A positioning calculation and optimization method

Abstract

The present invention relates to a positioning calculation and optimization method, comprising the following steps: establishing a positioning solution model based on TDOA; performing local positioning solution of nodes through the model to obtain local positioning information; introducing local positioning information into an absolute coordinate system based on a coordinate transformation model to achieve positioning solution of the entire network; and analyzing positioning accuracy based on the above positioning information. By using a conversion model based on the Rodriguez matrix in coordinate registration, the model is different from the traditional Bursa model and can be applied to three-dimensional coordinate transformation at any angle, introducing local positioning information into an absolute coordinate system, and achieving positioning solution of the entire network, thereby improving the positioning accuracy and robustness of the overall system. The establishment of a positioning solution model based on TDOA includes: constructing a relative coordinate system of a node network in a three-dimensional plane; including the following steps: establishing a three-dimensional node network consisting of n+1 nodes.

Description

Technical Field

[0001] The present invention relates to the field of navigation and positioning technology, and in particular to a positioning calculation and optimization method. Background Art

[0002] The Global Navigation Satellite System (GNSS) has made remarkable achievements in the field of positioning. However, in certain harsh environments, such as urban canyons, densely built areas, or between high-rise buildings, traditional GNSS positioning technology faces some challenges. These environments may cause multipath effects, signal blocking, and signal attenuation, which may affect the accuracy and stability of GNSS positioning. The current problems of traditional GNSS positioning methods are as follows:

[0003] (i) In densely built-up areas such as cities, GNSS signals are easily affected by multiple paths, causing the received signals to contain reflected signals, which can lead to deviations in traditional GNSS positioning. In scenes such as high-rise buildings or mountainous areas, terrain and buildings may block the propagation of satellite signals, making it difficult for the receiver to obtain sufficient satellite information, thereby reducing the availability and accuracy of positioning.

[0004] (ii) The performance of traditional GNSS positioning methods in denial environments is not satisfactory because these methods have limited anti-interference capabilities against multipath effects and signal attenuation. In some special environments, such as closed spaces or tunnels, the signal strength may be significantly attenuated or even fail to work properly, so traditional GNSS positioning methods cannot provide effective and accurate positioning information. Summary of the invention

[0005] In view of the above-mentioned shortcomings of the prior art, an object of the present invention is to provide a positioning calculation and optimization method to solve one or more problems in the prior art.

[0006] To achieve the above object, the technical solution of the present invention is as follows:

[0007] A positioning calculation and optimization method comprises the following steps:

[0008] Establish positioning solution model based on TDOA;

[0009] Perform node local positioning calculation through the model to obtain local positioning information;

[0010] Based on the seven-parameter coordinate transformation model, the local positioning information is introduced into the absolute coordinate system to realize the positioning solution of the entire network;

[0011] Analyze the positioning accuracy based on the above positioning information.

[0012] Furthermore, the establishment of a positioning solution model based on TDOA includes: constructing a relative coordinate system of a node network in a three-dimensional space;

[0013] The steps include:

[0014] Establish a three-dimensional network node consisting of n+1 nodes;

[0015] The line connecting nodes 0 and n is taken as the X-axis, the plane formed by the intersection of 01 and 0n is taken as the XOY plane, and the direction perpendicular to the plane is taken as the Z direction;

[0016] The distance difference between node i and j and node j and 0 is expressed as:

[0017]

[0018] The distance difference can be rewritten as: f(X)=ΔR+ε, where ε represents the distance difference measurement error.

[0019] Furthermore, the node local positioning solution is performed through the model to obtain local positioning information, including the following steps:

[0020] Perform Taylor linearization on f(X) to obtain a non-homogeneous linear system of equations;

[0021] The obtained nonhomogeneous linear equations are solved using the damped least squares method.

[0022] Furthermore, the non-homogeneous linear equation system is specifically: Gx=b, where G is Matrix of

[0023]

[0024] The damped least squares method is used to solve the obtained non-homogeneous linear equations to obtain: x = (G T G+μI) -1 G T b, where μ is a damping coefficient greater than 0 and I is the identity matrix.

