Positioning tracking method and device based on multi-channel multi-frequency magnetic field

Through the multi-channel and multi-frequency magnetic field method, the problem of magnetic field symbol confirmation in electromagnetic positioning technology is solved, large-scale movement and precise measurement of the receiving end are achieved, and the needs of indoor location information and real-time trajectory tracking are met.

CN116448107BActive Publication Date: 2025-09-05BEIJING HUAHANG RADIO MEASUREMENT & RES INST
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Patent Information

Application Number
CN202210024259.4
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2022-01-06
Publication Date
2025-09-05
Estimated Expiration
2042-01-06

AI Technical Summary

Technical Problem

Existing electromagnetic positioning technology has difficulty confirming the magnetic field sign under the condition of no reference phase, resulting in limited movement range of the receiving end and small measurement range, which cannot meet the precise measurement requirements of indoor location information and real-time trajectory tracking.

Method used

A multi-channel and multi-frequency magnetic field method is adopted. The receiving end determines the relative phase reference value between the frequencies of the receiving channel at the initial positioning point, calculates the relative phase between the frequencies and confirms the sign of the magnetic field. The pose candidate data is calculated in combination with the signed magnetic field of the receiving channel to realize electromagnetic positioning and tracking without the need for a reference phase.

Benefits of technology

It realizes the confirmation of magnetic field sign without reference phase conditions, allows the receiving end to move over a large range, expands the measurement range, and meets the precise measurement requirements of indoor location information and real-time trajectory tracking.

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Abstract

The present invention relates to a positioning and tracking method and device based on a multi-channel, multi-frequency magnetic field. The method comprises: at an initial positioning point, a receiving end uses three receiving channels to receive magnetic field signals of three different frequencies and determine a relative phase reference value between the frequencies; at subsequent positioning points, the relative phase between the frequencies is calculated for the unsigned magnetic field of the three frequencies in each receiving channel. Based on the relative phase reference value between the frequencies in that channel, the relative relationship between the signs of the three frequencies is determined to obtain two groups of signed magnetic fields with three frequencies; the three receiving channels are combined to obtain a total of eight groups of signed magnetic fields with three frequencies; the eight groups of signed magnetic fields are calculated separately to obtain eight candidate pose data; the eight candidate pose data at the current positioning point are compared with the pose data at the previous positioning point, and the pose data with the smallest difference is determined as the pose data for the current positioning point. The present invention implements electromagnetic positioning and tracking by confirming the sign of the magnetic field without a reference phase.
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Description

Technical Field

[0001] The present invention belongs to the technical field of electromagnetic positioning, and in particular relates to a positioning and tracking method and device based on multi-channel and multi-frequency magnetic fields. Background Art

[0002] Electromagnetic positioning uses electromagnetic fields to determine the position and posture of a target object. It is widely used in fields such as virtual reality, medical navigation, biomechanics, and motion analysis. It not only determines the target's position but also its angular posture. Its key advantages are high accuracy and freedom from line-of-sight obstructions.

[0003] When performing positioning, existing devices need to connect the transmitting channel and the receiving channel to determine the reference phase, thereby determining the magnetic field sign to calculate the positioning result. The disadvantage of this method is that the receiving end cannot move over a large range and the measurement range is small, which makes it inconvenient to use in the field of precise measurement of indoor position information and real-time trajectory tracking information. Summary of the Invention

[0004] In view of the above analysis, the present invention aims to disclose a positioning and tracking method and device based on multi-channel and multi-frequency magnetic fields, which solves the problem of confirming the magnetic field sign under the condition of no reference phase and realizes electromagnetic positioning and tracking.

[0005] The present invention discloses a positioning and tracking method based on a multi-channel and multi-frequency magnetic field, comprising:

[0006] At the initial positioning point where the posture data is known, the receiving end uses three receiving channels to receive magnetic field signals of three different frequencies and determines the relative phase reference value between the frequencies of each receiving channel;

[0007] At each subsequent positioning point, the receiving end calculates the relative phase between the three frequencies of the unsigned magnetic field of each receiving channel. Based on the relative phase reference value between the frequencies in the channel, the relative relationship between the signs of the three frequencies is determined to obtain two groups of signed magnetic fields with three frequencies. The three receiving channels are combined to obtain a total of eight groups of signed magnetic fields with three frequencies. The eight groups of signed magnetic fields are calculated separately to obtain eight candidate pose data.

