CN103412682B - Electronic whiteboard experimental system based on infrared ultrasonic co-located and localization method - Google Patents
Electronic whiteboard experimental system based on infrared ultrasonic co-located and localization method Download PDFInfo
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Abstract
一种基于红外超声联合定位的电子白板实验系统及定位方法,属于无线定位领域。本实验系统主要包括集成了红外发射器与超声波发射器的信号发射模块、集成了红外接收器与六个超声波接收器的信号接收模块、信号处理模块和上位机。信号笔会产生周期性红外、超声信号,接收端的红外接收器检测到红外信号,六个超声波接收器同时开始工作,分别检测各自接收到超声波信号所用的时间,传送给信号处理模块,采用Chan算法对经过BP神经网络校正的数据进行求解得到信号源。本发明大大节约了传感器的成本,且体积较小,能够及时准确的获取传感器的检测数据,同时可以作为高精度算法的实验平台,并为算法有效性等的研究提供了便利条件。
The invention relates to an electronic whiteboard experiment system and a positioning method based on combined infrared and ultrasonic positioning, which belong to the field of wireless positioning. The experimental system mainly includes a signal transmitting module integrating an infrared transmitter and an ultrasonic transmitter, a signal receiving module integrating an infrared receiver and six ultrasonic receivers, a signal processing module and a host computer. The signal pen will generate periodic infrared and ultrasonic signals. The infrared receiver at the receiving end detects the infrared signal. The six ultrasonic receivers start working at the same time. The signal source is obtained by solving the data corrected by the BP neural network. The invention greatly saves the cost of the sensor, has a small volume, can timely and accurately acquire the detection data of the sensor, can be used as an experimental platform for a high-precision algorithm, and provides convenient conditions for research on the effectiveness of the algorithm.
Description
技术领域 technical field
本发明是一种基于红外超声联合定位的电子白板实验系统及定位方法,属于无线定位领域。The invention relates to an electronic whiteboard experiment system and a positioning method based on combined infrared and ultrasonic positioning, and belongs to the field of wireless positioning.
背景技术 Background technique
电子白板是一种可以在板面上任意书写并能够被电子捕获的干擦拭白板,集黑板、多媒体、投影仪为一身,其功能远远大于三者之和,是近年来国际上推出的一款高科技产品。电子白板是对传统板书以及多媒体教室的一种突破,它与投影仪、计算机等的联机使用,利用计算机的数据处理功能和信息传输功能,可以轻松实现信息演示、编辑等功能。电子白板教学平台对比黑板及电教平台两种教学方式,保留了黑板的互动性及电教的丰富性,克服了黑板的单调性及电教的单向性的不足,从根本上解决了以往教学模式中存在的问题和不足,真正实现了“教与学的互动”,实现了高品质、高效率的教学模式。The electronic whiteboard is a dry-wipe whiteboard that can be written on the board and can be electronically captured. It integrates a blackboard, multimedia, and a projector. Its functions are far greater than the sum of the three. A high-tech product. The electronic whiteboard is a breakthrough to traditional blackboard writing and multimedia classrooms. It can be used online with projectors and computers, and can easily realize information presentation, editing and other functions by using the data processing function and information transmission function of the computer. The electronic whiteboard teaching platform compares the two teaching methods of the blackboard and the audio-visual platform, retains the interactivity of the blackboard and the richness of the audio-visual education, overcomes the lack of monotony of the blackboard and the unidirectionality of the audio-visual education, and fundamentally solves the problems in the previous teaching mode. The existing problems and deficiencies have truly realized the "interaction between teaching and learning" and realized a high-quality and efficient teaching model.
