CN114866165A - Method for quickly measuring and acquiring multi-band indoor signal distribution field - Google Patents
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Abstract
The invention discloses a method for quickly measuring and acquiring a multi-band indoor signal distribution field. Step 1: an LFM signal source is arranged indoors; step 2: based on the LFM signal source in the step 1, utilizing receiving equipment to carry out drive test sampling; and step 3: determining the position of the receiver based on the drive test sampling result in the step 2; and 4, step 4: and (3) utilizing the receiver for determining the position in the step 3 to perform signal processing and output of the measurement result. The invention overcomes the problems of operation complexity, model universality and measurement accuracy.
Description
Technical Field
The invention belongs to the field of signal coverage measurement; in particular to a method for quickly measuring and acquiring a multi-band indoor signal distribution field.
Background
Currently, for the problem of signal coverage measurement, there are several solutions: 1) depending on the way in which the user actively reports to the mobile operator; 2) minimization of Drive Test (MDT) based on environmental electromagnetic Maps (REMs); 3) solutions based on ray tracing or ray launching. The scheme based on the active reporting of the user is out of the discussion range of the scheme due to low efficiency and low accuracy. The remaining two modes will be briefly described next.
1) Minimization of drive tests scheme based on environmental electromagnetic map
The basic principle of such a scheme is that the ue periodically reports its geographical location to the network operator during communication, and performs relevant measurements. The difference from the traditional drive test method and MDT is that the traditional solution uses base station based user equipment positioning (base station level); while absolute geographical location information (GPS level) is used in MDT.
In indoor environments, such solutions expose the main drawbacks: for one, GPS information is not available and base station based positioning is highly inaccurate. Due to the fact that obstacles in an indoor environment are densely distributed, an electromagnetic environment is complex, distortion of base stations and GPS signals is serious, errors of positioning results are extremely high, and the obstacles cannot be effectively used as references. In the environment of underground parking stations or subway stations, even GPS signals cannot be effectively received, so that the method has obvious defects. Secondly, due to the complex electromagnetic environment and the obvious multipath effect, a pseudo-blind area phenomenon with smaller signal receiving intensity can also occur at a plurality of positions which are not signal receiving blind areas due to the influence of multipath deep fading.
2) Scheme based on ray tracing equal prediction model
The scheme mainly adopts the modeling of the scene to be measured by the signal distribution field to obtain physical propagation information such as indoor obstacle distribution, wall surface size distribution, loss coefficients of all obstacle materials, indoor signal attenuation coefficients and the like. And simulating the physical propagation of the signal so as to obtain a simulation result of the signal receiving intensity of the whole scene. In operation, the propagation process of the signal is equivalent to ray, and physical properties such as ray reflection, refraction and scattering are mainly adopted, so that the method is called ray tracing.
Under the indoor actual measurement environment, the disadvantages of using the scheme are mainly shown as follows: firstly, the scene modeling needs to be accurately performed, different modeling needs to be performed for different scenes, and the parameter measurement process is very complex. Therefore, the scheme has no universality. Secondly, the calculation complexity is high, and in order to obtain an accurate result, the higher the number of ray tracing, the greater the accuracy, so that the requirement is often met by depending on extremely high calculation power.
Disclosure of Invention
The invention provides a method for quickly measuring and acquiring a multi-band indoor signal distribution field, which overcomes the problems of operation complexity, model universality and measurement accuracy and can quickly and accurately obtain a signal receiving intensity measurement result of a specified area.
The invention is realized by the following technical scheme:
a fast measurement and acquisition method for a multi-band indoor signal distribution field comprises the following steps:
step 1: an LFM signal source is arranged indoors;
step 2: based on the LFM signal source in the step 1, utilizing receiving equipment to carry out drive test sampling;
and step 3: determining the position of the receiver based on the drive test sampling result in the step 2;
and 4, step 4: and (3) utilizing the receiver for determining the position in the step 3 to perform signal processing and output of the measurement result.
Further, the step 1 specifically includes that the LFM signal source is composed of a radio frequency device for transmitting a chirp signal and a control upper computer; the signal source can continuously transmit the initial frequency f 1 A termination frequency of f 2 The mathematical expression of the LFM signal is:
where Re { } denotes a real part, and T is a pulse period.
