- Email: [email protected]
Variable step least mean square adaptive filtering method for wireless capsule endoscopy positioning system
Accepted Manuscript Title: Variable step least mean square adaptive filtering method for wireless capsule endoscopy positioning system Authors: Lin Gan, He Zhang PII: DOI: Reference:
S0030-4026(18)30884-2 https://doi.org/10.1016/j.ijleo.2018.06.077 IJLEO 61080
To appear in: Received date: Accepted date:
27-4-2018 13-6-2018
Please cite this article as: Gan L, Zhang H, Variable step least mean square adaptive filtering method for wireless capsule endoscopy positioning system, Optik (2018), https://doi.org/10.1016/j.ijleo.2018.06.077 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Variable step least mean square adaptive filtering method for wireless capsule endoscopy positioning system Lin Gan, He Zhang Nanjing University of Science and Technology, School of Mechanical Engineering,Nanjing 210094,People’s Republic of China ([email protected])
Abstract The wireless capsule endoscope (WCE) is the main method to diagnose intestinal and gastrointestinal
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diseases, and the positioning system is an important part of WCE. The random electromagnetic interference（EMI） problem in WCE magnetic positioning method is discussed. A mathematical model
of magnetic dipole magnetic signal interference is established, the effect of random interference on magnetic signal is reduced by using the variable step least mean square(VS-LMS) self-adaptive
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filtering algorithm. The pulse width, peak power and occurrence time of the three influencing factors
are analyzed respectively. Finally, Monte Carlo experimental method was used to analyse the statistical distribution of magnetic interference signals.
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Keywords: wireless capsule endoscope; positioning system; EMI; minimum mean square algorithm;
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adaptive filtering
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1. Introduction Wireless capsule endoscopy (WCE) is now the focus of research in the fields of engineering and medicine. As an innovative technology without a cable connection, WCE can provide patients with a friendly, non-invasive, painless small intestine and other stomach intestinal examination [1]. It contains a miniature camera and lighting system for taking pictures and a transmission module [2]. When it moves along the gastrointestinal tract, it is important to know exactly where the capsule is, because the therapeutic effect depends on the accuracy of the spatial information. Therefore, a precise and reliable positioning system plays an important role in improving the effect of WCE. Magnetic positioning method is the most commonly used WCE localization method, which is divided into two major categories [3]. The first method places a permanent magnet in a capsule and uses an external magnetic sensor to measure the magnetic field [4], [5]. Although this method is safe and can achieve reasonable accuracy (the average error is 1.8mm) [4], there are interference problems in the magnetic drive system [6], [7]. Although time-multiplexed sensing and driving have been proposed to overcome the interference problem [8], this solution does not guarantee real-time tracking and timely feedback [9]. In the second group, magnetic sensors were placed inside the capsule to measure the magnetic field [10], [11], [12]-[14]. Its average distance measurement error is less than 5 mm and angle measurement error is less than 19°[14]. In this system, there seems to be no interference between the magnetic induction and the magnetic drive. However, one common disadvantage of this approach is that it is less compatible with other motion control systems for the capsules [11]. More importantly, the method will take up more space and consume more electricity [15]. Other positioning methods
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include computer vision [16], ultrasound [17][18], and magnetic resonance imaging (MRI)[19], each with potential defects. In this paper, the random interference problem in WCE magnetic positioning method is discussed. A mathematical model of magnetic dipole magnetic signal interference is established, and vss-lms algorithm is used to reduce the random interference of the pulse laser to the magnetic signal. The influence factors of three random disturbance signals are analyzed for different jamming signal pulse width, peak power and occurrence time. Finally, the statistical distribution of magnetic interference signals before and after filtering is analyzed by Monte Carlo experiment.
