CN116008976B

CN116008976B - A fusion ranging method for CHIRP signal

Info

Publication number: CN116008976B
Application number: CN202310301674.4A
Authority: CN
Inventors: 梁宏明; 李洋漾
Original assignee: Sichuan Silingke Microelectronics Co ltd
Current assignee: Sichuan Silingke Microelectronics Co ltd
Priority date: 2023-03-27
Filing date: 2023-03-27
Publication date: 2023-06-23
Anticipated expiration: 2043-03-27
Also published as: CN116008976A

Abstract

The invention discloses a fusion ranging method for CHIRP signals, aiming at that the TOA ranging estimation in the prior art cannot obtain a ranging accuracy exceeding 1/BW. The fingerprint matching algorithm based on RSS has a huge workload when measuring fingerprints offline. And the fusion weight adopts the distance between the measurement position and the base station, and does not consider the multipath influence caused by the environment. The technical solution of the present invention includes: obtaining the delay information estimated by TOA, and then obtaining TOA distance information through the delay information; obtaining RSSI information, and then modeling the relationship between RSSI information and distance according to the lognormal distribution model, and according to The environmental information is calculated to obtain the environmental RSSI information, and the distance information is deduced based on the lognormal distribution model through the environmental RSSI information to obtain the RSSI distance information; the TOA distance information and the RSSI distance information are fused to obtain the fusion ranging result .

Description

Fusion ranging method for CHIRP signal

Technical Field

The invention belongs to the technical field of wireless communication, and particularly relates to a fusion ranging method for CHIRP signals.

Background

In wireless communication, ranging and positioning are receiving more and more attention as the basis of intelligent awareness. Where ranging is the basis of positioning, ranging and positioning means for chirp signals mainly include RSSI (Received Signal Strength Indicator) based ranging or TOA (Time of Arrival) based ranging. In an implementation, RSSI or TOA is often employed alone to implement the ranging and positioning functions. There is little consideration in using a combination of two measurements for ranging and positioning.

The RSSI-based ranging method mainly comprises two types, namely fingerprint ranging, namely firstly rasterizing an area to be positioned in an off-line state, and collecting RSSI fingerprint information of each grid so as to obtain a one-to-one mapping relation of RSSI and position information. And matching the actually measured RSSI information with the off-line measured position fingerprint information in the on-line state, so as to obtain a positioning result under the RSSI.

The second method is to construct a geometric relation of RSSI and distance for ranging, construct a function of RSSI and distance through several calibration anchor points in an offline state, and calculate distance information by reading the information of RSSI of the to-be-positioned point and using the geometric relation acquired before. Because the RSSI information can be read in the equipment, the information is easy to obtain, and the calculation is simple no matter the RSSI positioning method is based on fingerprint ranging or geometric relation matching. However, since RSSI information is often affected by multipath in the environment, ranging and positioning accuracy is limited.

As for TOA ranging, the transmission distance can be obtained by calculating the transmission time of the air interface by two time stamps between transmission and reception and multiplying the transmission time by the speed of light. Compared with the RSSI scheme, TOA ranging is less affected by the environment, and ranging and positioning accuracy are higher. However, the time resolution of TOA is often affected by bandwidth. Typically, the minimum time resolution is 1/BW, where BW represents bandwidth. Due to the limitation of spectrum resources, the bandwidth of the system is often limited, resulting in limited TOA-based ranging and positioning accuracy.

In the prior art, an algorithm is disclosed that fuses TOF (Time of Flight) measurements with RSS (Received Signal Strength) location fingerprint information. The algorithm achieves obtaining distance information through TOF measurement values, and then measuring RSS values of User Equipment (UE) and a gateway and matching fingerprint information to obtain the distance information. And then carrying out weighted fusion on the measured distance and the positioning result obtained in the two modes respectively through twice weighted fusion. Thereby improving the final ranging and positioning accuracy.

The prior art has the following technical problems:

1. TOA ranging estimates cannot achieve ranging accuracy exceeding 1/BW.

2. The fingerprint matching algorithm based on RSS has huge workload when measuring fingerprints offline, and is difficult to realize in large-scale engineering application.

3. The fusion weight adopts the distance between the measuring position and the base station, and the larger weight is given to the measuring quantity and the positioning result which are closer to each other.

