CN109581281B - Moving target positioning method based on arrival time difference and arrival frequency difference - Google Patents

Abstract

The invention discloses a moving target positioning method based on arrival time difference and arrival frequency difference, which sets that 1 moving target for transmitting signals, 1 moving sensor for receiving signals and serving as a reference sensor and a plurality of moving sensors only for receiving signals exist; then calculating the distance difference and the distance difference change rate of the transmission distance from the moving target to each moving sensor only used for receiving signals and the transmission distance from the moving target to the reference sensor; then calculating the initial values of the position and the speed of the moving target; then determining the positioning problem of the moving target, and further solving to obtain an accurate estimation value of the position of the moving target; finally, optimizing the estimated value of the speed of the moving target by using the accurate estimated value of the position to obtain the accurate estimated value of the speed; the method has the advantages of capability of accurately estimating the position and the speed of the moving target, low calculation complexity and short running time.

Description

Moving target positioning method based on arrival time difference and arrival frequency difference

Technical Field

The invention relates to a target positioning technology, in particular to a moving target positioning method based on time difference of arrival and frequency difference of arrival, wherein the positioning content is the position and the speed of a moving target.

Background

In recent years, wireless sensor network positioning technology is widely applied in many fields, and has attracted much attention due to its wide application, and wireless positioning plays an important role in people's life, and can realize geographical measurement, navigation, emergency rescue, target tracking, etc. conveniently and quickly. In many practical applications, the unknown object is not stationary, that is, the unknown object is a moving object, and it is very important to accurately estimate the position of the moving object and also estimate the velocity of the moving object, so that research on a high-precision moving object positioning method in a wireless sensor network is necessary.

Currently, there are many basic methods for positioning a moving object, and a Time measurement method based on a Time Difference of Arrival (Time Difference of Arrival) and a doppler frequency offset measurement method based on a frequency Difference of Arrival (frequency Difference of Arrival) are often used in combination. The method for positioning the moving target has the advantages that the time measurement method is low in complexity, and high-precision position estimation can be realized; the Doppler frequency shift measurement method relates to the position and the speed of a moving target, can further improve the estimation precision of the position, and can also realize high-precision speed estimation. Therefore, most studies of moving object positioning methods are based on time difference of arrival measurements and frequency difference of arrival measurements.

The existing iteration constraint weighted least square method combines a time measurement method based on arrival time difference and a Doppler frequency offset measurement method based on arrival frequency difference, the iteration constraint weighted least square method can obtain a global optimal solution during iteration convergence, but the method cannot ensure convergence of each estimation, namely, the situation of iteration divergence exists, the method adopts the existing semi-positive definite relaxation method to remedy during iteration divergence, namely, the existing semi-positive definite relaxation method is used to obtain the position and speed estimation values of an unknown target. However, when the noise in the wireless sensor network is large, the possibility of iterative divergence of the iterative constrained weighted least square method becomes high, so that the number of times of using the semi-positive relaxation method becomes large, while the complexity of the semi-positive relaxation method is high, and the operation time is long, so that the computational complexity of the iterative constrained weighted least square method is high, and the operation time required for solving the iterative constrained weighted least square method is long.

Disclosure of Invention

The technical problem to be solved by the invention is to provide a moving target positioning method based on arrival time difference and arrival frequency difference, which can accurately estimate the position and the speed of a moving target under the condition that the moving target is distributed outside a moving sensor and the noise in a wireless sensor network is large, can obtain a global optimal solution, avoids the problems of local convergence and divergence, and has low calculation complexity and short running time.

The technical scheme adopted by the invention for solving the technical problems is as follows: a method for positioning a moving object based on a time difference of arrival and a frequency difference of arrival, comprising the steps of:

the method comprises the following steps: establishing a plane coordinate system as a reference coordinate system in a wireless sensor network environment, and setting that 1 moving target for transmitting signals, 1 moving sensor for receiving signals and serving as a reference sensor and N moving sensors only for receiving signals exist in the wireless sensor network environment; the coordinate position of the moving target in the reference coordinate system is recorded as x, and the moving speed of the moving target in the reference coordinate system is recorded as x

The coordinate position of the reference sensor in the reference coordinate system is recorded as s₀The moving speed of the reference sensor in the reference coordinate system is recorded as

The coordinate position correspondence of the N mobile sensors in the reference coordinate system is recorded as s₁,...,s_NThe moving speeds of the N moving sensors in the reference coordinate system are correspondingly recorded as