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2. Magnetic location signal model WCE localization method generally uses the permanent magnet sealed in the capsule to produce a stable and reliable magnetic field source. The magnetic sensor is placed outside the patient's body to measure these persistent magnetic signals. Based on the mathematical model of small magnet, the mathematical model of magnetic detection is established as follows. Set the center of the trajectory of the magnetic core as the origin, when the magnetic core and the sensor are in the right direction, it is stipulated that the direction of the central connecting line is the x-axis. The material of cylindrical core is NdFeB, it is counterclockwise scanning, the N, S pole respectively located on both ends, and the axis is located in the xoy plane. Using the HMC1021 magnetic sensor to detect the magnetic core, the magnetic core rotation signal is obtained. At the same time, defining the moving coordinate system omxmym of the magnetic core, the origin is the center of the magnetic core, setting the central axis as the ym axis, making the magnetization direction is the positive direction of the ym axis. Assuming that the magnetic core and Y-axis Angle are θ, the coordinates of the sensor are as follows:
（5）
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xm L sin ym L cos r
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The magnetic field distribution of the permanent magnet core in the above model can be described by the magnetic dipoles (MD) model.The magnetic source is regarded as a magnetic dipole,therefore, for a cylindrical permanent magnet core, the magnetic induction B at any position outside can be expressed as: B m, r 0 5 3 r m r r 2 m （6） 4 r
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Where m is the magnetic dipole moment, set as (0,m), m is the size of the magnetic
dipole moment, r is the vector between field sources. Each axial component of magnetic induction in follower coordinate system can be derived as:
3m0 Bxm 4 r 5 L sin L cos r Bym m0 2 L cos r 2 L2 sin 2 4 r 5
（7）
According to the concept of scalar magnetic bit, the magnetic induction intensity generated by the permanent magnet in any position is expressed as:
m 4
B
r
r dS
（9）
3
s
r is the field source spacing, S is the magnetic charge area, and m is the surface magnetic charge density, which can be expressed as:
m Br n
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（10）
Br is the residual magnetic induction intensity of the cylindrical permanent
the cylindrical permanent magnet. According to the above two types: r
r
s
3
dS
Br 4
r
r
3
dS
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Br 4
s
（11）
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B
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magnet, and n is the unit vector of the outer normal line on the boundary surface of
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r and r are the distance between the field point and the positive and negative
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magnetic charge points, and s and s are the area of positive and negative magnetic charge.
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For any point P in the model, the cylindrical coordinate is ( , , y ) , and the magnetic induction intensity of the cylindrical permanent magnet at that place is as follows:
0 4
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B P
y2 2
( M cos( ) r( , , y; , , y ))) Rd dy '
'
'
'
'
'
（12）
y1 0
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Among them:
r( , , y; ' , ' , y ' ) 1
2 '2 2 ' cos( ' ) ( y y ' )2
（13）
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The radial component, azimuth component and axial component of the magnetic flux density at p are solved by equations (12) and (13) y 2 0 MR 2 2 R(cos( ' )) cos( ' )G 3 ( , , y; ' , ' , y ' )d 'dy ' B ( , , y ) 4 y1 0 y 0 MR 2 2 2 B ( , , y ) cos( ' )sin( ' ) G 3 ( , , y; ' , ' , y ' )d 'dy ' （14） 4 y1 0 y2 B ( , , y ) 0 MR cos( ' )( y y ' ) G 3 ( , , y; ' , ' , y ' )d 'dy ' y 4 y1
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The transformation relationship between cylindrical coordinate system and magnetic core with moving coordinate system is: Bxm B ( , , y )sin( ) B ( , , y ) cos( ) （15） Bym By ( , , y ) B B ( , , y ) cos( ) B ( , , y )sin( ) zm NdFeB N35 cylindrical permanent magnet is selected, its volume is 1 x 1mm, and the relevant parameter Settings are shown in table 1. When the magnetic core is different from the sensor (10mm, 12mm, 14mm, 16mm), the magnetic core generated by the MD model and EMM model is shown in FIG. 2. It can be seen that when the distance between the magnetic core and the sensor is greater than 10mm, the magnetic signals obtained by the two models are less different, and the signal similarity increases with the increase of distance. Although the signals obtained by the MD model and the EMM model have little difference, the MD model solves the system of nonlinear primary functions. However, the EMM model mainly performs numerical integral operation, which requires much more computations than the former model. Therefore, the MD model is used in the subsequent analysis. 