Multi-dimensional scale unambiguous distance measurement positioning method for measuring incoming wave time difference

Abstract

The invention provides a multi-dimensional scale ambiguity-free distance measurement positioning method for measuring incoming wave time difference, and belongs to the technical field of wireless positioning, and the method comprises the steps: measuring the time difference of arriving at different nodes by using a radio signal in an environment, constructing a matrix and a vector for removing rotation and mirror image ambiguity, converting a nonlinear constraint into a solvable model, and carrying out the measurement of the incoming wave time difference. A double fitting error search mechanism is designed, through rotation angle lattice point search, the minimum fitting error of an original image and a mirror image is calculated and compared, the mirror image and rotation blur are judged and eliminated, and therefore the node positioning result after deblurring is determined. According to the scheme, the absolute coordinates of the nodes can be effectively solved without depending on satellite positioning, the positioning error is small, the self-positioning problem of the nodes of the wireless sensor network in the complex shielding environment is remarkably solved, and the self-positioning level of the nodes in the complex environment is improved.

Description

Technical Field

[0001] This invention relates to the field of wireless positioning technology, and in particular to a multidimensional scaling unambiguous ranging and positioning method for measuring the time difference of arrival. Background Technology

[0002] With the rapid development of sensor networks, Internet of Things (IoT) networks, and human-machine networks, the location information of each node in the network is of great significance for applications such as environmental perception, inter-node communication, dynamic planning, and task execution.

[0003] Satellite positioning is a common method for obtaining the location information of outdoor network nodes. However, due to the limited quality of satellite signal reception, the accuracy of satellite positioning drops significantly in environments with obstructions such as tunnels, indoors, and mountains, making it difficult to meet the needs of obtaining network node location information.

[0004] To avoid relying on satellite positioning, multidimensional scaling (MDS) ranging is a common method for obtaining the location information of network nodes. This method first measures the distance between any two nodes in the network, determining all elements of the distance measurement matrix. Then, using the eigenvectors and eigenvalues ​​of the distance measurement matrix, it determines the relative position coordinates of the network nodes. However, since the distance between any two nodes in the network is independent of translation, rotation, and mirror transformations of the network node position coordinates, MDS suffers from translation, rotation, and mirror ambiguity.

[0005] To eliminate translational, rotational, and mirror ambiguities inherent in multidimensional scaling (MLS) ranging and positioning methods, a common approach is to install satellite positioning modules on some nodes. The satellite positioning results of these nodes are then combined with the relative position coordinates from the MLS ranging and positioning data to determine the position coordinates of nodes in the network that do not have satellite positioning modules installed. However, this method is still limited by the quality of satellite signal reception. In environments with obstructed views, such as tunnels, indoor spaces, or mountainous terrain, satellite positioning accuracy degrades significantly, making it difficult to meet the requirement of eliminating translational, rotational, and mirror ambiguities inherent in MLS ranging and positioning methods.

[0006] In reality, besides satellite positioning signals, other radio signals also exist in the network environment. Therefore, it is necessary to utilize these other radio signals in the actual network environment to eliminate translation, rotation, and mirror ambiguity inherent in multidimensional scaling ranging and positioning methods. A common hyperbolic cross-location method first measures the time difference between the arrival waves of an unknown radio signal and multiple nodes with known coordinates, then uses hyperbolic cross-location to locate the radio signal. If only the arrival time differences of multiple known radio signals arriving at two unknown nodes are used, the hyperbolic cross-location method can also be used to locate the two nodes. However, this requires measuring the arrival time differences of at least four radio signals located at different positions to calculate the four coordinate values ​​of the two nodes, resulting in a large amount of measurement data and complex calculations. Summary of the Invention

[0007] To address the issues of translation, rotation, and mirror ambiguity in existing multidimensional scaling ranging and positioning methods that do not rely on satellite positioning, this invention proposes a multidimensional scaling unambiguous ranging and positioning method that measures the time difference of arrival. This method utilizes radio signals from the actual environment in which the network is located to eliminate the translation, rotation, and mirror ambiguity inherent in multidimensional scaling ranging and positioning methods. It is suitable for situations where the quality of satellite positioning signals is poor and cannot meet the positioning requirements of network nodes.

[0008] A multidimensional scaling unambiguous ranging and positioning method for measuring the time difference of arrival of waves includes the following steps:

[0009] Step S1, parameter settings: set the number of nodes in the network, the multidimensional scaling ranging and positioning results of the nodes, the number of rotation angle search grid points, the rotation angle search grid point number, the rotation angle search grid points, the number of radio signals in the environment where the network is located, the location coordinates of the radio signals, the radio propagation speed, the selection matrix and the de-rotation ambiguity constant matrix.

