model, the constructed model is a non-convex optimization problem. Therefore, the coordinate reincarnation descent algorithm based on the alternating direction multiplier method is used to solve the objective function, and the objective function is decomposed into sub-problems about the distance system error and sub-problems about the angle system error. For the distance system error sub-problem, the analytical solution is directly obtained, and for the angle system error sub-problem, the alternating direction multiplier method is used to solve it, so as to iteratively update each sub-problem, and obtain the optimal estimate of the system error of each base station, which effectively solves the system error correction problem before coordinated perception and data fusion of multi-base station network, improves the estimation accuracy of system error, and obtains good system tracking performance. This method can greatly improve the data fusion accuracy when the urban base station network is collaboratively perceived, and obtain higher positioning accuracy and more stable detection performance.

[0213] The correctness and effectiveness of the present invention are further illustrated by simulation data processing results.

[0214] (I) Simulation conditions

[0215] This embodiment is performed on a computer with a 3.20 GHz Intel(R) Core(TM) i7-8700 CPU and MATLAB 9.8.0 (2020a) installed.

[0216] (II) Simulation content

[0217] Reference Figure 3 , the spatial relationship diagram of the positions of each base station and the target position in the synaesthesia integration scenario set in this embodiment. Set the number of networking base stations N = 4, there is a cooperative moving target and two cooperative stationary targets in the monitoring coverage area, in the set scenario, the communication base station network works in an asynchronous manner, that is, each communication base station observes once every 2s but the observation start time is different, each base station observes 10 times, and the measurement attitude angle (rotation angle) of the four communication base stations is set to [α, β, γ] = [0, 0, 0] °, Table 1 gives the position, start time and system error parameters of each base station, and Table 2 gives the state parameters of each target.

[0218] Table 1 Sensor position and system error

[0219] Position / m Start time / s Δρ / m Δη / . Δα / . Δβ / . Δγ / . Sensor 1 [25,25,25] 0.5 -1 2 2 1 1 Sensor 2 [25,-25,25] 1 -2 -1 1 1 2 Sensor 3 [-25,25,25] 1.5 -1 -2 2 2 1 Sensor 4 [-25,-25,25] 2 2 1 1 1 2

[0220] Table 2 Target state parameters

[0221] Position / m Speed / m / s Sports Goals [100,8,0] [-10,0,0] Stationary Target 1 [50,35,15] / Stationary Target 2 [-60,-30,40] /

[0222] Assume the measurement noise of the communication base station is: ρ =0.5m, The noise intensity during the target movement is q = 0.5m 2 / s 3 In the simulation experiment, the root mean square error (RMSE) is used as an evaluation indicator to evaluate the estimation performance of the proposed correction algorithm. MC = The average of 100 independent Monte Carlo experiments. The iteration stop condition of the coordinate cyclic descent algorithm is set to the maximum error between two consecutive iteration results is less than 10 -5 The iteration stopping condition of the alternating direction multiplier method is that the original residual and the dual residual are less than 10 -9 The penalty parameter ρ of the alternating direction multiplier method is set to the matrix H T The average value of the diagonal elements of H. Next, the established model is simulated.

[0223] In order to illustrate the superiority of the system error correction method of this embodiment, the estimation performance of the system error correction method of this embodiment is simulated and compared with the estimation performance of an existing correction method-augmented Kalman filter method. Here, the augmented Kalman filter method regards the system error of the base station as an augmented state, and uses Kalman filtering to jointly estimate the base station system error and the target state. Afterwards, the extended Kalman filter algorithm is used for target tracking, and the tracking performance of the base station network before and after the base station system error correction is simulated and compared. In the experiment, the tracking error RMSE is used to measure the target tracking performance.

[0224] (III) Analysis of simulation results

[0225] See also Figure 5a-Figure 5e , Figure 5a-Figure 5e A comparison chart of estimation performance results of the augmented Kalman filter estimation algorithm provided by an embodiment of the present invention and the multi-sensor network system error correction method under the background of synaesthesia integration, Figure 5a is the distance system error RMSE, Figure 5b is the pitch angle system error RMSE, Figure 5c is the roll angle system error RMSE, Figure 5d is the tilt angle system error RMSE, Figure 5e is the yaw angle system error RMSE. Figure 5a-Figure 5e The results show that the root mean square error of the system error estimate of the method in this embodiment is significantly smaller than the root mean square error of the system error estimate of the augmented Kalman filter algorithm. This is because the augmented Kalman filter method is based on the nonlinearity in the first-order linear approximation processing model, which leads to the model mismatch problem. This also illustrates the superiority of the method in this embodiment.