3. Random interference signal adaptive filtering method based on LMS algorithm For periodically disturbing magnetic signals with statistical regularity, filtering or shielding can be done by means of wavelet, high-order statistics, empirical mode decomposition (EMD) and linear impedance stabilization network [20-22]. However, in addition to the above mentioned EMI signals, random EMI signals are difficult to be eliminated by the above methods. Adaptive filtering algorithms are widely used in noise cancellation, narrow-band interference suppression in wideband signals, random echo cancellation and other aspects of communication. The commonly used adaptive filtering algorithms include Least mean square (LMS) algorithm, Recursive Least square (RLS) algorithm etc. Both of the above algorithms have better adaptive filtering ability, while LMS algorithm is low in complexity and easy to implement in hardware [23]. Considering the requirements of real-time measurement and the limitation of volume and power consumption, based on LMS adaptive filtering theory [24], an adaptive filter is designed to filter out random EMI. One input of the adaptive filter is the mixed signal x(n) of the actual scanning magnetic signal d(n) and the interference signal s(n) and the other input is the estimated reference input d(n) to the scanning magnetic signal. The adaptive filtering of input x(n) is used to match the output of the filter with y(n) and d(n), and the first stage output error e(n) is the best estimate of the jamming signal. The best estimate is fed to the mixed signal x(n), and the final output is the actual scanning magnetic signal d(n). Let the length of the mixed signal x(n) and the reference signal d(n) be N, the number of filter taps is M, and let n be from M to N, repeat the following iterative process:
X n [ x (n ), x (n 1), , x ( n M 1)] y (n) W T (n) X (n) e( n ) d ( n ) y ( n ) W (n 1) W ( n) 2 X ( n )e(n )
（17）
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The initialization parameter of the algorithm is W (n)=0 , y(n)=0、e(n)=0、M=8. Using the error e(n), the filter weight vector is updated in real time to realize the adaptive filtering of complex background signals. However, the convergence rate and the steady-state error of the traditional LMS algorithm depend on the iteration step size μ [25]. In response to the above problems, researchers proposed a variable step size LMS adaptive filtering algorithm [26,27]. When canceling the random EMI, smaller iterative steps can obtain smaller steady-state errors. As the target appears, the difference between d(n) and x(n) rapidly increases. In this case, a larger iteration step can quickly track the local trend of the non-stationary signal. Therefore, we propose a variable step size least mean square algorithm which is suitable for the characteristics of random EMI signals and has the step memory effect. The variation of the step size is expressed as:
p(n ) a1[1 cos(a2 e(n ) 3 )]
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a
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(n) a4 (n-1)+a5 p(n)
（18）
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The trend of the iteration step μ(n) is determined by the parameters a1～a5. The signal characteristics are analyzed through the experimental conditions, taking a1=0.8、 a2=0.85、a3=0.9、a4=0.75、a5=0.6. It can be seen from the above deduction that after increasing the variable step size, the number of multiplications of the algorithm is increased by 4 times than the LMS method with fixed step size. Therefore, the complexity of VSS-LMS algorithm is less than the fixed-step LMS algorithm, and still has better real-time performance. 3.1 The influence of random EMI signal pulse width on filtering effect Firstly, the influence of the pulse width of the random EMI signal on the filtering effect is discussed. The amplitude of the random EMI signal is set to 0.75V, the emergence moment is 0.15ms, and the pulse width is 10ns, 20ns, 30ns and 40ns respectively. For the above interference signal, the signal processed by the VSS-LMS filtering method is as shown in FIG.3, and the filtered signals are respectively shifted to the right by 0.01 ms. The amplitude of the interference signals with different pulse widths is compressed to 0.086V, The signal jitter decreases and the signal smoothness increases. Therefore, the VSS-LMS filter proposed in this paper can effectively eliminate the random EMI signals of different pulse widths without losing the effective measurement magnetic signal. The variation of the step size in the VSS-LMS algorithm is shown in FIG.4. When the interfering signal appears, the iterative step size rapidly changes. The peak value of the step size factor appears at the moment when the interference occurs. As the pulse width increases, the peak value of the step size is slightly reduction. The rapidly increasing iteration step can quickly track the random EMI signal, and the rest of the iteration steps are small, which is beneficial to smoothing the demagnetization signal and extracting the random EMI signal.