Wherein N is more than or equal to 3, s₁Representing the coordinate position, s, of the 1 st motion sensor in the reference coordinate system_NIndicating the coordinate position of the nth motion sensor in the reference coordinate system,

represents the moving speed of the 1 st moving sensor in the reference coordinate system,

representing the moving speed of the Nth moving sensor in the reference coordinate system;

step two: in the wireless sensor network environment, signals transmitted by a moving target are received by a reference sensor and N moving sensors only used for receiving the signals; firstly, measuring the transmission time of a signal emitted by a moving target to reach a reference sensor and the transmission time of a signal emitted by the moving target to reach N moving sensors; calculating the time difference between the transmission time of the signal emitted by the moving target to reach each moving sensor and the transmission time of the signal emitted by the moving target to reach the reference sensor, and recording the time difference between the transmission time of the signal emitted by the moving target to reach the ith moving sensor and the transmission time of the signal emitted by the moving target to reach the reference sensor as t_i(ii) a Secondly, measuring the Doppler frequency of the signal received by each mobile sensor and the Doppler frequency of the signal received by the reference sensor; calculating the Doppler frequency and reference transmission of the signal received by each mobile sensorThe frequency difference of the Doppler frequency of the signal received by the sensor is recorded as f, the frequency difference of the Doppler frequency of the signal received by the i-th mobile sensor and the Doppler frequency of the signal received by the reference sensor_i(ii) a Finally, calculating the distance difference between the signal transmission distance from the signal emitted by the moving target to each moving sensor and the signal transmission distance from the signal emitted by the moving target to the reference sensor, and recording the distance difference between the signal transmission distance from the signal emitted by the moving target to the ith moving sensor and the signal transmission distance from the signal emitted by the moving target to the reference sensor as d_i，d_i＝c×t_i(ii) a Calculating the rate of change of the difference between the distance from the moving object to the moving sensor and the distance from the moving object to the reference sensor, and recording the rate of change of the difference between the distance from the moving object to the ith moving sensor and the distance from the moving object to the reference sensor

Wherein i is a positive integer, i is more than or equal to 1 and less than or equal to N, c represents the speed of light, f₀Indicating the frequency of the carrier wave, f₀The value of (a) is known;

step three: calculate x and

respective initial values, corresponding to

And

wherein, the superscript "T" is the transposition symbol, (A)^TW₀A)^-1Is represented by (A)^TW₀A) Inverse of (a), (b), (c), (d), (₀And

are all intermediate variables introduced, r₀And

are all a number, r₀＝||x-s₀||，

0_1×kA row vector of dimension 1 × k representing element values all 0, k being a positive integer, k ≧ 2, d₁A distance difference s representing a signal transmission distance between the signal emitted from the moving object and the 1 st moving sensor and a signal transmission distance between the signal emitted from the moving object and the reference sensor_iRepresenting the coordinate position of the i-th motion sensor in the reference coordinate system, d_NA distance difference between a signal transmission distance from the signal transmitted from the moving object to the nth moving sensor and a signal transmission distance from the signal transmitted from the moving object to the signal received by the reference sensor,

a distance difference change rate representing a distance between a signal transmission distance of the signal emitted from the moving object to the 1 st moving sensor and a signal transmission distance of the signal emitted from the moving object to the reference sensor,

represents the moving speed of the ith moving sensor in the reference coordinate system,

representing moving objectsA rate of change in a difference between a signal transmission distance of the emitted signal to the nth motion sensor and a signal transmission distance of the signal emitted from the moving object to the reference sensor,

is Q_αInverse of (2), Q_α＝diag(Q_t,Q_f)，diag(Q_t,Q_f) Represents Q_tAnd Q_fIs a diagonal element, Q_tCovariance matrix of measurement noise, Q, representing time difference of arrival_fA covariance matrix of the measurement noise representing the difference in arrival frequencies,

the symbol "| | |" is a symbol for solving euclidean norm;

step four: determining the positioning problem of the moving target, which is described as:

constraint of y₂ ^TEy₂-2e^Ty₂+||s₀||²When the position of the moving target is 0, the positioning problem of the moving target is a weighted least square problem; wherein the content of the first and second substances,

shows that (Gy)₂-h)^TW^-1(Gy₂-h) minimization, W^-1The inverse of W is shown as a result,