[0025] Furthermore, the seven-parameter coordinate transformation model is used to introduce local positioning information into the absolute coordinate system to achieve positioning solution of the entire network, including the following steps:

[0026] Assume two spatial rectangular coordinate systems O'-X'Y'Z' and O-XYZ;

[0027] The coordinate values ​​of n nodes in the coordinate systems O'-X'Y'Z' and O-XYZ are (X' i , Y' i , Z'i ) and (X i , Y, Z i ), where i=1, 2, ..., n;

[0028] Combining O'-X'Y'Z' and O-XYZ, we get a seven-parameter coordinate transformation model of n nodes in two coordinate systems:

[0029]

[0030] , where X0, Y0, Z0 are translation parameters, and R is the three rotation matrices R X (α), R Y (β), R Z The product of (γ) is:

[0031]

[0032] , where α, β, and γ are rotation parameters, representing the rotation angles in the three directions of X, Y, and Z, respectively.

[0033] According to the principle of Rodriguez matrix, the R matrix is ​​expressed as: R = (1 + S) (1-S) -1 , where S is an antisymmetric matrix, specifically:

[0034] Substitute the scale parameter, rotation parameter, translation parameter and coordinates to be transformed into the above coordinate relationship to complete the coordinate transformation.

[0035] Furthermore, the calculation of the scale parameter includes: calculating the corresponding distance through the coordinates, and obtaining the scale parameter through the distance ratio, including the following steps:

[0036] Select n common points P i =(i=1,2,…,n) calculate any two points P i , P j The ratio of distances in the coordinate systems O'-X'Y'Z' and O-XYZ is:

[0037]

[0038] Take the mean of the distance ratios as the value of the scale parameter:

[0039]

[0040] Where n is the number of common points;

[0041] The calculation of the rotation parameters includes: i , P j Substituting the coordinate values ​​in the coordinate systems O'-X'Y'Z' and O-XYZ into the above coordinate relationship, we obtain:

[0042]

[0043] Subtract the two equations in the above formula to eliminate the translation parameter and then substitute them into the above coordinate relationship to obtain:

[0044]

[0045] When there are three common points, the above formula is combined to obtain:

[0046]

[0047] According to the above formula, the least square method can be used to find the parameters a, b, c, and substitute them into the R matrix R = (1 + S) (1-S) -1 Find the rotation matrix R in

[0048] The calculation of the translation parameter includes: according to the obtained scale parameter and rotation matrix, together with the common point coordinates, into the above coordinate relationship to obtain:

[0049]

[0050] Further, analyzing the positioning accuracy according to the positioning information includes: deriving a precision reduction factor; judging the influence of the spatial distribution of nodes in the model on the positioning accuracy according to the precision reduction factor;

[0051] The derivation of the DOP factor comprises the following steps:

[0052] Get the ratio of the RMSE of the intra-cluster positioning result to the RMSE of the observation;

[0053] Get the ratio of the RMSE of the seven parameters to the RMSE of the common point coordinates;

[0054] Get the ratio of the RMSE of the coordinate point after the seven-parameter coordinate model transformation to the RMSE of the coordinate point before the transformation.

[0055] Furthermore, the method of obtaining the ratio of the RMSE of the intra-cluster positioning to the RMSE of the observed quantity includes:

[0056] According to the Gx=b obtained by Taylor linearization, the least square method is used to solve: T G) -1 G T b;

[0057] By deriving the geometric factors in GNSS, we can get H = (G T G) -1 , where H is a symmetric matrix of order 3n-6;

[0058]

[0059]

[0060] Further, the obtaining of the ratio of the RMSE of the seven parameters to the RMSE of the common point coordinates includes: processing the seven-parameter coordinate transformation model before derivation, including: obtaining according to the antisymmetric matrix property:

[0061]

[0062] Therefore: R T R=[(I+S)(IS) -1 ] T [(I+S)(IS) -1 ]=(I+S) -1 (IS)(I+S)(IS) -1 =I;

[0063] Substituting matrix S into matrix R, we get:

[0064]