[0226] See also Figure 6 , Figure 6 A comparison diagram of tracking performance results of a base station network before and after correcting system errors in a multi-sensor network system error correction method in the context of synaesthesia integration provided by an embodiment of the present invention.

[0227] Figure 6 The results show that after the system error correction, the target tracking error of the base station network is smaller than the target tracking error before the system error correction, and the tracking performance of the base station network is improved, which illustrates the effectiveness of the method of this embodiment.

[0228] The above contents are further detailed descriptions of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as falling within the protection scope of the present invention.

Claims

1. A multi-sensor network system error correction method under the background of synaesthesia integration, characterized in that: Includes steps: Step 1, determining the types of system errors existing in the base station network under the background of synaesthesia integration, wherein the base station network includes a plurality of base stations, the base station network is located in a global coordinate system, each base station is located in a respective local coordinate system, and the plurality of base stations observe the cooperative target in the global coordinate system in their respective spherical coordinate systems; Step 2, according to the position relationship between the position of the cooperation target in the local coordinate system of each base station and the position relationship in the global coordinate system, and combined with the transformation relationship between the global coordinate system and the spherical coordinate system, to determine the observation model of the base station in the global coordinate system; Step 2 includes: The relationship between the position of the cooperation target in the local coordinate system of each base station and the position in the global coordinate system is: x k '=R T (I n +DTH n )(ξ k -p n ) Among them, ξ k '=[x' k ,y' k ,z' k ] T represents the position of the target at time k in the local coordinate system of the base station, Θ n =(α n ,β n ,γ n ) represents the measured values ​​of the rotation angles of the coordinate system of the nth base station working at time k around the x, y, and z axes, respectively, ΔΘ n represents the systematic error of the coordinate axis rotation angle of the nth base station, ξ k =[x k ,y k ,z k ] T represents the position of the target at time k in the global Cartesian coordinate system, represents the position of the nth base station working at time k, and R represents the rotation matrix, which is used to transform the local coordinate system of the base station into the Cartesian global coordinate system, satisfying R -1 (θ)=R T The properties of (Θ), R(Θ) is defined as: Among them, (α, β, γ) represents the rotation angle, R x , R y , R z Represents the rotation matrix around the x, y, and z axes; The transformation relationship between the global coordinate system and the spherical coordinate system is: Among them, z k represents the actual measurement vector of the base station, ρ k Represents the actual measurement parameter of distance, φ k Represents the actual measurement parameter of azimuth, η k represents the actual measurement parameter of the pitch angle, c represents the propagation speed of electromagnetic waves, t k Indicates the real delay of electromagnetic wave propagation; Combining the position relationship and the transformation relationship, the observation model of the base station at time k in the global coordinate system is expressed as: Where h(·) represents the measurement function of the base station about the target at time k, Δz n =[Δρ n ,Δφ n ,△η n ] T represents the additive measurement system error of the nth base station, n k ∈R 3 is a zero-mean Gaussian error, whose probability distribution follows and are the measurement noise variances at range, azimuth and elevation, respectively, n,k represents the distance measurement vector of the nth base station in the presence of error, φ n,k represents the azimuth angle measurement vector of the nth base station in the presence of error, η n,k represents the pitch angle measurement vector of the nth base station in the presence of errors, c represents the electromagnetic wave propagation speed, t n,k It represents the measured value of electromagnetic wave propagation delay in the presence of errors; Step 3, determining a state transition model of the cooperative moving target according to the position vector and velocity vector of the cooperative moving target in the global coordinate system, and determining the position of the cooperative stationary target; Step 3 includes: In the global coordinate system, assuming that the cooperative motion target obeys the linear uniform motion model, the discrete state vector of the cooperative motion target is defined according to the position vector and velocity vector of the cooperative motion target in the global coordinate system: Among them, ξ k =[x k ,y k ,z k ] T and V k =[v x,k ,v y,k ,v z,k ] T They represent the position vector and velocity vector of the cooperative moving target at time k respectively; Determine the state transition model of the cooperative motion target according to the discrete state vector of the cooperative motion target: s k+1 =Fs k +oh k Where F is the state transfer matrix, T represents the base station observation time interval, represents the Kronecker operator, I3 represents the 3×3 dimensional identity matrix, ω k represents the motion noise of the target at time k; The covariance matrix of the motion process noise is: Where q represents the intensity of process noise; The positions of the cooperative stationary targets are: in, represents the position of the first cooperative stationary target, indicates the position of the second cooperative stationary target; Step 4, combining the observation model of the base station, the state transition model of the cooperative moving target and the position of the cooperative stationary target, and determining the objective function of the base station system error correction according to the position matching error of the cooperative target in the global coordinate system; Step 4 includes: According to the observation model of the base station and the unbiasedness of the unbiased coordinate conversion function, it is calculated that: E[ξ k -R(Θ n +DTH n )h -1 (z n,k +△z n )-p n ]=0 Among them, E represents the expectation, ξ k represents the position of the target in the global coordinate system at time k, R represents the rotation matrix, Θ n Represents the measured value of the coordinate axis rotation angle of the nth base station, ΔΘ n represents the coordinate axis rotation error of the nth base station, h -1 represents the unbiased coordinate transformation function, z n,k represents the measurement data of the nth base station at time k, Δz n represents the measurement error of the nth base station, p n represents the position of the nth base station working at time k; The cooperative target position is obtained by nonlinear transformation based on the observation model of the base station and the system error: x k =R(Θ n +DTH n )h -1 (z n,k +Δz n )+p n +e k Where R represents the rotation matrix, Θ n Represents the measured value of the axis rotation angle, ΔΘ n represents the coordinate axis rotation error of the nth base station, h -1 represents the unbiased coordinate transformation function, z n,k represents the measurement data of the nth base station at time k, Δz n represents the measurement error of the nth base station, p n represents the position of the nth base station working at time k, ε k represents the unmodeled zero-mean error; Based on the position of the cooperative target and in combination with the position matching error of the cooperative target in the global coordinate system, an objective function of base station system error correction is established: Where k = 1, 2...K represents the discrete observation time, ξ k represents the position of the target in the global coordinate system at time k, R represents the rotation matrix, R represents the rotation matrix, Θ n Represents the measured value of the coordinate axis rotation angle of the nth base station, ΔΘ n represents the coordinate axis rotation error of the nth base station, h -1 represents the unbiased coordinate transformation function, z n,k represents the measurement data of the nth base station at time k, Δz n Indicates the measurement error, p n represents the position of the nth base station working at time k, Φ n represents the system error parameter of the nth base station; Step 5: Solve the objective function using a coordinate cyclic descent algorithm based on an alternating direction multiplier method to obtain an optimal estimate of the system error parameters of each base station.

