基于双指数模型的超声定位算法及其应用研究
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摘要
定位精度不高和对环境因素敏感等缺点限制了超声定位技术的应用领域和范围。本文以超声定位技术的实际需求为牵引,以克服超声定位技术的缺陷为目的,对超声信号的经验模型、实时超声定位算法以及算法的实际应用等内容进行了深入研究,具体包括
(1)影响超声定位系统精度的主要因素,以及定位精度与系统参数和测量精度之间的定量关系;
(2)超声信号TOF的常速度模型以及阈值法中整周期误差的消除算法;
(3)采用双指数模型描述超声信号及双指数模型参数估计方法;
(4)基于超声信号双指数模型的TOF实时估计算法;
(5)多径环境下基于双指数模型的TOF估计算法;
(6)基于双指数模型的定位算法在超短基线二维超声定位系统中的应用与实现。
研究结果表明:与传统的混合指数模型相比,本文提出的超声信号双指数模型能够更细腻地刻划压电薄膜超声传感器产生的超声信号,为高精度超声定位算法研究提供了新的基础;提出的若干算法,从不同层面发挥了双指数模型的特性,在精度和实时性两方面都有良好的表现,为进一步研究与应用提供了参考。
The ultrasonic localization technology can be applied in mobile robot, virtual reality (VR), smart home, consumer electronics and other application fields with its advantages such as low price, minimal infrastructure, low maintenance cost and less electromagnetic pollution. But the application scope of this technology is restricted by its disadvantages, for example, low positioning accuracy and susceptible to environmental noise and multi-path problem. Therefore in order to widely use this technology, how the accurate ultrasonic localization can be obtainained has been a research focus for many years.
Successful operation of most ultrasonic localization systems relies on accurate ultrasonic pulse time-of-flight (TOF) measurements. The threshold and cross-correlation method are the common methods for TOF this measurements. The inherent drawback of threshold method is the integer signal periods errors. The localization system based on threshold method can not achieve high resolution because of the existence of integer signal periods errors. In the single path and white Gaussian noise case, the cross-correlation method is the optimal method. In this method the received ultrasonic pulse is assumed to be time shifted, amplitude scaled and noise corrupted replica of reference signal. Unfortunately there is not reference signal in many systems. To overcome this shortcoming, some special models such as Gaussian model and hybird exponential model are used. Gaussian model suits RF ultrasonic pulse for which the rising rate is almost equal to falling rate. The damped exponential model is used to describe low frequency narrow band ultrasonic pulse with slow falling rate. While the damped exponential model lacks flexibility to accurately describe the variety of the pulse shapes encountered in practice.
For further improvement of the accuracy of ultrasonic localization system, this paper first explores a new module of ultrasonic signal, and then developes several high performance algorithms based on this module. Our purpose is to provide a new theoretic basis for ultrasonic localization system design and realization .
In first chapter, the introduction and the analysis of the development and the present situations of ultrasonic localization technology are summarized. The theoretical significance and the practical values of purpose and contents of this dissertation are given.
In chapter two, the relationship between localization errors and system parameters and measuring accuracy are calculated. Discussions on the sources of the errors and the approaches to improve the accuracy are also presented.
A constant velocity model is proposed to describe the series of TOF estimation results in chapter three. The model parameters fit Laplace distribution according to statisticacs of the target trace with more than four million samples in a real system. It is proved that the sum of acceleration absolute value is an equivalent logarithm likelihood function, and maxim likelihood algorithm based on it to eliminate the integer signal periods error is presented. Simulations of the validation of this model are conducted.
In chapter four, the model of ultrasonic signal in localization system and the role of model in TOF estimation algorithm are introduced. The double exponential model is presented to describe ultrasonic pulse in the system. The reasonability of double exponential model is analyzed by means of Prony method, and parameters determination method is given. It is proved that double exponential model is suited for narrow band ultrasonic signal in this kind of system by the comparison with other model.