[0065] Where Δ=1+a 2 +b 2 +c 2 ;

[0066] According to the above formula and the properties of orthogonal matrix, we can get: R -1 =R T =[(I+S)(IS) -1 ] T =(I+S) -1 (IS);

[0067] After shifting the terms of the above coordinate relationship, multiply both sides by (I+S)R -1 , the coordinate relationship is transformed into:

[0068]

[0069] Expand the above formula to get:

[0070]

[0071] Put the above formula in Linearization can be obtained: V = Bx-l function form,

[0072] in,

[0073]

[0074] x=[dX0 dY0 dY0 da db dc dk]

[0075]

[0076] Assume that the single-direction error mean of the common point coordinates X, Y, and Z is 0 and the variance is σ 2 , so the three equations in the above formula are heteroscedastic equations, which are solved by weighted least squares method. When there are three sets of common points, a system of 9 equations can be formed, which can be solved by weighted least squares iteration:

[0077]

[0078] Among them, W is the weight matrix, W = Q -1 , Q is the covariance matrix of the observed value, and the variance covariance matrix Q is obtained by using the covariance propagation law:

[0079]

[0080] The Dilution of Precision factor is: σ para =DOP' para ·σ, where σ X =σ Y =σ Z =σ represents the mean error in each direction, the mean error of the point position σ p for:

[0081] Substitute the point error into σ para =DOP' para· σ can be obtained: Among them, DOP para Expressed as the amplification factor of the common point position error.

[0082] Further, the obtaining of the RMSE ratio of the coordinate point after the conversion to the RMSE ratio of the coordinate point before the conversion includes: the processed seven-parameter model is converted into:

[0083]

[0084] Transpose the formula and rewrite it in matrix form: Gx = b, where:

[0085]

[0086] Using the weighted least squares method, we can get: x = (G T WG) -1 G T Wb, where W is the weight matrix;

[0087] The error amplification factor of the seven parameters and the coordinates of the points to be converted is:

[0088] Compared with the prior art, the beneficial technical effects of the present invention are as follows:

[0089] (i) The present invention uses a transformation model based on the Rodriguez matrix in coordinate registration. This model is different from the traditional Bursa model and can be applied to three-dimensional coordinate transformation at any angle. It introduces local positioning information into the absolute coordinate system to achieve positioning solution for the entire network, thereby improving the positioning accuracy and consistency of the overall system.

[0090] (ii) Furthermore, the present invention can record the timestamp of each node receiving the signal through the ranging information between nodes under harsh conditions, establish the observation equation through the TDOA (time difference of arrival) positioning model, and use the damped least squares method to achieve local positioning solution, which can effectively cope with the complexity of the local environment and improve the positioning accuracy of the node.

[0091] (III) Furthermore, the present invention proposes a geometric precision reduction factor and a derivation process, and further optimizes the positioning accuracy and enhances the robustness of the system by starting from the geometric configuration of the node. By utilizing the ranging information between nodes and the TDOA (time difference of arrival) positioning model, it has better resistance to multipath effects and signal attenuation, making it more suitable for positioning in a denied environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0092] Figure 1 A schematic flow chart of a positioning calculation and optimization method according to an embodiment of the present invention is shown.

[0093] Figure 2 A schematic diagram of a three-dimensional node network in a positioning calculation and optimization method according to an embodiment of the present invention is shown. DETAILED DESCRIPTION

[0094] In order to make the purpose, technical scheme and advantages of the present invention clearer, the following is a further detailed description of a positioning calculation and optimization method proposed by the present invention in combination with the accompanying drawings and specific embodiments. According to the following description, the advantages and features of the present invention will be clearer. It should be noted that the accompanying drawings adopt a very simplified form and use non-precise proportions, which are only used to conveniently and clearly assist in explaining the purpose of the embodiments of the present invention. In order to make the purpose, features and advantages of the present invention more obvious and easy to understand, please refer to the accompanying drawings. It should be noted that the structure, proportion, size, etc. illustrated by the accompanying drawings of this specification are only used to match the content disclosed in the specification, so that people familiar with this technology can understand and read, and are not used to limit the limiting conditions for the implementation of the present invention, so they have no technical substantive significance. Any modification of the structure, change of the proportional relationship or adjustment of the size, without affecting the effect that the present invention can produce and the purpose that can be achieved, should still fall within the scope of the technical content disclosed by the present invention.