2. The multi-sensor network system error correction method under the background of synaesthesia integration according to claim 1 is characterized in that: The types of system errors include measurement errors and coordinate axis rotation errors, wherein the measurement errors include distance system errors, azimuth system errors and pitch angle system errors, and the coordinate axis rotation errors include roll rotation angle system errors, tilt rotation angle system errors and yaw rotation angle system errors.

3. The multi-sensor network system error correction method under the background of synaesthesia integration according to claim 1 is characterized in that: Step 5 includes: The objective function is decomposed into several sub-problems to be solved by block variables, wherein the block variables include the distance system error Δρ=[Δρ1, Δρ2...Δρ N ] T 、Pitch angle system error Δη=[Δη1,Δη2...Δη N ] T , roll angle system error Δα=[Δα1,Δα2...Δα N ] T 、Tilt angle system error Δβ=[Δβ1,Δβ2...Δβ N ] T and yaw angle system error Δγ=[Δγ1,Δγ2...Δγ N ] T , N represents the number of base stations; The objective function is decomposed and solved by using a coordinate cyclic descent algorithm. During the solving process, the subproblems of solving the plurality of block variables are divided into subproblems about distance system error and subproblems about angle system error. The subproblems about distance system error and subproblems about angle system error are alternately updated and solved iteratively to obtain the optimal estimate of the system error parameter of each base station, wherein: The subproblem about the distance system error is equivalent to an unconstrained linear least squares optimization problem, and the unconstrained linear least squares optimization problem is directly solved analytically to obtain an analytical solution to the subproblem about the distance system error; The subproblem about the angle system error is equivalent to a quadratic constrained quadratic programming problem, and the alternating direction multiplier method is used to solve the quadratic constrained quadratic programming problem to obtain the optimal solution to the subproblem about the angle system error.