In chapter five, in order to improve accuracy of TOF estimation, two algorithms based on double exponential model are presented with simulation to show the validation of the algorithms. The two algorithms are parameters estimation method and cross-correlation function method respectively. Computation complexity of the two algorithms is analyzed, and it is proved that the two algorithms can be realized in DSP.
In chapter six, the multi-path phenomena in electronic board is introduced. The method of the TOF estimation overlapping signal is reviewed. TOF estimation algorithm based on cepstrum and cross-correlation function for observed data and double exponential model are discussed. It is demonstrated through simulations that the proposed algorithm can accurately estimate TOF under multi-path environment.
In chapter seven, an ultrasonic localization system based on double exponential model is introduced with system structure, algorithm flow and testing results.
In the final chapter, a brief summary of this dissertation is given with the future expected work.
The innovation idea of this dissertation focus on the five aspects as follows:
The notion of representation of the discrete-time ultrasonic signals using double exponential model and the method of computing model parameters are proposed. The rise time and full width half maximum of double exponential model is discussed and the conparison with the hybrid exponential model is conducted. It is shown that flexibility of double exponent model is superior to hybrid exponential model. The measured data fitting and simulation of TOT prove that the double exponent model has better performance than that of the damped exponential model.
An algorithm of TOF estimation by means of estimating double exponential model parameters is proposed. To estimate the time delay in exponential term results in a nonlinear least square method. In the proposed algorithm, it is transformed into multiple parameters estimation in least square method with linear form. Thus this algorithm can been applied in embedded system.
A fast algorithm for cross correlation function of observed data and double exponential model is proposed. In this algorithm, a linear time-invariant system is fed with backward running signals to determine the reversal of the time axis. Because of this, the impulse response of the system is the temporal expression of double exponential model and the output of the system is the cross correlation function. This algorithm can improve the accuracy of TOF in embedded system.
A constant speed model is used to fit series of TOF acquired in a real ultrasonic localization system. The noise distribution of the model is confirmed as Laplace distribution according to statistical results. On the basis of the above work, the maxim likelihood algorithm is presented to eliminate the impact of integer signal periods errors.
Finally, the idea to improve positioning accuracy in short baseline system is proposed, which is basically to keep two TOF errors with the same sign. The validity of the idea is proved in a real system.
(1)影响超声定位系统精度的主要因素,以及定位精度与系统参数和测量精度之间的定量关系;
(2)超声信号TOF的常速度模型以及阈值法中整周期误差的消除算法;
(3)采用双指数模型描述超声信号及双指数模型参数估计方法;
(4)基于超声信号双指数模型的TOF实时估计算法;
(5)多径环境下基于双指数模型的TOF估计算法;
(6)基于双指数模型的定位算法在超短基线二维超声定位系统中的应用与实现。
研究结果表明:与传统的混合指数模型相比,本文提出的超声信号双指数模型能够更细腻地刻划压电薄膜超声传感器产生的超声信号,为高精度超声定位算法研究提供了新的基础;提出的若干算法,从不同层面发挥了双指数模型的特性,在精度和实时性两方面都有良好的表现,为进一步研究与应用提供了参考。
The ultrasonic localization technology can be applied in mobile robot, virtual reality (VR), smart home, consumer electronics and other application fields with its advantages such as low price, minimal infrastructure, low maintenance cost and less electromagnetic pollution. But the application scope of this technology is restricted by its disadvantages, for example, low positioning accuracy and susceptible to environmental noise and multi-path problem. Therefore in order to widely use this technology, how the accurate ultrasonic localization can be obtainained has been a research focus for many years.
Successful operation of most ultrasonic localization systems relies on accurate ultrasonic pulse time-of-flight (TOF) measurements. The threshold and cross-correlation method are the common methods for TOF this measurements. The inherent drawback of threshold method is the integer signal periods errors. The localization system based on threshold method can not achieve high resolution because of the existence of integer signal periods errors. In the single path and white Gaussian noise case, the cross-correlation method is the optimal method. In this method the received ultrasonic pulse is assumed to be time shifted, amplitude scaled and noise corrupted replica of reference signal. Unfortunately there is not reference signal in many systems. To overcome this shortcoming, some special models such as Gaussian model and hybird exponential model are used. Gaussian model suits RF ultrasonic pulse for which the rising rate is almost equal to falling rate. The damped exponential model is used to describe low frequency narrow band ultrasonic pulse with slow falling rate. While the damped exponential model lacks flexibility to accurately describe the variety of the pulse shapes encountered in practice.