Disclosure of Invention

Aiming at the problems in the prior art, the invention provides a fusion ranging method for CHIRP signals, which aims at: in a chirp spread spectrum based communication system, more reliable distance measurement information needs to be obtained, so as to achieve better ranging and positioning performance.

The technical scheme adopted by the invention for achieving the purpose is as follows: there is provided a fusion ranging method for a CHIRP signal, including: when Chirp sends signals, the front end of each signal is provided with a section of preamble signal, TOA distance information and RSSI distance information are obtained by using the preamble signal, and the specific process comprises the following steps:

s1: acquiring delay information of TOA estimation, wherein the delay information comprises integer delay and decimal delay, and then acquiring TOA distance information through the delay information;

s2: acquiring RSSI information, modeling the relation between the RSSI information and the distance according to a lognormal distribution model, calculating environmental RSSI information according to environmental information, and reversely solving the distance information based on the lognormal distribution model through the environmental RSSI information to obtain RSSI distance information;

s3: and fusing the TOA distance information and the RSSI distance information to obtain a fused ranging result.

Preferably, the step of obtaining the integer delay in the S1 of the present invention specifically includes:

s1.1: first, a preamble signal in a transmission signal is transmitted

And preamble signal in the received signal +.>

And carrying out integer delay operation, wherein the integer delay operation is as follows:

wherein, fft represents the fast fourier transform,

represents->

Is represented by absolute value;

s1.2: then find out

Subscript corresponding to the maximum value of +.>

The following formula is shown:

wherein,,

is an integer delay of 0<i<2^SF+1。

Preferably, in the S1, the decimal delay is obtained through a MUSIC algorithm, and the method specifically comprises the following steps:

s1.3: the autocorrelation matrix R is first calculated as follows:

wherein H represents a conjugate transpose;

s1.4: then, carrying out eigenvalue decomposition on the autocorrelation matrix R to obtain eigenvalues, wherein the eigenvalue decomposition is shown in the following formula:

wherein, eig represents eigenvalue decomposition of the autocorrelation matrix R;

the eigenvalue decomposition of the present invention is performed to decompose the signal space and the noise space, because the essence of the MUSIC algorithm is to use the orthogonality of the signal space and the noise space to obtain the super-resolution delay estimation. The formula of the MUSIC pseudo spectrum obtained in S1.6 uses the eigenvector of the noise space; in addition, the eigenvalue obtained after the decomposition is also used in the S1.6 formula when making the multipath number judgment.

S1.5: the steering vector is then calculated as follows:

wherein e represents natural logarithm, pi represents pi, fc represents carrier frequency of signal, n represents nth chip, and n has value range of 0<n<

+1 and n is an integer; m represents a guide vector corresponding to an mth delay point; here, a window is opened around the integer delay point, and the fractional delay point is searched as shown in the following formula:

-offset1≤m≤

+offset2 and m= = -j->

Wherein, 0 is less than or equal to

And->

For integers, offset1 and offset2 represent windows, stp represents step size, +.>

BW represents the bandwidth of the signal and SF represents the spreading factor;

s1.6: assume that the number of multipaths in the space isL, the method for obtaining the multipath number is as follows: sorting the characteristic values in the order from big to small, and defining the sorted characteristic values as

,

When the following formula holds:

l corresponding to the formula is the number of multipaths, and the calculated MUSIC pseudo spectrum is

Wherein H represents a conjugate transpose, and then a subscript corresponding to the maximum value in P (m) is found, as shown in the following formula:

obtaining

Is a fractional delay;

s1.7: finally, delay information is obtained, and the following formula is shown:

。

preferably, in the step S1, delay information is obtained through a phase inversion algorithm, and the method specifically comprises the following steps:

s1.8: based on the nth chip

+.1 with n+1 chips>

The phase change between them is performed in a phase-change manner,the transmission delay of the signal is calculated as follows:

wherein pi represents pi,

representing the determination of the different moments +.>

Phase of->

s1.9: and then, the transmission delays of the plurality of chips are averaged to obtain delay information, wherein the delay information is shown in the following formula:

。

preferably, the invention multiplies the obtained delay information by the speed of light to obtain TOA distance information, as shown in the following formula:

wherein c is the speed of light.

