CN105425206B - A Robust Least Squares Localization Method in Unsynchronized Wireless Networks - Google Patents

Abstract

The invention discloses a robust least squares positioning method in an asynchronous wireless network, which first acquires the measurement signal emitted by an unknown target source, propagates to each sensor in the sensor network, and then forwards and returns to the unknown target source after relay processing. The measured value of the equivalent transmission distance of the measurement signal based on the round-trip arrival time; then according to the measurement value of the equivalent transmission distance of the measurement signal corresponding to each sensor, the corresponding equivalent distance measurement model of each sensor is obtained; then according to the re-described distance The measurement model establishes a robust least squares problem; then, by introducing optimization variables and using the second-order cone relaxation technique, the robust least squares problem is relaxed into a second-order cone programming problem; finally, the interior point method is used to solve the second-order cone programming problem, The coordinate estimation value of the unknown target source is obtained; the advantage is that it can effectively suppress the influence of clock drift and transit time on the positioning accuracy, the positioning accuracy is high, and it has high high-precision positioning stability.

Description

A Robust Least Squares Localization Method in Unsynchronized Wireless Networks

technical field

The invention relates to a target positioning method, in particular to a robust least square positioning method in an asynchronous wireless network.

Background technique

Target positioning plays an indispensable role in the military field such as precise military strikes. In the era of mobile Internet in modern society, with the huge development of commercial market applications such as location-based services, more and more efficient and accurate target positioning research has been obtained. At the same time, target positioning technology has broad application prospects in military reconnaissance, traffic surveillance, home automation, industrial and agricultural control, biomedicine, emergency rescue and disaster relief, etc. Therefore, it is very important to study target positioning methods. As a good supplement to positioning systems such as GPS, object positioning in wireless networks is a classic research topic.

In target positioning, the positioning method based on the measured value of arrival time accounts for a large part. However, the premise of this positioning method to achieve target positioning is to assume that the entire positioning network is completely synchronized in time, and does not consider the asynchronous nature of the positioning network. In fact, due to various factors such as hardware conditions, the actual network is usually asynchronous, or in other words, it is impossible to be completely synchronized, so this positioning method is difficult to apply to the actual network. Other existing time-of-arrival positioning methods also require the initial transmission time of the network to be accurately known, but this requirement is relatively difficult to achieve or the cost is relatively high.

In order to solve the technical problems of positioning methods based on time-of-arrival measurements, positioning methods in asynchronous wireless networks emerged as the times require. In the localization method in asynchronous wireless network, since the sensor clock has clock bias and clock drift, it is difficult to solve the problem of jointly estimating them with the target position when the clock bias and clock drift are completely unknown. In order to overcome this problem, some schemes have been proposed. The mainstream ones are: one is positioning based on time difference of arrival (TDOA); the other is positioning based on round-trip time of arrival (TW-TOA). Figure 1 shows a typical A schematic diagram of the round-trip time-of-arrival (TW-TOA)-based positioning environment for . In the positioning method based on the time difference of arrival, the clock bias is removed, and finally only the joint estimation of the clock drift and the target position is needed, but it should be noted that this method still requires the sensors in the positioning network to be synchronized in time; in In the positioning method based on the round-trip arrival time, it does not require any synchronization between nodes in the positioning network, but it needs to consider the impact of the transit time in the measurement on the positioning results, such as the total feasible region method proposed by some scholars and the least squares method, the two methods first estimate the transit time, and finally obtain the estimated value of the target position through the joint estimation of the clock drift and the target source position, but the error in the transit time estimation will have a large impact on the positioning performance influences.

Contents of the invention

The technical problem to be solved by the present invention is to provide a robust least square positioning method in an asynchronous wireless network, the positioning is based on the round-trip arrival time, and the positioning accuracy is high.

