CN114666732B - Moving target positioning calculation and error evaluation method under noisy network - Google Patents
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Abstract
The invention discloses a method for positioning and calculating a moving target and evaluating errors under a noisy network, which comprises the steps of installing a tag on the moving target, determining a sensing base station set corresponding to the tag, solving a differential distance by combining a target motion model based on a signal arrival time difference between a base station and the tag, estimating a primary distance estimated value between the moving target and the base station under a noise signal by adopting unscented particle filtering, establishing a target distributed positioning and calculating a covariance matrix and a corresponding positioning error caused by uncertainty in the process of base station calibration and signal measurement based on a base station calibration error and signal ranging. The invention fully considers the uncertainty between the base station and the signal, introduces the unscented particle filter to perform primary positioning estimation of the moving target, solves the real-time position of the moving target by utilizing a primary distance estimation value and a separation variable method in order to avoid the positioning error caused by a pathological matrix, performs positioning sensing and positioning error evaluation on the moving target in real time, and can provide a basis for the cooperative positioning and autonomous movement of the target.
Description
Technical Field
The invention relates to distributed positioning of a moving target in a monitoring area, in particular to a method for positioning and resolving the moving target and evaluating errors under a noisy network.
Background
The target positioning technology is one of key technologies of cooperative automation, and can be applied to various industrial scenes to accurately detect the target position. Currently, there are several ways to position the target, such as an odometer, a visual positioning method, and an inertial measurement method, but there are problems that accumulated errors exist for a long time, image distortion is easily generated due to uneven illumination, and an external sensor is required to correct. With the widespread use of wireless communication technology, the use of wireless signals between sensors to locate a target is an effective means. In the positioning area, a monitoring network is constructed in a mode of deploying a certain number of sensor communication ad hoc networks, wherein the monitoring network can be divided into a base station and a tag according to whether the initial coordinates of the sensors are known. In the communication range of the base station, the tag arranged on the target is communicated with the base station in the communication range to obtain a wireless signal capable of indicating the geometric distance between the target and the base station, and meanwhile, the real-time coordinate of the tag is obtained by combining the initial accurate deployment of the coordinate of the base station and adopting a designed positioning resolving algorithm, so that the real-time coordinate of the target can be obtained.
In multi-base station target positioning, the target positioning method can be classified into a non-ranging-based positioning technique and a ranging-based positioning technique according to whether the distance or angle information between the base station and the tag is adopted. The positioning technology of non-ranging mainly comprises a centroid algorithm based on network connectivity, an approximate triangle interior point testing method based on relative positions, a positioning method based on a distance vector jump method, a convex planning method and the like, but the centroid algorithm has better precision only when a label is positioned at a geometric polygon centroid formed by base stations, the approximate triangle interior point testing method excessively depends on coverage rate of the base stations, the jump distance is utilized to replace the straight line distance between the base stations and the label based on the distance vector jump method, and the convex planning method has better positioning precision when the base stations are deployed at the edges of the network. Therefore, the positioning technology based on non-ranging is generally used in occasions with low positioning accuracy requirements due to low power consumption, less calculation amount and poor positioning performance. For some occasions with accurate positioning requirements, a positioning technology based on distance measurement is mostly adopted, and the currently commonly used wireless distance measurement technology is used for accurately solving the position of a moving target by measuring wireless signals of a base station and a tag base station, such as based on signal strength indication, signal arrival time difference and signal arrival angle information, by adopting a least square method, a Taylor series expansion method, a Kalman filtering method and the like.
Along with the increasingly severe and diverse application environments of base station and tag type positioning, targets are expanded from single targets to multiple targets, positioning requirements of the targets are also extended from accurate positioning of the single targets to cooperative positioning of the multiple targets, and cooperative operation tasks among moving targets are increasingly complex, so that the distributed positioning precision of the moving targets is improved, a new positioning technology is required to be adopted, a new positioning algorithm is designed, and the full-space distributed positioning sensing requirements of the moving targets are met.
Disclosure of Invention
The invention aims to: the invention provides a method for resolving and evaluating errors of moving targets in a noisy network, which adopts multi-source signals between a plurality of base stations and labels to locate the moving targets in real time and solves the problems of inaccuracy or partial area location failure in target location.