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3.2 The influence of random EMI signal energy on filter effect Secondly, the effect of random EMI signal energy on the filtering effect is studied. The pulse width of random EMI signal is set as 20ns and the emergence time is 0.15ms. The amplitudes are 0.6V, 0.8V, 1.0V and 1.2V respectively. The results of signal processing using the VSS-LMS filtering method are shown in FIG.5. The filtered signals are respectively shifted to the right by 0.01ms. The amplitude of the filtered interference signal increases with the original peak value. When the original peak value is 1.2V, the filtered peak value is 0.106V, when the original peak value is 0.6V, the filtered peak value is 0.059V. Therefore, the VSS-LMS filtering algorithm proposed in this paper can effectively eliminate random electromagnetic interference signals of different power. The variation of the step size in VSS-LMS algorithm is shown in FIG.6. Similarly, when the interference signal appears, the iterative step size changes rapidly. The peak value of the step size factor appears at the moment when the interference occurs, and the iteration steps are small in the rest of the time. Interfering with the increase of the signal peak, the peak value of the step factor slightly increases. 3.3 The influence of random EMI signal occurrence time on filter effect Due to the randomness of the interference, the influence of different random EMI moments on the filtering effect is investigated finally. The random EMI signal pulse width is 20ns, the amplitude is 0.8V, the occurrence time of random EMI are 0.11ms, 0.16ms, 0.21ms, 0.26ms and 0.31ms. The results of signal processing using the VSS-LMS filtering method are shown in FIG.7, it can be seen that the amplitude of the interference signal is suppressed to about 0.083V, and the signal smoothness of the position where the interference signal is located is improved. Therefore, the VSS-LMS filtering algorithm proposed in this paper can effectively eliminate the random EMI signals at different times. The variation of the step size in the VSS-LMS algorithm is shown in FIG.8. At different times when the interfering signal appears, the iterative step size rapidly changes. The peak value of the step size factor appears at the moment when the interference occurs, and the rest time steps are small. 4. Experimental Results and Discussions In order to further verify the performance of the above VSS-LMS filtering algorithm, the experimental measurement system is built. By adjusting the pulse width, power and occurrence time of interference signals, the experimental filter parameters are recorded under different state parameters. Monte Carlo method is used to carry out experiments. Each experiment is repeated 200 times to obtain the amplitude probability density distribution of the measured filtered interference signal. The filtering effect of the VSS-LMS method proposed in this paper is tested. Firstly, the interference signal pulse width was adjusted, and the amplitude of random electromagnetic interference was set at 0.8V, and the occurrence time was 0.15ms. When the pulse width was 10ns, 20ns, 30ns and 40ns, the filtered interference signals are measured. It can be seen that the amplitude distribution of the signal amplitude becomes more and more dispersed as the pulse width increases. Secondly, the pulse width of the random EMI signal is adjusted to 20ns, and the moment of emergence is 0.15ms. When the random disturbance amplitude is 1.2V,
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1.0V, 0.8V and 0.6V, the interference signal after VSS-LMS filtering is measured. It can be seen that with the increase of the amplitude of the interference signal, the amplitude-probability density curve of the filtered signal moves to the right and the distribution becomes divergent. Finally, the random electromagnetic interference signal pulse width is adjusted to 20ns, the signal amplitude is 0.8V, when the target azimuth are 0.11ms, 0.16ms, 0.21ms, 0.26ms and 0.31ms, the interference signal after VSS-LMS filtering is measured. With the increase of the slope of the curve at the moment when the interference signal appears, the distribution of the probability density curve of the filtered signal becomes concentrated. 5. Conclusion In this study, a VSS-LMS random EMI filtering method with step memory effect is designed for WCE magnetic localization system. Simulation and experiment are conducted respectively for three kinds of random disturbance factors such as different interference pulse width, peak power and occurrence time. Using Monte Carlo experimental method to get the statistical distribution of filtering signal. The results show that the VSS-LMS filtering algorithm proposed in this paper can effectively reduce the random electromagnetic interference signals with different pulse widths, different powers and different moments, it can effectively keep the measuring magnetic signals and improve the positioning accuracy.