然而市场上存在的电子白板由于其面向客户,大都是板面较大、高度集成,难以获取内部传感器信息,并没有适合进行实验研究的电子白板实验系统。因而当研究人员欲对电子白板核心技术(如定位精度、识别准确性等)展开研究时,必须要面对由于无法获取集成在白板硬件中的各传感器的采样信息而不能得到验证研究成果有效性所必须的精度、响应速度、准确性等反馈信息的难题,这是研究工作中一个较大的障碍,同时势必也会延迟电子白板的更新换代。However, most of the electronic whiteboards on the market are large and highly integrated because they are oriented to customers, and it is difficult to obtain internal sensor information. There is no electronic whiteboard experimental system suitable for experimental research. Therefore, when researchers want to conduct research on the core technology of electronic whiteboards (such as positioning accuracy, recognition accuracy, etc.), they must face the fact that the validity of the research results cannot be verified due to the inability to obtain the sampling information of each sensor integrated in the whiteboard hardware. The problem of feedback information such as the necessary precision, response speed, and accuracy is a major obstacle in research work, and it will inevitably delay the replacement of electronic whiteboards.
目前,电子白板的基本定位算法包括场强(RSSI)定位法、基于电波传播时间(TOA)或时间差(TDOA)的定位法、基于电波入射角(AOA)的定位法以及各类混合定位法。其中, 基于TDOA的定位法无严格时间同步要求,能适用于各种类型的系统,且应用成本较低,定位精度较高,受到广泛关注。但是,由于环境中存在各种干扰,实际测量得到的数据常常含有误差,导致定位精度降低甚至定位失败,因此有必要研究高精度的定位算法。At present, the basic positioning algorithms of electronic whiteboards include field strength (RSSI) positioning method, positioning method based on radio wave propagation time (TOA) or time difference (TDOA), positioning method based on radio wave incident angle (AOA) and various hybrid positioning methods. Among them, the positioning method based on TDOA has no strict time synchronization requirements, can be applied to various types of systems, and has low application cost and high positioning accuracy, which has attracted widespread attention. However, due to various disturbances in the environment, the actual measured data often contain errors, resulting in reduced positioning accuracy or even positioning failure. Therefore, it is necessary to study high-precision positioning algorithms.
发明内容 Contents of the invention
本发明提出了一种基于红外超声联合定位的电子白板实验系统及定位方法。本实验系统利用红外线发射传感器和超声波发射传感器模拟信号笔的发射原理产生红外线和超声波信号,信号接收端获取前述信号从信号笔发出到被接收传感器接收到之间的传播时间,进而由定位算法对数据求解得到信号笔的位置信息,从而达到信号笔定位的目的。本发明能够及时准确获取传感器的检测数据,可以弥补目前电子白板产品集成度高,不适合进行实验研究的缺陷,且具有体积小,成本低的特点;同时可以作为高精度算法的实验平台,为验证算法有效性等的研究提供便利的条件。同时,以本发明的电子白板实验系统作为硬件平台,提出一种基于BP神经网络与Chan算法的联合定位算法。The invention proposes an electronic whiteboard experiment system and a positioning method based on combined infrared and ultrasonic positioning. This experimental system uses the infrared emission sensor and ultrasonic emission sensor to simulate the emission principle of the signal pen to generate infrared and ultrasonic signals. The data is solved to obtain the position information of the signal pen, so as to achieve the purpose of positioning the signal pen. The invention can timely and accurately obtain the detection data of the sensor, can make up for the defects of high integration of current electronic whiteboard products and is not suitable for experimental research, and has the characteristics of small size and low cost; at the same time, it can be used as an experimental platform for high-precision algorithms. It provides convenient conditions for the research on the validity of the verification algorithm. At the same time, using the electronic whiteboard experiment system of the present invention as a hardware platform, a joint positioning algorithm based on BP neural network and Chan algorithm is proposed.
