CN116106638A - Long-baseline strong electromagnetic pulse anti-interference positioning method and system - Google Patents
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Abstract
The invention provides a long baseline strong electromagnetic pulse anti-interference positioning method, which comprises the following steps: acquiring position information of all sensors, and acquiring arrival time information of effective electromagnetic pulse signals acquired by all sensors; performing time correlation analysis and waveform correlation analysis of electromagnetic pulse signals according to the arrival time information, eliminating interference signals, and completing event identity judgment; constructing a time difference positioning mathematical model based on a time difference measurement equation and an optimization theory according to the sensor position information of the same observed event waveform; and obtaining optimal position information of the electromagnetic pulse signal source according to the enhanced Marquardt algorithm. The long baseline strong electromagnetic pulse anti-interference positioning method and the system can realize high-precision detection and positioning of the strong electromagnetic pulse.
Description
Technical Field
The invention relates to the technical field of wireless positioning, in particular to a long baseline strong electromagnetic pulse anti-interference positioning method, a system, electronic equipment and a storage medium.
Background
In the prior art, the electromagnetic pulse detection positioning system receives electromagnetic pulse signals by utilizing a plurality of sensors, transmits data to a processing center in real time, and then realizes positioning of an electromagnetic pulse signal source through a processing center positioning algorithm. Through the electromagnetic pulse detection positioning system, information such as the position and the occurrence time of an electromagnetic pulse signal source can be rapidly obtained in real time, and important support is provided for electromagnetic pulse event early warning. The performance of the electromagnetic pulse detection positioning system is mainly measured by positioning accuracy, and the positioning accuracy is determined by the adopted positioning algorithm.
At present, a large number of lightning locating systems are deployed at home and abroad, the existing systems mainly detect at short distance, and the distance for arranging the sensors is in the order of ten kilometers to hundred kilometers. The adopted positioning system is mainly based on a time difference positioning (TDOA) principle, the positioning algorithm is mainly a traditional Chan algorithm, a Fang algorithm and the like, and in recent years, a grid search algorithm is also adopted. However, in the existing algorithms, although the conventional algorithms such as Chan can obtain higher positioning accuracy in short-distance detection, errors are large in non-line-of-sight propagation, and the calculation efficiency of the grid search positioning algorithm is greatly reduced along with the increase of the grid number when the detection area is large.
The events such as super strong thunder and lightning can generate strong electromagnetic pulse signals, and the electric field amplitude is large, so that the events are easy to exceed the dynamic range of a sensor and cannot be positioned when the traditional short baseline detection positioning system is adopted. On the other hand, with the rapid development of industry, the frequently existing electromagnetic interference signals may cause "false signals" to be included in a real event, which seriously affects the normal use of the electromagnetic pulse detection positioning system, and causes the positioning accuracy to be drastically reduced or even not to be positioned. Sources of interference include lightning discharges, electrical machinery, electrical electronics, power transmission lines or internal combustion engine ignition, and the like.
Therefore, the existing positioning system and algorithm have certain defects when detecting and positioning strong electromagnetic pulses.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a long baseline strong electromagnetic pulse anti-interference positioning method and a system, which can realize high-precision detection and positioning of strong electromagnetic pulses.
In order to achieve the above purpose, the invention provides a long baseline strong electromagnetic pulse anti-interference positioning method, which comprises the following steps:
acquiring position information of all sensors, and acquiring arrival time information of effective electromagnetic pulse signals acquired by all sensors;
performing time correlation analysis and waveform correlation analysis of electromagnetic pulse signals according to the arrival time information, eliminating interference signals, and completing event identity judgment;
constructing a time difference positioning mathematical model based on a time difference measurement equation and an optimization theory according to the sensor position information of the same observed event waveform;
and obtaining optimal position information of the electromagnetic pulse signal source according to the enhanced Marquardt algorithm.
Further, in the step of performing time-dependent analysis and waveform-dependent analysis of electromagnetic pulse signals according to the arrival time information, excluding interference signals, completing event identity determination, comprising,
judging whether the time difference between the signals reaching different sensors exceeds the theoretical maximum transmission time difference, judging the signals exceeding theoretical expectation as interference and eliminating the interference;
if the time difference accords with the theoretically expected waveform, performing cross-correlation analysis, and judging the waveform correlation coefficient as interference and eliminating the waveform correlation coefficient when the waveform correlation coefficient is smaller than a set threshold value;
and screening all waveforms of the same event to finish event identity judgment.