The technical scheme is as follows: the invention relates to a method for positioning and resolving a moving target and evaluating errors under a noisy network, which comprises the following steps:
(1) Based on a sensing network formed by a tag installed on a moving target and a base station installed in a positioning area, solving a base station set which can be perceived by the corresponding moving target moving time mark;
(2) Solving the differential distance between the tag and the base station by adopting a signal arrival time difference, and estimating primary distance estimation values between different targets and the base station by using unscented particle filtering under a noisy wireless signal;
(3) Solving the real-time position of the moving target based on the primary distance estimation value and the separation variable method;
(4) And calculating a covariance matrix and a corresponding positioning error caused by uncertainty in the base station calibration and signal measurement processes by considering the base station reference coordinates and calibration errors, the signal ranging values and the ranging errors.
Further, the step (1) includes the steps of:
(11) The moving target positioning area is L multiplied by W multiplied by H; the base station set is AN S＝{AN1,AN2,…,ANm, wherein m is the number of base stations; the label set is MN S＝{MN1,MN2,…,MNn, wherein n is the number of labels;
(12) The signal arrival time difference is adopted for the sensing signals between the multiple base stations and the tag, and then the arrival time difference to differential distance conversion model between the base station AN i and the base station AN 1 and the tag MN j is expressed as follows:
Wherein t i represents the signal arrival time between the base station AN i and the tag MN j, t i-t1 represents the wireless signal arrival time difference between the base station and different tags, i ε m and j ε n;
(13) Different wireless signals from the base station are received by the target in the moving process, the base station is calibrated to obtain a coordinate value a i＝[axi,ayi,azi]T based on the label x j＝[uxj,uyj,uzj]T of the target in different positions as a circle center, and a corresponding perception base station set is obtained when the geometric distance between the label and the base station is equal to a i-xj||≤Rs, wherein R s is a perception radius.
Further, the step (2) includes the steps of:
(21) The state equation of the object based on the motion characteristic at the moment k is as follows:
xj(k)＝Fjxj(k-1)+wj(k-1)
wherein F j and w j (k-1) are the corresponding state transition matrix and process noise, respectively; the measurement equation is established at the time k based on the differential distance between the wireless arrival time differences as follows:
wherein v j (k) is the corresponding state equation noise; based on the motion characteristics of the target and a wireless differential distance equation, a nonlinear equation set for one-time estimation of the target is established, and the state estimation value of the target j at the moment k of the target is as follows:
Wherein, Is particle mean value/>The importance weight is normalized;
(22) Target j state estimate at time k Including the three-axis position and three-axis velocity of the target:
Calculating the geometric distance between the coordinate estimation value of the target MN j and the base station AN i at the moment k:
Wherein, the geometry distance between the target MN j and the base station a i is calculated as a function of.
Further, the step (3) includes the steps of:
(31) Decomposing the target coordinates to be estimated into x, y and z axis direction coordinates, and decomposing the matrix G into G 1、G2 and G 3:
G1＝-[ax2-ax1,ax3-ax1,…,axm-ax1]T
G2＝-[ay2-ay1,ay3-ay1,…,aym-ay1]T
G3＝-[az2-az1,az3-az1,…,azm-az1]T
At the same time, the covariance matrix C εε caused by uncertainty in the base station calibration process is decomposed into And/>Wherein ε 1、ε2 and ε 3 are row vectors of ε;
(33) The estimation result of the target x direction is:
the estimation result of the target y direction is:
The estimation result of the target z direction is:
Wherein:
G d is a column vector consisting of theoretical geometric differences between the base station AN i and the base station AN 1 and the tag MN j, i=2, 3,..m; h d is the range error, H is a matrix containing uncertainty in the wireless positioning process;
further, the step (4) includes the steps of:
(41) The calibration error of the base station reference coordinates is epsilon, the range error of the wireless signal is phi, the covariance matrix C φφ caused by the uncertainty of the wireless signal range is E [ phi & phi T ], the covariance matrix C εε caused by the uncertainty in the base station calibration process is E [ epsilon T & epsilon ], and the covariance matrix C εφ between the uncertainty error in the base station position calibration process and the measurement error in the wireless signal range process is E [ epsilon T phi ];
(42) When the base station coordinate calibration error epsilon and the wireless signal ranging error phi are not related, the covariance matrix C εφ can be equivalent to zero, the influence of the base station coordinate error calibration value on the wireless signal ranging value is ignored, and the wireless arrival time difference ranging estimated value and the tag coordinate estimated value are combined, wherein the expression is as follows:
(44) The positioning error caused by the uncertainty of the base station coordinate calibration is as follows:
Wherein, C i is an element of each row in H d; the positioning error caused by the uncertainty of the measurement of the arrival time difference of the wireless signal is as follows:
The beneficial effects are that: compared with the prior art, the invention has the beneficial effects that: the invention utilizes the ranging signals between multiple base stations and the tags, fully considers the uncertainty between the base stations and the signals, introduces unscented particle filtering, carries out positioning sensing on the moving target in real time and evaluates the positioning error of the moving target, and can provide a basis for the cooperative positioning and autonomous control of the target.