本发明的主体思路是:当信号笔在电子白板实验系统的书写区域按下开关开始书写,信号笔会产生周期性红外线、超声波信号,接收端的红外线接收传感器检测到红外线信号(由于距离较短且红外线传播速度接近光速,其传播时间可忽略不计),触发DSP中断,六个超声波接收传感器同时开始工作(认为是瞬时触发),分别检测各自接收到超声波信号所用的时间,传送给信号处理模块,利用Chan算法对经过BP神经网络校正的采样数据进行求解得到信号源(也即信号笔)在电子白板实验系统上的位置信息,从而达到对信号笔定位的目的。The main idea of the present invention is: when the signal pen presses the switch in the writing area of the electronic whiteboard experiment system to start writing, the signal pen will generate periodic infrared and ultrasonic signals, and the infrared receiving sensor at the receiving end detects the infrared signal (because the distance is short and the infrared The propagation speed is close to the speed of light, and its propagation time is negligible), triggering the DSP interrupt, and the six ultrasonic receiving sensors start working at the same time (considered as instantaneous triggering), respectively detect the time it takes for each to receive the ultrasonic signal, and send it to the signal processing module. The Chan algorithm solves the sampling data corrected by the BP neural network to obtain the position information of the signal source (that is, the signal pen) on the electronic whiteboard experimental system, so as to achieve the purpose of positioning the signal pen.
本发明采取的具体技术方案如下:包括信号发射模块(简称信号笔)、信号接收模块、信号处理模块、上位机软件,其特征在于:还包括红外线发射传感器、超声波发射传感器、红外线接收传感器、六个超声波接收传感器,红外线发射传感器和超声波发射传感器固定在信号笔中,由单片机控制发出周期性的红外线信号和超声波信号,红外线接收传感器和六个超声波接收传感器固定在信号接收模块,接收红外线信号和超声波信号,信号接收传感器模块的输出端与信号处理模块的输入端相连,信号处理模块采用DSP作为主控芯片,信号处理模块的输出端与上位机软件相连。The specific technical scheme adopted by the present invention is as follows: including a signal transmitting module (referred to as a signal pen), a signal receiving module, a signal processing module, and a host computer software, and is characterized in that: it also includes an infrared emitting sensor, an ultrasonic emitting sensor, an infrared receiving sensor, six One ultrasonic receiving sensor, the infrared emitting sensor and the ultrasonic emitting sensor are fixed in the signal pen, and the periodic infrared signal and ultrasonic signal are sent out by the single-chip microcomputer control, the infrared receiving sensor and six ultrasonic receiving sensors are fixed in the signal receiving module, receiving the infrared signal and Ultrasonic signal, the output end of the signal receiving sensor module is connected with the input end of the signal processing module, the signal processing module adopts DSP as the main control chip, and the output end of the signal processing module is connected with the host computer software.
上述电子白板实验系统的定位算法包括以下步骤:The positioning algorithm of the above-mentioned electronic whiteboard experimental system includes the following steps:
1)信号发射模块开关按下,红外线发射传感器和超声波发射传感器发出周期性的红外线信号和超声波信号;1) When the switch of the signal transmitting module is pressed, the infrared transmitting sensor and the ultrasonic transmitting sensor send out periodic infrared signals and ultrasonic signals;
2)信号接收端的红外线接收传感器检测到信号,触发六个超声波接收传感器同时开始工作,分别检测各自接收到超声波信号所用的时间ti,i=1,2,3,4,5,6;2) The infrared receiving sensor at the signal receiving end detects the signal, triggers the six ultrasonic receiving sensors to start working at the same time, and detects the time t i , i=1, 2, 3, 4, 5, 6 for each receiving the ultrasonic signal;
3)以第一个超声波接收传感器的数据为参考,采用TDOA算法计算获得5个TDOA值ti1,i=2,3,4,5,6;3) Taking the data of the first ultrasonic receiving sensor as a reference, use the TDOA algorithm to calculate and obtain 5 TDOA values t i1 , i=2,3,4,5,6;
4)利用不含误差的理论数据训练BP神经网络,用训练好的BP神经网络对5个TDOA值ti1,i=2,3,4,5,6进行修正;4) Use the theoretical data without errors to train the BP neural network, and use the trained BP neural network to correct the five TDOA values t i1 , i=2,3,4,5,6;
5)利用修正后的数据采用Chan算法进行位置估算,得到信号笔在电子白板实验系统上的位置信息,从而达到对信号笔定位的目的。5) Using the corrected data, use the Chan algorithm to estimate the position, and obtain the position information of the signal pen on the electronic whiteboard experimental system, so as to achieve the purpose of positioning the signal pen.