Further, in the step of constructing a moveout localization mathematical model based on the moveout measurement equation and the optimization theory based on the sensor position information of the same observed event waveform, comprising,
the position of a sensor for observing the waveform of the same event is R i Wherein i=1, 2,3,.., M; m is the number of sensors observing the same event waveform;
extracting the electromagnetic pulse signal intensity obtained by each sensor, and determining the point position of the sensor with the maximum pulse peak intensity as a reference point R 1 ；
Calculating each sensor and reference point R 1 Time difference of arrival between
And converts the time difference into a distance difference +.>
Wherein c is the speed of light;
the position of the electromagnetic pulse signal source is set as
The i-th sensor position is +.>
, wherein />
Indicate latitude>
Representing longitude, the set of measurement equations is available as follows:
wherein ,
representing the ellipsoidal distance between any two points, calculated by using an ellipsoidal coordinate model discrete approximate calculation function, ++>
and />
Respectively represent the firstiAnd (b)jThe positions of the individual sensors;
based on nonlinear optimization theory, constructing a nonlinear function through the measurement equation set, wherein the nonlinear function comprises the following formula:
wherein ,
，/>
；
constructing an objective function
Converting the moveout localization problem into a problem of minimizing the objective function, i.e. +.>
。
Further, the step of obtaining the optimal position information of the electromagnetic pulse signal source according to the enhanced Marquardt algorithm further comprises the following steps of,
acquiring initial position information of the electromagnetic pulse signal source based on a Fang algorithm;
acquiring iteration initial parameters of Marquardt algorithm based on historical information
And growth factor->
；
Acquiring an objective function improvement quantity of each step of iterative process based on a Marquardt algorithm;
and ending the iterative process according to the set convergence threshold value, and obtaining the optimal signal source position information.
Further, the iterative initial parameters of the Marquardt algorithm are obtained based on the historical information
And growth factor->
Further comprising the steps of (1) and (2),
the Marquardt algorithm sets an initial parameter greater than 0
And a growth factor of greater than 1 +.>
；
For each iteration, the parameters of the Marquardt algorithm are as follows
；
Observing by adopting a short baseline detection network and a long baseline detection network to obtain effective historical events, taking position information obtained by the short baseline detection network as a reference value, debugging parameters of a Marquardt algorithm used by the long baseline detection network until the comprehensive performance is optimal, and determining
and />
Is a function of the empirical value of (a).
Further, the step of obtaining the improvement of the objective function of each iteration process based on the Marquardt algorithm further comprises the steps of
The 1 st iteration uses the initial parameter +.>
Based on->
Calculate the matrix of the kth iteration +.>
, wherein ,/>
M is the number of equation of time difference measurement, n is the number of unknowns.
Further, the step of ending the iterative process according to the set convergence threshold to obtain the optimal signal source position information further comprises,
the improvement quantity of the objective function in the kth iteration process is calculated, and the calculation formula is as follows:
wherein ,
is an n-order identity matrix>
Is a positive real number, < >>
；
Optimizing the current position, wherein the calculation formula is as follows
。
In order to achieve the above object, the present invention further provides a long baseline strong electromagnetic pulse anti-interference positioning system, comprising,
the acquisition module is used for acquiring the position information of all the sensors in the detection network and the electromagnetic pulse signal information acquired by the sensors;
the interference processing module is used for eliminating interference signals, so that signals participating in positioning come from the same electromagnetic pulse event;
the algorithm enhancement module is used for acquiring an iteration initial value of the Marquardt algorithm based on the Fang algorithm and acquiring initial parameters and growth factors of the Marquardt algorithm based on the historical information;
and the optimal searching module is used for acquiring optimal position information of the electromagnetic pulse signal source by utilizing an enhanced Marquardt algorithm.
In order to achieve the above object, the present invention further provides an electronic device, including a memory and a processor, where the memory stores a program running on the processor, and the processor executes the steps of the long baseline strong electromagnetic pulse anti-interference positioning method when running the program.
In order to achieve the above object, the present invention further provides a computer readable storage medium having stored thereon computer instructions for executing the steps of the long baseline strong electromagnetic pulse anti-interference positioning method described above when the computer instructions are run.
The long baseline strong electromagnetic pulse anti-interference positioning method and system have the following beneficial effects:
on one hand, the influence of interference signals is eliminated by adding an interference processing module and an algorithm, and on the other hand, the optimal signal source position information is obtained by adopting a Marquardt algorithm fused with a Fang algorithm and historical information, so that the aims of simultaneously keeping high precision and fast convergence are fulfilled, and the robustness of a positioning algorithm is enhanced.
Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.
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The accompanying drawings are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate the invention and together with the embodiments of the invention, and do not limit the invention. In the drawings:
FIG. 1 is a flow chart of a long baseline strong electromagnetic pulse anti-interference positioning method according to an embodiment of the invention;
FIG. 2 is a flowchart of an enhanced Marquardt algorithm in accordance with an embodiment of the present invention;
FIG. 3 is a schematic diagram of a long baseline strong electromagnetic pulse anti-interference positioning system according to the present invention;
fig. 4 is a schematic structural view of an electronic device according to the present invention.
Detailed Description
The preferred embodiments of the present invention will be described below with reference to the accompanying drawings, it being understood that the preferred embodiments described herein are for illustration and explanation of the present invention only, and are not intended to limit the present invention.
Example 1
Fig. 1 is a flowchart of a long baseline strong electromagnetic pulse anti-interference positioning method according to the present invention, and the long baseline strong electromagnetic pulse anti-interference positioning method according to the present invention will be described in detail with reference to fig. 1.
In step 101, all sensor position information is acquired, and valid electromagnetic pulse signals acquired by all sensors are acquired, and then arrival time information is extracted from the signals.
Preferably, all sensor position information is acquired, S i (i=1, 2,3,., N), N being the number of all sensors in the observational network; acquiring effective electromagnetic pulse signals acquired by all sensors, extracting arrival time information of each sensor, and recording as t i 。
In this embodiment, in order to represent all the sensor positions in the observational network, the present invention adopts S i (i=1, 2,3,., N) to represent the location of the sensor, where N is the number of sensors; if a certain sensor collects effective electromagnetic pulse signals, the arrival time information of the signals is extracted and recorded as t i 。
In step 102, event identity determination is accomplished by excluding interfering signals through time correlation and waveform correlation.
Preferably, judging whether the time difference between the arrival of the signals at different sensors exceeds the theoretical maximum transmission time difference, and judging the signals exceeding theoretical expectation as interference and rejecting; if the time difference accords with the waveform expected by theory, further performing cross-correlation analysis, and judging the waveform as interference to be removed when the waveform correlation coefficient is smaller than a set threshold value; and screening all waveforms of the same event to finish event identity judgment.
In this embodiment, the waveform cross-correlation coefficient threshold is typically obtained through empirical statistics.
In step 103, a moveout location mathematical model is constructed based on the moveout measurement equation and the optimization theory.
Preferably, R is used i (i=1, 2,3,) M marks the sensors that acquired the same electromagnetic pulse event signal, M being the number of sensors that observe the same event waveform.
Extracting each sensorThe electromagnetic pulse signal intensity obtained by the device is determined to be a point position of a sensor with the maximum pulse peak intensity as a reference point, and is recorded as R 1 。
Calculating the time difference of arrival between each sensor and the reference point
And converting the time difference into a distance difference
Where c is the speed of light.
The position of the electromagnetic pulse signal source to be calculated is recorded as
The i-th sensor position is denoted +.>
The system of measurement equations is then obtained as follows:
calculating the ellipsoid distance between any two points by adopting an ellipsoid coordinate model two-point distance calculation discrete approximate calculation function
。
Based on nonlinear optimization theory, constructing a nonlinear function through a measurement equation set, wherein the nonlinear function is represented by the following formula:
wherein ,
，/>
。
constructing an objective function
Converting the moveout localization problem into a problem of minimizing the objective function, i.e. +.>
。
The above problem is a nonlinear least squares problem, and various solving algorithms have been developed.
In step 104, the enhanced Marquardt algorithm is used to calculate the optimal position information of the electromagnetic pulse signal source.
Preferably, to reduce the amount of calculation, the initial value is obtained based on the traditional TDOA algorithm, so that the comprehensive performance of the Marquardt algorithm is enhanced. Determining initial parameters of Marquardt algorithm based on historical information
And growth factor->
The robustness of the algorithm is further improved. And (5) performing iterative computation by using the enhanced Marquardt algorithm to obtain the optimal signal source position information.