0_N×Na square matrix of dimension N × N, B, representing all element values 0₁＝diag(r₁,...,r_N)，

diag(r₁,...,r_N) Is represented by r₁,...,r_NThe elements of the diagonal line are taken as the elements,

to represent

The elements of the diagonal line are taken as the elements,

are all intermediate variables that are introduced into the reactor,

are all a numerical value, and all the numerical values,

identity matrix with dimension k × k, 0_k×1Column vector of dimension k × 1, 0, representing all element values 0_k×kA square matrix of dimension k × k representing element values all 0, e ═ s₀ ^T,0_1×k,0]^T；

Step five: solving the positioning problem of the moving target by using a dichotomy to obtain the final estimated value sum of x

Is correspondingly expressed as

And

step six: to pair

Updating and optimizing to obtain

Is the final estimate of

Wherein the content of the first and second substances,

represents Q_fThe inverse of (a) is,

to represent

The inverse of (a) is,

the concrete process of the step five is as follows:

step a1, defining λ as the lagrange multiplier, and noting the function about λ as Φ (λ), which is described as: phi (lambda) ═ G^TW^-1G+λE)^-1(G^TW^-1h-λe)；

Step A2, solving matrix

And the characteristic value with the maximum value is recorded as u₁The minimum eigenvalue is designated as u₀(ii) a Then order

Wherein the content of the first and second substances,

and

are all intermediate variables that are introduced into the reactor,

step A3, order

Then will be

And

respectively substituting phi (lambda) into (G)^TW^-1G+λE)^-1(G^TW^{- 1}h- λ e), corresponding to

And

wherein the content of the first and second substances,

is an introduced intermediate variable;

step A4, judgment

If true, then order

Then a5 is executed; otherwise, it orders

Then a5 is executed; wherein the content of the first and second substances,

and

wherein, the symbol is an assignment symbol;

step A5, judgment

If yes, go to step A6; otherwise, returning to execute the step A3; wherein the symbol "|" is an absolute value symbol, representing a precision threshold;

step A6, mixing

As the optimum value for λ.

Compared with the prior art, the invention has the advantages that:

1) the method fully utilizes the measurement technology based on the arrival time difference to obtain the time difference between the transmission time of the signal transmitted by the moving target and the reference sensor, and jointly utilizes the measurement technology based on the arrival frequency difference to obtain the frequency difference between the Doppler frequency of the signal received by each moving sensor and the Doppler frequency of the signal received by the reference sensor, thereby further forming the positioning problem of the moving target, which is essentially a weighted least square problem, the weighted least square problem can be effectively solved, the global optimal solution can be obtained, and the problems of convergence to a local minimum point and divergence are avoided; the solving complexity is low, and the operation time is reduced.

2) The method combines a measurement technology based on time difference of arrival and a measurement technology based on frequency difference of arrival to construct a weighted least square problem, further solves and obtains an accurate estimation value of the coordinate position of the moving target, and then further updates speed estimation by using the accurate estimation value of the coordinate position of the moving target to obtain accurate speed estimation, so that the accurate position estimation value is ensured in the first step, and the position estimation value is also ensured for the accurate speed estimation in the second step, therefore, even under the condition that the moving target is distributed outside a moving sensor and the noise in a wireless sensor network is large, the method can accurately estimate the position and the speed of the moving target on the premise of ensuring low complexity.

Drawings

FIG. 1 is a general flow diagram of the process of the present invention;

FIG. 2 shows σ²Each value is 10^-2,10^-1.5,10^-1,10^-0.5,1,10^0.5,10¹Then, the method and the lower boundary of Clarame-Rou are utilized to estimate the position of the moving target;

FIG. 3 is a²Each value is 10^-2,10^-1.5,10^-1,10^-0.5,1,10^0.5,10¹In time, the method and Clarmei-The lower bound is a comparison graph of the root mean square error for estimating the velocity of a moving target.

Detailed Description

The invention is described in further detail below with reference to the accompanying examples.