本发明采用红外线传感器、超声波传感器作为获取定位信息的信号输入,大大节约了传感器的成本,同时减小了体积,能够及时准确的获取传感器信息。The present invention adopts an infrared sensor and an ultrasonic sensor as signal input for obtaining positioning information, which greatly saves the cost of the sensor, reduces the volume at the same time, and can obtain sensor information timely and accurately.
附图说明 Description of drawings
图1 电子白板实验系统的示意图Figure 1 Schematic diagram of the electronic whiteboard experimental system
图2 电子白板实验系统的原理框图Figure 2 The principle block diagram of the electronic whiteboard experiment system
图3 电子白板实验系统的系统结构框图Figure 3 System structure block diagram of the electronic whiteboard experiment system
图4 电子白板实验系统信号发射的软件流程图Figure 4 The software flow chart of the signal emission of the electronic whiteboard experiment system
图5 电子白板实验系统定位算法示意图Figure 5 Schematic diagram of positioning algorithm for electronic whiteboard experiment system
图6 电子白板实验系统定位算法原理框图Fig. 6 Principle block diagram of positioning algorithm of electronic whiteboard experiment system
图7 对TDOA值进行修正的BP神经网络模型Figure 7. The BP neural network model that corrects the TDOA value
图8 电子白板实验系统定位算法的软件流程图Figure 8 Software flow chart of the positioning algorithm of the electronic whiteboard experiment system
具体实施方式 detailed description
下面结合附图对本实验系统作进一步说明:The following is a further description of the experimental system in conjunction with the accompanying drawings:
如图1、图2所示,本发明的硬件结构比较简单,成本低,容易实现。As shown in Fig. 1 and Fig. 2, the hardware structure of the present invention is relatively simple, low in cost, and easy to implement.
为了减少信号发射端的体积,本实验系统中控制产生脉冲波形的单片机选择的是体积较小的Microchip公司的8位8引脚单片机PIC12F629。波形电路主要由单片机的GP0口和GP1口产生,由于驱动电路里的谐振回路对脉冲所含的80KHZ的频率分量谐振,而脉冲宽度与脉冲所含各频率分量的功率大小直接相关,同时脉冲越宽,功率越大,电池寿命越短;脉冲宽度太窄,脉冲所含80KHZ信号能量小,造成系统发射功率不足,因此本实验系统选用的脉冲宽度为400uS,红外二极管采用200uS宽度的脉冲信号完全可以驱动。脉冲信号的周期设定为10mS,保证了每秒可以发出100个信号,完全满足接受需要和视觉要求。单片机PIC12F629的GP0口发出脉宽为400uS、周期为10mS的脉冲信号,作为超声波传感器的驱动信号;GP1口发出脉宽为200uS、周期为10mS的脉冲信号,作为红外二极管的驱动信号。PIC单片机控制过程的软件实现流程如图4所示。In order to reduce the volume of the signal transmitting end, the single-chip microcomputer that controls the pulse waveform in this experimental system is selected as the 8-bit 8-pin single-chip microcomputer PIC12F629 of Microchip Company with a smaller volume. The waveform circuit is mainly generated by the GP0 port and GP1 port of the single-chip microcomputer. Since the resonant circuit in the drive circuit resonates with the 80KHZ frequency component contained in the pulse, the pulse width is directly related to the power of each frequency component contained in the pulse. wide, the greater the power, the shorter the battery life; the pulse width is too narrow, and the 80KHZ signal energy contained in the pulse is small, resulting in insufficient system transmission power. can be driven. The period of the pulse signal is set to 10mS, which ensures that 100 signals can be sent out per second, which fully meets the needs of reception and vision. The GP0 port of the microcontroller PIC12F629 sends out a pulse signal with a pulse width of 400uS and a period of 10mS as the driving signal of the ultrasonic sensor; GP1 port sends out a pulse signal with a pulse width of 200uS and a period of 10mS as the driving signal of the infrared diode. The software implementation process of the PIC microcontroller control process is shown in Figure 4.