[0095] A positioning calculation and optimization method comprises the following steps:

[0096] Step S1: Establish a positioning solution model based on TDOA (Time Difference of Arrival).

[0097] Step S2: Perform node local positioning calculation through the model to obtain local positioning information.

[0098] Step S3: Based on the seven-parameter coordinate transformation model, the local positioning information is introduced into the absolute coordinate system to realize the positioning solution of the entire network.

[0099] Step S4: Analyze the positioning accuracy based on the above positioning information.

[0100] Furthermore, the establishment of a positioning solution model based on TDOA includes: constructing a relative coordinate system of a node network in a three-dimensional space;

[0101] The relative coordinate system of the node network in the three-dimensional space is constructed as follows:

[0102] Step S11: Establish a three-dimensional network node consisting of n+1 nodes. Specifically, there is no anchor node in the node network.

[0103] Step S12: Please refer to Figure 2 , take the line connecting node 0 and node n as the X-axis, take the plane formed by the intersection of the straight lines 01 and 0n as the XOY plane, and according to the right-hand rule, take the direction perpendicular to the plane as the Z direction.

[0104] Step S13: The distance difference between nodes i and j and the distance difference between nodes j and 0 is expressed as:

[0105]

[0106] Step S14: The distance difference can be rewritten as: f(X)=ΔR+ε, where ε represents the distance difference measurement error, and ε~N(0,σ 2 ).

[0107] Furthermore, the node local positioning solution is performed through the model to obtain local positioning information, including the following steps:

[0108] Step S21: Perform Taylor linearization on f(X) to obtain a non-homogeneous linear equation system.

[0109] Step S22: using the damped least squares method to solve the obtained non-homogeneous linear equations.

[0110] Furthermore, the non-homogeneous linear equation system is specifically: Gx=b, where in a network with n+1 nodes, G is The matrix of .

[0111] Furthermore,

[0112]

[0113] Specifically, the damped least squares method is used to solve the obtained non-homogeneous linear equations to obtain: x = (G T G+μI) -1 G T b, where μ is a damping coefficient greater than 0 and I is the unit matrix. Furthermore, when solving the coordinates of each node by least squares, in order to prevent the matrix G T When G is singular or pathological, the damped least squares algorithm is introduced. The damped least squares algorithm mainly consists of two parts. First, a damping coefficient μ greater than 0 is added to the linearized matrix, that is, G T G+μI, where I is the unit matrix, and then the increment of the unknown parameter is calculated based on the modified matrix. The second is the adjustment algorithm of μ after each iteration. Since the set μ>0, the matrix G T G+μI is always symmetrical and positive. Therefore, the residual value always has a solution. In the actual algorithm process, μ is a tentative value. Generally, the current and previous iteration results are compared to decide how to adjust the parameters and damping coefficients. For a given μ value, the general adjustment method is: if the result reduces the error index function, then continue to reduce the μ value, otherwise increase the μ value. The specific steps are as follows:

[0114] Step S221: Initialization: Give the initial value θ 0 , set the iteration threshold ε>0, the damping coefficient μ>0, the adjustment coefficient β>0, and the iteration coefficient q=0.

[0115] Step S222: Linearization: Derivatively calculate the matrix G and the matrix C based on the observation equations and the current iteration value.

[0116] Step S223: Solve the linear equation system: Δθ q =(G T G+μI) -1 G T b|θ=θ q .

[0117] Step S224: Update the estimation result: θ q+1 =θ q +Δθ q .

[0118] Step S225: Determine whether the current iteration has converged: If ||Δθ q ||<ε, indicating that the iteration converges, the algorithm ends and the result is output; if ||Δθ q ||≥ε, proceed to the next step.