The general flow diagram of the method for positioning a moving target based on the time difference of arrival and the frequency difference of arrival provided by the invention is shown in fig. 1, and the method comprises the following steps:

the method comprises the following steps: establishing a plane coordinate system as a reference coordinate system in a wireless sensor network environment, and setting that 1 moving target for transmitting signals, 1 moving sensor for receiving signals and serving as a reference sensor and N moving sensors only for receiving signals exist in the wireless sensor network environment; the coordinate position of the moving target in the reference coordinate system is recorded as x, and the moving speed of the moving target in the reference coordinate system is recorded as x

The coordinate position of the reference sensor in the reference coordinate system is recorded as s₀The moving speed of the reference sensor in the reference coordinate system is recorded as

The coordinate position correspondence of the N mobile sensors in the reference coordinate system is recorded as s₁,...,s_NThe moving speeds of the N moving sensors in the reference coordinate system are correspondingly recorded as

N is not less than 3, in this embodiment, N is 4, s₁Representing the coordinate position, s, of the 1 st motion sensor in the reference coordinate system_NIndicating the coordinate position of the nth motion sensor in the reference coordinate system,

represents the moving speed of the 1 st moving sensor in the reference coordinate system,

representing the moving speed of the Nth moving sensor in the reference coordinate system; here, s₀And

and

known as x and

is unknown.

Step two: in the wireless sensor network environment, signals transmitted by a moving target are received by a reference sensor and N moving sensors only used for receiving the signals; firstly, measuring the transmission time of a signal emitted by a moving target to reach a reference sensor and the transmission time of a signal emitted by the moving target to reach N moving sensors; calculating the time difference between the transmission time of the signal emitted by the moving target to reach each moving sensor and the transmission time of the signal emitted by the moving target to reach the reference sensor, and recording the time difference between the transmission time of the signal emitted by the moving target to reach the ith moving sensor and the transmission time of the signal emitted by the moving target to reach the reference sensor as t_i(ii) a Secondly, measuring the Doppler frequency of the signal received by each mobile sensor and the Doppler frequency of the signal received by the reference sensor; calculating the frequency difference between the Doppler frequency of the signal received by each mobile sensor and the Doppler frequency of the signal received by the reference sensor, and recording the frequency difference between the Doppler frequency of the signal received by the ith mobile sensor and the Doppler frequency of the signal received by the reference sensor as f_i(ii) a Finally, calculating the distance difference between the signal transmission distance from the signal emitted by the moving target to each moving sensor and the signal transmission distance from the signal emitted by the moving target to the reference sensor, and recording the distance difference between the signal transmission distance from the signal emitted by the moving target to the ith moving sensor and the signal transmission distance from the signal emitted by the moving target to the reference sensor as d_i，d_i＝c×t_i(ii) a Calculating the rate of change of the difference between the distance from the moving object to the moving sensor and the distance from the moving object to the reference sensor, and recording the rate of change of the difference between the distance from the moving object to the ith moving sensor and the distance from the moving object to the reference sensor

Wherein i is a positive integer, i is more than or equal to 1 and less than or equal to N, c represents the speed of light, f₀Indicating the frequency of the carrier wave, f₀The value of (c) is known.

Step three: calculate x and

respective initial values, corresponding to

And

wherein, the superscript "T" is the transposition symbol, (A)^TW₀A)^-1Is represented by (A)^TW₀A) Inverse of (a), (b), (c), (d), (₀And

are all intermediate variables introduced, r₀And

are all a number, r₀＝||x-s₀||，

0_1×kA row vector of dimension 1 × k with element values all 0, k being a positive integer, k ≧ 2, where k is 2 and d is₁A distance difference s representing a signal transmission distance between the signal emitted from the moving object and the 1 st moving sensor and a signal transmission distance between the signal emitted from the moving object and the reference sensor_iRepresenting the coordinate position of the i-th motion sensor in the reference coordinate system, d_NA distance difference between a signal transmission distance from the signal transmitted from the moving object to the nth moving sensor and a signal transmission distance from the signal transmitted from the moving object to the signal received by the reference sensor,

a distance difference change rate representing a distance between a signal transmission distance of the signal emitted from the moving object to the 1 st moving sensor and a signal transmission distance of the signal emitted from the moving object to the reference sensor,

represents the moving speed of the ith moving sensor in the reference coordinate system,

representing a rate of change of a distance difference between a signal transmission distance of the signal emitted from the moving object to the nth moving sensor and a signal transmission distance of the signal emitted from the moving object to the reference sensor,

is Q_αInverse of (2), Q_α＝diag(Q_t,Q_f)，diag(Q_t,Q_f) Represents Q_tAnd Q_fIs a diagonal element, Q_tCovariance matrix of measurement noise, Q, representing time difference of arrival_fIs shown toThe covariance matrix of the measurement noise up to the frequency difference,

the symbol "| | |" is a symbol for solving euclidean norm.