Preferably, the invention adopts an alpha filter to obtain

Bag(s) or(s) of (are)>

The range of the values is as follows: 0</>

</>

+1, the TOA distance information obtained is shown in the following formula:

+

。

preferably, in the present invention S2, the specific steps for acquiring the RSSI distance information are:

s2.1: obtain RSSI information of the packet, assume that

TOA distance information derived from each packet is +.>

If->

-

threshold2 or dt (+)>

)-

>threshold2，

The value range of (2) is 0<

</>

+1, determining the TOA distance information as multipath information, determining the RSSI information corresponding to the packet as abnormal RSSI information, and deleting the abnormal RSSI information and multipath information corresponding to the packet;

s2.2: the total number of the remaining packets after the deletion is T, the RSSI information of the T-th packet is expressed as r (T), and the value range of T is 0<

<T+1, and then alpha filtering the multi-packet data using an alpha filter reduces the variance of the RSSI as shown in the following equation:

+

s2.3: and then modeling the relation between the RSSI information and the distance according to a lognormal distribution model, wherein the relation is shown in the following formula:

wherein,,

represents the filtered RSSI information received at a distance d,>

representing distance parameter>

Representative distance is->

RSSI information of time, ">

An environmental factor is represented by an environmental-related correction value;

s2.4: k RSSI information with distance measurement distance of near point and far point is selected to respectively solve correction values

K is a parameter and then is denoted as +.>

，0<k<K+1 and K is an integer, calculated +.>

The values are shown in the following formula:

s2.5: then, based on the obtained RSSI information, the distance information is reversely solved according to the lognormal model, and the RSSI distance information is obtained and expressed as: dr (1), dr (2) … dr

)。

Preferably, in the present invention S3, the obtained fusion ranging result is specifically:

s3.1: based on the T packet data obtained in S2.2, TOA distance information of the T packets is expressed as: dt (1), dt (2) … dt (T);

s3.2, calculating the mean value and standard deviation of the TOA distance information, wherein the mean value and standard deviation are respectively shown in the following formulas:

and calculating the mean value and standard deviation of the corresponding RSSI distance information, wherein the mean value and standard deviation are respectively shown in the following formula:

s3.3: and then carrying out weighted fusion on TOA distance information and RSSI distance information according to standard deviation, wherein the weighted fusion is shown in the following formula:

wherein the standard deviation is taken asThe weight is:

，

the criterion of weight selection is that the larger the standard deviation or variance is, the smaller the weight is given;

the fusion ranging result obtained after fusion is

。

Preferably, in the present invention S3.3, the TOA distance information and the RSSI distance information may be weighted and fused according to the variance, as shown in the following formula:

wherein, the variance is taken as the weight:

，

the fusion ranging result obtained after fusion is

。

Preferably, in the present invention S3.3, when the measurement error satisfies the gaussian distribution, a gaussian weight is used to fuse the TOA distance information and the RSSI distance information, as shown in the following formula:

wherein, the weight of TOA distance information is calculated as

The weight for calculating the RSSI distance information is +.>

；

The fusion ranging result obtained after fusion is

。

Compared with the prior art, the technical scheme of the invention has the following advantages/beneficial effects:

1. the TOA distance information is acquired through the super-resolution MUSIC algorithm, so that the time resolution and estimation capability exceeding 1/BW can be realized, and the estimation precision can be remarkably improved.

2. The method can also obtain TOA distance information through a phase inversion method, is simple and feasible, and can greatly reduce the calculated amount under the condition of ensuring the estimation accuracy by using a Yu Gaoxin-to-noise ratio scene.

3. The invention screens abnormal RSSI information through TOA distance information, can obviously improve the reliability of RSSI measurement results, and simultaneously has three weighting fusion methods with different weights, and can further improve the accuracy of system ranging by carrying out weighting fusion on TOA distance information and RSSI distance information.

Drawings

In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed in the embodiments will be briefly described below, it being understood that the following drawings only illustrate some examples of the present invention and therefore should not be considered as limiting the scope, and other related drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.

Fig. 1 is a schematic flow chart of the method for acquiring TOA distance information according to the present invention.

Fig. 2 is a flow chart of the invention for acquiring RSSI distance information.

Fig. 3 is a schematic flow chart of the weighted fusion of TOA distance information and RSSI distance information according to the present invention.