[0008] The eight pose candidate data at the current positioning point are compared with the pose data at the previous positioning point, and the pose candidate data with the smallest difference is determined as the pose data of the current positioning point.

[0009] Furthermore, the three receiving channels of the receiving end respectively use three mutually orthogonal single-axis magnetic induction coils to receive three orthogonal magnetic field signals of three different frequencies sent by the transmitting end.

[0010] Furthermore, at the initial positioning point, the unsigned magnetic field of each of the three frequencies actually measured by the receiving end is combined with the magnetic field sign obtained by theoretical calculation based on the posture relationship between the transmitting end and the receiving end to determine the signed magnetic field of the three frequencies of each receiving channel; based on the signed magnetic fields of the three frequencies, the relative phase reference value between the frequencies of each receiving channel is determined.

[0011] Furthermore, the process of determining the relative phase reference value between frequencies includes the following steps:

[0012] 1) Determine the position data of the transmitter and the receiver at the initial positioning point;

[0013] 2) The three receiving channels of the receiving end receive the magnetic field signals of three different frequencies transmitted by the transmitting end and measure nine unsigned magnetic fields;

[0014] 3) Based on the posture data and the three frequency data, nine magnetic field signs are obtained by theoretical calculation;

[0015] 3) Combining the signs of the nine magnetic fields obtained by theoretical calculation with the nine unsigned magnetic fields obtained by measurement to obtain nine signed magnetic fields;

[0016] 4) Compare the three signed magnetic fields in each receiving channel respectively to determine the nine relative phase reference values ​​between the three magnetic field frequencies of the three receiving channels at the initial positioning point.

[0017] Furthermore, the relative phase reference value between frequencies The receiving end channel number i = 1, 2, 3; is the signed magnetic field phase of frequency numbered j and k in the initial positioning point channel i; j / k = 1, 2, 3.

[0018] Furthermore, when determining the relative relationship of the symbols of the three frequencies of each receiving channel,

[0019] Each receiving channel uses the magnetic field frequency with the largest amplitude among the three measured frequencies as the reference frequency, calculates the relative phases between the other two frequencies and the reference frequency, and then compares them with the corresponding relative phase reference values ​​between the other two frequencies and the reference frequency to determine the relative sign relationship of the three frequencies of each receiving channel.

[0020] Furthermore, the method for obtaining two groups of signed magnetic fields with three frequencies comprises the following steps:

[0021] 1) From the three unsigned magnetic fields obtained from each channel at the receiving end, the frequency with the largest magnetic field amplitude is determined as the reference frequency;

[0022] 2) Taking the phase of the reference frequency as the reference phase, calculate the phase difference between the phase of the other two frequency magnetic fields and the reference phase is the frequency number, i=1,2,3 is the channel number;

[0023] 3) The phase difference Relative phase reference value between corresponding frequencies A comparison is performed, and the magnetic field sign relationship between the other two frequencies of the channel and the frequency with the largest induced magnetic field is determined based on the comparison results; when the magnetic field sign of the frequency with the largest induced magnetic field is positive or negative, two groups of signed magnetic fields with three frequencies with different signs are obtained.

[0024] Furthermore, the phase difference Relative phase reference value between corresponding frequencies The comparison method is when When , it is determined that the magnetic field signs of the two frequency points numbered j and k in the channel are opposite; otherwise, it is determined that the magnetic field signs of the two frequency points numbered j and k in the channel are the same, and D is the preset angle threshold.

[0025] The present invention also discloses a positioning and tracking device for confirming magnetic field symbols based on the phase relationship between channels, comprising a transmitting end, a receiving end, and a tracking and processing end;

[0026] The transmitter is used to transmit three orthogonal magnetic field signals of three frequencies at a set location;

[0027] The receiving end is used to receive the three orthogonal magnetic field signals from the transmitting end and output unsigned magnetic field signals to the tracking processing end;

[0028] The tracking processing end is used to execute the positioning tracking method based on the multi-channel multi-frequency magnetic field as described in any one of claims 1 to 8 to perform positioning tracking of the receiving end.