Further, step 2 is specifically that the receiving device is composed of a receiver for receiving the radio frequency signal and an upper mechanism for storing the received signal; during reception, the device samples the received signal for at least more than one pulse period T
Sending the coordinate information to an upper computer for storage, recording the coordinate information x of the current position when the coordinate information x is stored by the upper computer, and combining the coordinate information x and the received signal of the point into a two-dimensional tuple
Stored in a database.
Further, step 3 specifically includes, in the process of determining the position by the receiver, turning on the signal source, moving the receiving device, and receiving the chirp signal at the same time;
the determined position scheme includes, but is not limited to, a pre-measured and calibrated sampled position recording scheme or ultra-wideband (UWB) based high precision indoor positioning.
Further, the step 4 specifically comprises the following steps,
step 4.1: preprocessing signals received by a receiver;
and 4.2: and carrying out interpolation recovery of the signal receiving intensity field on the preprocessed signals.
Further, said step 4.1, using fractional order Fourier transform to focus the LFM signal,
step 4.1.1: for received signal
Performing energy focusing in the corresponding optimal fractional Fourier transform domain;
step 4.1.2: collecting the energy of each multipath peak of the energy focusing, and searching and superposing the energy;
step 4.1.3: and taking the superposition value of the step 4.1.2 as a received signal energy value of the current position.
Further, the process of performing focusing peak positioning in the optimal fractional fourier transform domain in step 4.1.1 is specifically that a focusing peak searching method is adopted, including but not limited to a data size comparison method around a peak value and a zero-crossing counting method for performing binarization at a given threshold value;
the peak obtained by searching is converted into time domain amplitude according to the conversion relation between the time domain and the fractional domain:
wherein v is max For the coordinate position, X, of a peak value of the LFM signal transformation result in the optimal fractional domain pmax (ν max ) The magnitude of the peak in the fractional domain; n is the number of signal sampling data points, and sin () represents a sine function; a is a time domain amplitude value corresponding to the fractional domain peak value; p is a radical of max The optimal fractional order Fourier transform order corresponding to the transmitted LFM signal is obtained;
p max slope of FM frequency with LFM signal
The relationship between them is:
wherein, f 1 Is the initial frequency, f, at which the signal source can transmit continuously 2 Is the termination frequency that the signal source can continuously transmit; t is the pulse period; cot () is a cotangent function;
the time domain amplitudes of the peak values are superposed to be used as the current signal receiving intensity value s x And stores the value in a two-dimensional tuple (x, s) together with the position x ) And storing.
Further, the interpolation recovery process of step 4.2 is specifically to arrange the sample data of all sample points (1,2, 3.) in order, and represent the sample data as (X | y):
for unknown point position X * Its signal reception intensity value y * Mean value of predicted results of (y) () * |X * X, y) is obtained by the following equation:
wherein, k (X) * X) is the kernel function adopted at position X * And the result of the calculation at X,
is the observed noise of the environment, I is the identity matrix, () -1 Is the inversion operation of the matrix;
variance σ of prediction result for uncertainty of prediction 2 (y * |X * X, y) represents:
the invention has the beneficial effects that:
the invention provides a low-cost and flexibly-distributed indoor signal field measuring and acquiring method, which has the advantages of obvious flexibility and high efficiency compared with the traditional drive test and user reporting modes highly depending on professional skills.
The invention can effectively deal with the problem of measurement errors introduced by indoor complex electromagnetic environment, obtains smooth signal field distribution and has good resistance effect on indoor strong multipath effect.
The invention adopts a scheme combining sampling and prediction, can effectively reduce the distribution quantity of sampling nodes, improves the measurement efficiency and reduces the measurement time.
Drawings
FIG. 1 is a flow chart of the present invention.
Fig. 2 is a physical diagram of a transceiver assembly of the present invention, wherein (a) the transmitter is physically depicted and (b) the receiver is physically depicted.
Fig. 3 is a schematic diagram of an application scenario of the present invention.
Fig. 4 is a diagram of an actual test scenario of the present invention, wherein (a) the left-hand scenario of the gate (facing the gate) and (b) the right-hand scenario of the gate (facing the gate).
Fig. 5 is a block diagram of a transmitter used in the present invention.
Fig. 6 is a block diagram of a receiver used in the present invention.
Fig. 7 is a time domain waveform and fractional domain focusing result diagram of an actual received signal of the present invention, wherein (a) the time domain waveform diagram under the multipath effect, and (b) the optimal fractional domain focusing result diagram under the multipath effect.
Fig. 8 is a sample node distribution diagram for reconstruction, in which (a) a median filtered sample processing result diagram, and (b) a sample processing result diagram according to the present invention.