Step four: determining the positioning problem of the moving target, which is described as:

constraint of y₂ ^TEy₂-2e^Ty₂+||s₀||²When the position of the moving target is 0, the positioning problem of the moving target is a weighted least square problem; wherein the content of the first and second substances,

shows that (Gy)₂-h)^TW^-1(Gy₂-h) minimization, W^-1The inverse of W is shown as a result,

0_N×Na square matrix of dimension N × N, B, representing all element values 0₁＝diag(r₁,...,r_N)，

diag(r₁,...,r_N) Is represented by r₁,...,r_NThe elements of the diagonal line are taken as the elements,

to represent

The elements of the diagonal line are taken as the elements,

are all intermediate variables that are introduced into the reactor,

are all a number, r₁＝||x-s₁||，

Identity matrix with dimension k × k, 0_k×1Column vector of dimension k × 1, 0, representing all element values 0_k×kA square matrix of dimension k × k representing element values all 0, e ═ s₀ ^T,0_1×k,0]^T。

Step five: solving the positioning problem of the moving target by using a dichotomy to obtain the final estimated value sum of x

Is correspondingly expressed as

And

in this embodiment, the specific process of step five is:

step a1, defining λ as the lagrange multiplier, and noting the function about λ as Φ (λ), which is described as: phi (lambda) ═ G^TW^-1G+λE)^-1(G^TW^-1h-λe)。

Step A2, solving matrix

And the characteristic value with the maximum value is recorded as u₁The minimum eigenvalue is designated as u₀(ii) a Then order

Wherein the content of the first and second substances,

and

are all intermediate variables that are introduced into the reactor,

step A3, order

Then will be

And

respectively substituting phi (lambda) into (G)^TW^-1G+λE)^-1(G^TW^{- 1}h- λ e), corresponding to

And

wherein the content of the first and second substances,

is an intermediate variable introduced.

Step A4, judgment

If true, then order

Then a5 is executed; otherwise, it orders

Then a5 is executed; wherein the content of the first and second substances,

and

wherein, the symbol is assigned.

Step A5, judgment

If yes, go to step A6; otherwise, returning to execute the step A3; the symbol "|" is an absolute value symbol, and represents an accuracy threshold, and in this embodiment, is 10 | "^-10。

Step A6, mixing

As the optimum value for λ.

Step six: to pair

Updating and optimizing to obtain

Is the final estimate of

Wherein the content of the first and second substances,

represents Q_fThe inverse of (a) is,

to represent

The inverse of (a) is,

in order to verify the feasibility and the effectiveness of the method, the method is subjected to simulation test.

Assuming that 5(N ═ 4) mobile sensors are provided, the coordinate position of the reference sensor in the reference coordinate system is at the origin (0, 0), the moving speed of the reference sensor in the reference coordinate system is 0m/s, 4 mobile sensors only receiving signals are uniformly distributed in a circle with the origin (0, 0) as the center and the radius of 300m, and the moving speed of the 4 mobile sensors only receiving signals in the reference coordinate system is not more than 10 m/s. The coordinate position of the moving object in the reference coordinate system is randomly selected within a circular ring region centered at the origin (0, 0) and having a radius of 300m and a radius of 1000m, and the unknown movementThe moving speed of the target in the reference coordinate system is not more than 10 m/s. Assuming that the measurement noise of the arrival time difference measurement model and the measurement noise of the arrival frequency difference measurement model are independent of each other, the covariance matrix of the measurement noise of the arrival time difference measurement model is:

the covariance matrix of the measurement noise of the arrival frequency difference measurement model is: q_f＝0.01Q_tWherein, I_NIdentity matrix with dimension N × N, 1_NColumn vector of dimension N × 1, σ, representing element values all 1²Power of measurement noise, σ, for time difference of arrival²Each value is 10^-2,10^-1.5,10^-1,10^-0.5,1,10^0.5,10¹。

On the basis of the experimental conditions, the method of the invention is respectively utilized to carry out simulation experiment comparison under the Clarame-Luo boundary.

