CN105929364B - Utilize the relative position measurement method and measuring device of radio-positioning - Google Patents
Utilize the relative position measurement method and measuring device of radio-positioning Download PDFInfo
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- CN105929364B CN105929364B CN201610257367.0A CN201610257367A CN105929364B CN 105929364 B CN105929364 B CN 105929364B CN 201610257367 A CN201610257367 A CN 201610257367A CN 105929364 B CN105929364 B CN 105929364B
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- 238000000691 measurement method Methods 0.000 title claims abstract description 17
- 238000005259 measurement Methods 0.000 claims abstract description 15
- 238000012545 processing Methods 0.000 claims abstract description 7
- 238000000034 method Methods 0.000 claims description 33
- 238000012937 correction Methods 0.000 claims description 4
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
- G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
- G01S5/0284—Relative positioning
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- Position Fixing By Use Of Radio Waves (AREA)
Abstract
The present invention provides a kind of relative position measurement method and apparatus using radio-positioning, including transmitting unit, receiving unit, and signal processing unit, through the spacing and each receiving unit that record the position of each receiving unit, each receiving unit at a distance from transmitting unit under original state, the reception signal for extracting each receiving unit solves phase information.According to the quadrilateral space geometrical relationship of receiving unit and transmitting unit, position of the transmitting unit relative to platform can be found out.The present invention solves phase fuzzy problem, and the measurement in the direction and relative position of transfer point can be realized by the transmitting signal of single-frequency；System realizes simple, high reliablity, influenced by extraneous factor it is smaller, can real-time control mobile node moving distance and position, can be widely applied to need in long term monitoring and early warning system.
Description
Technical field
The present invention relates to a kind of method and apparatus of determining relative position more particularly to a kind of phases using radio-positioning
To location measurement method and measuring device, belong to wireless positioning field.
Background technique
Now, it carried out investigations for a long time in some needs, supervised, communicated, searched and rescued, gone on patrol, taken photo by plane and industrial production etc.
In field, mobile node (being such as tethered at receiving node, industrial machine manpower) is usually mounted on platform (including surface car, ship
Warship, earth-fixed station, workshop etc.) cable or moveable arm on.For the ease of preferably handling target information, obtain
Real-time and accurate relative position information of the mobile node relative to platform, to the control such as spot hover of mobile node, automatic
Folding and unfolding etc. becomes particularly important.
In recent years, the development with rapid changepl. never-ending changes and improvements with science and technology, location technology also obtains swift and violent development, to target object
Positioning it is also more and more accurate.Existing widely used location technology, as GPS, Beidou satellite navigation, barometertic altimeter,
Optical alignment and wireless location etc., these method equipment costs are very high, are affected by the external environment larger, realize that process is more multiple
It is miscellaneous.And the wireless location technology based on Electromagnetic Wave Propagation, have system equipment simple, small power consumption, calculation amount and communication overhead it is small,
Stability is good, the advantages that interference is smaller and registration, has been widely used in the every field of society by environment.
Currently, radio-location technology is mainly divided into according to the difference of range measurement principle based on received signal strength (RSSI) side
Method is based on direction of arrival degree (AOA) method, is based on time of arrival (toa) (TOA) method, is based on signal arrival time difference
(TDOA) and based on signal phase difference (PDOA) method etc. is reached.Wherein for RSSI vulnerable to such environmental effects, multi-path jamming is tight
Weight, positioning accuracy are low；And AOA can provide azimuth information, can not but obtain range information, therefore cannot obtain accurate three-dimensional phase
To positional relationship；The range measurement principle of TOA is to carry out ranging by measuring the time of Electromagnetic Wave Propagation, if requiring range accuracy
It is higher, then need that its pulse width is very short or modulation bandwidth is very wide, system is realized very difficult, and needs base station and mobile node
Between accurate time synchronization；Although same TDOA relaxes the requirement of the time synchronization between base station and mobile node, but there is also surveys
The high problem of difficulty is realized away from system in situation with high accuracy；If according to multistation radar range finding principle in PDOA, transceiver is measured
Two signals of different location receiving antenna to calculate the direction of signal propagation, but do not have survey by their phase difference value
Away from ability；If the phase that the same antenna generates the continuous wave of different transmitting fixed frequencies is prolonged according to multifrequency radar range measurement principle
It is different late, distance is calculated by solution phase difference.Two ways generates phase winding, needs more complicated Used for Unwrapping Phase Ambiguity
Algorithm, and need to emit and receive several point-frequency signals of close proximity, system realizes that difficulty is also very high.
