WO2024108367A1 - 一种超声波主动式目标定位方法与装置 - Google Patents

一种超声波主动式目标定位方法与装置 Download PDF

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WO2024108367A1
WO2024108367A1 PCT/CN2022/133373 CN2022133373W WO2024108367A1 WO 2024108367 A1 WO2024108367 A1 WO 2024108367A1 CN 2022133373 W CN2022133373 W CN 2022133373W WO 2024108367 A1 WO2024108367 A1 WO 2024108367A1
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ultrasonic
ultrasonic sensor
sensors
target
coordinates
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French (fr)
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姜燕丹
邱奕臻
黄志尧
冀海峰
王保良
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Zhejiang University
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Zhejiang University
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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
    • G01S15/00—Systems using the reflection or reradiation of acoustic waves, e.g. sonar systems
    • G01S15/02—Systems using the reflection or reradiation of acoustic waves, e.g. sonar systems using reflection of acoustic waves
    • G01S15/06—Systems determining the position data of a target
    • 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
    • G01S5/18—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using ultrasonic, sonic or infrasonic waves
    • G01S5/22—Position of source determined by co-ordinating a plurality of position lines defined by path-difference measurements

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  • the invention relates to ultrasonic positioning technology, and in particular to an ultrasonic active target positioning method and device.
  • robotics With the development of computer science, sensor technology and artificial intelligence, robotics has played a vital role in manufacturing, transportation, outer space and deep sea exploration. As one of the key technologies in robotics, target positioning technology has received more and more attention.
  • ultrasonic positioning methods use a large number of ultrasonic sensors to obtain the arrival time or time difference of multiple received ultrasonic echoes, and use the obtained arrival time to solve the target position through relatively complex numerical algorithms. These methods have the problems of large amount of calculation, large number of sensors, and in most cases require prior knowledge and manual intervention.
  • the present invention aims to achieve target positioning by optimizing the ultrasonic sensor array configuration, using the least ultrasonic sensors and the simplest array structure, and using the most theoretically stable analytical method with the least computational effort.
  • the present invention proposes an ultrasonic active target positioning method and device, which involves an ultrasonic sensor array configuration and target position solution and distance measurement. It uses the least ultrasonic sensors, can ensure that there is a unique analytical solution for the three-dimensional target position, and has the advantages of a small number of sensors, the least theoretical computational effort and the best solution stability, a simple sensor configuration structure, and high positioning accuracy.
  • the present invention provides an ultrasonic active target positioning method and device.
  • the ultrasonic sensor array configuration in the positioning device can realize target positioning in three-dimensional space.
  • the present invention uses four ultrasonic sensors to form an ultrasonic sensor array.
  • the array adopts a one-transmit-multiple-receive signal transmission and reception mode.
  • One of the ultrasonic sensors is used as a reference ultrasonic sensor, which works in T/R dual mode, that is, it serves as both an ultrasonic transmitter and an ultrasonic receiver.
  • the remaining three ultrasonic sensors work in R mode, that is, they only serve as receivers.
  • the time difference is obtained by the time when the reference ultrasonic sensor transmits the ultrasonic wave and the arrival time when the sensor receives the ultrasonic echo, and the target position is solved.
  • the ultrasonic sensor array configuration and method have the advantages of simple configuration structure, minimum theoretical calculation amount, best solution stability, and high accuracy in target positioning.
  • the present invention first provides an ultrasonic active target positioning device, which includes an ultrasonic sensor array, a control module and a computer;
  • the ultrasonic sensor array includes four ultrasonic sensors that are not in the same plane; and one of the ultrasonic sensors is used as a reference ultrasonic sensor, which works in a transmitting/receiving dual mode, that is, it serves as both an ultrasonic transmitter and an ultrasonic receiver;
  • the control module controls each ultrasonic sensor to transmit and receive ultrasonic signals. Each sensor transmits a signal containing arrival time information to the control module. After obtaining the arrival time, the control module calculates the corresponding time difference based on the time when the reference ultrasonic sensor transmits the ultrasonic wave and the time when each ultrasonic sensor receives the ultrasonic echo, and communicates with the computer through a USB data cable, sending the time difference to the computer.
  • the computer uses the time difference to solve the three-dimensional coordinates of the target object and the distance from the target to the reference ultrasonic sensor, and displays and saves the positioning and ranging results.
  • the location of the reference ultrasonic sensor is taken as the coordinate origin
  • the other three ultrasonic sensors are respectively on three coordinate axes
  • the distances from the other three ultrasonic sensors to the reference ultrasonic sensor are equal.
  • the remaining three ultrasonic sensors operate in a receiving mode, that is, they only serve as ultrasonic receivers.