4. The multi-sensor network system error correction method under the background of synaesthesia integration according to claim 3 is characterized in that: The objective function is solved by using a coordinate cyclic descent algorithm, comprising the steps of: 1) For each block variable Δρ 0 ,Δη 0 ,Δα 0 ,Δβ 0 ,Δγ 0 Initialize, give the iteration stop condition, set the current iteration number to 1, where Δρ 0 ,Δη 0 ,Δα 0 ,Δβ 0 ,Δγ 0 Represents the initialization variables of block variables Δρ, Δη, Δα, Δβ, Δγ at the 0th iteration; 2) Fixed Δη 0 ,Δα 0 ,Δβ 0 ,Δγ 0 , Δρ 0 Substitute it into the objective function as an independent variable and solve it to obtain Then, Substitute into the objective function and fix Δα 0 ,Δβ 0 ,Δγ 0 , Δη 0 As an independent variable, we solve it to get And so on, until we get End this iteration; The five block variables of the tth iteration are expressed as: Where f represents the objective function, Δρ, Δη, Δα, Δβ, and Δγ represent five system error variables; 3) Determine whether the current iteration result meets the iteration stop condition. If so, terminate the iteration and output the Δρ obtained by the current iteration number. * ,Δη * ,Δα * ,Δβ * ,Δγ * As the optimal system error vector Φ * ; Otherwise, increase the number of iterations by 1 and repeat step 2).

5. The multi-sensor network system error correction method under the background of synaesthesia integration according to claim 3 is characterized in that: The subproblem of the distance system error is equivalent to an unconstrained linear least squares optimization problem, and the unconstrained linear least squares optimization problem is directly solved analytically to obtain an analytical solution to the subproblem of the distance system error, including: When (Δη, Δα, Δβ, Δγ) is fixed, the subproblem about the distance system error Δρ is equivalently expressed as an unconstrained linear least squares optimization problem, and the unconstrained linear least squares optimization problem is expressed in matrix form: Among them, the coefficient matrix represents a full rank matrix, the constant vector K represents the number of observations, and N represents the number of base stations; Directly solve the unconstrained linear least squares optimization problem and obtain the analytical expression for the distance system error subproblem: Δρ * =-(G T G) -1 G T c.

6. The multi-sensor network system error correction method under the background of synaesthesia integration according to claim 3 is characterized in that: The angle system error subproblem is equivalent to a quadratic constrained quadratic programming problem, and the quadratic constrained quadratic programming problem is solved by an alternating direction multiplier method to obtain an optimal solution to the angle system error subproblem, including: The angle system error subproblem is equivalent to a quadratic constrained quadratic programming problem: Where C is defined as Coefficient matrix H∈R 3K*2N represents a full rank matrix, c∈R 3K is a constant vector, c represents a constant matrix, K represents the number of observations, and N represents the number of base stations; The quadratic constrained quadratic programming problem is solved using the alternating direction multiplier method.

7. The multi-sensor network system error correction method under the background of synaesthesia integration according to claim 6 is characterized in that: Solving the quadratic constrained quadratic programming problem using an alternating direction multiplier method includes: 1) Initialize x 0 ,z 0 ,λ 0 , set ρ>0, where ρ is a predefined positive parameter to ensure that the augmented Lagrangian function is a convex function, where x 0 ,z 0 ,λ 0 are the initialization parameters for x, z, and λ at the 0th iteration, where x is the variable to be solved, z is the introduced auxiliary variable, and λ is the Lagrange multiplier; 2) Given the iteration stop condition and the maximum number of iterations, let the current number of iterations be 1; 3) An auxiliary variable z=x is introduced to reformulate the quadratic constrained quadratic programming problem. The augmented Lagrangian function of the reformulated quadratic constrained quadratic programming problem is: Among them, ρ>0 is the penalty parameter, λ∈R 2N is the Lagrange multiplier of the equality constraint x=z, g(z) represents the indicator function, 4) Solve the variables in parallel by iterative calculation. The kth iteration is: 4.1) The problem is an unconstrained strongly convex quadratic problem, and the solution is: Among them, x k+1 represents the optimization variable, L ρ represents the Lagrangian function, z k represents the optimization variable, λ k represents the Lagrange multiplier, H represents the coefficient matrix, ρ represents the penalty parameter, I represents the identity matrix, and c represents the constant matrix; 4.2) The problem is a projection problem, and the solution is: Among them, z k+1 represents the optimization variable, L ρ represents the Lagrangian function, x k+1 represents the optimization variable, λ k represents the Lagrange multiplier, ρ represents the penalty parameter, y represents the intermediate variable, I2 represents the 2*2 identity matrix, and N represents the number of base stations; 4.3) The update of Lagrange multiplier is: k+1 =λ k +ρ(x k+1 -z k+1 ); 5) Determine whether the original residual and the dual residual meet the iteration stop condition. If so, terminate the iteration and output the x obtained in the current iteration. * as the optimal variable solution for this subproblem; otherwise, the number of iterations is increased by 1 and step 4 is repeated).

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