Preferably, as shown in fig. 2, the step of "enhancing the Marquardt algorithm" may be specifically performed as:
s201: acquiring initial position information of a signal source based on a Fang algorithm;
s202: acquiring iteration initial parameters and growth factors of a Marquardt algorithm based on historical information;
s203: acquiring an objective function improvement quantity of each step of iterative process based on a Marquardt algorithm;
s204: and ending the iterative process according to the set convergence threshold value, and obtaining the optimal signal source position information.
The enhanced Marquardt algorithm provided by the invention adopts the traditional Fang algorithm to acquire the initial position on one hand, and acquires the experience initial parameters and the growth factors based on the historical information on the other hand, so that the positioning performance is more robust.
In this embodiment, step s201 specifically includes: the initial value is obtained by adopting the Fang algorithm, and the Fang algorithm is an optimal solution obtained by linearizing a hyperbolic observation equation, and is a time difference positioning method with the simplest principle and the fastest calculation speed. The initial value can be obtained rapidly by utilizing the Fang algorithm, so that the additional calculation amount is not increased greatly, and the convergence time of the nonlinear least square algorithm can be shortened.
In one embodiment, when the number of sensors is 3, the Fang algorithm is directly used for initial position calculation. When the number of the sensors is greater than 3, selecting 3 sensors with strongest signals, and then performing initial position calculation by using a Fang algorithm.
In the embodiment, the target position is assumed to be [ ] according to the time difference hyperbola positioning modelx,y) The position of the ith sensor is%x i ,y i ) Can obtain the observation equation
The two sides of the Chinese herbal medicine are square and can be obtained>
, wherein />
. Then introducing the time difference measurement value to obtain a nonlinear time difference positioning equation set:
from the above equation, only 3 sensors are needed to realize the two-dimensional position location of the target. In order to solve the nonlinear equation set, linearization processing can be performed on the nonlinear equation set. Will calculate
Is unfolded and simply processed to obtain
Will be%x,y,R 1 ) As an unknown, this equation is a system of linear equations. The Fang algorithm further simplifies the processing based on the above, and the specific method is as follows:
the coordinates of the three sensors are reset to be (0, 0),x 2 ,0)，(x 3 ,y 3 ) On the coordinates, there are
，/>
Substituting it into the above to obtain
The above two simple processes can be eliminatedR 1 Obtaining a simplified linear relation
Finally, utilize
The target position can be solvedx,y). Note that the solutionxOr (b)yTwo values may be obtained in the process of (a), and the correct value may be determined using a priori information.
In this embodiment, step s202 specifically includes:
for each iteration, the parameters of the Marquardt algorithm are
，/>
If the value is too small, the searching direction cannot be ensured to be the descending direction; if->
If the value is too large, the convergence speed is obviously slowed down. Thus initial parameters +.>
Growth factor->
These two parametersThe setting of the number has a significant impact on the performance of the algorithm.
In the embodiment, reasonable sensor network applicable to the distributed sensor network is obtained through early test analysis
and />
Is a function of the empirical value of (a).
In this embodiment, an existing short baseline detection network and the long baseline detection network are used to observe synchronously and independently, a batch of history events are obtained, the position information obtained by the short baseline detection network is used as a true value, the parameters of the Marquardt algorithm used by the long baseline detection network are debugged, and the determination is made until the comprehensive performance is optimal
and />
Is a function of the empirical value of (a).
In this embodiment, step s203 in the algorithm specifically includes:
order the
The 1 st iteration uses the initial parameter +.>
Based on->
Calculate the matrix of the kth iteration +.>
, wherein ,/>
M is the number of equation of time difference measurement, n is the number of unknowns. If the position information to be calculated includes only longitude and latitude information, n=2.
In this embodiment, step s204 in the algorithm specifically includes:
the improvement quantity of the objective function in the kth iteration process is calculated, and the calculation formula is as follows:
wherein ,
is an n-order identity matrix. Optimizing the current position, wherein the calculation formula is +.>
。
In this embodiment, the method further includes step s205:
based on optimized location
Calculating the optimized objective function value +.>
Comparison->
And->
Is of a size of (a) and (b).
In this embodiment, the method further includes step s206:
setting a convergence threshold
Calculate->
The method comprises the steps of carrying out a first treatment on the surface of the When->
In the case of->
Stopping the operation to obtain an optimal solution +.>
Whether or notThe process returns to step s203 to continue the next iteration calculation.
When (when)
In the case of->
Stopping the operation to obtain an optimal solution +.>
Otherwise let->
Returning to step s204, the iterative calculation of the present round is performed again.
Through the steps, the optimal position of the signal source can be obtained.