  • the present invention also provides an ultrasonic active target positioning method based on the above device, which comprises the following steps:
  • Step 1 Using the reference ultrasonic sensor in the ultrasonic sensor array to actively transmit ultrasonic waves, the ultrasonic waves are propagated to the target object and reflected, and the four ultrasonic sensors respectively receive the reflected ultrasonic waves, i.e., ultrasonic echoes, to obtain the arrival time;
  • Step 3 Calculate and obtain the analytical solution of the target coordinates (x, y, z);
  • Step 4 Calculate the analytical solution of the distance ⁇ from the target to the reference ultrasonic sensor.
  • the present invention has the following beneficial effects:
  • the present invention utilizes an analytical method to solve the target coordinates and adopts a new ultrasonic sensor array configuration, which satisfies the condition that the solution of the three-dimensional spatial coordinates of the target position exists and is unique, overcoming the problems of high computational cost, large number of sensors, relatively complex sensor arrays, and usually requiring prior knowledge and manual intervention in the existing ultrasonic positioning technology. It has the advantages of requiring a small number of ultrasonic sensors, a simple configuration structure, and not requiring prior knowledge and manual intervention.
  • the present invention arranges the ultrasonic sensor on the coordinate axis and optimizes the sensor coordinates from the perspective of the condition number, thereby effectively simplifying the analytical solution, reducing the amount of calculation, and improving the stability of the solution, so that the computational complexity of the target coordinate solution is low, the amount of calculation is minimal in theory, and it has the best numerical stability and high positioning accuracy.
  • the device of the present invention is easy to install, small in size, low in power consumption, low in price, and has a wide range of applications.
  • FIG1 is a schematic structural diagram of an ultrasonic active target positioning device
  • FIG2 is a schematic diagram of four ultrasonic sensors in the same plane
  • FIG3 is a schematic diagram of four ultrasonic sensors not in the same plane
  • FIG4 is a further optimized configuration of the ultrasonic sensor array spatial configuration shown in FIG3 ;
  • FIG. 5 is a further optimized configuration of the spatial configuration of the ultrasonic sensor array shown in FIG. 4 .
  • the present invention proposes a new ultrasonic sensor array configuration and a target positioning method for the configuration.
  • the method has the characteristics of a small number of ultrasonic sensors, a simple configuration, the smallest theoretical calculation amount, the best numerical stability, and high positioning accuracy.
  • the present invention provides a device for target positioning based on ultrasonic sensors, including an ultrasonic sensor array, a control module and a computer.
  • ultrasonic sensors form an array, and the configuration thereof satisfies the non-singular coefficient matrix of the linear equation group for solving the target position.
  • the configuration of the target positioning ultrasonic sensor array provided by the present invention includes four ultrasonic sensors, and the four ultrasonic sensors are not in the same plane.
  • any one of the four ultrasonic sensors is taken as a reference ultrasonic sensor, and its coordinates are set to (0,0,0); the reference ultrasonic sensor works in T/R dual mode, that is, it both transmits and receives ultrasonic waves; the remaining three ultrasonic sensors can at least work in R mode, that is, they need to be able to act as receivers. In a preferred embodiment, the remaining three ultrasonic sensors only work in R mode, that is, they only receive ultrasonic waves.
  • the four ultrasonic sensors are connected to the control module through wires to realize the power supply, control and transmission of arrival time information of the ultrasonic sensors.
  • the control module calculates the corresponding time difference according to the time when the reference ultrasonic sensor transmits the ultrasonic wave and the time when each ultrasonic sensor receives the ultrasonic echo, and communicates with the computer through a USB data cable to send the time difference to the computer.
  • the computer uses the time difference to solve the three-dimensional coordinates of the target object and the distance from the target to the reference ultrasonic sensor, and displays and saves the positioning and ranging results.
  • a basic model for three-dimensional target positioning is established based on the target and N ultrasonic sensors.
  • the present invention adopts a one-transmit-multiple-receive ultrasonic signal transceiving mode.
  • t0 be the time when the reference ultrasonic sensor S1 transmits the ultrasonic wave
  • c the speed of sound
  • ⁇ t 10 t 1 ⁇ t 0 .
  • the ultrasonic wave propagates from Si to the target object, is reflected by the target object, and the ultrasonic echo is received by the ultrasonic sensor Si . Therefore, the relationship between Si and the target coordinates can be expressed as the following equation.
  • T is the Celsius temperature of the environment, obtained by the temperature sensor, and the unit of sound speed is m/s.
  • equation (4) is usually converted into a linear equation system about the position coordinates (x, y, z) of the target P and then solved.
  • the coordinates (x i , y i , z i ) and the sound speed c of the ultrasonic sensor are known.