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Acknowledgements: This study was supported by National Natural Science Foundation of China (51605227) and the Fundamental Research Funds for the central universities(NUST30915011303).
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References 1 Than T D, Alici G, Zhou H, et al. A review of localization systems for robotic endoscopic capsules[J]. IEEE Transactions on Biomedical Engineering, 2012, 59(9): 2387-2399. 2 Iddan G, Meron G, Glukhovsky A, et al. Wireless capsule endoscopy[J]. Nature, 2000, 405(6785): 417. 3 Than T D, Alici G, Zhou H, et al. Enhanced Localization of Robotic Capsule Endoscopes Using Positron Emission Markers and Rigid-Body Transformation[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2017. 4 Hu C, Li M, Song S, et al. A cubic 3-axis magnetic sensor array for wirelessly tracking magnet position and orientation[J]. IEEE Sensors Journal, 2010, 10(5): 903-913. 5 Weitschies W, Blume H, Mönnikes H. Magnetic marker monitoring: high resolution real-time tracking of oral solid dosage forms in the gastrointestinal tract[J]. European Journal of Pharmaceutics and Biopharmaceutics, 2010, 74(1): 93-101. 6 Carpi F, Shaheed H. Grand challenges in magnetic capsule endoscopy[J]. Expert review of medical devices, 2013, 10(4): 433-436. 7 Keller J, Fibbe C, Rosien U, et al. Recent advances in capsule endoscopy: development of maneuverable capsules[J]. Expert review of gastroenterology &
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hepatology, 2012, 6(5): 561-566. 8 Wang X, Meng M Q H. Perspective of active capsule endoscope: actuation and localisation[J]. International Journal of Mechatronics and Automation, 2011, 1(1): 38-45. 9 Pahlavan K, Bao G, Ye Y, et al. Rf localization for wireless video capsule endoscopy[J]. International Journal of Wireless Information Networks, 2012, 19(4): 326-340. 10 Salerno M, Ciuti G, Lucarini G, et al. A discrete-time localization method for capsule endoscopy based on on-board magnetic sensing[J]. Measurement Science and Technology, 2011, 23(1): 015701. 11 Yim S, Sitti M. 3-D localization method for a magnetically actuated soft capsule endoscope and its applications[J]. IEEE Transactions on Robotics, 2013, 29(5): 1139-1151. 12 Kim M G, Hong Y S, Lim E J. Position and orientation detection of capsule endoscopes in spiral motion[J]. International Journal of Precision Engineering and Manufacturing, 2010, 11(1): 31-37. 13 Di Natali C, Beccani M, Valdastri P. Real-time pose detection for magnetic medical devices[J]. IEEE Transactions on Magnetics, 2013, 49(7): 3524-3527. 14 Popek K M, Mahoney A W, Abbott J J. Localization method for a magnetic capsule endoscope propelled by a rotating magnetic dipole field[C]//Robotics and Automation (ICRA), 2013 IEEE International Conference on. IEEE, 2013: 5348-5353. 15 Basar M R, Malek F, Juni K M, et al. Ingestible wireless capsule technology: A review of development and future indication[J]. International Journal of Antennas and Propagation, 2012, 2012. 16 Spyrou E, Iakovidis D K. Video-based measurements for wireless capsule endoscope tracking[J]. Measurement Science and Technology, 2013, 25(1): 015002. 17 Nagy Z, Fluckiger M, Ergeneman O, et al. A wireless acoustic emitter for passive localization in liquids[C]//Robotics and Automation, 2009. ICRA'09. IEEE International Conference on. IEEE, 2009: 2593-2598. 18 Gumprecht J D J, Lueth T C, Khamesee M B. Navigation of a robotic capsule endoscope with a novel ultrasound tracking system[J]. Microsystem technologies, 2013, 19(9-10): 1415-1423. 19 Krieger A, Iordachita I I, Guion P, et al. An MRI-compatible robotic system with hybrid tracking for MRI-guided prostate intervention[J]. IEEE Transactions on Biomedical Engineering, 2011, 58(11): 3049-3060. 