Fig. 9 is a comparison graph of the reconstruction results of the signal reception intensity field of the present invention, wherein (a) the median filtering reconstruction results are shown, and (b) the reconstruction results are shown.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Example 1
The working flow is shown in fig. 1, and a fast measurement and acquisition method of a multi-band indoor signal distribution field includes the following steps:
step 1: an LFM signal source is arranged indoors;
step 2: based on the LFM signal source in the step 1, utilizing receiving equipment to carry out drive test sampling;
and step 3: determining the position of the receiver based on the drive test sampling result in the step 2;
and 4, step 4: and (3) utilizing the receiver for determining the position in the step 3 to perform signal processing and output of the measurement result.
Further, the step 1 specifically includes that the LFM signal source is composed of a radio Frequency device for transmitting Linear Frequency Modulated (LFM) signals and a control upper computer; the signal source can continuously transmit the initial frequency f 1 A termination frequency of f 2 The mathematical expression of the LFM signal is:
where Re { } denotes a real part, and T is a pulse period.
In the actual test process, f is adjusted according to the signal field distribution test requirements of different frequency bands 1 And f 2 Thereby achieving the purpose of multi-band measurement; the placement of the signal source is determined by the actual need.
Further, step 2 is specifically that the receiving device is composed of a receiver for receiving the radio frequency signal and an upper mechanism for storing the received signal; during reception, the device samples the received signal for at least more than one pulse period T
Sending the coordinate information to an upper computer for storage, recording the coordinate information x of the current position when the coordinate information x is stored by the upper computer, and combining the coordinate information x and the received signal of the point into a two-dimensional tuple
Stored in a database.
Further, step 3 specifically includes, in the process of determining the position by the receiver, turning on the signal source, moving the receiving device, and receiving the chirp signal at the same time;
the determined location scheme includes, but is not limited to, a pre-measured and calibrated sampled location recording scheme or ultra-wideband UWB based high precision indoor positioning.
Further, the step 4 specifically comprises the following steps,
step 4.1: preprocessing signals received by a receiver;
step 4.2: and carrying out interpolation recovery of the received intensity field on the preprocessed signals.
Further, due to the complexity of the indoor electromagnetic environment, the effects of multipath are significant, and the signal may be enhanced or diminished at the receiving location depending on the relative size of the propagation path difference and wavelength between the multipath components. This causes a slight shift in the sampling point which results in a drastic change in the amplitude of the received signal. Therefore, the strength value of the direct sampling result of the received signal cannot be used as the signal receiving strength evaluation criterion of the current point, so that the received signal needs to be preprocessed;
said step 4.1, focusing of the LFM signal using a fractional fourier transform,
step 4.1.1: for received signal
Performing energy focusing in the corresponding optimal fractional Fourier transform domain, wherein the energy focusing is focusing peak/pulse;
step 4.1.2: collecting the energy of each multipath peak of the energy focusing, and searching and superposing the energy;
step 4.1.3: and taking the superposition value of the step 4.1.2 as a received signal energy value of the current position.
Further, the fractional fourier transform numerical calculation method adopted therein includes, but is not limited to, algorithms such as fractional fourier transform based on four-term weighting, fractional fourier transform based on eigenvalue decomposition, and closed-type fractional fourier transform. The process of performing the focusing peak positioning in the optimal fractional fourier transform domain in step 4.1.1 is specifically that a focusing peak searching method is adopted, including but not limited to a data size comparison method around a peak value (that is, a method of performing left and right adjacent position comparison of data points to position the peak value position by using the peak value as a highest point property in a local range); a zero-crossing counting method for binarization at a given threshold value; that is, a scheme of binarizing given data by 0-1 in accordance with a threshold value and then obtaining a peak position by recording a position where a zero point is crossed unidirectionally, and the like.
The peak obtained by searching is converted into time domain amplitude according to the conversion relation between the time domain and the fractional domain:
wherein, v max For the coordinate position, X, of a peak value of the LFM signal transformation result in the optimal fractional domain pmax (ν max ) Is the magnitude of the peak in the fractional domain; n is the number of signal sampling data points, and sin () represents a sine function; a is a time domain amplitude value corresponding to the fractional domain peak value; p is a radical of max The optimal fractional order Fourier transform order corresponding to the transmitted LFM signal is obtained;
p max slope of FM frequency with LFM signal
The relationship between them is:
wherein f is 1 Is the initial frequency, f, at which the signal source can transmit continuously 2 Is the termination frequency that the signal source can continuously transmit; t is the pulse period; cot () is a cotangent function;
the time domain amplitudes of the peak values are superposed to be used as the current signal receiving intensity value s x And stores the value in a two-dimensional tuple (x, s) together with the position x ) And storing.