  • ⁇ t 10 and ⁇ t i1 can be obtained from t 0 and ti . Therefore, the matrix G and the vector h are determined.
  • the target positioning can be achieved.
  • the distance ⁇ from the target to the reference ultrasonic sensor can be calculated by the following formula.
  • the condition for the three-dimensional space target coordinates (x, y, z) in formula (10) to have a unique analytical solution is that the matrix G is non-singular.
  • the four ultrasonic sensor coordinates in the configuration of the target positioning ultrasonic sensor array are configured to meet this condition, where the expression of the matrix G is:
  • the necessary and sufficient condition for the matrix G to be non-singular is that the four ultrasonic sensors in the ultrasonic sensor array are not in the same plane.
  • the specific proof is as follows:
  • the positional relationship of the four ultrasonic sensors S 1 , S 2 , S 3 and S 4 in space can be divided into two types: one is that the four ultrasonic sensors are in the same plane, and the other is that the four ultrasonic sensors are not in the same plane.
  • the necessary and sufficient condition for the matrix G to be non-singular is that the four ultrasonic sensors in the ultrasonic sensor array are not in the same plane. The proof is complete.
  • the target coordinates (x, y, z) can obtain a unique analytical solution by formula (11).
  • the present invention realizes positioning by solving formula (10). Since the computational complexity and stability of the analytical solution are important, the present invention ensures that the analytical solution of the target coordinates is simple in form, small in computational complexity and has good stability by reasonably selecting the coordinates of the four ultrasonic sensors.
  • the matrix G is designed as a diagonal matrix by setting S 2 , S 3 and S 4 on three coordinate axes respectively. As shown in FIG4 , let the coordinates of ultrasonic sensor S 2 be (x 2 ,0,0), the coordinates of ultrasonic sensor S 3 be (0,y 3 ,0), and the coordinates of ultrasonic sensor S 4 be (0,0,z 4 ).
  • the matrix G under this configuration is non-singular and has the form:
  • the coordinates of the four ultrasonic sensors can be optimized from the perspective of the condition number cond(G) of the matrix G.
  • This method achieves positioning by solving a system of linear equations with G as the coefficient matrix.
  • cond(G) is an important indicator of the stability of the solution.
  • a large cond(G) means that the measurement error may have a significant impact on the solution, and the fluctuation of the solution may be large.
  • a small cond(G) means that the measurement error has a small impact on the solution, and the solution is stable.
  • the minimum value of the condition number cond(G) of the matrix G is 1.
  • the present invention proposes a practical four-element ultrasonic sensor array configuration, which requires that S 2 , S 3 and S 4 are on three coordinate axes respectively, and the distances between these three ultrasonic sensors and the reference ultrasonic sensor (origin) are equal.
  • the corresponding matrix G can be expressed as:
  • the corresponding inverse matrix G -1 is:
  • the analytical expression of the target coordinates (x, y, z) corresponding to the actual four-element ultrasonic sensor array configuration, that is, the analytical solution of the target coordinates is:
  • the reference ultrasonic sensor is controlled by the control module to emit an ultrasonic pulse; the ultrasonic pulse is transmitted outward and reflected after encountering a target, and the reflected ultrasonic echo is received by four ultrasonic sensors; then the four sensors transmit a signal containing arrival time information to the control module; after obtaining the arrival time, the control module calculates the corresponding time differences ⁇ t 10 , ⁇ t 21 , ⁇ t 31 and ⁇ t 41 using the time t 0 when the reference ultrasonic sensor emits the ultrasonic wave and the arrival times t 1 , t 2 , t 3 and t 4 when the four ultrasonic sensors receive the ultrasonic echo; the control module communicates with the computer through a USB data cable and sends ⁇ t 10 , ⁇ t 21 , ⁇ t 31 and ⁇ t 41 to the computer, and the computer solves the coordinates of the target object according to formula (21) and solves the distance from the target to the reference ultrasonic
  • Step 1 Using the reference ultrasonic sensor in the ultrasonic sensor array to actively transmit ultrasonic waves, the ultrasonic waves are propagated to the target object and reflected, and the four ultrasonic sensors respectively receive the reflected ultrasonic waves, i.e., ultrasonic echoes, to obtain the arrival time;
  • Step 3 Calculate the analytical solution of the target coordinates (x, y, z) according to formula (21);
  • Step 4 Calculate the analytical solution of the distance ⁇ from the target to the reference ultrasonic sensor according to formula (22).
  • the target to be measured is a 20 ⁇ 20 cm plastic plate.
  • the center coordinates of the plastic plate are used as the positioning coordinates of the object to be measured.
