CN110658492A - Iteration method for optimizing positions of indoor target and scatterer - Google Patents

Abstract

The invention discloses an iteration method for optimizing positions of indoor targets and scatterers. Firstly, constructing an indoor scatterer and a multipath signal propagation model of a single AP according to multipath signal propagation characteristics; secondly, constructing a difference delta tof equation of the target position relative to each scatterer by using the position relation between the multipath signal parameter difference delta tof and the single AP, the target and each scatterer, and converting the performance optimization problem of the positioning system into a weighted least square solving problem; and finally, solving a difference delta tof equation by iteration by using a WLS algorithm to obtain the final estimated positions of the scatterers and the target. The method provides an indoor target and scatterer position optimization iteration method based on a WLS algorithm, solves the problem of low positioning accuracy in a multipath environment, and can enhance the robustness of a positioning system while reducing equipment deployment cost.

Description

Iteration method for optimizing positions of indoor target and scatterer

Technical Field

The invention relates to the technical field of indoor positioning, in particular to an iteration method for optimizing positions of an indoor target and a scatterer.

Background

Under the comprehensive evolution of factors such as technical development, demand change and industry fusion, along with the collision of multiple industries such as wireless communication, internet of things and artificial intelligence, the outdoor positioning technology cannot meet the demand of people on position information. The development of indoor positioning technology gradually presents a development trend of integration of various positioning technologies and integration of indoor and outdoor positioning technologies. The indoor positioning industrial chain is expanded and extended from a single line to a net structure, and then is developed to an indoor positioning system with higher positioning precision. Currently, in the research in the field of indoor positioning, position estimation is usually performed by means of signal parameter information such as Received Signal Strength (RSS), Angle of Arrival (AOA), Time of Arrival (ToF), or in combination with motion sensor data fusion information. In order to improve the accuracy of the positioning technique, fine-grained parameters such as time of flight and angle of arrival are generally used as signal parameters of the positioning system. In order to improve the estimation accuracy of the AoA-based positioning algorithm, multiple APs are usually deployed in a test environment, which increases the investment of equipment cost, and thus the positioning method based on a single AP is gradually applied to various positioning systems.

In an indoor complex environment, non-line-of-sight propagation is a main factor influencing the positioning accuracy of the WLAN, and currently, the research on the non-line-of-sight positioning of the WLAN mainly includes: a non-line-of-sight identification algorithm, a non-line-of-sight positioning algorithm based on scatterer information, and a non-line-of-sight positioning method with added inequality constraints. The multi-path information based on the scatterer channel model and the scatterer geometric position relation provides a new idea for the indoor positioning technology. In the positioning process, multipath information is often considered as interference information, so researchers usually adopt some techniques to suppress this part of information, and simultaneously improve the positioning accuracy of the system by deploying relevant positioning equipment. When signals are propagated in an indoor environment by various scatterers, the multipath signals contain abundant geometric information capable of reflecting indoor environment changes, so that the propagation characteristics of the scatterers can be combined to assist in positioning targets and positions of the scatterers.

Aiming at the problem that the existing indoor positioning technology is difficult to meet a plurality of performance requirements of a single AP positioning system, the invention provides an indoor target and scatterer position optimization iteration method. The method reduces the deployment cost of a plurality of APs and special multi-array antenna equipment in a positioning algorithm, and utilizes simple and easily-obtained scatterer position information in an indoor environment to construct a difference delta tof equation of a target position relative to each scatterer, and finally solves the equation through a WLS algorithm to obtain the target and scatterer position information. The method solves the problems that the existing positioning system needs to deploy a large number of APs and the robustness in a multipath environment is low, and has good effectiveness.

Disclosure of Invention

The invention aims to provide an iteration method for optimizing the positions of an indoor target and a scatterer, which is different from the conventional method for inhibiting multipath signals aiming at the limitations of the existing indoor positioning technology in the aspects of infrastructure overhead, system stability and the like.