[0119] Step S226: Update the damping coefficient: set the error index function to ||Δθ q ||, if ||Δθ q ||<||Δθ q-1 ||, then μ=μ / β. if||Δθ q ||≥||Δθ q-1 ||, then μ=μ*β.

[0120] Step S227: Update the iteration count q=q+1, and return to the linearization step to continue iterating.

[0121] Furthermore, the seven-parameter coordinate transformation model is used to introduce local positioning information into the absolute coordinate system to achieve positioning solution of the entire network, including the following steps:

[0122] Step S31: Assume two spatial rectangular coordinate systems O'-X'Y'Z' and O-XYZ.

[0123] Step S32: The coordinate values ​​of the n nodes in the coordinate systems O'-X'Y'Z' and O-XYZ are respectively (X' i , Y' i , Z' i ) and (X i , Y, Z i ), where i=1, 2,…, n.

[0124] Step S33: Fusing O'-X'Y'Z' and O-XYZ. Specifically, the two local coordinate systems can be fused by translation, rotation, and scaling to obtain a seven-parameter coordinate transformation model of n nodes in the two coordinate systems:

[0125]

[0126] , where X0, Y0, Z0 are translation parameters, and R is the three rotation matrices R X (α), R Y (β), R Z The product of (γ) is:

[0127]

[0128] , where α, β, and γ are rotation parameters, representing the rotation angles in the three directions of X, Y, and Z respectively. The seven parameters are the translation parameters X0, Y0, and Z0, the rotation parameters α, β, and γ, and the scale factor k, k = 1 + μ.

[0129] According to the principle of Rodriguez matrix, the R matrix is ​​expressed as: R = (1 + S) (1-S) -1 , where S is an antisymmetric matrix, specifically: Among them, a, b, and c are intermediate parameters used to replace the rotation parameters. According to the properties of the antisymmetric matrix, the rotation matrix is ​​replaced by abc to facilitate the subsequent derivation and calculation.

[0130] Step S34: Substitute the scale parameter, rotation parameter, translation parameter and coordinates to be converted into the above coordinate relationship to complete the coordinate conversion.

[0131] Furthermore, the calculation of the scale parameter includes: calculating the corresponding distance through the coordinates, and obtaining the scale parameter through the distance ratio, including the following steps:

[0132] Select n common points P i =(i=1,2,…,n) calculate any two points P i , P j The ratio of distances in the coordinate systems O'-X'Y'Z' and O-XYZ is:

[0133]

[0134] Take the mean of the distance ratios as the value of the scale parameter:

[0135]

[0136] Wherein, n is the number of common points. Specifically, there are n(n-1) / 2 distance ratios between n common points.

[0137] The calculation of the rotation parameters includes: i , P j Substituting the coordinate values ​​in the coordinate systems O'-X'Y'Z' and O-XYZ into the above coordinate relationship, we obtain:

[0138]

[0139] Subtract the two equations in the above formula to eliminate the translation parameter and then substitute them into the above coordinate relationship to obtain:

[0140]

[0141] When there are three common points, the above formula is combined to obtain:

[0142]

[0143] According to the above formula, the least square method can be used to find the parameters a, b, c, and substitute them into the R matrix R = (1 + S) (1-S) -1 The rotation matrix R is obtained. Specifically, in the present invention, when n>3, at most 3n equations can be listed to solve the rotation parameters.

[0144] The calculation of the translation parameter includes: according to the obtained scale parameter and rotation matrix, together with the common point coordinates, into the above coordinate relationship to obtain:

[0145]

[0146] Furthermore, analyzing the positioning accuracy based on the above positioning information includes: deriving a precision decay factor, specifically, the precision decay factor represents the ratio of the RMSE (root mean square error) of the positioning result to the RMSE of the observation; judging the influence of the spatial distribution of nodes in the model on the positioning accuracy according to the precision decay factor, the precision decay factor can quantitatively reflect the influence of the spatial distribution on the positioning accuracy, and the positioning accuracy can be optimized by dynamically adjusting the spatial distribution of the nodes through the value of the precision decay factor.