[0010] Step S2: Determine the time difference measurement of the radio signal arriving at the network node, thereby determining the unrotated ambiguity time difference vector and the unrotated ambiguity time difference matrix;

[0011] Step S3: Based on the multidimensional scaling ranging and positioning results of the nodes, determine the corresponding mirror positioning results, as well as the original image de-rotated fuzzy angle coordinate vector and the mirror image de-rotated fuzzy angle coordinates corresponding to the rotation angle search grid point; based on the radio signal position coordinates, determine the original image de-rotated fuzzy angle matrix and the mirror image de-rotated fuzzy angle matrix, the original image de-rotated fuzzy angle vector and the mirror image de-rotated fuzzy angle vector corresponding to the rotation angle search grid point, thereby determining the overall original image de-rotated fuzzy angle matrix and the overall mirror image de-rotated fuzzy angle matrix, the overall original image de-rotated fuzzy angle vector and the overall mirror image de-rotated fuzzy angle vector corresponding to the rotation angle search grid point.

[0012] Step S4: Determine the preimage fitting error and mirror image fitting error corresponding to the search grid points at the rotation angle;

[0013] Step S5: Determine the minimum value of the original image fitting error and the minimum value of the mirror image fitting error, along with their corresponding rotation angle search grid point numbers. Compare the minimum value of the mirror image fitting error with the minimum value of the original image fitting error to determine the node positioning results for removing mirror blur, rotation blur, and translation blur.

[0014] Furthermore, the selection matrix in step S1 is:

[0015] ;

[0016] The de-rotation fuzzy constant matrix is:

[0017] ;

[0018] in, It is an array where all elements are 1. Dimensional column vector.

[0019] Further, step S2 specifically includes:

[0020] Determine the first The first radio signal arrived at the network. The time difference measurement of each node is as follows , , Thus, the unrotated fuzzy time difference vector is determined. for:

[0021] , ;

[0022] in, For the speed of radio propagation, The time difference matrix for de-rotation fuzziness is:

[0023] .

[0024] Furthermore, step S3 specifically includes:

[0025] By the Multidimensional scaling and positioning results of each node Determine the first Mirror positioning results of each node for:

[0026] , ,

[0027] No. Search grid points by rotation angle The corresponding number The original image is rotated and blurred by the following angle coordinate vector:

[0028] ;

[0029] No. The angle coordinates of the mirror image after rotation and blurring are:

[0030] ;

[0031] By the radio signal location coordinates Determine the first Search grid points by rotation angle The corresponding number The preimage rotation blur angle matrix is:

[0032] ;

[0033] No. The mirror-image rotation blur angle matrix is:

[0034] ;

[0035] No. The preimage is rotated and blurred by the following angle vector:

[0036] ;

[0037] No. The mirror image is rotated and blurred by the following angle vector:

[0038] ;

[0039] Thus determine the first Search grid points by rotation angle The corresponding preimage rotation blur angle overall matrix is:

[0040] ;

[0041] The overall vector of the original image's rotation and blur angle is:

[0042] ;

[0043] Where, vector The elements are the de-rotated blur time difference vectors. The square of the corresponding element. ;

[0044] The overall matrix for mirroring and removing the rotation blur angle is:

[0045] ;

[0046] The overall vector for the mirror-image rotation blur angle is:

[0047] ;

[0048] in, .

[0049] Furthermore, step S4 specifically includes:

[0050] By the Search grid points by rotation angle The corresponding global matrix of the preimage rotation blur angle and the global vector of the preimage rotation blur angle are used to determine the first... Search grid points by rotation angle Corresponding preimage fitting error for:

[0051] ,

[0052] in, , ;

[0053] By the Search grid points by rotation angle The corresponding global matrix and global vector of the mirror-to-rotation blur angle are used to determine the first... Search grid points by rotation angle Corresponding mirror fit error for:

[0054] ,

[0055] in, , .