Detailed Description

To make the objects, technical solutions and advantages of the present invention more apparent, the technical solutions in the embodiments of the present invention will be clearly and completely described below, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments, based on the embodiments of the invention, which are apparent to those of ordinary skill in the art without inventive faculty, are intended to be within the scope of the invention. Accordingly, the detailed description of the embodiments of the invention provided below is not intended to limit the scope of the invention as claimed, but is merely representative of selected embodiments of the invention.

Example 1:

as shown in fig. 1-3, embodiment 1 provides a fusion ranging method for a CHIRP signal, including: when Chirp sends signals, the front end of each signal is provided with a section of preamble signal, TOA distance information and RSSI distance information are obtained by using the preamble signal, and the specific process comprises the following steps:

s1: as shown in fig. 1, delay information of TOA estimation is obtained, the delay information includes integer delay and decimal delay, and then TOA distance information is obtained through the delay information; the step of obtaining the integer delay is specifically:

s1.1: first, a preamble signal in a transmission signal is transmitted

And preamble signal in the received signal +.>

wherein, fft represents the fast fourier transform,

represents->

Is represented by absolute value;

s1.2: then find out

Subscript corresponding to the maximum value of +.>

The following formula is shown:

wherein,,

is an integer delay of 0<i<2^SF+1。

Then the decimal delay is obtained through a MUSIC algorithm, and the method specifically comprises the following steps:

s1.3: the autocorrelation matrix R is first calculated as follows:

wherein H represents a conjugate transpose;

S1.5: the steering vector is then calculated as follows:

-offset1≤m≤

+offset2 and m= = -j->

Wherein, 0 is less than or equal to

And->

BW represents the bandwidth of the signal and SF represents the spreading factor; the sizes of the windows offset1 and offset2 and the step stp in embodiment 1 can be selected according to practical requirements.

S1.6: assuming that the number of the multipath in the space is L, the method for acquiring the number of the multipath is as follows: sorting the characteristic values in the order from big to small, and defining the sorted characteristic values as

,

When the following formula holds:

obtaining

Is a fractional delay;

。

multiplying the obtained delay information by the speed of light to obtain TOA distance information, wherein the TOA distance information is shown in the following formula:

wherein c is the speed of light.

When obtaining

（（0</>

</>

+1)) packets, a batch of delay estimation measures can be obtained>

(1),

(2),…

(

)。

In order to reduce fluctuation of delay estimation results caused by environmental noise and improve ranging accuracy, an alpha filter is adopted:

+

in this embodiment 1, a packet refers to one data block in communication, i.e., a group of data transmitted. In this embodiment 1, through multi-packet positioning, abnormal RSSI information in some packets or multipath information in TOA distance information can be removed, i.e. multiple measurements are used to remove some sporadic noise or abnormal values.

in this embodiment 1, the specific steps of acquiring RSSI information are as follows:

s2.1: obtain RSSI information of the packet, assume that

TOA distance information derived from each packet is +.>

If->

-

threshold2 or dt (+)>

)-

>threshold2，

The value range of (2) is 0<

</>

+1, determining the TOA distance information as multipath information, determining the RSSI information corresponding to the packet as abnormal RSSI information, and deleting the abnormal RSSI information and multipath information corresponding to the packet; does not participate in subsequent operations. threshold2 is a threshold.

+

wherein,,

represents the filtered RSSI information received at a distance d,>

representing distance parameter>

Representative distance is->

RSSI information of time, ">

For the correction values related to the environment, ++>

Represents an environmental factor; environmental factor->

The classical values of (2) are shown in table 1:

TABLE 1

K is a parameter and then is denoted as +.>

，0<k<K+1 and K is an integer, calculated +.>

The values are shown in the following formula:

)。

S3: and fusing the TOA distance information and the RSSI distance information to obtain a fused ranging result. The method comprises the following steps:

s3.3: then, the TOA distance information and the RSSI distance information are subjected to weighted fusion according to standard deviation or variance, and the larger the standard deviation or variance is, the smaller the given weight is, as shown in the following formula:

the first way to select the weights is to use the standard deviation as the weight:

，

；

the second weight is selected by taking the variance as the weight:

，

；

a third way to select weights is when the measurement error satisfies a gaussian distribution, then the gaussian weights can be used to fuse the TOA and RSSI measurements. The weights for TOA are calculated as:

the weight for calculating RSSI is +.>

。

The fusion ranging result obtained after fusion is

。

In this embodiment 1, by using the weighted fusion method of the three different weights, the accuracy of the system ranging can be further improved by using the weighted fusion of the RSSI ranging information and the TOA ranging information.