The technical solution adopted by the present invention to solve the above-mentioned technical problems is: a robust least squares positioning method in an asynchronous wireless network, which is characterized in that it comprises the following steps:

① Establish a two-dimensional coordinate system or a three-dimensional coordinate system as a reference coordinate system in an asynchronous wireless network environment, and assume that there is an unknown target source and N sensors with known positions in the asynchronous wireless network environment, and the unknown target source The coordinate in the reference coordinate system is x, and the coordinates of N sensors in the reference coordinate system correspond to s ₁ , s ₂ ,...,s _N , where N≥n+1, n represents the dimension of the reference coordinate system s ₁ represents the coordinates of the first sensor in the reference coordinate system, s ₂ represents the coordinates of the second sensor in the reference coordinate system, s _N represents the coordinates of the Nth sensor in the reference coordinate system;

②In the asynchronous wireless network environment, the measurement signal is transmitted by the unknown target source, and the measurement signal is transmitted to each sensor and then forwarded back to the unknown target source after relay processing. First, it is determined that the measurement signal transmitted by the unknown target source reaches each The time difference between the time point when a sensor forwards back to the unknown target source after relay processing and the time point when the unknown target source emits the measurement signal, the measurement signal emitted by the unknown target source is propagated to the i-th sensor and then processed by relay The time difference between the time point when the forwarding returns to the unknown target source and the time point when the unknown target source transmits the measurement signal is 2t _i , in seconds, then Among them, 1≤i≤N, w represents the clock drift of the unknown target source, s _i represents the coordinates of the i-th sensor in the reference coordinate system, c is the speed of light, and T _i represents the i-th sensor’s relay processing of the unknown target source The transit time required to measure the signal, Indicates that the measurement signal transmitted by the unknown target source propagates to the i-th sensor, and then forwards and returns to the unknown target source after being transferred. The variance of the entire transmission path is The Gaussian distribution noise, the symbol "‖‖" is the Euclidean 2 norm; then calculate the round-trip arrival rate when the measurement signal emitted by the unknown target source propagates to each sensor and then forwards back to the unknown target source after relay processing The measurement value of the equivalent transmission distance of the measurement signal of time, the measurement signal transmitted by the unknown target source is propagated to the i-th sensor and then forwarded back to the unknown target source after the relay processing, and the measurement signal equivalent transmission distance measurement based on the round-trip arrival time The value is 2d _i , the unit is meter, then in, Indicates the influence of T _i on d _i , n _i represents the noise in d _i , n _i obeys the Gaussian distribution, and the variance of n _i is

③ Obtain the distance measurement model corresponding to each sensor. For the i-th sensor, the corresponding distance measurement model acquisition process is: let w=1+δ, and require δ to satisfy the condition |δ|≤δ _max << 1, and determine The range of values is then unite and w=1+δ, get reunion and w=1+δ, get Then according to and |δ|≤δ _max <<1, we get Assume again then according to with ,get joint later with get again Subtract both sides of the approximate equal sign median of get final order and order Will Simplified to and will As the distance measurement model corresponding to the i-th sensor; where, δ represents the clock drift of the unknown target source relative to the standard clock, the symbol "||" is the absolute value symbol, the symbol "<<" is much smaller than the symbol, δ _max Indicates the maximum value of the clock drift of the unknown target source relative to the standard clock, a _i and b _i correspond to represent The upper and lower bounds of the values,

④ Re-describing the distance measurement model corresponding to each sensor, for the distance measurement model corresponding to the i-th sensor The specific process of re-describing it is: Into then to Squaring both sides of the approximately equal sign of , and assuming then omit the quadratic term of n _i get then Into: which is re-described as

⑤According to the re-described distance measurement model, establish a robust least squares problem, described as: Then order according to with Will Into Then according to Describe the robust least squares problem as: in, express to make the smallest value of x, express to make {e _i } with the largest value, {e _i } refers to the set composed of e ₁ ,e ₂ ,…,e _N , f(e _i ) means to take the e _i that makes the value of f(e _i ) the largest;