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FIG. 1 is a flow chart of the present invention;
Fig. 2 is a schematic diagram of a base station deployment proposed by the present invention;
Fig. 3 is a positioning schematic of the present invention.
Detailed Description
The technical scheme of the present invention will be described in detail below with reference to the accompanying drawings.
As shown in fig. 1 to 3, the invention provides a method for resolving and evaluating the positioning of a moving target in a noisy network, wherein a wireless distributed network is formed by base stations and labels to position the target, a plurality of base stations are distributed in a positioning area according to a certain deployment strategy, and the coordinates of each base station are measured by adopting a manual calibration method; meanwhile, a plurality of moving targets are in a positioning area for executing operation tasks, a label is deployed on each target body for positioning the moving targets in real time, and a base station perception set of different targets is built based on a target motion model; the method comprises the steps of calculating the differential distance between a label and a base station by using a wireless arrival time difference signal between an anchor node with a known coordinate position and the label, and establishing a target solving equation, wherein the solving equation comprises an unknown quantity exceeding the number of equation sets, and the first distance estimation value between different targets and the base station is estimated by using unscented particle filtering. The method specifically comprises the following steps:
Step S1: and solving a base station set which can be perceived by the moving target movement time mark correspondence based on a sensing network formed by the tag arranged on the moving target and the base station arranged in the positioning area. The method specifically comprises the following steps:
(1) The moving target positioning area is L multiplied by W multiplied by H; the base station set is AN S＝{AN1,AN2,…,ANm, wherein m is the number of base stations; the label set is MN S＝{MN1,MN2,…,MNn, wherein n is the number of labels; the signal arrival time difference is adopted for the sensing signals between the multiple base stations and the tag, and then the arrival time difference to differential distance conversion model between the base station AN i and the base station AN 1 and the tag MN j can be expressed as:
Wherein t i represents the signal arrival time between the base station AN i and the tag MN j, and t i-t1 represents the wireless signal arrival time difference between the base station and different tags, i e m and j e n.
(2) Different wireless signals from the base station are received by the target in the moving process, the base station is calibrated to a coordinate value a i＝[axi,ayi,azi]T based on the label x j＝[uxj,uyj,uzj]T of the target at different positions as a circle center, and a corresponding perception base station set is obtained when the geometric distance between the label and the base station is equal to a i-xj||≤Rs, wherein R s is a perception radius.
Step S2: the differential distance between the tag and the base station is solved by adopting the signal arrival time difference, and the primary distance estimation value between different targets and the base station is estimated by using unscented particle filtering under the noisy wireless signal, and the method specifically comprises the following steps:
(1) The state equation of the object based on the motion characteristic at the moment k is as follows:
xj(k)＝Fjxj(k-1)+wj(k-1)
The corresponding state transition matrix and process noise are F j and w j (k-1), respectively, and a measurement equation is established at the time k based on the differential distance between the wireless arrival time differences, and is as follows:
The corresponding state equation noise is v j (k), and a nonlinear equation set for one-time estimation of the target is established based on the motion characteristic of the target and a wireless differential distance equation;
(2) Performing one-time positioning estimation on the state of the target j, transforming sampling points at the moment k through UT, and obtaining a particle mean value according to KF And corresponding covariance/>Then obtain probability density function of approximate Gaussian distributionThereby obtaining the sample particle as/>Calculating normalized importance weight/>Changing the sample set with the weight into the sample set with the equal weight after the sample particles are degraded, wherein the state estimation value of the target j at the moment k can be expressed as:
(3) Target j state estimate at time k Including the three-axis position and three-axis velocity of the target, namely:
calculating the geometric distance between the estimated value of the coordinates of the target MN j at the k moment and the base station AN i Can be expressed asCalculating a function of the geometric distance between the target MN j and the base station a i, and calculating the geometric distance/>, between the target MN j and the base stationSubstituting the target location calculation result into the formula (2) in the step 3.