[0147] The derivation of the DOP factor comprises the following steps:

[0148] Step S41: complete the intra-cluster positioning of each cluster through the distance difference information, and obtain the RMSE ratio of the intra-cluster positioning result to the RMSE of the observed quantity.

[0149] Furthermore, the ratio of the RMSE of the intra-cluster positioning result to the RMSE of the observed quantity includes:

[0150] According to the Gx=b obtained by Taylor linearization, the least square method is used to solve: T G) -1 G T b.

[0151] By deriving the geometric factors in GNSS, we can get H = (G T G) -1, where H is a symmetric matrix of order 3n-6.

[0152]

[0153] Among them, DOP pos It is the ratio of the RMSE of the intra-cluster positioning result to the RMSE of the observed value.

[0154] Step S42: Use the least squares model to solve the seven parameters and obtain the ratio of the RMSE of the seven parameters to the RMSE of the common point coordinates.

[0155] Further, the obtaining of the ratio of the RMSE of the seven parameters to the RMSE of the common point coordinates includes: processing the seven-parameter coordinate transformation model before derivation, including: obtaining according to the antisymmetric matrix property:

[0156]

[0157] Therefore: R T R=[(I+S)(IS) -1 ] T [(I+S)(IS) -1 ]=(I+S) -1 (IS)(I+T)(IS) -1 =I.

[0158] Substituting matrix S into matrix R, we get:

[0159]

[0160] Where Δ=1+a 2 +b 2 +c 2 ;

[0161] According to the above formula and the properties of orthogonal matrix, we can get: R -1 =R T =[(I+S)(IS) -1 ] T =(I+S) -1 (IS);

[0162] After shifting the terms of the above coordinate relationship, multiply both sides by (I+S)R -1 , the coordinate relationship is transformed into:

[0163]

[0164] Where k = 1 + μ;

[0165] Expand the above formula to get:

[0166]

[0167] Put the above formula in Linearization can be obtained: V = Bx-l function form,

[0168] in,

[0169]

[0170] x=[dX0 dY0 dY0 da db dc dk]

[0171]

[0172] Assume that the single-direction error mean of the common point coordinates X, Y, and Z is 0 and the variance is σ 2 , so the three equations in the above formula are heteroscedastic equations, which are solved by weighted least squares method. When there are three sets of common points, a system of 9 equations can be formed, which can be solved by weighted least squares iteration:

[0173]

[0174] Among them, W is the weight matrix, W = Q -1 , Q is the covariance matrix of the observed value, and the variance covariance matrix Q is obtained by using the covariance propagation law:

[0175]

[0176] The Dilution of Precision factor is: σ para =DOP' para ·σ, where σ X =σ Y =σ Z =σ represents the mean error in each direction, the mean error of the point position σ p for:

[0177] Substitute the point error into σ para =DOP' para ·σ can be obtained: Among them, DOP para That is, the ratio of the RMSE of the seven parameters to the RMSE of the common point coordinates.

[0178] Step S43: according to the solved seven parameters, the seven-parameter coordinate transformation model is brought back to perform coordinate transformation on other points, and the ratio of the RMSE of the coordinate point after transformation to the RMSE of the coordinate point before transformation is obtained.

[0179] Further, the obtaining of the RMSE ratio of the coordinate point after the conversion to the RMSE ratio of the coordinate point before the conversion includes: the processed seven-parameter model is converted into:

[0180]

[0181] Transpose the formula and rewrite it in matrix form: Gx = b, where:

[0182]

[0183] Using the weighted least squares method, we can get: x = (G T WG) -1 G T Wb, where W is the weight matrix.

[0184] The ratio of the RMSE of the coordinate point after transformation to the RMSE of the coordinate point before transformation is:

[0185] The technical features of the above-described embodiments may be arbitrarily combined. To make the description concise, not all possible combinations of the technical features in the above-described embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0186] The above-mentioned embodiments only express several implementation methods of the present invention, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention shall be subject to the attached claims.