In conclusion in actual application, needing a kind of while there is high-precision, high reliability and be easy to engineering reality
Existing relative position wireless location system solves real-time and accurate relative position information of the mobile node relative to platform.
Summary of the invention
The problem to be solved in the present invention is to provide a kind of relative position measurement sides using radio-positioning being easily achieved
Method and measuring device solve the problems, such as that phase is wound, have good positioning accuracy.
In order to solve the above technical problems, the technical solution adopted by the present invention is that：A kind of relative position measurement method, feature
It is：Three-dimensional system of coordinate is established using any point as coordinate origin, is arranged on testee for emitting radio signal
Transmitting unit, the transmitting unit is mobile with testee, is arranged at least in same xoy plane or yoz plane or xoz plane
At least four receiving unit is arbitrarily arranged in 3 receiving units in space, and the receiving unit is used to receive radio signal,
And at least three receiving unit is not arranged on the same straight line, the relative position measurement method includes the following steps：
1) testee coordinate and transmitting unit of transmitting unit and each receiving unit and each in initial position are calculated
Initial distance between receiving unit；
2) testee uses solution commissioning to the radio reception signal that receiving unit receives after initial position movement
Phase method calculates the phase value of t moment radio reception signal, and the radio reception signal by the t-1 moment to t moment
Phase change value；
3) according to formulaThe t-1 moment is calculated to t moment transmitting unit and the by the phase change value
The distance between i receiving unit changing value Δ Ri,t, and the initial distance between transmitting unit and each receiving unit is combined, meter
The distance between transmitting unit and each receiving unit after calculation testee is mobile, whereinIt is the i-th of the t-1 moment to t moment
The phase change value of the radio reception signal of a receiving unit, λ are the wavelength of radio reception signal, wherein i >=3；
4) after being moved by the coordinate of each receiving unit, the testee between transmitting unit and each receiving unit
Distance calculates the coordinate of transmitting unit after testee movement, the coordinate of the testee after being moved；
5) the mobile relative distance of testee is calculated.
In above-mentioned technical proposal, in the step 2), the solution commissioning phase method is that phase method is surveyed in quadrature demodulation.
In above-mentioned technical proposal, it further includes method for correcting phase that phase method is surveyed in the quadrature demodulation, the phasing side
Method includes：
1) setting jump thresholding α and phase correcting value k；
2) if the absolute value of the phase change of radio reception signal is greater than jump thresholding, according to phase correcting value to phase
Position is corrected, and initial value k=0, then the phase value after the radio reception signal of i-th of receiving unit of t moment is calibrated
For
Wherein,Phase after being corrected for the radio reception signal that i-th of receiving unit of t-1 moment receives
Corrected value,For the phase value for the radio reception signal that i-th of receiving unit of t moment receives,It is connect for i-th of t moment
Receive the phase correcting value after the radio reception signal that unit receives is corrected.
The present invention also provides a kind of relative position measurement devices using radio-positioning, which is characterized in that including hair
Unit, receiving unit and signal processing unit are penetrated, wherein：
Transmitting unit：For emitting radio signal, the transmitting unit is set on testee the transmitting unit,
And it is mobile with testee；
Receiving unit：The receiving unit is flat in same xoy for receiving the radio signal, the receiving unit
At least three receiving unit being arranged or at least four being arbitrarily arranged in space receive single on face or yoz plane or xoz plane
Member, and at least three receiving unit is not arranged on the same straight line；
And signal processing unit：For calculating the coordinate of each receiving unit, calculate transmitting unit and each receiving unit it
Between initial distance, by the received radio reception signal of each receiving unit carry out solution commissioning phase, calculate radio reception signal
Phase change value, and calculate it is mobile after transmitting unit and the distance between each receiving unit；And according to each receiving unit
The distance between transmitting unit and each receiving unit after coordinate, movement, the coordinate of the transmitting unit after calculating movement；Calculate hair
Penetrate the moving distance of unit.