⑥ Determine the maximum value of f(e _i ), if Then the maximum value of f(e _i ) is max(f(-ρ _i ),f(ρ _i )); if Then the maximum value of f(e _i ) is then according to and the maximum value of f(e _i ), get in photogenic form, describing

for: Among them, the symbol "||" is the absolute value symbol, and max() is the maximum value function, where express to make The smallest value of x,{η _i }, η _i is The i-th optimization variable introduced in , {η _i } is the set of N optimization variables introduced, and "st" means "subject to the condition of";

⑦ joint and with

get

⑧ in Introduce the optimization variable y, y=||x|| ² , and then use the second-order cone relaxation technique to relax y=||x|| ² to ||x|| ² ≤ y, and obtain the second-order cone programming problem, described for: in, express to make x, y, {η _i } with the smallest value, the symbol “[]” is a vector representation symbol, is the transpose vector of _si ;

⑨Using interior point method technology to Carry out the solution to obtain the estimated values corresponding to x, y, {η _i }, correspondingly denoted as

The determination process of the value of a _i in the described step 3. and the value of _bi is:

③-1. Assume that there are N sensors whose location information is known in the asynchronous wireless network tested;

③-2. The measurement signal is sent from the j'th sensor to the i'th sensor, and the measurement signal transmitted by the j'th sensor is calculated and propagated to the i'th sensor, and then forwarded back to the j'th sensor after being processed The time difference between the time point of the sensor and the time point when the j'th sensor initially emits the measurement signal is 2t _{j', the product of i'} and the speed of light c, denoted as Among them, 1≤i'≤N, 1≤j'≤N, i'≠j';

③-3. According to the position information of the N sensors, calculate the real distance between the j'th sensor and the i'th sensor, denoted as d _j',i' ; then calculate the measurement signal emitted by the j'th sensor After reaching the i'th sensor, the equivalent transmission distance in the transit time of the i'th sensor is denoted as d _T,j',i' ,

③-4. Randomly select a sensor from N sensors, assuming that the selected sensor is the i'th sensor, then set a _i =min(d _T,j',i' |1≤j'≤N, j'≠i'), and let b _i =max(d _T,j',i' |1≤j'≤N,j'≠i'), where min() is the minimum value function, max( ) is the maximum value function.

Compared with the prior art, the present invention has the advantage that: compared with the existing total feasible region method and the least squares method, the present invention utilizes the robust least squares method to treat the clock drift and transit time as an irrelevant variable robustly, Only estimate the coordinate value of the unknown target source in the reference coordinate system, so that the influence of clock drift and transit time on the positioning accuracy can be effectively suppressed, and the positioning accuracy is high; at the same time, the robust least squares problem The relaxation is described as a second-order cone programming problem, which can ensure that the global optimal solution is not affected by local convergence, and thus has high high-precision positioning stability.

Description of drawings

FIG. 1 is a schematic diagram of a typical positioning environment based on round trip time of arrival (TW-TOA);

Fig. 2 is the overall flow chart of the inventive method;

Fig. 3 is the change schematic diagram of root mean square error with noise size in the measurement of the inventive method and existing total feasible region method and least squares method;

Fig. 4 is a schematic diagram of the change of the root mean square error with the number of sensors (anchor nodes) in the measurement of the method of the present invention, the existing total feasible region method and the least square method.

detailed description

The present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments.

A robust least squares positioning method in an asynchronous wireless network proposed by the present invention, its overall flow diagram is as shown in Figure 2, and it includes the following steps:

① Establish a two-dimensional coordinate system or a three-dimensional coordinate system as a reference coordinate system in an asynchronous wireless network environment, and assume that there is an unknown target source and N sensors with known positions in the asynchronous wireless network environment, and the unknown target source The coordinate in the reference coordinate system is x, and the coordinates of N sensors in the reference coordinate system correspond to s ₁ , s ₂ ,...,s _N , where N≥n+1, n represents the dimension of the reference coordinate system number, n=2 or n=3, that is, n=2 when the reference coordinate system is a two-dimensional coordinate system, n=3 when the reference coordinate system is a three-dimensional coordinate system, s ₁ represents the coordinates of the first sensor in the reference coordinate system , s ₂ represents the coordinates of the second sensor in the reference coordinate system, and s _N represents the coordinates of the Nth sensor in the reference coordinate system.