Further, the interpolation recovery process of step 4.2 is specifically that the purpose of this step is to reduce the number of sampling points, and utilize a small number of sampling point results (x, s) x ) By means of a predictive modelThe signal reception strength predictions in the remaining ranges. And performing interpolation recovery of the received intensity field by adopting a Gaussian process regression model, wherein kernel functions adopted in the prediction process include, but are not limited to, various forms of rational secondary kernels, Gaussian kernels, Matern covariance functions and kernels formed by combining the kernel functions. The sample data for all sample points (1,2, 3.) are arranged in order and denoted as (X | y):
for unknown point position X * Its signal reception intensity value y * Mean value of predicted results of (y) () * |X * X, y) is obtained by the following equation:
wherein, k (X) * X) is the kernel function adopted at position X * And the result of the calculation at X,
is the observed noise of the environment, I is the identity matrix, () -1 Is the inversion operation of the matrix;
variance σ of prediction result for uncertainty of prediction 2 (y * |X * X, y) represents:
example 2
The demonstration verification scene is an indoor scene of 1018 rooms in the scientific park 2A of Harbin university of Industrial science, and the scene setting schematic diagram and the actual scene are respectively shown in FIG. 3 and FIG. 4.
In fig. 3, the area of the floor on the left side of the gate is about 25.2m 2 The area of the right side field is about 12.6m 2 . The transmitter site is placed on the desk to the right of the gate of figure 3, the receiverRandomly sampled in the scene. In order to artificially manufacture the communication blind area, the gate is closed during testing. Because the gate is made of metal, signals are greatly attenuated under the action of electromagnetic shielding when passing through the gate, and a communication blind area is formed on the other side of the gate. The specific test process is as follows: 1. the transmitter is fixed at the scene position shown in fig. 3 and then cyclically transmits a chirp (LFM) signal. 2. The receiver adopts a trolley to push random dispersion to carry out sparse sampling in a scene. And during sampling, recording the position information of the down-sampling and the linear frequency modulation signal data obtained by sampling, and storing the position information and the linear frequency modulation signal data into a preset data format after all the sampling is finished for later-stage processing. 3. And importing all the sampled data into a notebook computer, completing the whole subsequent signal processing process (mainly aiming at the multipath effect) with the assistance of Python and MATLAB, and reconstructing according to the discrete sampling result to obtain the signal distribution condition of the whole scene. The detailed transmitter and receiver construction, signal generation and acquisition, and data processing procedures will be described separately.
1. Transceiver composition and signal generation and acquisition process
The transceiver consists of a USRP-2920 device of National Instruments company which is connected with an upper computer (notebook computer) through an Ethernet port. The USRP is responsible for sending (receiving) linear frequency modulation signals, the upper computer plays the roles of parameter configuration, transceiving control and receiving data storage in the experimental process, and sends parameter setting and control commands to the USRP through the Ethernet port. During the experiment, the transmitter is fixed on the test bed and kept still. The receiver is placed on an experimental trolley with the length, width and height of 90cm, 70cm and 70cm respectively, and then the mobile measurement receives the transmitter signals at different positions in the test environment. And storing the received signal data information and the current receiving position into an upper computer, and performing a signal processing process after the reception is finished. The transceiver is constructed as shown in figure 2.