Example 2

Based on embodiment 1, embodiment 2 further proposes a phase inversion algorithm to obtain TOA distance information;

the TOA distance information is acquired through the MUSIC algorithm, so that super-resolution ranging performance can be realized, namely, the delay estimation precision acquired by the method can be far better than 1/BW, however, the calculation amount of the algorithm is large, and the main calculation amount is concentrated on eigenvalue decomposition of the autocorrelation matrix R. Therefore, when the signal-to-noise ratio is smaller than or equal to a preset threshold value, the MUSIC algorithm is adopted to acquire TOA distance information, and when the signal-to-noise ratio is larger than the threshold value, the phase inversion algorithm is adopted, and the method specifically comprises the following steps:

s1.8: based on the nth chip

+.1 with n+1 chips>

The phase change between them, calculate the transmission delay of the signal, as shown in the following formula:

wherein,,

representing the determination of the different moments +.>

Phase of->

。

and multiplying the delay information obtained by one of the two methods by the speed of light to obtain TOA distance information.

Of course, the MUSIC method can be used alone under different signal-to-noise ratio conditions in the case of sufficient computing resources. Or under the condition of limited calculation resources, under the condition of different signal to noise ratios, the phase inversion method is singly used, and the two methods are also within the protection scope of the patent.

The foregoing is merely a preferred embodiment of the present invention, and it should be noted that the above-mentioned preferred embodiment should not be construed as limiting the invention, and the scope of the invention should be defined by the appended claims. It will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the spirit and scope of the invention, and such modifications and adaptations are intended to be comprehended within the scope of the invention.

Claims

1. A fusion ranging method for CHIRP signals, characterized in that, when transmitting Chirp signals, each signal has a preamble signal at the beginning, and TOA distance information and RSSI distance information are obtained by using the preamble signal. The specific process includes the following steps:

S1: Obtain the delay information for TOA estimation, including integer delay and fractional delay, and then obtain the TOA distance information through the delay information;

The specific steps to obtain the integer delay are as follows:

S1.1: First, perform an integer delay operation between the preamble signal tx _pre in the transmitted signal and the preamble signal rx _pre in the received signal, as shown in the following formula:

Here, fft represents Fast Fourier Transform.

represents the conjugate of rx and _pre , and || represents the absolute value;

S1.2: Then find the index idx _int corresponding to the maximum value in x _corr , as shown in the following formula:

Where idx _int is the integer delay, 0 < i <2^SF+1;

The decimal delay is obtained using the MUSIC algorithm, and the specific steps are as follows:

S1.3: First, calculate the autocorrelation matrix R, as shown in the following formula:

R = x _corr * x _corr ^H

Where H represents the conjugate transpose;

S1.4: Then, perform eigenvalue decomposition on the autocorrelation matrix R to obtain the eigenvalues, as shown in the following equation:

[eigenval,eigenvec] = eig(R)

Where eig represents the eigenvalue decomposition of the autocorrelation matrix R;

S1.5: Then calculate the guide vector, using the formula shown below:

Where e represents the natural logarithm, pi represents π, fc represents the carrier frequency of the signal, n represents the chip number, and the value of n is in the range of 0 < n < ^2SF + 1 and n is an integer; m represents the delay point number; here, a window is opened around the integer delay points to search for the fractional delay points, as shown in the following formula:

idx _int -offset1≤m≤idx _int +offset2 and

in,

And l' is an integer, offset1 and offset2 represent the window, stp represents the step size, f _delta = BW/2 ^SF , BW represents the bandwidth of the signal, and SF represents the spreading factor;

S1.6: Assuming the number of multipaths in the space is L, the method to obtain the number of multipaths is: sort the eigenvalues in descending order, and define the sorted eigenvalues as eigenval(1), eigenval(2)...eigenval( ^2SF ), when the following formula holds:

In the formula, L represents the number of multipath paths, and the calculated MUSIC pseudospectrum is...