20 Aggarwal R, Singh J K, Gupta V K, et al. Noise reduction of speech signal using wavelet transform with modified universal threshold[J]. International Journal of Computer Applications, 2011, 20(5): 14-19. 21 Inoue T, Saruwatari H, Takahashi Y, et al. Theoretical analysis of musical noise in generalized spectral subtraction based on higher order statistics[J]. IEEE Transactions on Audio, Speech, and Language 22 Wu Z, Huang N E. Ensemble empirical mode decomposition: a noise-assisted data analysis method[J]. Advances in adaptive data analysis, 2009, 1(01): 1-41. 23 BoyanHuang,YeguiXiao,YapingMa, et al. Asimplifiedvariablestep-size
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LMSalgorithmfor Fourier analysis and its statistical properties[J]. Signal Processing, 2015, 117: 69-81. [24] Kwong R H, Johnston E W. A variable step size LMS algorithm[J]. IEEE Transactions on signal processing, 1992, 40(7): 1633-1642. [25] Zhang Y. Adaptive algorithms and structures with potential application in reverberation time estimation in occupied rooms[M]. Cardiff University (United Kingdom), 2007. [26]Mader A, Puder H, Schmidt G U. Step-size control for acoustic echo cancellation filters–an overview[J]. Signal Processing, 2000, 80(9): 1697-1719. [27] Shin H C, Sayed A H, Song W J. Variable step-size NLMS and affine projection algorithms[J]. IEEE signal processing letters, 2004, 11(2): 132-135.
z
zm ym om
θ
P(ζ,β,y)
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Figure 1. Mathematical model of rotating scanning magnetic signal
Figure 2. The y-axis direction magnetic field component in the MD model and EMM model: (a),(b),(c) and (d) are the distance between the core and the sensor is 10mm, 12mm, 14mm and 16mm
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Figure 3. Simulation of different EMI filters with different pulse widths
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Figure 4. Change of step factor in VSS-LMS algorithm
Figure 5. Simulation of different EMI filters with different power
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Figure 6. Change of step factor in VSS-LMS algorithm
Figure 7. Simulation of EMI filters with different occurrence time Figure 8. Change of step factor in VSS-LMS algorithm
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Figure 9. Probability density distribution of EMI signals with different pulse widths after filtering
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Figure 10. Probability density distribution of EMI signals with different energy after filtering
Figure 11. Probability density distribution of EMI signals with different occurrence time after
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filtering
Table 1.System parameters
Parameter
Value
Parameter
Value
Gain
200
5
8.72×10
Br/T
1.02
Threshold Level/mV
-150
r/mm
1
Magnetic resolution/μT
0.012
L/mm
12
Sensitivity/(mV/(V·Gauss))
1.18
σN/mV
45
Sensor bandwidth/MHz
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m/(A/m)
S0030-4026(18)30884-2 https://doi.org/10.1016/j.ijleo.2018.06.077 IJLEO 61080
To appear in: Received date: Accepted date:
27-4-2018 13-6-2018
Please cite this article as: Gan L, Zhang H, Variable step least mean square adaptive filtering method for wireless capsule endoscopy positioning system, Optik (2018), https://doi.org/10.1016/j.ijleo.2018.06.077 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Variable step least mean square adaptive filtering method for wireless capsule endoscopy positioning system Lin Gan, He Zhang Nanjing University of Science and Technology, School of Mechanical Engineering,Nanjing 210094,People’s Republic of China ([email protected])