Step S3: the method for solving the real-time position of the moving target based on the primary distance estimation value and the separation variable method specifically comprises the following steps:
(1) Decomposing the target coordinates to be estimated into x, y and z-axis direction coordinates, and decomposing the matrix G into G 1、G2 and G 3, wherein:
G1＝-[ax2-ax1,ax3-ax1,…,axm-ax1]T
G2＝-[ay2-ay1,ay3-ay1,…,aym-ay1]T
G3＝-[az2-az1,az3-az1,…,azm-az1]T
At the same time, the covariance matrix C εε caused by uncertainty in the base station calibration process is decomposed into And/>Wherein ε 1、ε2 and ε 3 are row vectors of ε;
(2) The estimation of the target x-direction can be expressed as:
the estimation of the target y-direction can be expressed as:
the estimation of the target z-direction can be expressed as:
Wherein:
G d is a column vector consisting of theoretical geometric differences between the base station AN i and the base station AN 1 and the tag MN j, i=2, 3. H d is the range error and H is the matrix containing the uncertainty in the wireless positioning process.
Step S4: taking reference coordinates and calibration errors of a base station, signal ranging values and ranging errors into consideration, and calculating covariance matrixes and corresponding positioning errors caused by uncertainty in the base station calibration and signal measurement processes, wherein the method specifically comprises the following steps of:
(1) The calibration error of the base station reference coordinates is epsilon, the range error of the wireless signal is phi, the covariance matrix C φφ caused by the uncertainty of the wireless signal range is E [ phi & phi T ], the covariance matrix C εε caused by the uncertainty in the base station calibration process is E [ epsilon T & epsilon ], and the covariance matrix C εφ between the uncertainty error in the base station position calibration process and the measurement error in the wireless signal range process is E [ epsilon T phi ];
(2) When the base station coordinate calibration error epsilon and the wireless signal ranging error phi are not related, the covariance matrix C εφ can be equivalent to zero, the influence of the base station coordinate error calibration value on the wireless signal ranging value is ignored, the wireless arrival time difference ranging estimated value and the tag coordinate estimated value are combined, and the joint expression of the coordinates can be written as follows:
(3) The positioning error caused by the uncertainty of the base station coordinate calibration can be expressed as:
Wherein:
Wherein c i refers to the elements of each row in H d; the positioning error caused by the uncertainty of the wireless signal arrival time difference measurement can be expressed as:
the target wireless distributed positioning accuracy is mainly introduced by the uncertainty of the measurement of the arrival time difference of the wireless signals, and the positioning accuracy of the target is also affected by the uncertainty of the deployment of wireless nodes and the calibration of the base station coordinates.