The invention relates to an iteration method for optimizing the positions of an indoor target and a scatterer, which comprises the following steps:

step one, constructing an indoor multipath signal propagation model according to signal propagation characteristics under an indoor multipath environment, wherein m (m is more than or equal to 3, and m is an integer) scatterers containing position errors are deployed in the model and are expressed as

The ith scatterer is noted as

(i is not more than m, i is an integer) and the coordinate is recorded as

Single AP coordinate is denoted as s₁＝(x₁，y₁，z₁) The target position coordinate is denoted as (x, y, z).

Step two, based on the primary position of the scatterer in the step one(i is not more than m, i is an integer), constructing a group with the position coordinates of each scatterer as particles by utilizing a particle swarm optimization algorithm in the group intelligent optimization algorithm, and continuously and iteratively updating the speed and the position of each particle in the groupFinally, m initial scatterer position coordinates containing position errors and with the optimal group are searched and recorded as s_i ⁽¹⁾＝(x_i ⁽¹⁾，y_i ⁽¹⁾，z_i ⁽¹⁾)，i＝，…，m。

Step three, based on the preliminary estimated positions of the m scatterers obtained in the step two, calculating a distance set C_i；

The method specifically comprises the following steps:

and step three (one), because the energy loss of the signal after multiple reflections is large, only a single reflection path is considered in the model provided by the patent. The signal is reflected by the ith scatterer and then reaches the AP S₁Distance r of reflection path from signal terminal to scatterer_iIt can be calculated by the following formula:

step three (two), based on the signal reflection path r in step three (one)_iLet the distance d of the reflection path from the scatterer to the single AP_iIt can be calculated by the following formula:

step three, the direct-view distance r of the signal from the target to the single AP₁It can be calculated by the following formula:

constructing a distance set C_j＝{r_i，d_i，r₁In which C is_jMiddle is distance element r_i，d_iAnd r₁。

Step four, based on the distance set C in step three_jConstruction of the differential Δ tof_i，1An equation; the method specifically comprises the following steps:

step four (one), in the distance set C_jIn (1), traverse all scatterers in the setReflection path distance r with position as calculation parameter_iAnd a distance d_i。

Step four (step two), in the multipath environment with a plurality of scatterers distributed indoors, the time difference between the target signal reflected by the scatterers and the direct path obtained through actual measurement is recorded as delta tof_i，1Constructing a differential Δ tof_i，1The equation is as follows:

cΔtof_i，1＝r_i+d_i-r₁ (4)

where c represents the speed of light.

Step five, based on the difference delta tof in the step four_i，1An equation is combined with the position relation among the single AP, the target and the scatterer to construct a pi_1，e ⁽¹⁾A set of localization equations for the unknown variables; the method specifically comprises the following steps:

step five (one), defining vector pi_1，e ⁽¹⁾Is expressed as pi_1，e ⁽¹⁾＝[x⁽⁰⁾，y⁽⁰⁾，z⁽⁰⁾，r₁]^TThe vector including a preliminary target position u⁽⁰⁾＝(x⁽⁰⁾，y⁽⁰⁾，z⁽⁰⁾) And direct viewing radial distance r₁。

Step five (two), based on the vector pi in step five (one)_1，e ⁽¹⁾And constructing a positioning equation set, wherein the formula is as follows:

h_1，e ⁽¹⁾＝G_1，e ⁽¹⁾π_1，e ⁽¹⁾ (5)

wherein the content of the first and second substances,

l_m，1＝s_m ^(1)Ts_m ⁽¹⁾-s₁ ^Ts₁and m represents the number of scatterers.

Step six, based on the stepsCalculating a preliminary target position u by using the positioning equation set in the fifth step⁽⁰⁾＝(x⁽⁰⁾，y⁽⁰⁾，z⁽⁰⁾) (ii) a The method specifically comprises the following steps:

step six (one), defining weight matrix W_1，e ⁽¹⁾The calculation formula is as follows:

W_1，e ⁽¹⁾＝B_1，e ^-TQ^-1B_1，e ^-1 (6)

wherein, B_1，e＝2diag{r₂，r₃，…r_MQ is c of the known differential Δ tof noise error n²And (4) doubling.