For further improvement of the accuracy of ultrasonic localization system, this paper first explores a new module of ultrasonic signal, and then developes several high performance algorithms based on this module. Our purpose is to provide a new theoretic basis for ultrasonic localization system design and realization .
In first chapter, the introduction and the analysis of the development and the present situations of ultrasonic localization technology are summarized. The theoretical significance and the practical values of purpose and contents of this dissertation are given.
In chapter two, the relationship between localization errors and system parameters and measuring accuracy are calculated. Discussions on the sources of the errors and the approaches to improve the accuracy are also presented.
A constant velocity model is proposed to describe the series of TOF estimation results in chapter three. The model parameters fit Laplace distribution according to statisticacs of the target trace with more than four million samples in a real system. It is proved that the sum of acceleration absolute value is an equivalent logarithm likelihood function, and maxim likelihood algorithm based on it to eliminate the integer signal periods error is presented. Simulations of the validation of this model are conducted.
In chapter four, the model of ultrasonic signal in localization system and the role of model in TOF estimation algorithm are introduced. The double exponential model is presented to describe ultrasonic pulse in the system. The reasonability of double exponential model is analyzed by means of Prony method, and parameters determination method is given. It is proved that double exponential model is suited for narrow band ultrasonic signal in this kind of system by the comparison with other model.
In chapter five, in order to improve accuracy of TOF estimation, two algorithms based on double exponential model are presented with simulation to show the validation of the algorithms. The two algorithms are parameters estimation method and cross-correlation function method respectively. Computation complexity of the two algorithms is analyzed, and it is proved that the two algorithms can be realized in DSP.
In chapter six, the multi-path phenomena in electronic board is introduced. The method of the TOF estimation overlapping signal is reviewed. TOF estimation algorithm based on cepstrum and cross-correlation function for observed data and double exponential model are discussed. It is demonstrated through simulations that the proposed algorithm can accurately estimate TOF under multi-path environment.
In chapter seven, an ultrasonic localization system based on double exponential model is introduced with system structure, algorithm flow and testing results.
In the final chapter, a brief summary of this dissertation is given with the future expected work.
The innovation idea of this dissertation focus on the five aspects as follows:
The notion of representation of the discrete-time ultrasonic signals using double exponential model and the method of computing model parameters are proposed. The rise time and full width half maximum of double exponential model is discussed and the conparison with the hybrid exponential model is conducted. It is shown that flexibility of double exponent model is superior to hybrid exponential model. The measured data fitting and simulation of TOT prove that the double exponent model has better performance than that of the damped exponential model.
An algorithm of TOF estimation by means of estimating double exponential model parameters is proposed. To estimate the time delay in exponential term results in a nonlinear least square method. In the proposed algorithm, it is transformed into multiple parameters estimation in least square method with linear form. Thus this algorithm can been applied in embedded system.
A fast algorithm for cross correlation function of observed data and double exponential model is proposed. In this algorithm, a linear time-invariant system is fed with backward running signals to determine the reversal of the time axis. Because of this, the impulse response of the system is the temporal expression of double exponential model and the output of the system is the cross correlation function. This algorithm can improve the accuracy of TOF in embedded system.
A constant speed model is used to fit series of TOF acquired in a real ultrasonic localization system. The noise distribution of the model is confirmed as Laplace distribution according to statistical results. On the basis of the above work, the maxim likelihood algorithm is presented to eliminate the impact of integer signal periods errors.
Finally, the idea to improve positioning accuracy in short baseline system is proposed, which is basically to keep two TOF errors with the same sign. The validity of the idea is proved in a real system.
引文
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