The parameter configuration of the transceiver radio signal is controlled by Labview software, and the structure of the transmitter is shown in figure 5. Wherein, the whole transmitter can be divided into a baseband Linear Frequency Modulation (LFM) signal generator and a Labview built-in LFM signal modulation methodThe radio frequency USRP interface module. The LFM signal is generated mainly by using the ramp signal generator in fig. 5. It receives four parameters, the number of samples, the start frequency, the end frequency and the type of linear sampling. It should be noted that in inputting the parameters, the value of the number of samples divided by the value of the duration is actually the sampling rate at which the LFM signal is sampled. This calculated sampling rate should be at least 5-10 times the input termination frequency in order for the transmitted sample to recover the waveform of the LFM signal. Assuming a starting frequency f 1 A termination frequency of f 2 The duration is T and the number of samples is n. The frequency modulation slope can be obtained
After the two signals are generated, the phases of the two signals which are multiplied as complex exponential signals are connected to the phase input end of the polar coordinate to complex number conversion module. In order to prevent overflow errors of the DSP in the USRP, the amplitude of the baseband complex signal should not exceed 1, so that the amplitude of the complex exponential signal is set to 1. After this polar to complex conversion, the signal is input to the interface module of the USRP. The USRP interface module mainly comprises four sub-modules: niUSRP Open Tx session. vi, niUSRP configuration signal. vi, niUSRP Write Tx data. vi, and niUSRP Close session. vi. Wherein, niUSRP Open Tx session. vi receives the device name parameter (mainly IP address of USRP), starts a transmission session niUSRP configuration signal. vi between the host and the USRP for signal transmission parameters and signal samples, receives parameters related to signal transmission, such as IQ symbol rate, carrier frequency, antenna name and antenna gain for transmission, from the input control of the front panel, and transmits the configuration parameters to the USRP. niUSRPWrite Tx data. vi accepts the LFM signal sample data previously generated and sends it to USRP. Vi ends the session after completing the data transfer between the host and USRP and reports errors that may occur. After completing the transmission of the configuration parameters and the signal samples, the USRP performs configuration according to the parameters to process the baseband signals through the radio frequency link and then transmits the baseband signals out of the antenna.
The receiver architecture is shown in fig. 6. The receiver part mainly comprises five sub-modules corresponding to a transmitting terminal: niUSRP Open Rx session. vi, niUSRP configuration signal. vi, niUSRPFetch Rx data. vi, niusrpabort. vi, and niUSRP Close session. vi. And the niUSRP Open Rx session.vi receives the device name parameter as the corresponding transmitter subvi and starts a transmission session between the USRP and the host for receiving the signal parameter and the sample data of the received signal. niUSRP configuration signal.vi is to obtain corresponding IQ symbol rate, carrier frequency, and antenna name and antenna gain parameters for receiving from the input control of the front panel and transmit these parameters to the USRP for configuring the receiving hardware. niUSRPFetch Rx data. vi receives the number of samples specified by the corresponding input control in a front panel and transmits a number of baseband symbols equal to the specified number from USRP to the host. niusrpabort. vi is used to clear the buffered data in preparation for receiving the next data. Vi Close session of USRP and host and report possible errors. And finally, the waveform chart module circularly displays the acquired IQ two-path baseband signal waveform each time.
The parameters employed by the transceiver are as follows. The LFM signal of the transmitter has the parameters of 2048 samples, 1kHz starting frequency, 2kHz ending frequency and 2 multiplied by 10 sampling rate 4 Hz, frequency modulation slope 19540.8Hz/s, IQ symbol rate 400k symbols/s, carrier frequency 915MHz, and transmitting antenna gain 20 dB. The receiver parameter settings correspond to the transmitter and the antenna gain is set to 20 dB. The number of samples received each time in the sampling test process is 2048.
2. Data processing procedure
The received data is firstly subjected to fractional Fourier transform processing, so that the influence caused by multipath effect can be effectively resisted. By utilizing the focalization of the fractional Fourier transform to the linear frequency modulation signal, a peak with good focalization can be obtained in the optimal fractional Fourier transform domain, and the amplitude of the peak is measured to obtain accurate signal intensity information of the receiving point position.
Fig. 7 shows the time-domain waveform of the actual received signal and its focusing result in the optimal fractional domain. The focusing effect of the fractional fourier transform on the chirp signal is evident from fig. 7. When the signal acquisition point is located in a region where the multipath effect is strong, more than one focusing spike will occur in the optimal fractional domain. And then, reconstructing a signal receiving intensity field in the whole area by utilizing Gaussian process regression, thereby achieving the effect of reducing sampling points required by signal distribution. In order to visually compare the effect difference between the scheme and the traditional scheme, the traditional median filtering processing is adopted as comparison. The sample node processing results for reconstruction are shown in fig. 8. The processed data are input into a gaussian process regression model for training, and the prediction result is obtained as shown in fig. 9.
Comparing the in-gate parts of fig. 9a) and 9b), it can be seen that due to the presence of multipath effects, the signal experiences deep attenuation where no significant attenuation should occur, due to phase cancellation; the scheme based on fractional Fourier transform can effectively remove the influence of the points. Therefore, it can be found that the scheme can have a good multipath effect resistance effect compared with the median filtering scheme. In addition, due to the existence of the iron gate, a large-area blind area is generated in the area behind the iron gate due to the influence of shadow fading, and the signal blind area reconstruction result conforms to the actual scene, so that the effectiveness of the scheme can be verified.