Step six (two), based on the weight matrix W in step six (one)_1，e ⁽¹⁾Solving the unknown vector pi by using a weighted least square algorithm_1，e ⁽¹⁾The calculation formula is as follows:

π_1，e ⁽¹⁾＝(G_1，e ^(1)TW_1，e ⁽¹⁾G_1，e ⁽¹⁾)^-1G_1，e ^(1)TW_1，e ⁽¹⁾h_1，e ⁽¹⁾ (7)

step seven, based on the positioning equation set in the step five, calculating the current initial target position u⁽⁰⁾For its true position u₁ ^(0)oTime, vector pi_1，e ⁽¹⁾The covariance matrix of (a); the method specifically comprises the following steps:

step seven (one), recording delta tof_i，1 ^o、ΔT_iRespectively differential arrival time Δ tof_i，1True value and error term of d_i ^o、Δd_iRespectively representing the real distance between the scatterer and the single AP and a distance error term (because the position of the scatterer has an error), and ignoring a high-order error term in analysis; the calculation formula is as follows:

step seven (two), based on the preliminary scatterer position error term in step seven (one)It is expressed in vector form as follows:

wherein, B_1，e＝2diag{r₂，r₃，…r_M}。

Step seven (three), vector expression formula epsilon based on preliminary scatterer position error term in step seven (two)₁(i) Updating the calculation weight matrix W_2，e ⁽¹⁾The formula is as follows:

step seven (four), based on the weight matrix W in step seven (three)_2，e ⁽¹⁾Calculating pi_1，e ⁽¹⁾The covariance matrix formula of (a) is as follows:

cov(π_1，e ⁽¹⁾)＝(G_1，e ⁽¹⁾W_2，e ⁽¹⁾G_1，e ⁽¹⁾)^-1 (11)

step eight, reestablishing the standard value of pi_2，e ⁽¹⁾A set of positioning equations for the unknown vector; the method specifically comprises the following steps:

step eight (one), vector expression is pi_2，e ⁽¹⁾＝[(x⁽⁰⁾-x₁)²，(y⁽⁰⁾-y₁)²，(z⁽⁰⁾-z₁)²]The element in the vector is the difference between the preliminary target position and the single AP position.

Step eight (two), based on the vector pi in step eight (one)_2，e ⁽¹⁾And updating a positioning equation set, wherein the formula is as follows:

h_2，e ⁽¹⁾＝G_2，e ⁽¹⁾π_2，e ⁽¹⁾ (12)

wherein the content of the first and second substances,

step nine, based on the positioning equation set in step eight and the covariance matrix cov (pi) in step seven (four)_1，e ⁽¹⁾) Calculating the updated initial target position u by using a weighted least square algorithm⁽¹⁾(ii) a The method specifically comprises the following steps:

step nine (one), updating and calculating weight matrix W_1，e ⁽²⁾The formula is as follows:

W_1，e ⁽²⁾＝B_2，e ^-Tcov(π_1，e ⁽¹⁾)B_2，e ^-1 (13)

wherein, B_2，e＝2diag{(x⁽⁰⁾-x₁)，(y⁽⁰⁾-y₁)，(z⁽⁰⁾-z₁)，r₁}

Step nine (two), based on W in step nine (one)_1，e ⁽²⁾And calculating an unknown vector by using a weighted least square algorithm, wherein the formula is as follows:

π_2，e ⁽¹⁾＝(G_2，e ^(1)TW_1，e ⁽²⁾G_2，e ⁽¹⁾)^-1G_2，e ^(1)TW_1，e ⁽²⁾h_2，e ⁽¹⁾ (14)

step nine (three), variable pi based on solution in step nine (two)_2，e ⁽¹⁾Calculating the updated preliminary target position u⁽¹⁾Comprises the following steps:

where T is a sign factor, which acts to eliminate the ambiguity problem of the root in equation (15), and is expressed as:

T＝diag{sgn(π_2，e ⁽¹⁾(1)-x₁)，sgn(π_2，e ⁽¹⁾(2)-y₁)，sgn(π_2，e ⁽¹⁾(3)-z₁)}

step ten, based on the updated preliminary target position u obtained in the step nine⁽¹⁾Updating a positioning equation set by a sum difference delta tof equation, and iteratively calculating a final scatterer position coordinate s of the system_i＝(x_i，y_i，z_i) I is 2, …, m; the method specifically comprises the following steps:

step ten (one), based on the updated preliminary target position u obtained in the step nine⁽¹⁾＝(x⁽¹⁾，y⁽¹⁾，z⁽¹⁾) The final scatterer position is expressed as:

s_i＝s^o _i+Δs_i (16)

wherein s is^o _iAs true coordinates of the scatterers, Δ s_iIs the position coordinate error of the scatterer;

the following new difference Δ tof equation is given as the following equation (18):

(cΔtof_i，1 ^o-d_i ^o)²+2(cΔtof_i，1 ^o-d_i ^o)r₁＝s_i ^oTs_i ^o-s₁ ^oTs₁ ^o-2(s_i ^o-s₁ ^o)^Tu⁽¹⁾ (17)

step ten (two), based on the formula (19) in the step ten (one), establishing a positioning equation set with z as an unknown vector, wherein elements in z comprise final scatterer position coordinates, and the positioning equation set is as follows:

h_t＝G_tz (20)

wherein s is₁ ^o，…s_i ^oI 2, …, m being the true position coordinates of the scatterer,

step ten (three), based on the positioning equation set in the step ten (two), calculating an unknown vector z containing the position coordinates of the final scatterer by using a least square algorithm:

z＝G₁ ^-1h_t (21)

thus, the final scatterer coordinates of the present system are i, i ═ 2, …, m elements in the variable z.

Step eleven, based on the formula (18) in the step eleven, calculating an error term of the final scatterer position coordinate obtained by utilizing the initial target position inverse iteration and recording the error term as epsilon_tThe calculation formula is as follows:

will delta d_iSpread out at each scatterer:

the error term can be written as:

ε_t＝UΔψ (24)

wherein the content of the first and second substances,

α_i＝2r_i，

Δψ＝[ΔT₂ ΔT₃ … ΔT_m Δs₁ ^T Δs₂ ^T … Δs_m ^T]^T。

step twelve, based on the final scattering obtained in step tenBody position coordinate s_i＝(x_i，y_i，z_i) And step five is repeated, a positioning equation set with the final target position u as an unknown variable is constructed, and the coordinate u of the final target position is solved as (x, y, z).

Advantageous effects

The invention has the beneficial effects that: firstly, constructing an indoor scatterer and a multipath signal propagation model of a single AP; then, constructing a differential delta tof positioning equation by using the multipath signal parameter differential delta tof according to the triangular geometric position relation among the single AP, the target and each scatterer, and converting the positioning system performance optimization problem into a weighted least square solving problem; and finally, iteration is carried out by utilizing a WLS algorithm to obtain the estimated positions of the scatterers and the targets. The method solves the problem of low positioning accuracy in a multipath environment, and can enhance the robustness of a positioning system while reducing equipment deployment cost.

Drawings

FIG. 1 is a flow chart of the present invention;

FIG. 2 is a WLAN single AP based multi-scatterer positioning model according to the present invention;

detailed description of the preferred embodiments

The invention will be further described with reference to the accompanying drawings in which:

as shown in fig. 1, an iterative method for optimizing the position of an indoor target and a scatterer includes the following steps:

step one, in an indoor multipath environment, an indoor multipath signal propagation model is constructed according to signal propagation characteristics, as shown in fig. 2. M (m is more than or equal to 3, m is an integer) scatterers containing position errors are arranged in the model and are expressed as

The ith scatterer is noted as

(i is not more than m, i is an integer) and the coordinate is recorded as

Single AP coordinate is denoted as s₁＝(x₁，y₁，z₁) The target position coordinate is denoted as (x, y, z).