The present invention can be used for determining the relative positional relationship of mobile node and platform, have the advantages and positive effects of：
(1) the phase unwrapping winding method realized using Phase Tracking, solves phase fuzzy problem；
(2) measurement in the direction and relative position of transfer point can be realized by the transmitting signal of single-frequency；
(3) compared to existing location technology, system is realized simple, high reliablity, is influenced by extraneous factor smaller；
It (4), can real-time control mobile node by the continuous measurement to transmitting unit and its initial position after movement
Moving distance and position can be widely applied to need in long term monitoring and early warning system；
(5) wireless location distance measuring method is simplified.
Detailed description of the invention
Fig. 1 is the relative position measurement schematic device of the invention using radio-positioning；
Fig. 2 is the flow chart of the relative position measurement method of the invention using radio-positioning；
Fig. 3 is that the relative position measurement method of the embodiment of the present invention 1 calculates diagram；
Fig. 4 is that the relative position measurement method of the embodiment of the present invention 2 calculates diagram.
Specific embodiment
The present invention will be further explained below with reference to the attached drawings.
As shown in Figure 1 to Figure 3, the present invention provides a kind of relative position measurement devices using radio-positioning, including
Transmitting unit, receiving unit and signal processing unit, for emitting radio signal, transmitting unit is set to transmitting unit
On testee, and it is mobile with testee；Receiving unit is for receiving the radio signal, and receiving unit can there are many sides
At least three receiving unit can be arranged in case in same xoy plane or yoz plane or xoz plane, can also be any in space
At least four receiving unit is set, but the condition that at least three receiving unit is not arranged on the same straight line need to be met；Signal processing list
Member calculates transmitting unit S and each receiving unit T for calculating the coordinate of each receiving unitiBetween initial distance, by each reception
Unit TiReceived radio reception signal carries out solution commissioning phase, calculates the phase change value of radio reception signal, and calculates
Transmitting unit S and each receiving unit T after movementiThe distance between；And according to each receiving unit TiCoordinate, it is mobile after hair
Penetrate cell S and each receiving unit TiThe distance between, the coordinate of the transmitting unit S after calculating movement；Calculate the first of transmitting unit S
Beginning position and it is mobile after transmitting unit S coordinate between relative distance.
Embodiment 1：The relative position measurement method and measuring device of at least three receiving unit are set
As shown in Fig. 1-Fig. 3, three-dimensional system of coordinate is established using any point as coordinate origin；Hair is installed on testee
Penetrate cell S, transmitting unit S can tranmitting frequency be f single-frequency radio signal, transmitting unit is mobile with testee；Same
At least three receiving unit T is set in xoy plane or yoz plane or xoz planei, wherein i >=3, and at least three receiving unit is not
On same straight line.The motion profile of transmitting unit S has continuity, and transmitting unit S successively emits single-frequency radio
Signal can obtain transmitting unit S and each receiving unit T by lasting observationiThe distance between.
This, which is sentenced, is arranged at least three receiving unit T in same xoy planeiFor, it is set in same yoz plane or xoz plane
Set receiving unit TiThe case where it is similar with method herein.
Relative position measurement method of the invention includes：
(1) initial distance between initial coordinate values and transmitting unit and each receiving unit is calculated
The coordinate for calculating testee transmitting unit in initial position is S0(x0,y0,z0), calculate each receiving unit Ti's
Coordinate Ti(xi,yi, 0), and calculate transmitting unit S and each receiving unit TiBetween initial distance be
(2) phase value for the radio reception signal that initial position and each receiving unit of t moment receive is calculated, by t-1
After phase correcting value and testee movement after moment to the phase change value and correction of the radio reception signal of t moment
The distance between transmitting unit and each receiving unit.
For testee in initial position, the radio signal that transmitting unit S is emitted is by all reception lists on platform
First TiIt receives, extracts all receiving unit TiRadio reception signal, phase method is surveyed with quadrature demodulation to it, is calculated each
A receiving unit TiThe initial phase value of the radio signal received
The transmitting unit S is mobile with mobile platform, while each receiving unit TiTransmitting unit S is emitted with frequency f
Signal is received, to each receiving unit TiThe radio reception signal received calculates with solution commissioning phase method and receives list
First TiIn the phase value for the radio reception signal that t moment receivesAnd when t=0, transmitting unit S is located at the t=0 moment
Initial position.