The long baseline strong electromagnetic pulse anti-interference positioning method provided by the invention is used for supporting long baseline electromagnetic pulse signal source positioning, integrates the traditional TDOA algorithm and the optimized intelligent search algorithm, and provides a method with both accuracy and robustness for long baseline time difference positioning.
Example 2
Fig. 3 is a schematic diagram of a long baseline strong electromagnetic pulse anti-interference positioning system according to the present invention, as shown in fig. 3, the long baseline strong electromagnetic pulse anti-interference positioning system of the present invention includes an acquisition module 301, an interference processing module 302, an algorithm enhancing module 303, and an optimal searching module 304.
The acquisition module 301 is configured to acquire location information of all sensors in the detection network, and electromagnetic pulse signal information acquired by each sensor.
The interference processing module 302 is configured to reject the interference signal, and ensure that the signals involved in positioning all come from the same electromagnetic pulse event.
The algorithm enhancement module 303 is configured to obtain, on the one hand, the iteration initial value of the Marquardt algorithm based on the Fang algorithm, and on the other hand, the initial parameter and the growth factor of the Marquardt algorithm based on the history information.
An optimal search module 304 for resolving electromagnetic pulse signal source optimal position information using an enhanced Marquardt algorithm.
Example 3
Fig. 4 is a schematic structural diagram of an electronic device according to the present invention, as shown in fig. 4, the electronic device includes: a processor 401, a memory 402, a communication bus 403 and a communication interface 404, wherein,
the processor 401 is configured to invoke logic instructions in the memory 402 to perform a long baseline strong electromagnetic pulse anti-interference positioning method, the method comprising: acquiring position information of all sensors, acquiring effective electromagnetic pulse signals acquired by all sensors, and extracting arrival time information from the signals; removing interference signals through time correlation and waveform correlation, and completing event identity judgment; constructing a time difference positioning mathematical model based on a time difference measurement equation and an optimization theory; and solving the optimal position information of the electromagnetic pulse signal source by adopting an enhanced Marquardt algorithm.
The logic instructions in memory 402 may be implemented in the form of software modules or software products. The software modules or products may be stored on various storage media such as optical discs, U-discs, removable hard disks, etc. that can be used to store program code. Software modules stored on the storage medium may invoke all or part of the steps of the methods described in all embodiments of the present invention through a single computer device.
Communication bus 403 is used to accomplish data or instruction transfer between processor 401, memory 402, and communication interface 404. The communication interface 404 is used for information transfer between the electronic device and other associated devices, including electromagnetic pulse information sent by the sensor, and the like. The invention also provides a computer readable storage medium, on which computer instructions are stored, the computer instructions execute the steps of the long baseline strong electromagnetic pulse anti-interference positioning method, and the long baseline strong electromagnetic pulse anti-interference positioning method is referred to the description of the previous section and is not repeated.
Those of ordinary skill in the art will appreciate that: the foregoing description is only a preferred embodiment of the present invention, and the present invention is not limited thereto, but it is to be understood that modifications and equivalents of some of the technical features described in the foregoing embodiments may be made by those skilled in the art, although the present invention has been described in detail with reference to the foregoing embodiments. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (10)
1. A long baseline strong electromagnetic pulse anti-interference positioning method comprises the following steps:
acquiring position information of all sensors, and acquiring arrival time information of effective electromagnetic pulse signals acquired by all sensors;
performing time correlation analysis and waveform correlation analysis of electromagnetic pulse signals according to the arrival time information, eliminating interference signals, and completing event identity judgment;
constructing a time difference positioning mathematical model based on a time difference measurement equation and an optimization theory according to the sensor position information of the same observed event waveform;
and obtaining optimal position information of the electromagnetic pulse signal source according to the enhanced Marquardt algorithm.
2. The method of claim 1, wherein the step of performing time-dependent analysis and waveform-dependent analysis of electromagnetic pulse signals based on the arrival time information, excluding interference signals, and performing event identity determination comprises,
judging whether the time difference between the signals reaching different sensors exceeds the theoretical maximum transmission time difference, judging the signals exceeding theoretical expectation as interference and eliminating the interference;
if the time difference accords with the theoretically expected waveform, performing cross-correlation analysis, and judging the waveform correlation coefficient as interference and eliminating the waveform correlation coefficient when the waveform correlation coefficient is smaller than a set threshold value;
and screening all waveforms of the same event to finish event identity judgment.