Step two, based on the primary position of the scatterer in the step one

(i is not more than m, i is an integer), a group taking the position coordinates of each scatterer as particles is constructed by utilizing a particle swarm optimization algorithm in the group intelligent optimization algorithm, the speed and the position of each particle in the group are continuously updated in an iterative manner, and finally m initial scatterer position coordinates containing position errors and optimal in the group are searched out and are recorded as s_i ⁽¹⁾＝(x_i ⁽¹⁾，y_i ⁽¹⁾，z_i ⁽¹⁾)，i＝2，…，m。

Step three, based on the preliminary estimated positions of the m scatterers obtained in the step two, calculating a distance set C_j(ii) a The method specifically comprises the following steps:

and step three (one), because the energy loss of the signal after multiple reflections is large, only a single reflection path is considered in the model provided by the patent. The signal is reflected by the ith scatterer and then reaches the AP S₁Distance r of reflection path from signal terminal to scatterer_iIt can be calculated by the following formula:

step three (two), based on the signal reflection path r in step three (one)_iLet the distance d of the reflection path from the scatterer to the single AP_iIt can be calculated by the following formula:

step three, the direct-view distance r of the signal from the target to the single AP₁It can be calculated by the following formula:

constructing a distance set C_j＝{r_i，d_i，r₁In which C is_jMiddle is distance element r_i，d_iAnd r₁。

Step four, based on the distance set C in step three_jConstruction of the differential Δ tof_i，1An equation; the method specifically comprises the following steps:

step four (one), in the distance set C_jTraversing all reflection path distances r in the set by using the scattering position as a calculation parameter_iAnd a distance d_i。

Step four (step two), in the multipath environment with a plurality of scatterers distributed indoors, the time difference between the target signal reflected by the scatterers and the direct path obtained through actual measurement is recorded as delta tof_i，1Constructing a differential Δ tof_i，1The equation is as follows:

cΔtof_i，1＝r_i+d_i-r₁ (4)

where c represents the speed of light.

Step five, based on the difference delta tof in the step four_i，1An equation is combined with the position relation among the single AP, the target and the scatterer to construct a pi_1，e ⁽¹⁾A set of localization equations for the unknown variables; the method specifically comprises the following steps:

step five (one), defining vector pi_1，e ⁽¹⁾Is expressed as pi_1，e ⁽¹⁾＝[x⁽⁰⁾，y⁽⁰⁾，z⁽⁰⁾，r₁]^TThe vector including a preliminary target position u⁽⁰⁾＝(x⁽⁰⁾，y⁽⁰⁾，z⁽⁰⁾) And direct viewing radial distance r₁。

Step five (two), based on the vector pi in step five (one)_1，e ⁽¹⁾And constructing a positioning equation set, wherein the formula is as follows:

h_1，e ⁽¹⁾＝G_1，e ⁽¹⁾π_1，e ⁽¹⁾ (5)

wherein the content of the first and second substances,

l_m，1＝s_m ^(1)Ts_m ⁽¹⁾-s₁ ^Ts₁and m represents the number of scatterers.

Step six, calculating a preliminary target position u based on the positioning equation set in the step five⁽⁰⁾＝(x⁽⁰⁾，y⁽⁰⁾，z⁽⁰⁾) (ii) a The method specifically comprises the following steps:

step six (one), defining weight matrix W_1，e ⁽¹⁾The calculation formula is as follows:

W_1，e ⁽¹⁾＝B_1，e ^-TQ^-1B_1，e ^-1 (6)

wherein, B_1，e＝2diag{r₂，r₃，…r_MQ is c of the known differential Δ tof noise error n²And (4) doubling.