[0029] Furthermore, the transmitting end includes three orthogonal transmitting coils, which use a frequency division transmission mode to send three orthogonal magnetic field signals of three different frequencies.

[0030] The present invention can achieve at least one of the following beneficial effects:

[0031] The invention eliminates the need for synchronization between the transmitting and receiving channels, eliminates the need for phase reference, and confirms the magnetic field sign to achieve electromagnetic positioning tracking. Furthermore, the receiving end can move over a wide range, thus enabling wide-range measurement. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] The accompanying drawings are only for the purpose of illustrating particular embodiments and are not to be considered limiting of the present invention. Like reference symbols denote like parts throughout the drawings.

[0033] Figure 1 Flowchart of a positioning and tracking method based on a multi-channel and multi-frequency magnetic field in an embodiment of the present invention;

[0034] Figure 2 Flowchart of a method for obtaining two groups of three-frequency signed magnetic fields in an embodiment of the present invention;

[0035] Figure 3 This is an example diagram of combining signed magnetic fields of receiving channels in an embodiment of the present invention;

[0036] Figure 4 is a flow chart of the positioning and tracking process in an embodiment of the present invention;

[0037] Figure 5 This is a schematic block diagram of a positioning and tracking device based on a multi-channel and multi-frequency magnetic field in an embodiment of the present invention. DETAILED DESCRIPTION

[0038] The preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, which constitute a part of this application and are used to illustrate the principles of the present invention together with the embodiments of the present invention.

[0039] One embodiment of the present invention discloses a positioning and tracking method based on a multi-channel and multi-frequency magnetic field, such as Figure 1 Shown, including:

[0040] Step S1: At the initial positioning point where the posture data is known, the receiving end uses three receiving channels to receive magnetic field signals of three different frequencies, and determines the relative phase reference value between the frequencies of each receiving channel;

[0041] Step S2: At each subsequent positioning point, the receiving end calculates the relative phase between the frequencies for the unsigned magnetic fields of the three frequencies of each receiving channel. Based on the relative phase reference value between the frequencies in the channel, the relative relationship between the signs of the three frequencies is determined to obtain two groups of signed magnetic fields with three frequencies. The three receiving channels are combined to obtain a total of eight groups of signed magnetic fields with three frequencies. The eight groups of signed magnetic fields are calculated separately to obtain eight candidate pose data.

[0042] Step S3: Compare the eight pose candidate data at the current positioning point with the pose data at the previous positioning point, and determine the pose candidate data with the smallest difference as the pose data of the current positioning point.

[0043] That is, at the second positioning point after the initial positioning point, eight pose candidates are calculated based on the eight groups of three-frequency signed magnetic fields from the three receiving channels of the receiver. Each group of signed magnetic fields can be used to calculate a corresponding pose candidate. The eight pose candidates at the second positioning point are compared with the pose data of the initial positioning point, and the pose candidate with the smallest difference is determined as the pose data of the second positioning point. This process is repeated in this way to obtain the pose data of the receiver at all positioning points, thus achieving positioning and tracking of the receiver.

[0044] Specifically, in order to enable the receiving end moving in the magnetic field to sense the magnetic field signal in any posture, the three receiving channels of the receiving end in this embodiment respectively use three mutually orthogonal single-axis magnetic induction coils to receive three orthogonal magnetic field signals of three different frequencies sent by the transmitting end;

[0045] The transmitter is fixed in position and includes three mutually orthogonal magnetic field generating coils. It uses a frequency division transmission mode to send three orthogonal magnetic field signals of three different frequencies f1, f2 and f3.

[0046] Specifically, the magnetic field signal induced by the uniaxial magnetic induction coil at the receiving end is an unsigned magnetic field signal. In step S1, at the initial positioning point, the unsigned magnetic field actually measured by the receiving end is combined with the magnetic field sign calculated based on the pose relationship between the transmitting and receiving ends to determine the measured signed magnetic field for each receiving channel. The relative phase between different frequencies in a receiving channel is determined based on the signed magnetic field.

[0047] More specifically, the process of determining the relative phase between different magnetic field frequencies includes the following steps:

[0048] 1) Determine the position data of the transmitter and the receiver at the initial positioning point;

[0049] Mount the transmitter so that its magnetic field signal covers the receiver's motion range. Place the receiver in the magnetic field at a preset position. Determine the receiver's position data, including its three-axis position data in the magnetic field coordinate system and its three-axis attitude data, including azimuth, pitch, and roll. For example, [3,0,0,90,0,0].