[0056] Further, step S5 specifically includes:

[0057] right ,Sure The minimum value is The corresponding rotation angle search grid point number is ,Sure The minimum value is The corresponding rotation angle search grid point number is ;when At that time, determine the first step of de-mirror blur and de-rotation blur. The location results for each node are as follows:

[0058] ,

[0059] Determine the first step of de-mirror blur, de-rotation blur, and de-translation blur. The location results for each node are as follows:

[0060] , ;

[0061] in, for Order selection matrix, ;

[0062] Otherwise, when At that time, determine the first step of de-mirror blur and de-rotation blur. The location results for each node are as follows:

[0063] ;

[0064] Determine the first step of de-mirror blur, de-rotation blur, and de-translation blur. The location results for each node are as follows:

[0065] , ;

[0066] in, .

[0067] This invention provides a multidimensional scaling unambiguous ranging and positioning method for measuring the time difference of arrival (TDOA). This method utilizes radio signals in the environment to measure the time difference of arrival at different nodes, constructs matrices and vectors to remove rotation and mirror ambiguity, transforms nonlinear constraints into a solvable model, and designs a dual fitting error search mechanism. Through rotation angle grid point search, it calculates and compares the minimum fitting error between the original image and the mirror image, identifies and eliminates mirror and rotation ambiguity, thereby determining the unambiguous node positioning result. This invention utilizes radio signals in the actual environment where the network is located to eliminate translation, rotation, and mirror ambiguity inherent in multidimensional scaling ranging and positioning methods. It is suitable for situations where satellite positioning signal quality is poor and cannot meet the positioning requirements of network nodes. It can effectively solve the absolute coordinates of nodes without relying on satellite positioning, with small positioning errors. It significantly solves the self-localization problem of wireless sensor network nodes in complex occlusion environments and improves the autonomous positioning level of nodes in complex environments. Attached Figure Description

[0068] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0069] Figure 1 This is a flowchart of a multi-dimensional scaling unambiguous ranging and positioning method for measuring the time difference of arrival waves, provided by an embodiment of the present invention. Detailed Implementation

[0070] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0071] This embodiment provides a multi-dimensional scaling unambiguous ranging and positioning method for measuring the time difference of arrival of waves, such as... Figure 1 As shown, the method includes the following steps:

[0072] Step 1: Set the number of nodes in the network to [number]. , No. The multidimensional scaling and localization results of each node are represented as a two-dimensional column vector. , The number of grid points searched by rotation angle is Rotation angle search grid point number , No. The rotation angle search grid points are: The number of radio signals in the environment where the network is located is , No. The location coordinates of each radio signal are represented by a two-dimensional column vector. , The speed of radio propagation is , The order selection matrix is:

[0073] ;

[0074] The order derotation fuzzy constant matrix is:

[0075] ;

[0076] in, It is an array where all elements are 1. Dimensional column vector.

[0077] Step 2, the The time difference measurement module of the nth node determines the nth The first radio signal arrived at the network. The time difference measurement of each node is as follows , , Thus, the unrotated fuzzy time difference vector is determined. for:

[0078] , ;

[0079] in, For the speed of radio propagation, The time difference matrix for de-rotation fuzziness is:

[0080] .

[0081] Step 3, from the first Multidimensional scaling and positioning results of each node Determine the corresponding mirror positioning result for:

[0082] , ,

[0083] Determine the first Search grid points by rotation angle The corresponding number The original image is rotated and blurred by the following angle coordinate vector:

[0084] ,

[0085] No. The angle coordinates of the mirror image after rotation and blurring are:

[0086] ;

[0087] By the radio signal location coordinates Determine the first Search grid points by rotation angle The corresponding number The preimage rotation blur angle matrix is:

[0088] ,

[0089] No. The mirror-image rotation blur angle matrix is:

[0090] ,

[0091] No. The preimage is rotated and blurred by the following angle vector:

[0092] ,

[0093] No. The mirror image is rotated and blurred by the following angle vector:

[0094] ,

[0095] Thus determining the first Search grid points by rotation angle The corresponding preimage rotation blur angle overall matrix is:

[0096]

[0097] The overall vector of the original image's rotation and blur angle is:

[0098]

[0099] Where, vector The elements are the de-rotated blur time difference vectors. The square of the corresponding element. ;

[0100] The overall matrix for mirroring and removing the rotation blur angle is:

[0101]

[0102] The overall vector for the mirror-image rotation blur angle is:

[0103] ,

[0104] in, .

[0105] Step 4, from the first Search grid points by rotation angle The corresponding global matrix of the preimage rotation blur angle and the global vector of the preimage rotation blur angle are used to determine the first... Search grid points by rotation angle Corresponding preimage fitting error for:

[0106] ,

[0107] in, , ;

[0108] By the Search grid points by rotation angle The corresponding global matrix and global vector of the mirror-to-rotation blur angle are used to determine the first... Search grid points by rotation angle Corresponding mirror fit error for:

[0109] ,

[0110] in, , .