  • the ambient temperature of the experiment is 25°C.
  • the method and device can realize the positioning and ranging of the target object with good positioning and ranging accuracy.
  • the absolute errors of the positioning coordinates x, y, z and the distance ⁇ from the measured object to the reference ultrasonic sensor are all within 3.0cm.
  • ultrasonic sensors constitute a sensor array, and the configuration of the array satisfies the condition that there is a unique analytical solution for solving the target position coordinates.
  • the ultrasonic sensor array configuration of the present invention and the target position solving method based on the arrival time of the ultrasonic signal, the positioning and ranging of the target object in three-dimensional space can be realized.
  • this method has the characteristics of requiring fewer ultrasonic sensors, simpler configuration, the smallest theoretical calculation amount, the best numerical stability, and high positioning accuracy.

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  • Engineering & Computer Science (AREA)
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Abstract

本发明公开了一种超声波主动式目标定位方法与装置，装置包括超声波传感器阵列、控制模块以及计算机。本发明采用四个超声波传感器组成阵列，其构型满足目标位置坐标解析解存在且唯一条件，该阵列采用一发多收式信号收发模式，其中一个超声波传感器作为基准超声波传感器，工作在发射/接收双模式，其余三个超声波传感器工作在接收模式。本发明确定了一个实际超声波传感器阵列构型，通过该构型实现三维目标坐标的求解以及目标与基准超声波传感器之间距离的测量。本发明具有传感器阵列构型结构简单、所需超声波传感器数量最少、目标坐标求解理论上计算量最小且具有最好的数值稳定性。

Description

一种超声波主动式目标定位方法与装置 技术领域
本发明涉及超声波定位技术，尤其涉及一种超声波主动式目标定位方法与装置。
背景技术
随着计算机科学、传感器技术以及人工智能的发展，从制造业、交通运输业到对外太空以及深海的探索研究，机器人技术都起到了至关重要的作用。目标定位技术作为机器人技术中的关键技术之一，越来越受到重视。
目前，视觉传感器、激光传感器以及超声波传感器是机器人目标定位技术中采用的几种主流传感器。视觉传感器获得信息丰富，然而在弱光或黑暗条件下难以正常工作。激光传感器精度较高，但其存在安全风险、成本较高且无法实现对透明目标的测量。与其他传感器相比，超声波传感器具有成本低、功耗低、体积小和重量轻等优点，且适用范围很广，可适用于透明物体，并能适用于低能见度或黑暗环境，因此超声波传感器在机器人目标定位领域的研究和应用相当普及。
然而在实际应用中超声波定位技术仍然存在一些问题需要解决。目前，多数超声波定位方法是采用较多数量的超声波传感器获得多个收到超声回波的到达时间或时间差，并通过相对复杂的数值算法利用获得的到达时间求解目标位置。这些方法存在计算量较大、传感器数量较多的问题，并且多数情况下需要先验知识和人工干预。