本实验系统的超声波发射传感器要求360度全向传播,并且要求在全向范围内具有良好的传播特性,因此本系统选用美国EMAS传感器公司生产的压电薄膜超声波传感器PT80KHZ—01。该传感器在满足上述要求的同时还具有频响高、动态范围好、输出电压高、稳定性好、耐冲击、不易老化等特点,满足本实验系统的各种要求。The ultrasonic transmitter sensor of this experimental system requires 360-degree omnidirectional transmission and good propagation characteristics in the omnidirectional range. Therefore, this system uses the piezoelectric thin film ultrasonic sensor PT80KHZ-01 produced by the American EMAS sensor company. While meeting the above requirements, the sensor also has the characteristics of high frequency response, good dynamic range, high output voltage, good stability, impact resistance, and not easy to age, which meets the various requirements of this experimental system.
本实验系统所需的红外线发射传感器同样要求360度全向传播,但市场上没有满足条件的红外线发射传感器,因此本实验系统选用红外线发射二极管SFH426,它的发射角度为120度,使用4个SFH426让其均匀分布一周可以实现360度全向发射。The infrared emitting sensor required by this experimental system also requires 360-degree omnidirectional transmission, but there is no infrared emitting sensor that meets the conditions on the market, so this experimental system uses infrared emitting diode SFH426, its emission angle is 120 degrees, and four SFH426 are used Let it be evenly distributed for a week to achieve 360-degree omnidirectional emission.
超声波接收传感器采用美国EMAS传感器公司的SR80KHZ—01,它也是一款压电薄膜传感器,具有接收信号大范围、较大的方向角与带宽等优点。The ultrasonic receiving sensor adopts SR80KHZ-01 from EMAS Sensor Company of the United States, which is also a piezoelectric film sensor, which has the advantages of wide range of receiving signals, large direction angle and bandwidth.
红外线接收传感器采用的是SFH506—38,它是外形很小的红外远距离控制系统接收传感器,PIN二极管和前置放大器装在焊接外壳里,环氧材料封装。该接收传感器输出的调制信号可以直接被微处理器解调。其最主要的优点是,在有干扰的环境中仍具有可靠性,外壳具有屏蔽作用抗电磁干扰。The infrared receiving sensor adopts SFH506-38, which is a small infrared remote control system receiving sensor. The PIN diode and preamplifier are installed in the welding shell and encapsulated by epoxy material. The modulated signal output by the receiving sensor can be directly demodulated by the microprocessor. Its main advantage is that it still has reliability in an environment with interference, and the shell has a shielding effect against electromagnetic interference.
下面结合图3说明本实验系统的信号处理模块,包括电源管理模块、DSP主控制电路。其中红外线接收传感器与DSP的一个I/O口相连,超声波接收传感器与DSP中具有捕获功能的I/O口相连,利用捕获中断来获取超声波传播时间。在DSP中进行算法实现,对采样数据进行求解后,输出信号笔的位置信息,通过RS232串口传输至上位机软件。The signal processing module of this experimental system is described below in conjunction with Figure 3, including the power management module and the DSP main control circuit. Among them, the infrared receiving sensor is connected with an I/O port of the DSP, and the ultrasonic receiving sensor is connected with the I/O port with the capture function in the DSP, and the ultrasonic propagation time is obtained by using the capture interrupt. The algorithm is realized in DSP, and after solving the sampling data, the position information of the signal pen is output, which is transmitted to the host computer software through the RS232 serial port.