②In the asynchronous wireless network environment, as shown in Figure 1, the measurement signal is transmitted by the unknown target source, and the measurement signal is propagated to each sensor and then forwarded back to the unknown target source after relay processing. First, determine the source of the unknown target source The time difference between the time point when the measurement signal is transmitted to each sensor and then forwarded back to the unknown target source after relay processing and the time point when the unknown target source transmits the measurement signal, the measurement signal transmitted by the unknown target source arrives at the i-th The time difference between the time point when the sensor forwards back to the unknown target source after the relay processing and the time point when the unknown target source initially transmits the measurement signal is 2t _i , and the unit is second, then Among them, 1≤i≤N, w represents the clock drift of the unknown target source, where the value of w is unknown, s _i represents the coordinates of the i-th sensor in the reference coordinate system, c is the speed of light, T _i represents the i-th sensor the relay time required to relay a measurement signal emitted by an unknown target source, where the value of T _i is unknown, Indicates that the measurement signal transmitted by the unknown target source propagates to the i-th sensor, and then forwards and returns to the unknown target source after being transferred. The variance of the entire transmission path is Gaussian noise, the symbol "‖‖" is the Euclidean 2 norm; then calculate the round-trip arrival time based on when the measurement signal emitted by the unknown target source propagates to each sensor and then forwards back to the unknown target source after relay processing The measurement value of the equivalent transmission distance of the measurement signal, the measurement signal transmitted by the unknown target source is propagated to the i-th sensor and then forwarded back to the unknown target source when the measurement signal is transmitted back to the unknown target source based on the round-trip arrival time. is 2d _i , the unit is meter, then in, Indicates the influence of T _i on d _i , n _i represents the noise in d _i , n _i obeys the Gaussian distribution, and the variance of n _i is (i.e. the power of noise _ni in 2d _i ),

③ Obtain the distance measurement model corresponding to each sensor. For the i-th sensor, the corresponding distance measurement model acquisition process is: let w=1+δ, and require δ to satisfy the condition｜δ｜≤δ _max << 1, and determine The range of values is then unite and w=1+δ, get reunion and w=1+δ, get Then according to and |δ|≤δ _max <<1, we get Assume again then according to with get joint later with get again Subtract both sides of the approximate equal sign median of get final order and order Will Simplified to and will As the distance measurement model corresponding to the i-th sensor; where, δ represents the clock drift of the unknown target source relative to the standard clock, the symbol "||" is the absolute value symbol, the symbol "" is much smaller than the symbol, and δ _max represents the unknown The maximum value of the clock drift of the target source relative to the standard clock, where the value of δ _max is known, and a and b correspond to represent The upper and lower bounds of the values, the values of a _i and b _i are known, |e _i |≤ρ _i ,

In this specific embodiment, the determination process of the value of a _i and the value of _bi in step 3. is:

③-1. Assume that the tested asynchronous wireless network has N sensors whose location information is known, and the location information of the sensors can be obtained by GPS positioning.

③-2. The measurement signal is sent from the j'th sensor to the i'th sensor, and the measurement signal transmitted by the j'th sensor is calculated and propagated to the i'th sensor, and then forwarded back to the j'th sensor after being processed The product of the time difference 2t _j',i' and the speed of light c between the time point of the sensor and the time point when the j'th sensor initially emits the measurement signal is expressed as Wherein, 1≤i'≤N, 1≤j'≤N, i'≠j'.