The record testee radio reception that all receiving units receive during beginning to move into this section of t moment
Signal.The phase of t moment radio reception signal can survey phase method by quadrature demodulation and acquire, but phase method institute is surveyed in quadrature demodulation
The phase value that can be measured is in [- π, π] range.And in actual observation, due to the variation (or flight path) of positions of mobile nodes
With continuity, when the phase value of signal is more than [- π, π] range, phase winding will occur, phase ambiguity occur, it cannot
Obtain true phase information.Unwrapping must be carried out to phase ambiguity thus, the phase of signal is corrected, it is true to obtain
Real phase information.When being more than [- π, π] range, phase information will be jumped, and in entire motion process, phase letter
Breath will not mutate, and the phase of signal once mutates, i.e., the big Mr. Yu of absolute value of the difference of two adjacent phases
When a threshold value, then the integral multiple of 2 π is added in the phase.
Method for correcting phase of the invention is as follows：It is given phase hit thresholding that α, which is arranged, and integer k is phasing system
Number, is corrected phase value, and the initial value k=0 of k.It is assumed that a certain receiving unit of t moment receives radio reception signal
Phase correcting value after calibrated isAnd t moment is to receiving the demodulated signal phase value of signal
ForCheck the phase value of adjacent moment, then t moment receiving unit TiIt is received it is calibrated after signal phase valueFor
Until all phase informations are disposed in the entire motion process of mobile node, the measurement of phase is completed.Wherein,Phase correcting value after being corrected for the radio reception signal that i-th of receiving unit of t-1 moment receives,For t
The phase value for the radio reception signal that i-th of receiving unit of moment receives,It is received for i-th of receiving unit of t moment
Radio reception signal be corrected after phase correcting value.
After the present invention obtains true phase information, phase value is replaced to be calculated using phase correcting value.If certain is for the moment
When to carve each receiving unit received signal phase value with corresponding each initial phase value difference be the integral multiple of 2 π, then emit
Cell S is located at the surface of its initial position.
On entire orthogonal plane, only phase can mutate on the negative semiaxis of horizontal axis, i.e., phase herein is not
Continuously.When the in-phase component that quadrature demodulation is surveyed in phase method is negative, quadrature component is+0 or smaller positive number, then phase
Position is some value near+π or+π, and when quadrature component is some smaller negative near -0, then phase is near-π
Some value.
It calculates by the t-1 moment to t moment receiving unit TiThe phase change value of the radio reception signal receivedBy carrying out long-time observation to receiving unit, by phase change valueThe t-1 moment is calculated to t moment
The distance change value of transmitting unit and i-th of receiving unitThen t moment transmitting unit S and receiving unit Ti
The distance between be Ri,t=Ri,0+ΔRi,1+ΔRi,2+……+ΔRi,t；
(3) any 3 receiving unit T being not arranged on the same straight line are chosen1(x1,y1,0)、T2(x2,y2,0)、T3(x3,
y3, 0), measurement transmitting unit S and each receiving unit T1、T2、T3The distance between be respectively R1,t、R2,t、R3,t, t moment transmitting list
The coordinate of member is S (x, y, z), establishes equation group
Since 3 receiving units are not arranged on the same straight line, the order of the coefficient matrix of above formula is 3, therefore is had
Unique solution can solve x, y, z value, and thus solving and obtaining the coordinate of t moment transmitting unit S is S (x, y, z), that is, after moving
The coordinate of testee is (x, y, z), then the mobile relative distance of testee is
Coordinate origin can also be set by the initial position of transmitting unit S, can correspondingly simplify calculating.
Embodiment 2：The relative position measurement method and measuring device of at least four receiving unit are set
As shown in Figure 1, Figure 2 and Figure 4, three-dimensional system of coordinate is established using any point as coordinate origin；Pacify on testee
Fill transmitting unit S, transmitting unit S can tranmitting frequency be f single-frequency radio signal, transmitting unit is mobile with testee；?
At least four receiving unit T is arbitrarily set in spacei, wherein i >=4, and at least three receiving unit is not arranged on the same straight line.Hair
The motion profile for penetrating cell S has continuity, and transmitting unit S successively emits single-frequency radio signal, by lasting observation,
Transmitting unit S and each receiving unit T can be obtainediThe distance between.