寻求一种使用相对较少的超声波传感器且计算成本较低的目标定位方法是研究者们一直以来的目标。本发明旨在通过优化超声波传感器阵列构型，采用最少的超声波传感器和最简单的阵列结构，以理论上计算量最小且最稳定的解析方法来实现目标定位。本发明提出了一种超声波主动式目标定位方法与装置，该方法涉及一种超声波传感器阵列构型和目标位置解算与距离测量，其使用最少的超声波传感器，能保证三维目标位置的求解存在唯一的解析解，并具有传感器数量少、理论上计算量最小且解的稳定性最好、传感器构型结构简单、定位准确性高等优点。
发明内容
本发明针对基于多超声波传感器的目标定位技术的现状，提供了一种超声波主动式目标定位方法与装置，该定位装置中的超声波传感器阵列构型能够实现三维空间中的目标定位。本发明采用四个超声波传感器组成超声波传感器阵列，该阵列采用一发多收式信号收发模式， 其中一个超声波传感器作为基准超声波传感器，工作在T/R双模式，即既作为超声波发射器，又作为超声波接收器，其余三个超声波传感器工作在R模式，即只作为接收器。通过基准超声波传感器发射超声波的时间以及传感器收到超声回波的达到时间获得时间差，求解得到目标位置。该超声波传感器阵列构型和方法在目标定位方面具有构型结构简单、理论上计算量最小且解的稳定性最好、准确性高等优势。
本发明的技术方案如下：
本发明首先提供了一种超声波主动式目标定位的装置，其包括超声波传感器阵列、控制模块以及计算机；
所述超声波传感器阵列包括四个不在同一个平面内的超声波传感器；且其中一个超声波传感器作为基准超声波传感器，其工作在发射/接收双模式下，即既作为超声波发射器，又作为超声波接收器；
控制模块操控各超声波传感器发射和接收超声波信号，每个传感器将包含到达时间信息的信号传送至控制模块，控制模块获得到达时间后根据基准超声波传感器发射超声波的时间以及各超声波传感器接收超声回波的时间计算相应的时间差，并通过USB数据线与计算机进行通信，将该时间差发送给计算机，计算机利用该时间差求解目标物体的三维坐标以及目标到基准超声波传感器的距离，并显示和保存定位及测距的结果。
作为本发明的优选方案，以基准超声波传感器所在位置为坐标原点，另外三个超声波传感器分别在三个坐标轴上，并且另外三个超声波传感器到基准超声波传感器的距离相等。
作为本发明的优选方案，其余三个超声波传感器工作在接收模式下，即只作为超声波接收器。
本发明还提供了一种基于上述装置的超声波主动式目标定位方法，其包括如下步骤：
步骤一：采用所述超声波传感器阵列中的基准超声波传感器主动发射超声波，超声波传播至目标物体处发生反射，四个超声波传感器分别接收反射回来的超声波，即超声回波，获得到达时间；
步骤二：根据基准超声波传感器发射超声波的时间t 0以及四个超声波传感器收到超声回波的到达时间t 1、t 2、t 3和t 4，计算相应的时间差Δt 10、Δt 21、Δt 31和Δt 41；Δt 10＝t 1-t 0，Δt i1＝t i-t 1，i＝2，3，4；
步骤三：计算获得目标坐标(x,y,z)的解析解；
步骤四：计算获得目标到基准超声波传感器的距离ρ的解析解。
本发明与现有技术相比具有的有益效果：
1)本发明利用解析方法求解目标坐标，采用了一种新的超声波传感器阵列构型，该构型满足目标位置三维空间坐标的解存在且唯一的条件，克服了现有超声波定位技术中计算代价较高、传感器数量较多、传感器阵列相对复杂、通常需要先验知识和人工干预的问题，从而具有需要的超声波传感器数量少、构型结构简单、并且不需要先验知识和人工干预的优点。
2)本发明通过将超声波传感器布置在坐标轴上并从条件数的角度对传感器坐标进行优化，有效简化了解析解、减小了计算量、提高了解的稳定性，使得目标坐标求解的计算复杂度低、理论上计算量最小且具有最好的数值稳定性、定位精度高。
3)本发明装置安装方便、体积小、功耗低、价格低，可应用范围广。
附图说明
图1是一种超声波主动式目标定位装置的结构示意图；
图2是四个超声波传感器在同一平面内时的示意图；
图3是四个超声波传感器不在同一平面内时的示意图；
图4是图3所示超声波传感器阵列空间构型的一个进一步优化构型；
图5是图4所示超声波传感器阵列空间构型的一个进一步优化构型。
具体实施方式
本发明在基于超声波信号到达时间的目标定位问题的基础上，提出了一种新的超声波传感器阵列构型，以及针对该构型的目标定位方法。该方法较现有方法具有超声波传感器数量少，构型简单，理论上计算量最小且具有最好的数值稳定性，定位精度高的特点。
如图1所示，本发明提供了一种基于超声波传感器的目标定位的装置，包括超声波传感器阵列、控制模块以及计算机。四个超声波传感器组成阵列，其构型满足目标位置解算线性方程组的系数矩阵非奇异。本发明提供了的目标定位超声波传感器阵列的构型，其包含四个超声波传感器，这四个超声波传感器不在同一个平面内。取四个超声波传感器中的任意一个作为基准超声波传感器，其坐标定为(0,0,0)；基准超声波传感器工作在T/R双模式，即既发射超声波也接收超声波；其余的三个超声波传感器至少能够工作在R模式，即其需要能够作为接收器。在优选实施例中，其余三个超声波传感器仅工作在R模式，即只接收超声波。四个超声波传感器通过导线与控制模块相连，实现超声波传感器的供电、控制以及到达时间信息的传输。控制模块获得到达时间后根据基准超声波传感器发射超声波的时间以及各超声波传感器接收超声回波的时间计算相应的时间差，并通过USB数据线与计算机进行通信，将该时间差发送给计算机。计算机利用该时间差求解目标物体的三维坐标以及目标到基准超声波传感器的距离，并显示和保存定位及测距的结果。