FIG. 2 shows σ²Each value is 10^-2,10^-1.5,10^-1,10^-0.5,1,10^0.5,10¹Then, the method and the lower boundary of Clarame-Rou are utilized to estimate the position of the moving target; FIG. 3 shows σ²Each value is 10^-2,10^-1.5,10^-1,10^-0.5,1,10^0.5,10¹The present invention is used in the estimation of moving target speed in the lower Clarmet-Row boundary. As can be seen from fig. 2, when the noise in the wireless sensor network is small, i.e., σ²From 10^-2Change to 10^-1.5In the method, the root mean square error of the estimation result value can reach the lower bound of the Clarame-Rou, namely the position estimation value of the method has high accuracy; when the noise in the wireless sensor network is medium and large, i.e. sigma²From 10^-1.5Change to 10¹The root mean square error of the estimation of the unknown target position is close to the Clarmet-Louvre boundary, which shows that the method has high accuracy of the position estimation. As can be seen from the view in figure 3,when the root mean square error of the estimated speed value estimated by the method is small in noise in the wireless sensor network, sigma is²From 10^-2Change to 10^-1The method is always attached to the lower Cramer-Rao bound, which shows that the accuracy of the speed estimation value of the method is higher, and when the noise in the wireless sensor network is increased, the root mean square error of the speed estimation of the method is always attached to the lower Cramer-Rao bound and does not greatly deviate from the lower Cramer-Rao bound. The feasibility and the effectiveness of the method are fully shown through simulation results.

Claims (2)

1. A method for positioning a moving object based on a time difference of arrival and a frequency difference of arrival, comprising the steps of:

the method comprises the following steps: establishing a plane coordinate system as a reference coordinate system in a wireless sensor network environment, and setting that 1 moving target for transmitting signals, 1 moving sensor for receiving signals and serving as a reference sensor and N moving sensors only for receiving signals exist in the wireless sensor network environment; the coordinate position of the moving target in the reference coordinate system is recorded as x, and the moving speed of the moving target in the reference coordinate system is recorded as x

The coordinate position of the reference sensor in the reference coordinate system is recorded as s₀The moving speed of the reference sensor in the reference coordinate system is recorded as

The coordinate position correspondence of the N mobile sensors in the reference coordinate system is recorded as s₁,...,s_NThe moving speeds of the N moving sensors in the reference coordinate system are correspondingly recorded as

Wherein N is more than or equal to 3, s₁Representing the coordinate position, s, of the 1 st motion sensor in the reference coordinate system_NIndicating that the Nth motion sensor is in the parameterBy reference to the coordinate position in the coordinate system,

represents the moving speed of the 1 st moving sensor in the reference coordinate system,

representing the moving speed of the Nth moving sensor in the reference coordinate system;

step two: in the wireless sensor network environment, signals transmitted by a moving target are received by a reference sensor and N moving sensors only used for receiving the signals; firstly, measuring the transmission time of a signal emitted by a moving target to reach a reference sensor and the transmission time of a signal emitted by the moving target to reach N moving sensors; calculating the time difference between the transmission time of the signal emitted by the moving target to reach each moving sensor and the transmission time of the signal emitted by the moving target to reach the reference sensor, and recording the time difference between the transmission time of the signal emitted by the moving target to reach the ith moving sensor and the transmission time of the signal emitted by the moving target to reach the reference sensor as t_i(ii) a Secondly, measuring the Doppler frequency of the signal received by each mobile sensor and the Doppler frequency of the signal received by the reference sensor; calculating the frequency difference between the Doppler frequency of the signal received by each mobile sensor and the Doppler frequency of the signal received by the reference sensor, and recording the frequency difference between the Doppler frequency of the signal received by the ith mobile sensor and the Doppler frequency of the signal received by the reference sensor as f_i(ii) a Finally, calculating the distance difference between the signal transmission distance from the signal emitted by the moving target to each moving sensor and the signal transmission distance from the signal emitted by the moving target to the reference sensor, and recording the distance difference between the signal transmission distance from the signal emitted by the moving target to the ith moving sensor and the signal transmission distance from the signal emitted by the moving target to the reference sensor as d_i，d_i＝c×t_i(ii) a Calculating the signal transmission distance of the signal emitted by the moving target to each moving sensor andthe rate of change of the distance difference between the transmission distance of the signal emitted from the moving target to the reference sensor and the transmission distance of the signal emitted from the moving target to the i-th moving sensor and the reference sensor is recorded as