③-3. According to the position information of the N sensors, calculate the real distance between the j'th sensor and the i'th sensor, denoted as d _j',i' ; then calculate the measurement signal emitted by the j'th sensor After reaching the i'th sensor, the equivalent transmission distance in the transit time of the i'th sensor is denoted as d _T,j',i' ,

③-4. Randomly select a sensor from N sensors, assuming that the selected sensor is the i'th sensor, then set a _i =min(d _T,j',i' |1≤j'≤N, j'≠i'), and let b _i =max(d _T,j',i' |1≤j'≤N,j'≠i'), where min() is the minimum value function, max( ) is the maximum value function.

④ Re-describing the distance measurement model corresponding to each sensor, for the distance measurement model corresponding to the i-th sensor The specific process of re-describing it is: Into then to Squaring both sides of the approximately equal sign, and assuming Then the quadratic term of n _i can be omitted get then Into: which is re-described as

⑤According to the re-described distance measurement model, establish a robust least squares problem, described as: Then order according to with Will Into Then according to Describe the robust least squares problem as: in, express to make the smallest value of x, express to make {e _i } with the largest value, {e _i } refers to the set composed of e ₁ ,e ₂ ,…,e _N , the symbol "||" is the absolute value symbol, f(e _i ) means taking e _i that maximizes the value of f(e _i ).

⑥ Determine the maximum value of f(e _i ), if Then the maximum value of f(e _i ) is max(f(-ρ _i ),f(ρ _i )); if Then the maximum value of f(e _i ) is then according to and the maximum value of f(e _i ), get The photographic form of , described as: Among them, the symbol "||" is the absolute value symbol, max() is the maximum value function, express to make The smallest value of x,{η _i }, η _i is The i-th optimization variable introduced in , {η _i } is the set of N optimization variables introduced, and "st" means "subject to the condition of".

⑦ joint and with get

⑧ in Introduce the optimization variable y, y=||x|| ² , and then use the second-order cone relaxation technique to relax y=||x|| ² to ||x|| ² ≤y, and obtain the second-order cone programming problem, describe for: in, express to make x, y, {η _i } with the smallest value, the symbol “[]” is a vector representation symbol, is the transpose vector of _si .

⑨Using interior point method technology to Carry out the solution to obtain the estimated values corresponding to x, y, {η _i }, correspondingly denoted as

In order to verify the feasibility and effectiveness of the method of the present invention, the method of the present invention is simulated.

1) Test the variation of the performance of the method of the present invention with the size of the measurement noise. Assuming that 8 sensors are used for measurement, the measurement method is: first establish a plane rectangular coordinate system, and the 8 sensors are respectively at (40,40), (40, -40), (-40, 40), (-40 , -40), (40, 0), (0, 40), (40, 0), (0, -40) (unit: m), and the unknown target source is randomly distributed at (-40, 40)× (-40,40)m ² coordinate area. In the simulation, the clock drift w of the unknown target source is randomly distributed in the range of [0.99,1.01], that is, the maximum value of the clock drift of the unknown target source relative to the standard clock δ _max =0.01, while Assume that the range of random distribution is [24,36]m, 1≤i≤8, in addition, assuming that the noise power in the equivalent transmission distance measurement value of the corresponding measurement signal of all sensors is the same, that is, Among them, σ refers to the standard deviation of the noise represented by the abscissa in Fig. 3 .

Fig. 3 shows the schematic diagram of the variation of the root mean square error with the size of the noise in the measurement of the method of the present invention, the existing total feasible region method and the linear least squares method. It can be seen from Fig. 3 that the positioning performance of the method of the present invention is better than that of the existing total feasible region method (GTR) and the linear least squares (LLS) algorithm in the process of changing the noise from small to large. Specifically, when the standard deviation of the noise is 1m and 9m, the root mean square error can be reduced by 0.5m and 2.1m.