本发明的超声波传感器阵列构型的确定过程如下：
根据目标和N个超声波传感器建立三维目标定位的基本模型。定义目标P的坐标为(x,y,z)，第i个超声波传感器S i的坐标为(x i,y i,z i)(i＝1，2，…，N)。出于对定位实时性的考虑，本发明采用一发多收式超声波信号收发模式。令超声波传感器S 1为基准超声波传感器(坐标为(0,0,0))，其可以为N个超声波传感器中的任意一个；基准超声波传感器工作在T/R双模式，即既发射超声波也接收超声波；其余的超声波传感器S i(i＝2，3，…，N)工作在R模式，即只接收超声波。
令t 0为基准超声波传感器S 1发射超声波的时刻，t i为第i个超声波传感器S i接收到超声回波的时刻(i＝1，2，…，N)，即到达时间。因为本发明是一个主动式的测量过程，t 0和t i是已知量。
对于基准超声波传感器S 1，它接收到的是自己发射的超声波的回波，因此它与目标坐标(x,y,z)之间的关系可以表示为以下方程。
Figure PCTCN2022133373-appb-000001
其中，c为声速，Δt 10＝t 1-t 0。
对于其余的只接收超声波的超声波传感器S i(i＝2，3，…，N)，超声波从S 1传播到目标物体，经过目标物体反射，超声回波被超声波传感器S i接收。因此，S i与目标坐标之间的关系可以表示为以下方程。
Figure PCTCN2022133373-appb-000002
其中，Δt i1＝t i-t 1，i＝2，3，…，N。
公式(1)和(2)中的声速由下式计算得到。
Figure PCTCN2022133373-appb-000003
其中，T为环境的摄氏温度，由温度传感器获得，获得的声速单位为m/s。
由此，目标定位问题可以归结为以下方程。
Figure PCTCN2022133373-appb-000004
直接求解方程(4)所描述的非线性方程组的计算代价是相对较高的。因此，通常将方程 (4)转化成关于目标P的位置坐标(x,y,z)的线性方程组再进行求解。
首先，将公式(4)两边取平方并展开，得到：
Figure PCTCN2022133373-appb-000005
然后，将公式(5)中的第2至N个方程依次减去第一个方程(即基准超声波传感器确定的方程)，通过整理可得：
Figure PCTCN2022133373-appb-000006
将公式(6)转换为关于未知数p＝[x,y,z] T的线性方程组的形式：
Gp＝h       (7)
其中，
Figure PCTCN2022133373-appb-000007
Figure PCTCN2022133373-appb-000008
超声波传感器的坐标(x i,y i,z i)和声速c是已知的。Δt 10和Δt i1可以由t 0和t i获得。因此矩阵G和向量h是确定的。通过求解方程(7)就可以实现目标定位。
根据线性代数可知，如果方程(7)有唯一解，则矩阵G应当是一个3×3的方阵并且非奇异。这就意味着对于本发明中的一发多收式超声波传感器阵列，需要四个超声波传感器，即N＝4。那么公式(7)就可以简化为：
Figure PCTCN2022133373-appb-000009
当满足方程中G非奇异，此时可以得到目标P的坐标(x,y,z)的解析表达式，即目标坐标的解析解为：
Figure PCTCN2022133373-appb-000010
相应的，目标到基准超声波传感器的距离ρ可以通过下式计算。
Figure PCTCN2022133373-appb-000011
根据上文所述，公式(10)中三维空间目标坐标(x,y,z)有唯一解析解的条件为矩阵G非奇异，所述目标定位超声波传感器阵列的构型中四个超声波传感器坐标被配置为满足该条件，其中矩阵G的表达式为：
Figure PCTCN2022133373-appb-000012
矩阵G非奇异的充要条件是超声波传感器阵列中的四个超声波传感器不在同一个平面内。具体的证明如下：
定义超声波传感器S 2、S 3和S 4的位置向量分别为s 2＝[x 2,y 2,z 2]，s 3＝[x 3,y 3,z 3]和s 4＝[x 4,y 4,z 4]。根据公式(13)，可以看出向量s 2，s 3和s 4就是矩阵G的三个行向量。
四个超声波传感器S 1、S 2、S 3和S 4在空间中的位置关系可以分为两种，一种是四个超声波传感器在同一个平面内，另一种是四个超声波传感器不在同一个平面内。