Claims

1. A positioning calculation and optimization method, characterized in that: The following steps are involved: Establish positioning solution model based on TDOA; Perform node local positioning calculation through the model to obtain local positioning information; Based on the seven-parameter coordinate transformation model, the local positioning information is introduced into the absolute coordinate system to realize the positioning solution of the entire network; Analyze the positioning accuracy according to the above positioning information; The establishment of a positioning solution model based on TDOA includes: constructing a relative coordinate system of a node network in a three-dimensional space; The relative coordinate system of the node network in the three-dimensional space is constructed as follows: Establish a three-dimensional network node consisting of n+1 nodes; The line connecting nodes 0 and n is taken as the X-axis, the plane formed by the intersection of 01 and 0n is taken as the XOY plane, and the direction perpendicular to the plane is taken as the Z direction; The method of performing local node positioning calculation through the model to obtain local positioning information includes the following steps: Perform Taylor linearization on f(X) to obtain a non-homogeneous linear system of equations; The obtained non-homogeneous linear equations are solved using the damped least squares method; The method of introducing local positioning information into the absolute coordinate system based on the seven-parameter coordinate transformation model to realize the positioning solution of the entire network includes the following steps: Assume two spatial rectangular coordinate systems O'-X'Y'Z' and O-XYZ; The coordinate values ​​of n nodes in the coordinate systems O'-X'Y'Z' and O-XYZ are (X' i , Y' i , Z' i ) and (X i , Y i , Z i ), where i = 1, 2, ..., n; Combining O'-X'Y'Z' and O-XYZ, we get a seven-parameter coordinate transformation model of n nodes in two coordinate systems: ， Among them, X0, Y0, Z0 are translation parameters, and R is the three rotation matrices R X (α), R Y (β), R Z The product of (γ) is: ， Among them, α, β, and γ are rotation parameters, representing the rotation angles in the three directions of X, Y, and Z respectively; According to the principle of Rodriguez matrix, the R matrix is ​​expressed as: R = (1 + S) (1-S) -1 , where S is an antisymmetric matrix, and a, b, and c are all process parameters, specifically: Substitute the scale parameter, rotation parameter, translation parameter and coordinates to be transformed into the above coordinate relationship to complete the coordinate transformation.

2. A positioning calculation and optimization method as claimed in claim 1, characterized in that: The distance difference between node i and j and node j and 0 is expressed as: The distance difference can be rewritten as: f(X)=ΔR+ε, where ε represents the distance difference measurement error; where x i ,y i 、z i represents the spatial position of node i, x j ,y j 、z j represents the spatial position of node j, R ij Represents the distance between node i and node j, R j0 Represents the distance between node j and node 0.

3. A positioning calculation and optimization method as claimed in claim 1, characterized in that: The non-homogeneous linear equation system is specifically: Gx=b, where G is Matrix of The damped least squares method is used to solve the obtained non-homogeneous linear equations to obtain: x = (G T G+μI) -1 G T b, where μ is a damping coefficient greater than 0, I is the unit matrix; where X i , Y i , Z i represents the spatial position of node i, R ij represents the distance between node i and node j, and b represents a constant matrix.

4. A positioning calculation and optimization method as claimed in claim 1, characterized in that: The calculation of the scale parameter includes: calculating the corresponding distance through the coordinates, and obtaining the scale parameter through the distance ratio, including the following steps: Select n common points P i =(i=1,2,…,n) calculate any two points P i , P j The ratio of distances in the coordinate systems O'-X'Y'Z' and O-XYZ is: Take the mean of the distance ratios as the value of the scale parameter: Where n is the number of common points; The calculation of the rotation parameters includes: i , P j Substituting the coordinate values ​​in the coordinate systems O'-X'Y'Z' and O-XYZ into the above coordinate relationship, we get: Subtract the two equations in the above formula to eliminate the translation parameter and then substitute them into the above coordinate relationship to obtain: When there are three common points, the above formula is combined to obtain: According to the above formula, the least square method can be used to find the parameters a, b, c, and substitute them into the R matrix R = (1 + S) (1-S) -1 Find the rotation matrix R in The calculation of the translation parameter includes: according to the obtained scale parameter and rotation matrix, together with the common point coordinates, into the above coordinate relationship to obtain: Where X i , Y i , Z i Represents the coordinate value of node i in the coordinate system 0-XYZ, where X i ', Y i ', Z i ' represents the coordinate value of node i in the coordinate system 0-X'Y'Z', X j , Y j , Z j Represents the coordinate value of node j in the coordinate system 0-XYZ, where X j ', Y j ', Z j ' represents the coordinate value of node j in the coordinate system 0-X'Y'Z'.

