A recursive least squares-based demodulator for electrical tomography

Xu, Lijun; Zhou, Haili; Cao, Zhang

doi:10.1063/1.4799971

Cited by 21 publications

(14 citation statements)

References 19 publications

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“…Specialized measurement methods were elaborated by several groups to overcame problems with very small capacitance measurement in ECT [5,7,10,17,33]. New ECT and EIT hardware was developed to increase the throughput of contemporary data acquisition systems [3,9,28,30,38].…”

Section: Introductionmentioning

confidence: 99%

Evaluation of the Electrical Capacitance Tomography System for Measurement Using 3d Sensor

Kryszyn

Wanta

Smolik

2019

IAPGOS

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Further tests of EVT4 data acquisition system for electrical capacitance tomography are presented. The modular system, which can have up to 32 channels with an individual analogue to digital converter, was designed to ensure small uncertainty of capacitance measurement at high speed of imaging. The system’s performance in the context of 3D imaging was experimentally verified. In particular, we show that the measurement of changes in capacitance due to a small change of an electric permittivity distribution for the most distant electrodes in a suitably designed 3D sensor is possible using our system. Cross-plane measurements together with the measurements for the pairs of most distant electrodes are essential for accurate reconstruction of 3D distributions. Due to sensitivity of capacitance measurements obtained in the hardware, the measurements for all electrode pairs can be used in the inverse problem – the system of equations can be extended. Although the numerical condition number of a matrix of such a system is high, image reconstruction is possible from the data obtained in our system. The results of 3D image reconstruction for simple test objects are shown.

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Section: Introductionmentioning

confidence: 99%

Evaluation of the Electrical Capacitance Tomography System for Measurement Using 3d Sensor

Kryszyn

Wanta

Smolik

2019

IAPGOS

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“…Here, it should be noted that when the number of samples used for demodulation is fixed, (19) in the RLS method can be calculated offline, which are not included in Table I. 2) Non-recursive methods, including the quadrature, DFT and FFT methods If M =N/2 and the frequencies are equally-spaced, the quadrature demodulation method requires the same number of multiplications and additions as the DFT method. In the quadrature demodulation method, the number of multiplications and additions can be reduced when less frequency components are required to be measured.…”

Section: Number Of Additionsmentioning

confidence: 99%

“…To deal with the problem that the quadrature method requires one complete or integer periods of a sinusoid for demodulation, a recursive least squares method [19] and an information-filtering method [1], [20] were ever proposed for the demodulation of a singlefrequency signal by the research group of the authors. Each of the two methods can output a preliminary demodulation 2 result using the first two samples although the accuracy is very low.…”

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confidence: 99%

A Recursive Demodulator for Real-Time Measurement of Multiple Sinusoids

Sun

Cao

et al. 2018

IEEE Sensors J.

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Abstract-A fast demodulator for real-time measurement of the amplitudes and phases of multiple sinusoids is highly desired in many applications. When the sampling frequency is fixed, the number of samples needed for demodulation determines the time consumption and hence the demodulation speed. In this paper, a quadrature demodulation method is firstly presented, which requires that the samples cover exactly integer periods of the multi-frequency signal. Secondly, a new recursive demodulation method is proposed, which can not only overcome the limitation of the quadrature method, but also provide greater flexibility between accuracy and speed, i.e. either to obtain a higher speed at an expense of a lower accuracy, or vice versa. The proposed method can work with a sample series of any length as long as more than twice the number of sinusoids and generate demodulation results for all sinusoids simultaneously. Thirdly, a resource-saving and fast implementation of the recursive demodulator was proposed and constructed on a DSP/FPGA, which enables in-situ and on-line application of the recursive demodulator. Experiments were carried out to investigate the performance of the proposed demodulator, including relative error, standard deviation and their variations with the number of samples involved in the demodulation, and compare with other conventional methods.Index Terms-Recursive demodulator, Quadrature method, Demodulation speed, DSP/FPGA I. INTRODUCTION n the active measurement of various object parameters, an external excitation signal is applied on the target object through a sensor. By measuring the response signal that carries the information of the object's characteristic parameters, the parameters to be measured can be derived. Sinusoid is a kind of commonly used excitation signal. To quickly obtain the target parameters of the object under excitation of a series of given frequencies, multiple sinusoids of the given frequencies can be combined as an excitation signal so that the unknowns are measured simultaneously. Because the response sensor signal is also composed of multiple sinusoids with the same frequencies and the frequencies are pre-known, only the amplitudes and phases of the sinusoids need to be obtained. The active measurement is required in many industrial and biomedical applications, such as industrial process tomography [1]- [3], bio-impedance measurement [4]- [6], eddy current testing [7], [8] and built-in self-test [9], etc. Because the characteristic parameters of the target object are often rapidly changing, real-time and fast measurement of the amplitudes and phases of multiple sinusoids in the response sensor signal is highly desired in sensor data processing.The demodulation process can be implemented using an analog method [10], which consists of multiplexers and filters. However, the demodulation speed is restricted by the highorder low-pass filters. In recent years, digital demodulators have been widely used, including the synchronous sampling method [11], the DFT, FFT [12]- [14] and...

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“…As a result, the dynamic range and the measurement sensitivity are limited. Xu et al [4] presented an approach to realize fast impedance measurements. Based on recursive modulation techniques, preliminary demodulation results on amplitude and phase of a sinusoidal signal can be determined by processing only the first two sampling data.…”

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confidence: 99%

Fast Electrical Impedance Tomography Based on Code-Division-Multiplexing Using Orthogonal Codes

Gevers

Gebhardt

Westerdick

et al. 2015

IEEE Trans. Instrum. Meas.

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Electrical impedance tomography (EIT) is used to determine the spatial conductivity distribution of a measurement environment that involves several applications in the areas of process engineering and medical diagnostics. In common EIT systems, the measurements are performed by means of current patterns which are injected into the measurement environment using a serial time-division-multiplexing (TDM) scheme for the excitation of different electrodes. The measurement rate can be increased by performing parallel excitation using orthogonal signals. In this paper, a code-divisionmultiplexing (CDM) measurement procedure is presented. To optimize the separation between different measurement channels and the dynamic range, orthogonal Walsh-Hadamard codes are used. The measurements are conducted with a fast EIT system with nine parallel excitation sources and 18 parallel measurement channels. The measured crosstalk rejection between different channels is larger than 98 dB. The maximum absolute deviation between different measurement sets for repeated measurements is less than 24 µV with a mean standard deviation of less than 8.2 µV. The dynamic range for impedance measurements based on different excitation procedures (TDM, frequencydivision-multiplexing, and CDM) has been determined. Furthermore, reconstructed conductivity distributions based on measurements with the different excitation procedures have been compared with each other for different measurement scenarios (a root mean square difference of less than 1.2%). Finally, the influences of frequency-dependent measurement objects on the excitation procedures have been discussed.

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A recursive least squares-based demodulator for electrical tomography

Cited by 21 publications

References 19 publications

Evaluation of the Electrical Capacitance Tomography System for Measurement Using 3d Sensor

Evaluation of the Electrical Capacitance Tomography System for Measurement Using 3d Sensor

A Recursive Demodulator for Real-Time Measurement of Multiple Sinusoids

Fast Electrical Impedance Tomography Based on Code-Division-Multiplexing Using Orthogonal Codes

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