Step six (two), based on the weight matrix W in step six (one)_1，e ⁽¹⁾Solving the unknown vector pi by using a weighted least square algorithm_1，e ⁽¹⁾The calculation formula is as follows:

π_1，e ⁽¹⁾＝(G_1，e ^(1)TW_1，e ⁽¹⁾G_1，e ⁽¹⁾)^-1G_1，e ^(1)TW_1，e ⁽¹⁾h_1，e ⁽¹⁾ (7)

step seven, based on the positioning equation set in the step five, calculating the current initial target position u⁽⁰⁾For its true position u₁ ^(0)oTime, vector pi_1，e ⁽¹⁾The covariance matrix of (a); the method specifically comprises the following steps:

step seven (one), recording delta tof_i，1 ^o、ΔT_iRespectively differential arrival time Δ tof_i，1True value and error term of d_i ^o、Δd_iRespectively representing the real distance between the scatterer and the single AP and a distance error term (because the position of the scatterer has an error), and ignoring a high-order error term in analysis; the calculation formula is as follows:

step seven (two), based on the preliminary scatterer position error term in step seven (one)

It is expressed in vector form as follows:

wherein, B_1，e＝2diag{r₂，r₃，…r_M}。

Step seven (three), vector expression formula epsilon based on preliminary scatterer position error term in step seven (two)₁(i) Updating the calculation weight matrix W_2，e ⁽¹⁾The formula is as follows:

step seven (four), based on the weight matrix W in step seven (three)_2，e ⁽¹⁾Calculating pi_1，e ⁽¹⁾The covariance matrix formula of (a) is as follows:

cov(π_1，e ⁽¹⁾)＝(G_1，e ⁽¹⁾W_2，e ⁽¹⁾G_1，e ⁽¹⁾)^-1 (11)

step eight, reestablishing the standard value of pi_2，e ⁽¹⁾A set of positioning equations for the unknown vector; the method specifically comprises the following steps:

step eight (one), vector expression is pi_2，e ⁽¹⁾＝[(x⁽⁰⁾-x₁)²，(y⁽⁰⁾-y₁)²，(z⁽⁰⁾-z₁)²]The element in the vector is the difference between the preliminary target position and the single AP position.

Step eight (two), based on the vector pi in step eight (one)_2，e ⁽¹⁾And updating a positioning equation set, wherein the formula is as follows:

h_2，e ⁽¹⁾＝G_2，e ⁽¹⁾π_2，e ⁽¹⁾ (12)

wherein the content of the first and second substances,

step nine, based on the positioning equation set in step eight and the covariance matrix cov (pi) in step seven (four)_1，e ⁽¹⁾) Calculating the updated initial target position u by using a weighted least square algorithm⁽¹⁾(ii) a The method specifically comprises the following steps:

step nine (one), updating and calculating weight matrix W_1，e ⁽²⁾The formula is as follows:

W_1，e ⁽²⁾＝B_2，e ^-Tcov(π_1，e ⁽¹⁾)B_2，e ^-1 (13)

wherein, B_2，e＝2diag{(x⁽⁰⁾-x₁)，(y⁽⁰⁾-y₁)，(z⁽⁰⁾-z₁)，r₁}

Step nine (two), based on W in step nine (one)_1，e ⁽²⁾And calculating an unknown vector by using a weighted least square algorithm, wherein the formula is as follows:

π_2，e ⁽¹⁾＝(G_2，e ^(1)TW_1，e ⁽²⁾G_2，e ⁽¹⁾)^-1G_2，e ^(1)TW_1，e ⁽²⁾h_2，e ⁽¹⁾ (14)

step nine (three), variable pi based on solution in step nine (two)_2，e ⁽¹⁾Calculating the updated preliminary target position u⁽¹⁾Comprises the following steps:

where T is a sign factor, which acts to eliminate the ambiguity problem of the root in equation (15), and is expressed as:

T＝diag{sgn(π_2，e ⁽¹⁾(1)-x₁)，sgn(π_2，e ⁽¹⁾(2)-y₁)，sgn(π_2，e ⁽¹⁾(3)-z₁)}

step ten, based on the initial target position u obtained in the step nine⁽¹⁾Updating a positioning equation set by a sum difference delta tof equation, and iteratively calculating a final scatterer position coordinate s of the system_i＝(x_i，y_i，z_i) I is 2, …, m; the method specifically comprises the following steps:

step ten (one), based on the updated preliminary target position u obtained in the step nine⁽¹⁾＝(x⁽¹⁾，y⁽¹⁾，z⁽¹⁾) The final scatterer position is expressed as:

s_i＝s^o _i+Δs_i (16)

wherein s is^o _iAs true coordinates of the scatterers, Δ s_iIs the position coordinate error of the scatterer;

the following new difference Δ tof equation is given as the following equation (18):