5. A positioning calculation and optimization method as claimed in claim 1, characterized in that: Analyzing the positioning accuracy according to the positioning information includes: deriving a precision reduction factor; judging the influence of the spatial distribution of nodes in the model on the positioning accuracy according to the precision reduction factor; The derivation of the DOP factor comprises the following steps: Get the ratio of the RMSE (root mean square error) of the intra-cluster positioning result to the RMSE of the observed quantity; Get the ratio of the RMSE of the seven parameters to the RMSE of the common point coordinates; Get the ratio of the RMSE of the coordinate point after the seven-parameter coordinate model transformation to the RMSE of the coordinate point before the transformation.

6. A positioning calculation and optimization method as claimed in claim 5, characterized in that: The method of obtaining the ratio of the RMSE of the intra-cluster positioning to the RMSE of the observed quantity includes: According to the Gx=b obtained by Taylor linearization, the least square method is used to solve: T G) -1 G T b; By deriving the geometric factors in GNSS, we can get H = (G T G) -1 , where H is a symmetric matrix of order 3n-6; Where σ represents the mean error, h represents the coefficient matrix, and DOP pos Indicates the precision factor of solving the spatial point, G represents the coefficient matrix, G T is the transpose of the coefficient matrix.

7. A positioning calculation and optimization method as claimed in claim 5, characterized in that: The method of obtaining the ratio of the RMSE of the seven parameters to the RMSE of the common point coordinates includes: processing the seven-parameter coordinate transformation model before derivation, including: obtaining according to the antisymmetric matrix property: Therefore: R T R = [(I + S)(I - S) -1 T [(I + S)(I - S) -1 = (I + S) -1 (I - S)(I + S)(I - S) -1 = I;​ Substituting matrix S into matrix R, we get: Where, Δ=1+a 2 +b 2 +c 2 ; According to the above formula and the properties of orthogonal matrix, we can get: R -1 =R T =[(I+S)(IS) -1 ] T =(I+S) -1 (IS); After shifting the terms of the above coordinate relationship, multiply both sides by (I+S)R -1 , the coordinate relationship is transformed into: Expand the above formula to get: Put the above formula in Linearization can be obtained: V = Bx-l function form, in, x=[dX0 dY0 dY0 da db dc dk] Assume that the single-direction error mean of the common point coordinates X, Y, and Z is 0 and the variance is σ 2 , so the three equations in the above formula are heteroscedastic equations, which are solved by weighted least squares method. When there are three sets of common points, a system of 9 equations can be formed, which can be solved by weighted least squares iteration: Among them, W is the weight matrix, W = Q -1 , Q is the covariance matrix of the observed value, and the variance covariance matrix Q is obtained by using the covariance propagation law: The Dilution of Precision factor is: σ para =DOP′ para ·σ, where σ X =σ Y =σ Z =σ represents the mean error in each direction, the mean error of the point position σ p for: Substitute the point error into σ para =DOP′ para ·σ can be obtained: Among them, DOP para It is expressed as the amplification factor of the common point position error, where I represents the unit matrix, k represents the conversion coefficient, and a, b, and c represent process parameters.

8. A positioning calculation and optimization method as claimed in claim 7, characterized in that: The method of obtaining the ratio of the RMSE of the coordinate point after the seven-parameter coordinate model conversion to the RMSE of the coordinate point before the conversion comprises the following steps: the processed seven-parameter model is converted into: Transpose the formula and rewrite it in matrix form: Gx = b, where: Using the weighted least squares method, we can get: x = (G T WG) -1 G T Wb, where W is the weight matrix, and the error amplification factor of the seven parameters and the coordinates of the points to be converted is:

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