先考虑这四个超声波传感器在同一个平面内的情况。不失一般性地，如图2所示，假设它们都在xOy平面内，即z 2＝z 3＝z 4＝0。此时矩阵G可以表示为
Figure PCTCN2022133373-appb-000013
G的行列式det(G)＝0，即G是奇异的。
再考虑这四个超声波传感器不在同一个平面内的情况。不失一般性地，如图3所示，假设S 1、S 2和S 3在xOy平面内而S 4在该平面外，即z 2＝z 3＝0且z 4≠0。此时G可以表示为
Figure PCTCN2022133373-appb-000014
G的行列式为
det(G)＝z 4(x 2y 3-x 3y 2)         (16)
由于z 4≠0，det(G)＝0的充要条件是x 2y 3-x 3y 2＝0。但是x 2y 3-x 2y 2＝0意味着S 1、S 2和S 3共线，S 1、S 2、S 3和S 4在同一平面内。然而这和四个超声波传感器不在同一个平面内的前提矛盾。因此det(G)≠0，即G是非奇异的。
因此，矩阵G非奇异的充要条件是超声波传感器阵列中的四个超声波传感器不在同一个平面内。证明完毕。
事实上，根据线性代数，从向量的角度我们也可以获得相同的结论。如果这四个超声波传感器在同一个平面内，向量s 2，s 3和s 4线性相关，即矩阵G的三个行向量线性相关。因此det(G)＝0，即G是奇异的。如果这四个超声波传感器不在同一个平面内，向量s 2，s 3和s 4线性无关，即矩阵G的三个行向量线性无关。因此det(G)≠0，即G是非奇异的。所以G是非奇异的当且仅当这四个超声波传感器不在同一个平面内。
基于上述讨论，当且仅当这四个超声波传感器不在同一个平面内时，目标坐标(x,y,z)可以由公式(11)获得唯一的解析解。
本发明通过求解公式(10)来实现定位。由于解析解的计算量和稳定性是重要的，本发明通过合理选择四个超声波传感器的坐标，确保目标坐标的解析解形式简单、计算量小并且稳定性好。为了简化解析解的表达式、减小计算量，通过将S 2、S 3和S 4分别设置在三个坐标轴上，将矩阵G设计为对角阵。如图4所示，令超声波传感器S 2的坐标为(x 2,0,0)，超声波传感器S 3的坐标为(0,y 3,0)，超声波传感器S 4的坐标为(0,0,z 4)。该构型下的矩阵G非奇异，且形式为：
Figure PCTCN2022133373-appb-000015
进一步的，为了提高求解目标坐标(x,y,z)的数值稳定性，可以从矩阵G的条件数cond(G)的角度优化这四个超声波传感器的坐标。
本方法通过求解以G为系数矩阵的线性方程组实现定位。根据线性代数可知cond(G)是解的稳定性的重要指标。cond(G)大意味着测量误差可能对解产生显著的影响，解的波动就可能很大。cond(G)小意味着测量误差对解的影响就小，解就稳定。根据线性代数，不论在何种范数意义下，矩阵G的条件数cond(G)的最小值是1，当cond(G)＝1时，解的稳定性达到最好。
基于以上两点考虑，本发明提出了一个实际的四元超声波传感器阵列构型，其要求S 2、S 3和S 4分别在三个坐标轴上，并且这三个超声波传感器到基准超声波传感器(原点)的距离 相等。令x 2＝y 3＝z 4＝a，即超声波传感器S 2的坐标为(a,0,0)，超声波传感器S 3的坐标为(0,a,0)，超声波传感器S 4的坐标为(0,0,a)，a为S 2、S 3和S 4到基准超声波传感器的距离，所提出的阵列构型的坐标如图5所示。
相应的矩阵G可以表示为：
Figure PCTCN2022133373-appb-000016
此时，G的对角线元素相等，不论在何种范数意义下的矩阵G的条件数为都为1，cond(G)＝1，矩阵G的条件数达到最小值，解的稳定性最好。
对应的逆矩阵G -1为：
Figure PCTCN2022133373-appb-000017
相应的向量h为：
Figure PCTCN2022133373-appb-000018
该实际四元超声波传感器阵列构型相应的目标坐标(x,y,z)的解析表达式，即目标坐标的解析解为：
Figure PCTCN2022133373-appb-000019
相应的，目标到基准超声波传感器的距离ρ的解析解表达式为：
Figure PCTCN2022133373-appb-000020
本发明方法的实施过程中，首先通过控制模块操控基准超声波传感器发射超声脉冲；超声脉冲向外传输并在遇到目标后发生反射，反射后的超声回波由四个超声波传感器接收；之后这四个传感器将包含到达时间信息的信号传送至控制模块；控制模块获得到达时间后，利用基准超声波传感器发射超声波的时间t 0以及四个超声波传感器收到超声回波的到达时间t 1、t 2、t 3和t 4，计算相应的时间差Δt 10、Δt 21、Δt 31和Δt 41；控制模块通过USB数据线与计算机进行通信，将Δt 10、Δt 21、Δt 31和Δt 41发送给计算机，计算机根据公式(21)求解目标物体的坐标以及根据公式(22)求解目标到基准超声波传感器的距离，并显示和保存定位及测距的 结果。