(cΔtof_i，1 ^o-d_i ^o)²+2(cΔtof_i，1 ^o-d_i ^o)r₁＝s_i ^oTs_i ^o-s₁ ^oTs₁ ^o-2(s_i ^o-s₁ ^o)^Tu⁽¹⁾ (17)

step ten (two), based on the formula (19) in the step ten (one), establishing a positioning equation set with z as an unknown vector, wherein elements in z comprise final scatterer position coordinates, and the positioning equation set is as follows:

h_t＝G_tz (20)

wherein s is₁ ^o，…s_i ^oI 2, …, m being the true position coordinates of the scatterer,

step ten (three), based on the positioning equation set in the step ten (two), calculating an unknown vector z containing the position coordinates of the final scatterer by using a least square algorithm:

z＝G_t ^-1h_t (21)

thus, the final scatterer coordinates of the present system are i, i ═ 1, …, m elements in the variable z.

Step eleven, based on the formula (18) in the step eleven, calculating an error term of the final scatterer position coordinate obtained by utilizing the initial target position inverse iteration and recording the error term as epsilon_tThe calculation formula is as follows:

will delta d_iSpread out at each scatterer:

the error term can be written as:

ε_t＝UΔψ (24)

wherein the content of the first and second substances,α_i＝2r_i，

Δψ＝[ΔT₂ ΔT₃ … ΔT_m Δs₁ ^T Δs₂ ^T … Δs_m ^T]^T。

step twelve, based on the position coordinates s of the final scatterer obtained in the step ten_i＝(x_i，y_i，z_i) And step five is repeated, a positioning equation set with the final target position u as an unknown variable is constructed, and the coordinate u of the final target position is solved as (x, y, z).

Claims (4)

1. An iterative method for optimizing the positions of an indoor target and a scatterer is characterized by comprising the following steps;

step one, constructing an indoor multipath signal propagation model according to signal propagation characteristics in an indoor multipath environment, wherein m (m is more than or equal to 3, and m is an integer) scatterers containing position errors are deployed in the model

2, …, m, single APs₁A target u;

step two, constructing a group with each preliminary scatterer position as a particle by utilizing a particle swarm algorithm, continuously and iteratively updating the speed and the position of each particle in the group, and searching out m preliminary scatterer positions s containing position errors_i ⁽¹⁾，i＝2,…,m；

Step three, constructing a distance set C by taking the reflection path distance of each scatterer as a set element_j；

Step four, based on the elements in the distance set in step three, and the time difference delta tof between the target signal obtained through actual measurement and the direct path after the target signal is reflected by the scatterer_i,1Constructing a differential Δ tof_i,1An equation;

step five, based on the difference delta tof in the step four_i,1Equation and join sheetThe position relation among the AP, the target and the scatterer is constructed by taking the initial target position and the direct-view distance as unknown variables pi_1,e ⁽¹⁾The system of positioning equations of (1);

step six, calculating a preliminary target position u based on the positioning equation set in the step five⁽⁰⁾；

Step seven, obtaining a preliminary target position u based on the step six⁽⁰⁾Calculating the vector pi_1,e ⁽¹⁾The covariance matrix of (a);

step eight, updating by pi_2,e ⁽¹⁾A set of positioning equations for the unknown vector;

step nine, positioning equation set based on step eight and seven covariance matrix cov (pi)_1,e ⁽¹⁾) Calculating a preliminary target position u using a weighted least squares algorithm⁽¹⁾；

Step ten, based on the initial target position u obtained in the step nine⁽¹⁾Updating a positioning equation set by a sum difference delta tof equation, and iteratively calculating a final scatterer position coordinate s of the system_i，i＝2,…,m；

Eleven, based on the updated positioning equation set in the step ten, calculating an error term of the final scatterer position coordinate obtained by utilizing the inverse iteration of the initial target position and recording the error term as epsilon_t；

Step twelve, based on the position coordinates s of the final scatterer obtained in the step ten_i＝(x_i,y_i,z_i) And step five is repeated, a positioning equation set with the final target position u as an unknown variable is constructed, and the coordinate u of the final target position is solved as (x, y, z).