Claims (8)
1. A fast measurement and acquisition method for a multi-band indoor signal distribution field is characterized by comprising the following steps:
step 1: an LFM signal source is arranged indoors;
step 2: based on the LFM signal source in the step 1, utilizing receiving equipment to carry out drive test sampling;
and step 3: determining the position of the receiver based on the drive test sampling result in the step 2;
and 4, step 4: and (3) utilizing the receiver for determining the position in the step 3 to perform signal processing and output of the measurement result.
2. The method of claim 1The method for quickly measuring and acquiring the multi-band indoor signal distribution field is characterized in that the step 1 specifically comprises the steps that an LFM signal source consists of radio frequency equipment for sending linear frequency modulation signals and a control upper computer; the signal source can continuously transmit the initial frequency f 1 A termination frequency of f 2 The mathematical expression of the LFM signal is:
where Re { } denotes a real part, and T is a pulse period.
3. The method for fast measurement and acquisition of the distribution field of signals in the multi-band indoor set of claim 1, wherein the step 2 is embodied in that the receiving device comprises a receiver for receiving the radio frequency signal and a host computer for storing the received signal; during reception, the device samples the received signal for at least more than one pulse period T
Sending the coordinate information to an upper computer for storage, recording the coordinate information x of the current position when the coordinate information x is stored by the upper computer, and combining the coordinate information x and the received signal of the point into a two-dimensional tuple
Stored in a database.
4. The method according to claim 1, wherein step 3 is specifically, during the process of determining the position of the receiver, the signal source is turned on, the receiving device moves, and the chirp signal is received at the same time;
the determined position scheme includes, but is not limited to, a pre-measured and calibrated sampled position recording scheme or ultra-wideband (UWB) based high precision indoor positioning.
5. The method of claim 3, wherein the step 4 comprises the following steps,
step 4.1: preprocessing signals received by a receiver;
step 4.2: and carrying out interpolation recovery of the signal receiving intensity field on the preprocessed signals.
6. The method of claim 5, wherein step 4.1, focusing LFM signal by fractional Fourier transform,
step 4.1.1: for received signal
Performing energy focusing in the corresponding optimal fractional Fourier transform domain;
step 4.1.2: collecting the energy of each multipath peak of the energy focusing, and searching and superposing the energy;
step 4.1.3: and taking the superposition value of the step 4.1.2 as a received signal energy value of the current position.
7. The method as claimed in claim 6, wherein the step 4.1.1 for locating the focusing peak in the optimal fractional Fourier transform domain is implemented by using a focusing peak search method including, but not limited to, a data size comparison method around the peak value and a zero-crossing counting method for binarization at a given threshold;
the peak obtained by searching is converted into time domain amplitude according to the conversion relation between the time domain and the fractional domain:
wherein, v max Is an optimal scoreThe LFM signal in the domain transforms the coordinate location where a certain peak is located,
the magnitude of the peak in the fractional domain; n is the number of signal sampling data points, and sin () represents a sine function; a is a time domain amplitude value corresponding to the fractional domain peak value; p is a radical of max The optimal fractional order Fourier transform order corresponding to the transmitted LFM signal is obtained;
p max slope of FM frequency with LFM signal
The relationship between them is:
wherein f is 1 Is the initial frequency, f, at which the signal source can transmit continuously 2 Is the termination frequency that the signal source can continuously transmit; t is the pulse period; cot () is a cotangent function;
the time domain amplitudes of the peak values are superposed to be used as the current signal receiving intensity value s x And stores the value in a two-dimensional tuple (x, s) together with the position x ) And storing.
8. The method of claim 5, wherein the interpolation recovery process of step 4.2 is specifically to arrange the sampled data of all the sampling points (1,2, 3.) in order and expressed as (X | y):
for unknown point position X * Its signal reception intensity value y * Mean value of predicted results of (y) () * |X * X, y) is obtained by the following equation:
wherein, k (X) * X) is the kernel function adopted at position X * And the result of the calculation at X,
is the observed noise of the environment, I is the identity matrix, () -1 Is the inversion operation of the matrix;
variance σ of prediction result for uncertainty of prediction 2 (y * |X * X, y) represents:
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