[0111] Step 5, for ,Sure The minimum value is The corresponding rotation angle search grid point number is ,Sure The minimum value is The corresponding rotation angle search grid point number is ;when At that time, determine the first step of de-mirror blur and de-rotation blur. The location results for each node are as follows:

[0112] ,

[0113] Determine the first step of de-mirror blur, de-rotation blur, and de-translation blur. The location results for each node are as follows:

[0114] , ;

[0115] in, for Order selection matrix, ;

[0116] Otherwise, when At that time, determine the first step of de-mirror blur and de-rotation blur. The location results for each node are as follows:

[0117] ,

[0118] Determine the first step of de-mirror blur, de-rotation blur, and de-translation blur. The location results for each node are as follows:

[0119] , ;

[0120] in, .

[0121] The following specific embodiments demonstrate the experimental verification of the present invention:

[0122] In this embodiment, the number of nodes in the network is set to 6, and the actual x-coordinates of the 6 nodes are as follows:

[0123] -47.01, -244.69, -186.78, 131.52, -280.23, -429.39;

[0124] The actual position coordinates are as follows:

[0125] 203.68, 311.05, 316.49, -125.62, 418.87, -275.71;

[0126] The x-axis of the multidimensional scaling ranging and positioning results are as follows:

[0127] -55.61, -172.76, -175.57, 282.72, -282.08, 403.30;

[0128] The ordinates of the multidimensional scaling ranging and positioning results are as follows:

[0129] -132.3128, 58.8918, 1.8582, -292.5849, 88.9972, 275.1505;

[0130] The coordinate units mentioned above are all in meters;

[0131] The number of grid points searched by rotation angle is 360° rotation angle search grid point sequence number , No. The rotation angle search grid points are: Degree; There are 3 radio signals in the environment where the network is located. The x-coordinates of the radio signal locations are known to be:

[0132] 13.21, 53.22, -8.51;

[0133] The ordinates are as follows:

[0134] 64.14, 193.65, -10.77;

[0135] The coordinates of the radio signal locations mentioned above are all in meters, and the speed of radio propagation... .

[0136] In this embodiment, the time difference measurements for the arrival of the first radio signal at the network node are determined as follows:

[0137] 0, 0.6818, 0.5649, 0.2370, 1.0262, 1.3517;

[0138] The time difference measurements for the arrival of the second radio signal at the network node are as follows:

[0139] 0, 0.7372, 0.5685, 0.7656, 1.0111, 1.9139;

[0140] The time difference measurements for the arrival of the third radio signal at the network node are as follows:

[0141] 0, 0.6014, 0.5130, -0.1255, 0.9653, 0.9286;

[0142] All time difference measurements mentioned above are in microseconds.

[0143] The x-coordinates of the node positions in the network determined by the multi-dimensional scaling unambiguous ranging and positioning method for measuring the time difference of arrival of waves according to the present invention are as follows:

[0144] -46.22, -243.30, -186.49, 131.54, -279.08, -429.11;

[0145] The ordinates are as follows:

[0146] 204.41, 311.40, 317.19, -125.06, 418.99, -275.19;

[0147] Compared to the actual location of the network node, the positioning errors are as follows:

[0148] 1.08, 1.44, 0.76, 0.56, 1.15, 0.59;

[0149] All coordinates mentioned above are in meters.

[0150] As can be seen, the node position error determined by the multidimensional scaling unambiguous ranging and positioning method of the present invention for measuring the time difference of arrival is less than 1.45 meters. The positioning error is small, which can effectively utilize the radio signals in the environment where the network is located, eliminate the translation, rotation and mirror ambiguity existing in the multidimensional scaling ranging and positioning method, and improve the autonomous positioning level of nodes in complex environments.