为了实现超声波时延精确提取算法,本实验系统信号处理电路的核心芯片采用的是TI公司生产的一款TMS320C28X系列浮点DSP控制器TMS320F28335,其具有150MHz的高速处理能力,完全满足本实验系统的实时性要求。与以往的定点DSP相比,该器件具有精度高,成本低,功耗低,性能高,外设集成度高,数据以及程序存储量大,A/D转换更精确快速等优点。TMS320F28335具备32位浮点处理单元,6个DMA通道支持ADC、McBSP和EMIF,有多达18路的PWM输出,其中有6路为TI特有的更高精度的PWM输出,12位16通道ADC。得益于其浮点运算单元,用户可快速编写控制算法而无需在处理小数操作上耗费过多的时间和精力,与前代DSC相比,平均性能提高50%,从而简化软件开发,缩短开发周期,降低开发成本。In order to realize the accurate extraction algorithm of ultrasonic time delay, the core chip of the signal processing circuit of this experimental system adopts a TMS320C28X series floating-point DSP controller TMS320F28335 produced by TI Company, which has a high-speed processing capability of 150MHz, which fully meets the requirements of this experimental system. Real-time requirements. Compared with the previous fixed-point DSP, this device has the advantages of high precision, low cost, low power consumption, high performance, high peripheral integration, large data and program storage, and more accurate and fast A/D conversion. TMS320F28335 has a 32-bit floating-point processing unit, 6 DMA channels supporting ADC, McBSP and EMIF, and up to 18 PWM outputs, of which 6 are TI-specific higher-precision PWM outputs, and 12-bit 16-channel ADC. Thanks to its floating point operation unit, users can quickly write control algorithms without spending too much time and energy on dealing with decimal operations. Compared with the previous generation DSC, the average performance is increased by 50%, thus simplifying software development and shortening the development time. cycle and reduce development costs.
电源管理模块采用的是集成的DC-DC变压电路,它的主要作用是将电池电压(12v)转换成DSP控制板、红外线接收传感器、超声波接收传感器所需要的电压(5v、3.3v)。The power management module uses an integrated DC-DC transformer circuit, its main function is to convert the battery voltage (12v) into the voltage (5v, 3.3v) required by the DSP control board, infrared receiving sensor, and ultrasonic receiving sensor.
以本发明的电子白板实验系统作为硬件平台,提出一种基于BP神经网络与Chan算法的联合定位算法。方法如图5~7所示,以书写区域左上角为原点,分别以水平和竖直方向为X,Y轴,建立平面直角坐标系。算法的具体实现为:Taking the electronic whiteboard experiment system of the present invention as the hardware platform, a joint positioning algorithm based on BP neural network and Chan algorithm is proposed. The method is as shown in Figures 5-7, with the upper left corner of the writing area as the origin, and the horizontal and vertical directions as the X and Y axes, respectively, to establish a plane Cartesian coordinate system. The specific implementation of the algorithm is:
1)信号笔开关按下,红外线发射传感器和超声波发射传感器发出周期性的红外线信号和超声波信号;1) When the switch of the signal pen is pressed, the infrared emission sensor and the ultrasonic emission sensor send out periodic infrared signals and ultrasonic signals;
2)信号接收端的红外线接收传感器检测到红外线信号产生中断,触发六个超声波接收传感器同时开始工作,分别检测各自接收到超声波信号所用的时间ti,i=1,2,3,4,5,6;2) The infrared receiving sensor at the signal receiving end detects that the infrared signal is interrupted, triggers six ultrasonic receiving sensors to start working at the same time, and respectively detects the time t i , i=1,2,3,4,5, 6;
3)以第一个超声波接收传感器为参考,采用TDOA算法计算获得5个TDOA值ti1=ti-t1,i=2,3,4,5,6;3) Taking the first ultrasonic receiving sensor as a reference, use the TDOA algorithm to calculate and obtain 5 TDOA values t i1 =t i -t 1 , i=2,3,4,5,6;
4)用BP神经网络进行数据修正,具体如下:4) Carry out data correction with BP neural network, as follows:
a.设计BP神经网络:由输入层、隐含层和输出层组成。输入层由6个超声波接收传感器提供的5个TDOA测量值组成;隐含层神经元数目可以由经验公式获得,隐含层传递函数选择Sigmoid型函数;输出层由5个神经元构成,采用线性传递函数,输出值为修正后的TDOA值a. Design BP neural network: It consists of input layer, hidden layer and output layer. The input layer is composed of 5 TDOA measurement values provided by 6 ultrasonic receiving sensors; the number of neurons in the hidden layer can be obtained by empirical formula, and the transfer function of the hidden layer is selected as a Sigmoid function; the output layer is composed of 5 neurons, using linear Transfer function, the output value is the corrected TDOA value
b.训练BP神经网络:输入层的测量值采用定点测量所获取的无误差数据;输出层的输出值与输入层相同。b. Training BP neural network: the measurement value of the input layer adopts the error-free data obtained by fixed-point measurement; the output value of the output layer is the same as that of the input layer.