3. The method of claim 1, wherein in the step of constructing a time difference localization mathematical model based on a time difference measurement equation and an optimization theory based on sensor position information of the same observed event waveform,
the position of a sensor for observing the waveform of the same event is R i Wherein i=1, 2,3,; m is the number of sensors observing the same event waveform;
extracting the electromagnetic pulse signal intensity obtained by each sensor, and determining the point position of the sensor with the maximum pulse peak intensity as a reference point R 1 ；
Calculating each sensor and reference point R 1 Time difference of arrival between
And converting the time difference into a distance difference
Wherein c is the speed of light;
the position of the electromagnetic pulse signal source is set as
The i-th sensor position is +.>
, wherein />
Indicate latitude>
Representing longitude, the set of measurement equations is available as follows:
wherein ,
representing the ellipsoidal distance between any two pointsLeaving, calculating by using an ellipsoidal coordinate model discrete approximate calculation function>
and />
Respectively represent the firstiAnd (b)jThe positions of the individual sensors;
based on nonlinear optimization theory, constructing a nonlinear function through the measurement equation set, wherein the nonlinear function comprises the following formula:
wherein ,
，/>
；/>
constructing an objective function
Converting the moveout location problem to a problem of minimizing the objective function, i.e
。
4. The method for locating an electromagnetic pulse with long baseline and strong electromagnetic pulse according to claim 1, wherein the step of obtaining the optimal position information of the electromagnetic pulse signal source according to the enhanced Marquardt algorithm further comprises,
acquiring initial position information of the electromagnetic pulse signal source based on a Fang algorithm;
acquiring iteration initial parameters of Marquardt algorithm based on historical information
And increaseLong factor->
；
Acquiring an objective function improvement quantity of each step of iterative process based on a Marquardt algorithm;
and ending the iterative process according to the set convergence threshold value, and obtaining the optimal signal source position information.
5. The method for locating long baseline strong electromagnetic pulse interference according to claim 4, wherein the iterative initial parameters of Marquardt algorithm are obtained based on historical information
And growth factor->
Further comprising the steps of (1) and (2),
the Marquardt algorithm sets an initial parameter greater than 0
And a growth factor of greater than 1 +.>
；
For each iteration, the parameters of the Marquardt algorithm are as follows
；
Observing by adopting a short baseline detection network and a long baseline detection network to obtain effective historical events, taking position information obtained by the short baseline detection network as a reference value, debugging parameters of a Marquardt algorithm used by the long baseline detection network until the comprehensive performance is optimal, and determining
and />
Is a function of the empirical value of (a).
6. The method for locating an interference-free position of a long baseline strong electromagnetic pulse according to claim 5, wherein said step of obtaining an improvement of an objective function of each iterative process based on a Marquardt algorithm further comprises the steps of
The 1 st iteration uses the initial parameter +.>
Based on->
Calculate the matrix of the kth iteration +.>
, wherein ,
m is the number of equation of time difference measurement, n is the number of unknowns.
7. The method for locating long baseline strong electromagnetic pulse interference according to claim 6, wherein said step of ending the iterative process according to the set convergence threshold to obtain the optimal signal source position information further comprises,
the improvement quantity of the objective function in the kth iteration process is calculated, and the calculation formula is as follows:
wherein ,
is an n-order identity matrix>
Is a positive real number, < >>
；
Optimizing the current position, wherein the calculation formula is as follows
。
8. A long baseline strong electromagnetic pulse anti-interference positioning system is characterized by comprising,
the acquisition module is used for acquiring the position information of all the sensors in the detection network and the electromagnetic pulse signal information acquired by the sensors;
the interference processing module is used for eliminating interference signals, so that signals participating in positioning come from the same electromagnetic pulse event;
the algorithm enhancement module is used for acquiring an iteration initial value of the Marquardt algorithm based on the Fang algorithm and acquiring initial parameters and growth factors of the Marquardt algorithm based on the historical information;
and the optimal searching module is used for acquiring optimal position information of the electromagnetic pulse signal source by utilizing an enhanced Marquardt algorithm.
9. An electronic device comprising a memory and a processor, the memory having stored thereon a program for execution on the processor, the processor executing the steps of the long baseline strong electromagnetic pulse anti-interference positioning method of any one of claims 1-7 when the program is executed.
10. A computer readable storage medium having stored thereon computer instructions which, when run, perform the steps of the long baseline strong electromagnetic pulse anti-interference positioning method according to any one of claims 1-7.
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