Wherein i is a positive integer, i is more than or equal to 1 and less than or equal to N, c represents the speed of light, f₀Represents a frequency of a carrier wave;

step three: calculate x and

respective initial values, corresponding to

And

wherein, the superscript "T" is the transposition symbol, (A)^TW₀A)^-1Is represented by (A)^TW₀A) Inverse of (a), (b), (c), (d), (₀And

are all intermediate variables introduced, r₀And

are all a number, r₀＝||x-s₀||，

a₁＝[(s₁-s₀)^T0_1×kd₁0]，a_i＝[(s_i-s₀)^T0_1×kd_i0]，a_N＝[(s_N-s₀)^T0_1×kd_N0]，

0_1×kA row vector of dimension 1 × k representing element values all 0, k being a positive integer, k ≧ 2, d₁A distance difference s representing a signal transmission distance between the signal emitted from the moving object and the 1 st moving sensor and a signal transmission distance between the signal emitted from the moving object and the reference sensor_iRepresenting the coordinate position of the i-th motion sensor in the reference coordinate system, d_NA distance difference between a signal transmission distance from the signal transmitted from the moving object to the nth moving sensor and a signal transmission distance from the signal transmitted from the moving object to the signal received by the reference sensor,

a distance difference change rate representing a distance between a signal transmission distance of the signal emitted from the moving object to the 1 st moving sensor and a signal transmission distance of the signal emitted from the moving object to the reference sensor,

represents the moving speed of the ith moving sensor in the reference coordinate system,

representing a rate of change of a distance difference between a signal transmission distance of the signal emitted from the moving object to the nth moving sensor and a signal transmission distance of the signal emitted from the moving object to the reference sensor,

is Q_αInverse of (2), Q_α＝diag(Q_t,Q_f)，diag(Q_t,Q_f) Represents Q_tAnd Q_fIs a diagonal element, Q_tCovariance matrix of measurement noise, Q, representing time difference of arrival_fA covariance matrix of the measurement noise representing the difference in arrival frequencies,

the symbol "| | |" is a symbol for solving euclidean norm;

step four: determining the positioning problem of the moving target, which is described as:

constraint of y₂ ^TEy₂-2e^Ty₂+||s₀||²When the position of the moving target is 0, the positioning problem of the moving target is a weighted least square problem; wherein the content of the first and second substances,

shows that (Gy)₂-h)^TW^-1(Gy₂-h) minimization, W^-1The inverse of W is shown as a result,

g₁＝[(s₁-s₀)^T0_1×kd₁]，g_i＝[(s_i-s₀)^T0_1×kd_i]，g_N＝[(s_N-s₀)^T0_1×kd_N]，

W＝BQ_αB，

0_N×Na square matrix of dimension N × N, B, representing all element values 0₁＝diag(r₁,...,r_N)，

diag(r₁,...,r_N) Is represented by r₁,...,r_NThe elements of the diagonal line are taken as the elements,

to represent

Is a diagonal element, r₁、r_N、

Are all intermediate variables introduced, r₁、r_N、

Are all a number, r₁＝||x-s₁||，r_N＝||x-s_N||，

I_kIdentity matrix with dimension k × k, 0_k×1Column vector of dimension k × 1, 0, representing all element values 0_k×kA square matrix of dimension k × k representing element values all 0, e ═ s₀ ^T,0_1×k,0]^T；

Step five: solving the positioning problem of the moving target by using a dichotomy to obtain the final estimated value sum of x

Is correspondingly expressed as

And

step six: to pair

Updating and optimizing to obtain

Is the final estimate of

Wherein the content of the first and second substances,

represents Q_fThe inverse of (a) is,

to represent

The inverse of (a) is,

2. the method according to claim 1, wherein the specific process of step five is as follows:

step a1, defining λ as the lagrange multiplier, and noting the function about λ as Φ (λ), which is described as:

φ(λ)＝(G^TW^-1G+λE)^-1(G^TW^-1h-λe)；

step A2, solving matrix

And the characteristic value with the maximum value is recorded as u₁The minimum eigenvalue is designated as u₀(ii) a Then order

Wherein the content of the first and second substances,

and

are all intermediate variables that are introduced into the reactor,

step A3, order

Then will be

And

respectively substituting phi (lambda) into (G)^TW^-1G+λE)^-1(G^TW^-1h- λ e), corresponding to

And

wherein the content of the first and second substances,

is an introduced intermediate variable;

step A4, judgment

If true, then order

Then a5 is executed; otherwise, it orders

Then a5 is executed;wherein the content of the first and second substances,

and

wherein, the symbol is an assignment symbol;

step A5, judgment

If yes, go to step A6; otherwise, returning to execute the step A3; wherein the symbol "|" is an absolute value symbol, representing a precision threshold;

step A6, mixing

As the optimum value for λ.

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