[0050] 2) The three receiving channels of the receiving end receive the magnetic field signals of three different frequencies transmitted by the transmitting end and measure nine unsigned magnetic fields;

[0051] 3) Based on the posture data and the three frequency data, nine magnetic field signs are obtained by theoretical calculation;

[0052] The sign of the magnetic field induced by the uniaxial magnetic induction coil in the spatial magnetic field, which is determined according to the known position and posture in the magnetic field coordinate system, can be achieved using any existing technology in the field and applied to this embodiment without affecting the scope of protection of the present invention.

[0053] 3) Combining the signs of the nine magnetic fields obtained by theoretical calculation with the nine unsigned magnetic fields obtained by measurement to obtain nine signed magnetic fields;

[0054] 4) Compare the three signed magnetic fields in each receiving channel respectively to determine the nine relative phase reference values ​​between the three magnetic field frequencies of the three receiving channels at the initial positioning point.

[0055] Specifically, the relative phase reference value between frequencies The receiving end channel number i = 1, 2, 3; is the signed magnetic field phase of frequency numbered j and k in the initial positioning point channel i; j / k = 1, 2, 3.

[0056] That is, according to the phase relationship formula, the three frequencies in the three channels can be determined to include The phase relationship between 9 different frequencies including.

[0057] Specifically, in step S2, when determining the relative relationship between the signs of the three frequencies of each receiving channel, each receiving channel uses the magnetic field frequency with the largest amplitude in the magnetic field signals of the three frequencies measured as the reference frequency, and calculates the relative phases of the other two frequencies and the reference frequency; then compares them with the corresponding relative phase reference values ​​between the other two frequencies and the reference frequency to determine the relative relationship between the signs of the three frequencies of each receiving channel.

[0058] Specifically, in step S2, two groups of three-frequency signed magnetic field methods are obtained, such as Figure 2 As shown, the following steps are included:

[0059] 1) From the three frequencies of unsigned magnetic field obtained from each channel at the receiving end, determine the frequency with the largest magnetic field amplitude: f1, f2 or f3.

[0060] 2) Taking the phase of the induced magnetic field of this frequency as the reference phase, calculate the phase difference between the phases of the magnetic fields of the other two frequencies and the reference phase is the frequency number, i=1,2,3 is the channel number;

[0061] When the frequency of the induced magnetic field is the largest, calculate the phase difference between frequency f1 and frequencies f2 and f3.

[0062] When the frequency of the induced magnetic field is the largest, calculate the phase difference between frequency f2 and frequencies f1 and f3.

[0063] When the frequency of the induced magnetic field is the largest, calculate the phase difference between frequency f3 and frequencies f1 and f2.

[0064] is the unsigned phase of frequencies f1, f2, and f3 in channel i.

[0065] 3) The phase difference The corresponding relative phase A comparison is performed, and the magnetic field sign relationship between the other two frequencies of the channel and the frequency with the largest induced magnetic field is determined based on the comparison results; when the magnetic field sign of the frequency with the largest induced magnetic field is positive or negative, two groups of signed magnetic fields with three frequencies with different signs are obtained.

[0066] Specifically, the comparison method is when When , it is determined that the magnetic fields of the two frequency points in the channel are in opposite phases, otherwise it is determined that the magnetic fields of the two frequency points numbered j and k in the channel have the same signs, and D is the preset angle threshold.

[0067] At non-initial positioning points, the receiver's attitude is uncertain, so the sign of the measured maximum-amplitude magnetic field is also uncertain, including both positive and negative conditions. Therefore, each receiving channel obtains one set of signed magnetic fields for three frequencies when the sign of the maximum-amplitude magnetic field is positive, and another set of signed magnetic fields for three frequencies when the sign of the maximum-amplitude magnetic field is negative, for a total of two sets of signed measured magnetic fields for three frequencies.