(1) initial distance between initial coordinate values and transmitting unit and each receiving unit is calculated
The coordinate for calculating testee transmitting unit in initial position is S0(x0,y0,z0), calculate each receiving unit Ti's
Coordinate Ti(xi,yi,zi), and calculate transmitting unit S and each receiving unit TiBetween initial distance be
(2) phase value for the radio reception signal that initial position and each receiving unit of t moment receive is calculated, by t-1
After phase correcting value and testee movement after moment to the phase change value and correction of the radio reception signal of t moment
The distance between transmitting unit and each receiving unit.
Calculating process is same as Example 1 herein.
(3) any 4 receiving unit T are chosen1(x1,y1,z1)、T2(x2,y2,z2)、T3(x3,y3,z3)、T4(x4,y4,z4),
And wherein at least 3 receiving units are not arranged on the same straight line, measurement transmitting unit S and each receiving unit T1、T2、T3、T4Between
Distance be respectively R1,t、R2,t、R3,t、R4,t, the coordinate of t moment transmitting unit is S (x, y, z), establishes equation group
The above-mentioned equation group of abbreviation, obtains,
Since at least three receiving unit is not arranged on the same straight line, the coefficient matrix of above formulaOrder be 3, therefore above formula has unique solution, can solve x, y, z value, obtain t
The coordinate of moment transmitting unit is S (x, y, z), that is, the coordinate of the testee after moving is (x, y, z), then testee is mobile
Relative distance be
Embodiment 3：The moving direction and moving distance of testee are controlled
In actual application, the mobile real-time and accurate relative position letter of some testee is if desired obtained
Breath, or need to control the moving direction and moving distance of testee, when such as spot hover, automatic deploying and retracting, then only need
Transmitting unit S is set on testee, using relative position measurement method described in above-described embodiment 1 or 2, can be obtained
Obtain the mobile relative position information of real-time testee.When need to carry out spot hover, then real-time measurement testee moves
Relative position information operates corresponding control structure and its is enabled to stop movement when testee reaches required position.
The embodiments of the present invention have been described in detail above, but content is only the preferred embodiment of the present invention,
It should not be considered as limiting the scope of the invention.All changes and improvements made in accordance with the scope of the present invention, should all
It still belongs within this patent covering scope.
Claims (4)
1. a kind of relative position measurement method using radio-positioning, it is characterised in that：It is built using any point as coordinate origin
The transmitting unit for emitting radio signal is arranged in vertical three-dimensional system of coordinate on testee, and the transmitting unit is with tested
Object is mobile, and at least three receiving unit is arranged in same xoy plane or yoz plane or xoz plane or arbitrarily sets in space
At least four receiving unit is set, the receiving unit is for receiving radio signal, and at least three receiving unit is not in same
On straight line, the relative position measurement method includes the following steps：
1) the testee coordinate and transmitting unit of transmitting unit and each receiving unit and each reception in initial position are calculated
Initial distance between unit；
2) testee uses solution commissioning phase side to the radio reception signal that receiving unit receives after initial position movement
Method calculates the phase value of the radio reception signal of i-th of receiving unit of t moment, and i-th by the t-1 moment to t moment
The phase change value of the radio reception signal of receiving unit
3) according to formulaThe t-1 moment is calculated to t moment transmitting unit and i-th by the phase change value
The distance between receiving unit changing value Δ Ri,t, and the initial distance between transmitting unit and each receiving unit is combined, under utilization
After formula calculating testee is mobile at a distance from t moment transmitting unit is between each receiving unit
Ri,t=Ri,0+ΔRi,1+ΔRi,2+……+ΔRi,t,
WhereinFor the phase change value of the radio reception signal of i-th of receiving unit at t-1 moment to t moment, λ is nothing
Line electricity receives the wavelength of signal, i=1,2,3 ... ..., N, N >=3, Ri,0For transmitting unit and i-th receiving unit it is initial away from
From；
4) by the coordinate of each receiving unit, the testee after mobile between transmitting unit and each receiving unit away from
From the coordinate of transmitting unit, the coordinate of the testee after being moved after calculating testee is mobile；
5) the mobile relative distance of testee is calculated.