Abstract The wireless capsule endoscope (WCE) is the main method to diagnose intestinal and gastrointestinal
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diseases, and the positioning system is an important part of WCE. The random electromagnetic interference（EMI） problem in WCE magnetic positioning method is discussed. A mathematical model
of magnetic dipole magnetic signal interference is established, the effect of random interference on magnetic signal is reduced by using the variable step least mean square(VS-LMS) self-adaptive
SC R
filtering algorithm. The pulse width, peak power and occurrence time of the three influencing factors
are analyzed respectively. Finally, Monte Carlo experimental method was used to analyse the statistical distribution of magnetic interference signals.
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Keywords: wireless capsule endoscope; positioning system; EMI; minimum mean square algorithm;
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adaptive filtering
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1. Introduction Wireless capsule endoscopy (WCE) is now the focus of research in the fields of engineering and medicine. As an innovative technology without a cable connection, WCE can provide patients with a friendly, non-invasive, painless small intestine and other stomach intestinal examination [1]. It contains a miniature camera and lighting system for taking pictures and a transmission module [2]. When it moves along the gastrointestinal tract, it is important to know exactly where the capsule is, because the therapeutic effect depends on the accuracy of the spatial information. Therefore, a precise and reliable positioning system plays an important role in improving the effect of WCE. Magnetic positioning method is the most commonly used WCE localization method, which is divided into two major categories [3]. The first method places a permanent magnet in a capsule and uses an external magnetic sensor to measure the magnetic field [4], [5]. Although this method is safe and can achieve reasonable accuracy (the average error is 1.8mm) [4], there are interference problems in the magnetic drive system [6], [7]. Although time-multiplexed sensing and driving have been proposed to overcome the interference problem [8], this solution does not guarantee real-time tracking and timely feedback [9]. In the second group, magnetic sensors were placed inside the capsule to measure the magnetic field [10], [11], [12]-[14]. Its average distance measurement error is less than 5 mm and angle measurement error is less than 19°[14]. In this system, there seems to be no interference between the magnetic induction and the magnetic drive. However, one common disadvantage of this approach is that it is less compatible with other motion control systems for the capsules [11]. More importantly, the method will take up more space and consume more electricity [15]. Other positioning methods
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include computer vision [16], ultrasound [17][18], and magnetic resonance imaging (MRI)[19], each with potential defects. In this paper, the random interference problem in WCE magnetic positioning method is discussed. A mathematical model of magnetic dipole magnetic signal interference is established, and vss-lms algorithm is used to reduce the random interference of the pulse laser to the magnetic signal. The influence factors of three random disturbance signals are analyzed for different jamming signal pulse width, peak power and occurrence time. Finally, the statistical distribution of magnetic interference signals before and after filtering is analyzed by Monte Carlo experiment.