c.用训练好的BP神经网络对(3)中的5个TDOA值ti1,i=2,3,4,5,6进行修正c. Use the trained BP neural network to correct the five TDOA values t i1 in (3), i=2,3,4,5,6
5)利用修正后的距离值采用Chan算法进行位置估算,得到超声波信号源(也即信号笔)在电子白板实验系统上的位置信息,从而达到对信号笔定位的目的。具体如下:5) Using the corrected distance value, use the Chan algorithm to estimate the position, and obtain the position information of the ultrasonic signal source (that is, the signal pen) on the electronic whiteboard experimental system, so as to achieve the purpose of positioning the signal pen. details as follows:
设(x,y)为待求信号笔的位置,(xi,yi)为第i个超声波接收传感器的已知位置,C为超声波传播速度,Ri表示信号笔到第i个超声波接收传感器的距离,Ri1表示信号笔到第i个超声波接收传感器与信号笔到第1个超声波接收传感器的距离之差,则:Let (x, y) be the position of the signal pen to be requested, ( xi , y i ) is the known position of the i-th ultrasonic receiving sensor, C is the propagation speed of the ultrasonic wave, R i represents the signal pen to the i-th ultrasonic receiving sensor The distance of the sensor, R i1 represents the difference between the distance from the signal pen to the i-th ultrasonic receiving sensor and the distance from the signal pen to the first ultrasonic receiving sensor, then:
两边平方整理可得:Square both sides to get:
其中xi1=xi-x1,yi1=yi-y1, ,i=2,3,4,5,6where x i1 =x i -x 1 , y i1 =y i -y 1 , ,i=2,3,4,5,6
设Za=[x,y,R1]T为未知向量,此时方程(2)为关于这三个变量的三元一次方程,从而可以得到误差矢量:Let Z a =[x,y,R 1 ] T be an unknown vector, then equation (2) is a ternary linear equation about these three variables, so that the error vector can be obtained:
其中,
定义无噪声时{*}的表达形式为{*}0,则:When defining no noise, the expression form of {*} is {*} 0 , then:
其中ni1=ni-n1,ni为第i个超声波接收传感器检测时间的系统误差。Among them, n i1 =n i -n 1 , and n i is the systematic error of the detection time of the i-th ultrasonic receiving sensor.
由此可得误差矢量为:From this, the error vector can be obtained as:
其中,
Ψ=E[ψψT]=C2BQB (5)Ψ=E[ψψ T ]=C 2 BQB (5)
其中,Q=E[nn]为TDOA的协方差矩阵,利用WLS求得式(4)的近似解为:Among them, Q=E[nn] is the covariance matrix of TDOA, and the approximate solution of formula (4) obtained by using WLS is:
信号笔与超声波接收传感器距离较远时,定义一个R0,使其与各个 近似,此时B=R0I,Za可替代为:When the distance between the signal pen and the ultrasonic receiving sensor is relatively long, define a R 0 to make it compatible with each Approximately, at this time B=R 0 I, Z a can be replaced by:
信号笔与超声波接收传感器距离较近时,首先计算B的值,然后由式(6)得到信号笔的位置。至此,第一次WLS结束。When the distance between the signal pen and the ultrasonic receiving sensor is relatively close, the value of B is calculated first, and then the position of the signal pen is obtained by formula (6). So far, the first WLS is over.
利用第一次WLS估计值以及约束关系进行第二次WLS:Use the first WLS estimate and the constraint relationship for the second WLS:
其中,
最终解得信号笔的位置估计为:Finally, the estimated position of the signal pen is obtained as:
在本实验系统中,信号笔只在第一象限运动,所以(9)式计算得到的结果只取正值,由此实现定位。In this experimental system, the signal pen only moves in the first quadrant, so the result calculated by formula (9) only takes a positive value, thereby realizing positioning.
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