具体的，可按如下步骤进行：
步骤一：采用所述超声波传感器阵列中的基准超声波传感器主动发射超声波，超声波传播至目标物体处发生反射，四个超声波传感器分别接收反射回来的超声波，即超声回波，获得到达时间；
步骤二：根据基准超声波传感器发射超声波的时间t 0以及四个超声波传感器收到超声回波的到达时间t 1、t 2、t 3和t 4，计算相应的时间差Δt 10、Δt 21、Δt 31和Δt 41；Δt 10＝t 1-t 0，Δt i1＝t i-t 1，i＝2，3，4；
步骤三：根据公式(21)计算获得目标坐标(x,y,z)的解析解；
步骤四：根据公式(22)计算获得目标到基准超声波传感器的距离ρ的解析解。
为了验证该方法与装置的有效性和定位效果，开展了目标定位实验。
根据图5所示的坐标设计了一个实际的超声波传感器阵列，其中a＝8cm。待测目标为20×20cm的塑料板。塑料板的中心坐标，作为被测对象的定位坐标。实验的环境温度为25℃。
实验表明，在3.0m的测试范围内，该方法与装置能够实现对目标物体的定位和测距，且定位与测距的精度较好。定位坐标x、y、z以及被测对象到基准超声波传感器的距离ρ的绝对误差均在3.0cm以内。
本发明中四个超声波传感器构成传感器阵列，该阵列的构型满足目标位置坐标的求解存在唯一解析解的条件。通过本发明的超声波传感器阵列构型和基于超声波信号到达时间的目标位置求解方法，可以实现三维空间中目标物体的定位及测距。该方法较现有方法具有需要的超声波传感器数量少，构型简单，理论上计算量最小且具有最好的数值稳定性，定位精度高的特点。

Claims (6)

  1. 一种超声波主动式目标定位的装置，其特征在于包括超声波传感器阵列、控制模块以及计算机；
    所述超声波传感器阵列包括四个不在同一个平面内的超声波传感器；且其中一个超声波传感器作为基准超声波传感器，其工作在发射/接收双模式下，即既作为超声波发射器，又作为超声波接收器；
    控制模块操控各超声波传感器发射和接收超声波信号，每个传感器将包含到达时间信息的信号传送至控制模块，控制模块获得到达时间后根据基准超声波传感器发射超声波的时间以及各超声波传感器接收超声回波的时间计算相应的时间差，并通过USB数据线与计算机进行通信，将该时间差发送给计算机，计算机利用该时间差求解目标物体的三维坐标以及目标到基准超声波传感器的距离，并显示和保存定位及测距的结果。
  2. 根据权利要求1所述的超声波主动式目标定位的装置，其特征在于，以基准超声波传感器所在位置为坐标原点，另外三个超声波传感器分别在三个坐标轴上，并且另外三个超声波传感器到基准超声波传感器的距离相等。
  3. 根据权利要求1或2所述的超声波主动式目标定位的装置，其特征在于，其余三个超声波传感器工作在接收模式下，即只作为超声波接收器。
  4. 一种权利要求2所述装置的超声波主动式目标定位方法，其特征在于，包括如下步骤：
    步骤一：采用所述超声波传感器阵列中的基准超声波传感器主动发射超声波，超声波传播至目标物体处发生反射，四个超声波传感器分别接收反射回来的超声波，即超声回波，获得到达时间；
    步骤二：根据基准超声波传感器发射超声波的时间t 0以及四个超声波传感器收到超声回波的到达时间t 1、t 2、t 3和t 4，计算相应的时间差Δt 10、Δt 21、Δt 31和Δt 41；Δt 10＝t 1-t 0，Δt i1＝t i-t 1，i＝2，3，4；
    步骤三：计算获得目标坐标(x,y,z)的解析解；
    步骤四：计算获得目标到基准超声波传感器的距离ρ的解析解。
  5. 根据权利要求4所述的超声波主动式目标定位方法，其特征在于，所述的步骤三，具体为：四个超声波传感器分别记为S 1、S 2、S 3和S 4，令超声波传感器S 1为基准超声波传感器，其坐标为(0,0,0)，S 2、S 3和S 4的坐标分别为(a,0,0)、(0,a,0)、(0,0,a)，其中a为S 2、S 3和S 4到基准超声波传感器的距离；被测对象P的坐标(x,y,z)用如下解析解表示：
    Figure PCTCN2022133373-appb-100001
    Figure PCTCN2022133373-appb-100002
    Figure PCTCN2022133373-appb-100003
    其中c为声速。
  6. 根据权利要求4所述的超声波主动式目标定位方法，其特征在于，所述的步骤四，被测对象到基准超声波传感器的距离ρ具体为：
    Figure PCTCN2022133373-appb-100004
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