[0151] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A multi-dimensional scaling unambiguous ranging and positioning method for measuring the time difference of arrival, characterized in that, The method includes: Step S1, parameter settings: set the number of nodes in the network, the multidimensional scaling ranging and positioning results of the nodes, the number of rotation angle search grid points, the rotation angle search grid point number, the rotation angle search grid points, the number of radio signals in the environment where the network is located, the location coordinates of the radio signals, the radio propagation speed, the selection matrix and the de-rotation ambiguity constant matrix. Step S2: Determine the time difference measurement of the radio signal arriving at the network node, thereby determining the unrotated ambiguity time difference vector and the unrotated ambiguity time difference matrix; Step S3: Based on the multidimensional scaling ranging and positioning results of the nodes, determine the corresponding mirror positioning results, as well as the original image de-rotated fuzzy angle coordinate vector and the mirror image de-rotated fuzzy angle coordinates corresponding to the rotation angle search grid point; based on the radio signal position coordinates, determine the original image de-rotated fuzzy angle matrix and the mirror image de-rotated fuzzy angle matrix, the original image de-rotated fuzzy angle vector and the mirror image de-rotated fuzzy angle vector corresponding to the rotation angle search grid point, thereby determining the overall original image de-rotated fuzzy angle matrix and the overall mirror image de-rotated fuzzy angle matrix, the overall original image de-rotated fuzzy angle vector and the overall mirror image de-rotated fuzzy angle vector corresponding to the rotation angle search grid point. Step S4: Determine the preimage fitting error and mirror image fitting error corresponding to the search grid points at the rotation angle; Step S5: Determine the minimum value of the original image fitting error and the minimum value of the mirror image fitting error, along with their corresponding rotation angle search grid point numbers. Compare the minimum value of the mirror image fitting error with the minimum value of the original image fitting error to determine the node positioning results for removing mirror blur, rotation blur, and translation blur.

2. The multidimensional scaling unambiguous ranging and positioning method for measuring the time difference of arrival of waves according to claim 1, characterized in that, The selection matrix in step S1 is: ； The de-rotation fuzzy constant matrix is: ； in, It is an array where all elements are 1. Dimensional column vector.

3. The multidimensional scaling unambiguous ranging and positioning method for measuring the time difference of arrival of waves according to claim 1, characterized in that, Step S2 further includes: Determine the first The first radio signal arrived at the network. The time difference measurement of each node is as follows , , Thus, the unrotated fuzzy time difference vector is determined. for: ， ； in, For the speed of radio propagation, The time difference matrix for de-rotation fuzziness is: 。 4. The multidimensional scaling unambiguous ranging and positioning method for measuring the time difference of arrival of waves according to claim 3, characterized in that, Step S3 further includes: By the Multidimensional scaling and positioning results of each node Determine the first Mirror positioning results of each node for: ， ； No. Search grid points by rotation angle The corresponding number The original image is rotated and blurred by the following angle coordinate vector: ； No. The angle coordinates of the mirror image after rotation and blurring are: ； By the radio signal location coordinates Determine the first Search grid points by rotation angle The corresponding number The preimage rotation blur angle matrix is: ； No. The mirror-image rotation blur angle matrix is: ； No. The preimage is rotated and blurred by the following angle vector: ； No. The mirror image is rotated and blurred by the following angle vector: ； Thus determine the first Search grid points by rotation angle The corresponding preimage rotation blur angle overall matrix is: ； The overall vector of the original image's rotation and blur angle is: ； Where, vector The elements are the de-rotated blur time difference vectors. The square of the corresponding element. ; The overall matrix for mirroring and removing the rotation blur angle is: ； The overall vector for the mirror-image rotation blur angle is: ； in, .

5. The multidimensional scaling unambiguous ranging and positioning method for measuring the time difference of arrival of waves according to claim 4, characterized in that, Step S4 further includes: By the Search grid points by rotation angle The corresponding global matrix of the preimage rotation blur angle and the global vector of the preimage rotation blur angle are used to determine the first... Search grid points by rotation angle Corresponding preimage fitting error for: ； in, , ; By the Search grid points by rotation angle The corresponding global matrix and global vector of the mirror-to-rotation blur angle are used to determine the first... Search grid points by rotation angle Corresponding mirror fit error for: ； in, , .

6. The multidimensional scaling unambiguous ranging and positioning method for measuring the time difference of arrival of waves according to claim 5, characterized in that, Step S5 further includes: right ,Sure The minimum value is The corresponding rotation angle search grid point number is ,Sure The minimum value is The corresponding rotation angle search grid point number is ;when At that time, determine the first step of de-mirror blur and de-rotation blur. The location results for each node are as follows: ； Determine the first step of de-mirror blur, de-rotation blur, and de-translation blur. The location results for each node are as follows: ， ； in, for Order selection matrix, ; Otherwise, when At that time, determine the first step of de-mirror blur and de-rotation blur. The location results for each node are as follows: ； Determine the first step of de-mirror blur, de-rotation blur, and de-translation blur. The location results for each node are as follows: ， ； in, .

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