P(m)＝1/((steer _vec (m,:)*eigenvec(:,L+1:2 ^SF )*eigenvec(:,L+1:2 ^SF ) ^H *steer _vec (m,:) ^H )

Where H represents the conjugate transpose, then find the index corresponding to the maximum value in P(m), as shown in the following formula:

The idx _frac is obtained as a decimal delay;

S1.7: The final delay information is shown in the following formula:

idx _accu =idx _int -offset1+stp*(idx _frac );

An α filter is used to obtain t' packets, where t' ranges from 0 to t' to T'+1, and T' is the total number of packets required for one localization operation. The resulting TOA distance information is shown in the following formula:

dt(t')=dt'(t')*α+dt'(t'-1)*(1-α);

S2: Obtain RSSI information, then model the relationship between RSSI information and distance based on the log-normal distribution model, and calculate environmental RSSI information based on environmental information. Then, solve the distance information based on the log-normal distribution model using the environmental RSSI information to obtain RSSI distance information.

The specific steps to obtain RSSI distance information are as follows:

S2.1: Obtain the RSSI information of the packet. Assume that the TOA distance information obtained from the t'th packet is dt(t'). If dt(t')-dt(t'-1)>threshold or

If the value of t' is 0 <t'<T' + 1, then the TOA distance information is determined to be multipath information, the RSSI information corresponding to the packet is determined to be abnormal RSSI information, and the abnormal RSSI information and multipath information corresponding to the packet are deleted.

S2.2: After deletion, the total number of packets remaining is T. The RSSI information of the t-th packet is represented as r(t), where t ranges from 0 to t and from 0 to T+1. Then, an α filter is used to filter the multi-packet data to reduce the variance of RSSI, as shown in the following formula:

r _alpha (t)＝r(t)*α+r(t-1)*(1-α)

S2.3: Then, the relationship between RSSI information and distance is modeled according to the log-normal distribution model, as shown in the following formula:

Where r _alpha represents the filtered RSSI information received at a distance of d, d ₀ represents the distance parameter, P ₀ represents the RSSI information at a distance of d ₀ , ξ is the environment-related correction value, and n' represents the environmental factor;

S2.4: Select K RSSI data points with distances of near and far points to calculate their correction values ξ, where K is a parameter, and then denote them as ξ(k), where 0 < k < K+1 and k is an integer. The calculated ξ values are shown in the following formula:

S2.5: Then, based on the obtained RSSI information, the distance information is solved by inverse log-normal model, that is, the RSSI distance information is obtained, which is represented as: dr(1), dr(2)...dr(T);

S3: The TOA distance information and RSSI distance information are weighted and fused according to the standard deviation, variance or Gaussian weight to obtain the fused ranging result.

2. The fusion ranging method for CHIRP signals according to claim 1, characterized in that the obtained delay information is multiplied by the speed of light to obtain the TOA distance information, as shown in the following formula:

dt = idx _accu *c

Where c is the speed of light.

3. The fusion ranging method for CHIRP signals according to claim 1, characterized in that, in S3, obtaining the fusion ranging result specifically involves:

S3.1: Based on the T packets of data obtained in S2.2, the TOA distance information of these T packets is represented as: dt(1), dt(2)...dt(T);

S3.2: Then calculate the mean and standard deviation of these TOA distance information, as shown in the following formulas:

The mean and standard deviation of the corresponding RSSI distance information are calculated as follows:

S3.3: Then, the TOA distance information and RSSI distance information are weighted and fused according to the standard deviation.

Use standard deviation as the weight:

The criterion for weight selection is that the larger the standard deviation, the smaller the weight should be.

The fused ranging result obtained after fusion is

4. The fusion ranging method for CHIRP signals according to claim 3, characterized in that, in S3.3, alternatively, the TOA distance information and RSSI distance information are weighted and fused according to variance, with the variance used as the weight:

The criterion for weight selection is that the larger the variance, the smaller the weight should be.

The fused ranging result obtained after fusion is

5. A fusion ranging method for CHIRP signals according to claim 3, characterized in that, in S3.3, alternatively, when the measurement error satisfies a Gaussian distribution, Gaussian weights are used to fuse TOA distance information and RSSI distance information, and the weight of the TOA distance information is calculated as follows:

The weights for calculating RSSI distance information are:

The fused ranging result obtained after fusion is