2. The iterative method for optimizing the positions of the indoor target and the scatterer based on the method as claimed in claim 1, wherein the fourth step is specifically;

step four, based on the distance set C in step three_jConstruction of the differential Δ tof_i,1An equation; the method specifically comprises the following steps:

step four (one), in the distance set C_jTraversing all reflection path distances r in the set by using the scattering position as a calculation parameter_iAnd a distance d_i。

Step four (step two), in the multipath environment with a plurality of scatterers distributed indoors, the time difference between the target signal reflected by the scatterers and the direct path obtained through actual measurement is recorded as delta tof_i,1Constructing a differential Δ tof_i,1The equation is as follows:

cΔtof_i,1＝r_i+d_i-r₁ (4)

where c represents the speed of light.

3. The iterative method for optimizing the positions of the indoor target and the scatterer based on the method as claimed in claim 1, wherein the fifth step is specifically;

step five, based on the difference delta tof in the step four_i,1An equation is combined with the position relation among the single AP, the target and the scatterer to construct a pi_1,e ⁽¹⁾A set of localization equations for the unknown variables; the method specifically comprises the following steps:

step five (one), defining vector pi_1,e ⁽¹⁾Is expressed as pi_1,e ⁽¹⁾＝[x⁽⁰⁾,y⁽⁰⁾,z⁽⁰⁾,r₁]^TThe vector including a preliminary target position u⁽⁰⁾＝(x⁽⁰⁾,y⁽⁰⁾,z⁽⁰⁾) And direct viewing radial distance r₁。

Step five (two), based on the vector pi in step five (one)_1,e ⁽¹⁾And constructing a positioning equation set, wherein the formula is as follows:

h_1,e ⁽¹⁾＝G_1,e ⁽¹⁾π_1,e ⁽¹⁾ (5)

wherein the content of the first and second substances,

l_m,1＝s_m ^(1)Ts_m ⁽¹⁾-s₁ ^Ts₁and m represents the number of scatterers.

4. The iterative method for optimizing the positions of the indoor target and the scatterer based on the method as claimed in claim 1, wherein the step ten is specifically;

step ten, based on the updated preliminary target position u obtained in the step nine⁽¹⁾Updating a positioning equation set by a sum difference delta tof equation, and iteratively calculating a final scatterer position coordinate s of the system_i＝(x_i,y_i,z_i) I is 2, …, m; the method specifically comprises the following steps:

step ten (one), based on the updated preliminary target position u obtained in the step nine⁽¹⁾＝(x⁽¹⁾,y⁽¹⁾,z⁽¹⁾) The final scatterer position is expressed as:

s_i＝s^o _i+Δs_i (16)

wherein s is^o _iAs true coordinates of the scatterers, Δ s_iIs the position coordinate error of the scatterer;

the following new difference Δ tof equation is given as the following equation (18):

(cΔtof_i,1 ^o-d_i ^o)²+2(cΔtof_i,1 ^o-d_i ^o)r₁＝s_i ^oTs_i ^o-s₁ ^oTs₁ ^o-2(s_i ^o-s₁ ^o)^Tu⁽¹⁾ (17)

step ten (two), based on the formula (19) in the step ten (one), establishing a positioning equation set with z as an unknown vector, wherein elements in z comprise final scatterer position coordinates, and the positioning equation set is as follows:

h_t＝G_tz (20)

wherein s is₁ ^o,…s_i ^oI 2, …, m being the true position coordinates of the scatterer,

step ten (three), based on the positioning equation set in the step ten (two), calculating an unknown vector z containing the position coordinates of the final scatterer by using a least square algorithm:

z＝G_t ^-1h_t (21)

thus, the final scatterer coordinates of the present system are i, i ═ 1, …, m elements in the variable z.

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