The foregoing has shown and described the basic principles and main features of the present invention and the advantages of the present invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, and that the above embodiments and descriptions are merely illustrative of the principles of the present invention, and various changes and modifications may be made without departing from the spirit and scope of the invention, which is defined in the appended claims. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (3)
1. A method for calculating the positioning of a moving target and evaluating the errors under a noisy network is characterized by comprising the following steps:
(1) Based on a sensing network formed by a tag installed on a moving target and a base station installed in a positioning area, solving a base station set which can be perceived by the corresponding moving target moving time mark;
(2) Solving the differential distance between the tag and the base station by adopting a signal arrival time difference, and estimating primary distance estimation values between different targets and the base station by using unscented particle filtering under a noisy wireless signal;
(3) Solving the real-time position of the moving target based on the primary distance estimation value and the separation variable method;
(4) Taking reference coordinates and calibration errors of a base station, signal ranging values and ranging errors into consideration, and calculating covariance matrixes and corresponding positioning errors caused by uncertainty in the calibration and signal measurement processes of the base station;
the step (2) comprises the following steps:
(21) The state equation of the object based on the motion characteristic at the moment k is as follows:
xj(k)＝Fjxj(k-1)+wj(k-1)
wherein F j and w j (k-1) are the corresponding state transition matrix and process noise, respectively; the measurement equation is established at the time k based on the differential distance between the wireless arrival time differences as follows:
wherein v j (k) is the corresponding state equation noise; based on the motion characteristics of the target and a wireless differential distance equation, a nonlinear equation set for one-time estimation of the target is established, and the state estimation value of the target j at the moment k of the target is as follows:
Wherein, Is particle mean value/>The importance weight is normalized;
(22) Target j state estimate at time k Including the three-axis position and three-axis velocity of the target:
Calculating the geometric distance between the coordinate estimation value of the target MN j and the base station AN i at the moment k:
The method comprises the steps of calculating a function of geometric distance between a target MN j and a base station a i;
The step (3) comprises the following steps:
(31) Decomposing the target coordinates to be estimated into x, y and z axis direction coordinates, and decomposing the matrix G into G 1、G2 and G 3:
G1＝-[ax2-ax1,ax3-ax1,…,axm-ax1]T
G2＝-[ay2-ay1,ay3-ay1,…,aym-ay1]T
G3＝-[az2-az1,az3-az1,…,azm-az1]T
At the same time, the covariance matrix C εε caused by uncertainty in the base station calibration process is decomposed into Wherein ε 1、ε2 and ε 3 are row vectors of ε;
(32) The estimation result of the target x direction is:
the estimation result of the target y direction is:
The estimation result of the target z direction is:
Wherein:
Hd＝h+Gdd1 j(k)
G d is a column vector formed by theoretical geometric differences between the base station AN i and the base station AN 1 and the tag MN j, i=2, 3, …, m; h d is the range error, H is a matrix containing uncertainty in the wireless positioning process;
2. the method for solving and evaluating the positioning errors of a moving object in a noisy network according to claim 1, wherein the step (1) comprises the steps of:
(11) The moving target positioning area is L multiplied by W multiplied by H; the base station set is AN S＝{AN1,AN2,…,ANm, wherein m is the number of base stations; the label set is MN S＝{MN1,MN2,…,MNn, wherein n is the number of labels;
(12) The signal arrival time difference is adopted for the sensing signals between the multiple base stations and the tag, and then the arrival time difference to differential distance conversion model between the base station AN i and the base station AN 1 and the tag MN j is expressed as follows:
Wherein t i represents the signal arrival time between the base station AN i and the tag MN j, t i-t1 represents the wireless signal arrival time difference between the base station and different tags, i ε m and j ε n;
(13) Different wireless signals from the base station are received by the target in the moving process, the base station is calibrated to obtain a coordinate value a i＝[axi,ayi,azi]T based on the label x j＝[uxj,uyj,uzj]T of the target in different positions as a circle center, and a corresponding perception base station set is obtained when the geometric distance between the label and the base station is equal to a i-xj||≤Rs, wherein R s is a perception radius.
3. The method for solving and evaluating the positioning errors of a moving object in a noisy network according to claim 1, wherein the step (4) comprises the steps of:
(41) The calibration error of the base station reference coordinates is epsilon, the range error of the wireless signal is phi, the covariance matrix C φφ caused by the uncertainty of the wireless signal range is E [ phi & phi T ], the covariance matrix C εε caused by the uncertainty in the base station calibration process is E [ epsilon T & epsilon ], and the covariance matrix C εφ between the uncertainty error in the base station position calibration process and the measurement error in the wireless signal range process is E [ epsilon T phi;
(42) When the base station coordinate calibration error epsilon and the wireless signal ranging error phi are not related, the covariance matrix C εφ can be equivalent to zero, the influence of the base station coordinate error calibration value on the wireless signal ranging value is ignored, and the wireless arrival time difference ranging estimated value and the tag coordinate estimated value are combined, wherein the coordinate expression is as follows:
(43) The positioning error caused by the uncertainty of the base station coordinate calibration is as follows:
Wherein, C i is an element of each row in H d; the positioning error caused by the uncertainty of the measurement of the arrival time difference of the wireless signal is as follows:
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