2) Test the variation of the positioning accuracy of the method of the present invention as the number of sensors increases. The measurement method is: assume that there are 8 sensors in a plane Cartesian coordinate system and the 8 sensors are respectively at (40,40), (40,-40), (-40,40), (-40,-40) , (40, 0), (0, 40), (40, 0), (0, -40) (unit: m), and the unknown target source is randomly distributed at (-40, 40) × (-40, 40) Within the coordinate area of ^m2 , take the first 5 to 8 sensors for positioning test. In addition, it is assumed that the standard deviation of the noise in the measured value of the equivalent transmission distance of the measurement signal corresponding to all the sensors is the same, that is, σ ₁ =σ ₂ =...=σ ₈ =4m.

Fig. 4 shows the schematic diagram of the change of the root mean square error with the number of sensors (anchor nodes) in the measurement of the method of the present invention, the existing total feasible region method (GTR) and the linear least square method (LLS). In the process of gradually increasing the number of sensors from 5 to 8, the method of the invention is superior to the existing total feasible region method and the linear least square algorithm in terms of positioning accuracy. Specifically, when the number of sensors is less than 8, the performance of the total feasible region method and linear least squares deteriorates sharply, so that positioning cannot be completed, while the method of the present invention can still complete relatively accurate positioning.

It can be seen from the above simulation results that the method of the present invention has good performance. Compared with the existing total feasible region method and the linear least squares method, the method of the present invention can effectively reduce the root mean square error and improve the positioning accuracy, and the increase of noise power will not significantly weaken the positioning performance , which reflects the robustness of positioning; in addition, relatively accurate positioning can still be performed when there are relatively few sensors in the network, which further illustrates the feasibility and effectiveness of the method of the present invention.

Claims (2)