2. the relative position measurement method according to claim 1 using radio-positioning, it is characterised in that：The step
It is rapid 2) in, the solution commissioning phase method be quadrature demodulation survey phase method.
3. the relative position measurement method according to claim 2 using radio-positioning, it is characterised in that：It is described orthogonal
Solving commissioning phase method further includes method for correcting phase, and the method for correcting phase includes：
1) setting jump thresholding α and phase correction coefficient k, and initial value k=0；
2) if the absolute value of the phase change value of radio reception signal is greater than jump thresholding, according to phase correction coefficient to phase
Position is corrected, then the phase correcting value after the radio reception signal of i-th of receiving unit of t moment is calibrated is
Wherein,Phasing after being corrected for the radio reception signal that i-th of receiving unit of t-1 moment receives
Value,For the phase value for the radio reception signal that i-th of receiving unit of t moment receives,List is received for i-th of t moment
The radio reception signal that member receives be corrected after phase correcting value.
4. a kind of relative position measurement device using radio-positioning, which is characterized in that including transmitting unit, receiving unit,
And signal processing unit, wherein：
Transmitting unit：For emitting radio signal, the transmitting unit is set on testee the transmitting unit, and with
Testee is mobile；
Receiving unit：The receiving unit for receiving the radio signal, the receiving unit be in same xoy plane or
At least three receiving unit being arranged or at least four receiving unit being arbitrarily arranged in space in yoz plane or xoz plane, and
At least three receiving unit is not arranged on the same straight line；
And signal processing unit：For calculating the coordinate of testee transmitting unit and each receiving unit in initial position,
The initial distance between transmitting unit and each receiving unit is calculated, the received radio reception signal of each receiving unit is solved
Commissioning phase calculates the phase value of the radio reception signal of i-th of receiving unit of t moment, calculates by the t-1 moment to t moment
The phase change value of the radio reception signal of i-th of receiving unitAccording to formulaBy the phase
Changing value calculates the t-1 moment to the distance between t moment transmitting unit and i-th of receiving unit changing value Δ Ri,t, and combine hair
The initial distance between unit and each receiving unit is penetrated, formula R is utilizedi,t=Ri,0+ΔRi,1+ΔRi,2+……+ΔRi,tIt calculates
Transmitting unit after testee is mobile in the t moment distance R between each receiving uniti,t, whereinFor the t-1 moment to t
The phase change value of the radio reception signal of i-th of receiving unit at moment, wavelength of the λ for radio reception signal, i=1,
2,3 ... ..., N, N >=3, Ri,0For the initial distance of transmitting unit and i-th of receiving unit；And according to the seat of each receiving unit
The distance between transmitting unit and each receiving unit after mark, movement, the coordinate of the transmitting unit after calculating movement；Calculate transmitting
The moving distance of unit is to obtain the mobile relative distance of testee.
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| EP3521962B1 (en) * | 2016-09-27 | 2021-07-21 | Nissan Motor Co., Ltd. | Self-position estimation method and self-position estimation device |
| CN106604391A (en) * | 2016-11-14 | 2017-04-26 | 上海斐讯数据通信技术有限公司 | Indoor wifi positioning method and server |
| WO2018198441A1 (en) * | 2017-04-26 | 2018-11-01 | 三菱電機株式会社 | Movement-distance measurement device |
| CN108036745B (en) * | 2018-01-30 | 2020-02-07 | 长沙深之瞳信息科技有限公司 | Error compensation method for microwave interference deformation measurement |
| CN108877128A (en) * | 2018-06-26 | 2018-11-23 | 北京和协导航科技有限公司 | A kind of forest fire protection alarm system based on radio-positioning |
| CN111474553B (en) * | 2020-06-22 | 2020-11-27 | 深圳市汇顶科技股份有限公司 | Time-of-flight ranging method and device |
| CN115792184B (en) * | 2022-12-01 | 2024-05-24 | 山东科技大学 | Wireless stress and displacement measurement system and method for similar material simulation experiment |
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| US7990314B2 (en) * | 2008-06-30 | 2011-08-02 | Liao Henry H | Method and system for locating a geographical position using broadcast frequency modulation signals |
| US8786440B2 (en) * | 2009-10-02 | 2014-07-22 | Checkpoint Systems, Inc. | Calibration of beamforming nodes in a configurable monitoring device system |
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