[0068] For example, the frequency with the largest induced magnetic field in receiving channel 1 is f1;

[0069] Then, the phase difference between the calculated frequency f1 and the frequencies f2 and f3 is

[0070] Then, judge If yes, the sign of the magnetic field at frequency f2 is opposite to that of the magnetic field at frequency f1; if no, the sign of the magnetic field at frequency f2 is the same as that of the magnetic field at frequency f1;

[0071] judge If yes, the sign of the magnetic field at frequency f3 is opposite to the sign of the magnetic field at frequency f1; if no, the sign of the magnetic field at frequency f3 is the same as the sign of the magnetic field at frequency f1.

[0072] When the signs of the magnetic field at frequency f1 are respectively positive, two sets of signed measured magnetic fields at frequencies f1, f2, and f3 are obtained;

[0073] When the signs of the magnetic field at the frequency f1 are respectively negative, two sets of signed measured magnetic fields at the frequencies f1, f2, and f3 are obtained.

[0074] The preset angle threshold D may be set according to actual conditions including hardware processing accuracy, and is preferably in the range of 30° to 60°.

[0075] Each receiving channel obtains 2 groups of 3-frequency signed magnetic fields; the magnetic fields in the 3 receiving channels are combined to obtain 2 3 = 8 groups of signed magnetic fields with 3 frequencies;

[0076] like Figure 3 The figure shows an example of combining two groups of three-frequency signed magnetic fields per receive channel to generate eight groups of signed magnetic fields. In the figure, "+" and "-" represent the signs of the magnetic fields. The order of each frequency group is f1, f2, and f3. For example, in group 1, f1 is "+", f2 is "-", and f3 is "+".

[0077] Using these 8 groups of signed magnetic fields with 3 frequencies and the previous pose data as the initial value, the position and pose of the receiving end are calculated respectively using the Newton iteration method to obtain 8 pose candidate data.

[0078] Since only one of the eight pose candidate data is calculated by a magnetic field with completely correct signs, and the receiving end cannot undergo sudden changes during movement, in step S3, the eight pose candidate data at the current positioning point are compared with the pose data at the previous positioning point, and the pose candidate data with the smallest difference is determined as the pose data of the current positioning point. Similarly, the pose data of the receiving end at all positioning points after the initial positioning point are obtained to achieve positioning tracking of the receiving end. The specific positioning tracking process is as follows: Figure 4 shown.

[0079] In summary, in this embodiment of the present invention, the transmitting and receiving channels can be synchronized without a wire connection or phase reference to confirm the magnetic field sign and achieve electromagnetic positioning tracking. Furthermore, the receiving end can move over a wide range, thus enabling wide-range measurement.

[0080] Another embodiment of the present invention discloses a positioning tracking device based on a multi-channel multi-frequency magnetic field, such as Figure 5 Shown, including:

[0081] Including transmitting end, receiving end and tracking processing end;

[0082] The transmitter is used to transmit three orthogonal magnetic field signals of three frequencies at a set location;

[0083] The receiving end is used to receive the three orthogonal magnetic field signals from the transmitting end and output unsigned magnetic field signals to the tracking processing end;

[0084] The tracking processing end is used to execute the positioning tracking method based on the multi-channel multi-frequency magnetic field as described in the previous embodiment to perform positioning tracking of the receiving end.

[0085] Specifically, the transmitting end includes three orthogonal transmitting coils, which use a frequency division transmission mode to send three orthogonal magnetic field signals of three different frequencies.

[0086] The specific details and beneficial effects of this embodiment are the same as those of the previous embodiment, please refer to, and will not be described in detail here.

[0087] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by any technician familiar with this technical field within the technical scope disclosed by the present invention should be covered by the scope of protection of the present invention.