1. a robust least squares positioning method in an asynchronous wireless network, characterized in that it may further comprise the steps: ① Establish a two-dimensional coordinate system or a three-dimensional coordinate system as a reference coordinate system in an asynchronous wireless network environment, and assume that there is an unknown target source and N sensors with known positions in the asynchronous wireless network environment, and the unknown target source The coordinate in the reference coordinate system is x, and the coordinates of N sensors in the reference coordinate system correspond to s ₁ , s ₂ ,...,s _N , where N≥n+1, n represents the dimension of the reference coordinate system s ₁ represents the coordinates of the first sensor in the reference coordinate system, s ₂ represents the coordinates of the second sensor in the reference coordinate system, s _N represents the coordinates of the Nth sensor in the reference coordinate system; ②In the asynchronous wireless network environment, the measurement signal is transmitted by the unknown target source, and the measurement signal is transmitted to each sensor and then forwarded back to the unknown target source after relay processing. First, it is determined that the measurement signal transmitted by the unknown target source reaches each The time difference between the time point when a sensor forwards back to the unknown target source after relay processing and the time point when the unknown target source emits the measurement signal, the measurement signal emitted by the unknown target source is propagated to the i-th sensor and then processed by relay The time difference between the time point when the forwarding returns to the unknown target source and the time point when the unknown target source transmits the measurement signal is 2t _i , in seconds, then Among them, 1≤i≤N, w represents the clock drift of the unknown target source, s _i represents the coordinates of the i-th sensor in the reference coordinate system, c is the speed of light, and T _i represents the i-th sensor’s relay processing of the unknown target source The transit time required to measure the signal, Indicates that the measurement signal transmitted by the unknown target source propagates to the i-th sensor, and then forwards and returns to the unknown target source after being transferred. The variance of the entire transmission path is The Gaussian distribution noise, the symbol "||||" is the Euclidean 2 norm; then calculate the measurement signal transmitted by the unknown target source to each sensor and then forwarded back to the unknown target source based on The measurement signal equivalent transmission distance measurement value of the round-trip arrival time, the measurement signal transmitted by the unknown target source is propagated to the i-th sensor and then forwarded back to the unknown target source when the measurement signal is transmitted back to the unknown target source. The equivalent transmission of the measurement signal based on the round-trip arrival time The distance measurement is 2d _i in meters, then in, Indicates the influence of T _i on d _i , n _i represents the noise in d _i , n _i obeys the Gaussian distribution, and the variance of n _i is ③ Obtain the distance measurement model corresponding to each sensor. For the i-th sensor, the corresponding distance measurement model acquisition process is: let w=1+δ, and require δ to satisfy the condition |δ|≤δ _max =1 ,And determines The range of values is then unite and w=1+δ, get reunion and w=1+δ, get Then according to and |δ|≤δ _max = 1, we get Assume again then according to with get joint later with get again Subtract both sides of the approximate equal sign median of get final order and order Will Simplified to and will As the distance measurement model corresponding to the i-th sensor; where, δ represents the clock drift of the unknown target source relative to the standard clock, the symbol "||" is the symbol for taking the absolute value, the symbol "=" is much smaller than the symbol, and δ _max represents The maximum value of the clock drift of the unknown target source relative to the standard clock, a _i and b _i correspond to represent The upper and lower bounds of the value, |e _i |≤ρ _i , ④ Re-describing the distance measurement model corresponding to each sensor, for the distance measurement model corresponding to the i-th sensor The specific process of re-describing it is: Into then to Squaring both sides of the approximately equal sign, and assuming then omit the quadratic term of n _i get then Into: which is re-described as ⑤According to the re-described distance measurement model, establish a robust least squares problem, described as: Then order according to Will Into Then according to Describe the robust least squares problem as: in, express to make the smallest value of x, express to make {e _i } with the largest value, {e _i } refers to the set composed of e ₁ ,e ₂ ,…,e _N , Indicates to take the e _i that makes the value of f(e _i ) the largest; ⑥ Determine the maximum value of f(e _i ), if Then the maximum value of f(e _i ) is max(f(-ρ _i ),f(ρ _i )); if Then the maximum value of f(e _i ) is then according to and the maximum value of f(e _i ), get The photographic form of , described as: Among them, the symbol "||" is the absolute value symbol, and max() is the maximum value function, where express to make The smallest value of x,{η _i }, η _i is The i-th optimization variable introduced in , {η _i } is the set of N optimization variables introduced, and "st" means "subject to the condition of"; ⑦ joint and with get ⑧ in Introduce the optimization variable y, y=||x|| ² , and then use the second-order cone relaxation technique to relax y=||x|| ² to ||x|| ² ≤ y, and obtain the second-order cone programming problem, described for: in, express to make x, y, {η _i } with the smallest value, the symbol “[]” is a vector representation symbol, is the transpose vector of _si ; ⑨Using interior point method technology to Carry out the solution to obtain the estimated values corresponding to x, y, {η _i }, correspondingly denoted as 2. the robust least squares location method in a kind of asynchronous wireless network according to claim 1, it is characterized in that step 3. the determination process of the value of a _i and the value of b _i is: ③-1. Assume that there are N sensors whose location information is known in the asynchronous wireless network tested; ③-2. The measurement signal is sent from the j'th sensor to the i'th sensor, and the measurement signal transmitted by the j'th sensor is calculated and propagated to the i'th sensor, and then forwarded back to the j'th sensor after being processed The product of the time difference 2t _j',i' and the speed of light c between the time point of the sensor and the time point when the j'th sensor initially emits the measurement signal is expressed as Among them, 1≤i'≤N, 1≤j'≤N, i'≠j'; ③-3. According to the position information of the N sensors, calculate the real distance between the j'th sensor and the i'th sensor, denoted as d _j',i' ; then calculate the measurement signal emitted by the j'th sensor After reaching the i'th sensor, the equivalent transmission distance in the transit time of the i'th sensor is denoted as d _T,j',i' , ③-4. Randomly select a sensor from N sensors, assuming that the selected sensor is the i'th sensor, then set a _i =min(d _T,j',i' |1≤j'≤N, j'≠i'), and let b _i =max(d _T,j',i' |1≤j'≤N,j'≠i'), where min() is the minimum value function, max( ) is the maximum value function.