Claims

1. A positioning and tracking method based on multi-channel and multi-frequency magnetic fields, characterized in that: include: At the initial positioning point where the posture data is known, the receiving end uses three receiving channels to receive magnetic field signals of three different frequencies and determines the relative phase reference value between the frequencies of each receiving channel; At each subsequent positioning point, the receiving end calculates the relative phase between the three frequencies of the unsigned magnetic field of each receiving channel. Based on the relative phase reference value between the frequencies in the receiving channel, the relative relationship between the signs of the three frequencies is determined to obtain two groups of signed magnetic fields with three frequencies. The three receiving channels are combined to obtain a total of eight groups of signed magnetic fields with three frequencies. The eight groups of signed magnetic fields are calculated separately to obtain eight candidate pose data. Compare the eight pose candidate data at the current positioning point with the pose data at the previous positioning point, and determine the pose candidate data with the smallest difference as the pose data of the current positioning point; At the initial positioning point, the unsigned magnetic field of each of the three frequencies measured by the receiving end is combined with the magnetic field sign obtained by theoretical calculation based on the posture data of the transmitting end and the receiving end to determine the signed magnetic field of the three frequencies of each receiving channel; based on the signed magnetic field of the three frequencies, the relative phase reference value between the frequencies of each receiving channel is determined; The process of determining the relative phase reference value between frequencies includes the following steps: 1) Determine the pose data of the transmitter and the receiver at the initial positioning point; 2) The three receiving channels of the receiving end receive the magnetic field signals of three different frequencies transmitted by the transmitting end and measure nine unsigned magnetic fields; 3) Based on the posture data and the three frequencies, the nine magnetic field signs are theoretically calculated; 4) Combining the signs of the nine magnetic fields obtained by theoretical calculation with the nine unsigned magnetic fields obtained by measurement, nine signed magnetic fields are obtained; 5) Compare the three signed magnetic fields in each receiving channel respectively to determine the nine relative phase reference values ​​between the three magnetic field frequencies of the three receiving channels at the initial positioning point; When determining the relative relationship of the symbols of the three frequencies of each receiving channel, Each receiving channel uses the induced magnetic field frequency in the measured magnetic field signal of the three frequencies as the reference frequency, calculates the relative phases of the other two frequencies and the reference frequency; then compares them with the corresponding relative phase reference values ​​between the other two frequencies and the reference frequency to determine the relative relationship of the signs of the three frequencies of each receiving channel.

2. The positioning tracking method according to claim 1, characterized in that: The three receiving channels of the receiving end respectively use three mutually orthogonal single-axis magnetic induction coils to receive three orthogonal magnetic field signals of three different frequencies sent by the transmitting end.

3. The positioning tracking method according to claim 1, wherein: The relative phase reference value between frequencies ; The receiving channel number i=1,2,3; 、 is the signed magnetic field phase of frequencies j and k in channel i at the initial positioning point; j / k=1,2,3.

4. The positioning tracking method according to claim 1, wherein: The method for obtaining two groups of signed magnetic fields with three frequencies comprises the following steps: 1) From the three frequencies of unsigned magnetic field obtained from each receiving channel at the receiving end, determine the frequency with the largest induced magnetic field as the reference frequency; 2) Taking the phase of the reference frequency as the reference phase, calculate the phase difference between the phases of the other two frequency magnetic fields and the reference phase , j / k=1,2,3 are frequency numbers, i=1,2,3 are receiving channel numbers; 3) The phase difference Relative phase reference value between corresponding frequencies A comparison is performed, and the magnetic field sign relationship between the other two frequencies of the receiving channel and the frequency with the largest induced magnetic field is determined based on the comparison results; when the magnetic field sign of the frequency with the largest induced magnetic field is positive or negative, two groups of signed magnetic fields with three frequencies with different signs are obtained.

5. The positioning tracking method according to claim 4, characterized in that: Phase difference Relative phase reference value between corresponding frequencies The comparison method is ;when When , it is determined that the magnetic field signs of the two frequency points numbered j and k in the receiving channel are opposite; otherwise, it is determined that the magnetic field signs of the two frequency points numbered j and k in the receiving channel are the same. is the preset angle threshold.

6. A positioning tracking device for confirming the magnetic field sign based on the phase relationship between channels, characterized in that: Including transmitting end, receiving end and tracking processing end; The transmitter is used to transmit three orthogonal magnetic field signals of three frequencies at a fixed position; The receiving end is used to receive the three orthogonal magnetic field signals from the transmitting end and output unsigned magnetic field signals to the tracking processing end; The tracking processing end is used to execute the positioning tracking method based on the multi-channel multi-frequency magnetic field as described in any one of claims 1 to 5 to perform positioning tracking of the receiving end.

7. The positioning tracking device according to claim 6, characterized in that: The transmitter includes three orthogonal transmitting coils, which use a frequency division transmission mode to send three orthogonal magnetic field signals of three different frequencies.

Citation Information

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