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2. Magnetic location signal model WCE localization method generally uses the permanent magnet sealed in the capsule to produce a stable and reliable magnetic field source. The magnetic sensor is placed outside the patient's body to measure these persistent magnetic signals. Based on the mathematical model of small magnet, the mathematical model of magnetic detection is established as follows. Set the center of the trajectory of the magnetic core as the origin, when the magnetic core and the sensor are in the right direction, it is stipulated that the direction of the central connecting line is the x-axis. The material of cylindrical core is NdFeB, it is counterclockwise scanning, the N, S pole respectively located on both ends, and the axis is located in the xoy plane. Using the HMC1021 magnetic sensor to detect the magnetic core, the magnetic core rotation signal is obtained. At the same time, defining the moving coordinate system omxmym of the magnetic core, the origin is the center of the magnetic core, setting the central axis as the ym axis, making the magnetization direction is the positive direction of the ym axis. Assuming that the magnetic core and Y-axis Angle are θ, the coordinates of the sensor are as follows:
（5）
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xm L sin ym L cos r
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The magnetic field distribution of the permanent magnet core in the above model can be described by the magnetic dipoles (MD) model.The magnetic source is regarded as a magnetic dipole,therefore, for a cylindrical permanent magnet core, the magnetic induction B at any position outside can be expressed as: B m, r 0 5 3 r m r r 2 m （6） 4 r
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Where m is the magnetic dipole moment, set as (0,m), m is the size of the magnetic
dipole moment, r is the vector between field sources. Each axial component of magnetic induction in follower coordinate system can be derived as:
3m0 Bxm 4 r 5 L sin L cos r Bym m0 2 L cos r 2 L2 sin 2 4 r 5
（7）
According to the concept of scalar magnetic bit, the magnetic induction intensity generated by the permanent magnet in any position is expressed as:
m 4
B
r
r dS
（9）
3
s
r is the field source spacing, S is the magnetic charge area, and m is the surface magnetic charge density, which can be expressed as:
m Br n
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（10）
Br is the residual magnetic induction intensity of the cylindrical permanent
the cylindrical permanent magnet. According to the above two types: r
r
s
3
dS
Br 4
r
r
3
dS
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Br 4
s
（11）
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magnet, and n is the unit vector of the outer normal line on the boundary surface of
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r and r are the distance between the field point and the positive and negative
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magnetic charge points, and s and s are the area of positive and negative magnetic charge.
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For any point P in the model, the cylindrical coordinate is ( , , y ) , and the magnetic induction intensity of the cylindrical permanent magnet at that place is as follows:
0 4
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B P
y2 2
( M cos( ) r( , , y; , , y ))) Rd dy '
'
'
'
'
'
（12）
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Among them:
r( , , y; ' , ' , y ' ) 1
2 '2 2 ' cos( ' ) ( y y ' )2
（13）
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The radial component, azimuth component and axial component of the magnetic flux density at p are solved by equations (12) and (13) y 2 0 MR 2 2 R(cos( ' )) cos( ' )G 3 ( , , y; ' , ' , y ' )d 'dy ' B ( , , y ) 4 y1 0 y 0 MR 2 2 2 B ( , , y ) cos( ' )sin( ' ) G 3 ( , , y; ' , ' , y ' )d 'dy ' （14） 4 y1 0 y2 B ( , , y ) 0 MR cos( ' )( y y ' ) G 3 ( , , y; ' , ' , y ' )d 'dy ' y 4 y1
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The transformation relationship between cylindrical coordinate system and magnetic core with moving coordinate system is: Bxm B ( , , y )sin( ) B ( , , y ) cos( ) （15） Bym By ( , , y ) B B ( , , y ) cos( ) B ( , , y )sin( ) zm NdFeB N35 cylindrical permanent magnet is selected, its volume is 1 x 1mm, and the relevant parameter Settings are shown in table 1. When the magnetic core is different from the sensor (10mm, 12mm, 14mm, 16mm), the magnetic core generated by the MD model and EMM model is shown in FIG. 2. It can be seen that when the distance between the magnetic core and the sensor is greater than 10mm, the magnetic signals obtained by the two models are less different, and the signal similarity increases with the increase of distance. Although the signals obtained by the MD model and the EMM model have little difference, the MD model solves the system of nonlinear primary functions. However, the EMM model mainly performs numerical integral operation, which requires much more computations than the former model. Therefore, the MD model is used in the subsequent analysis. 3. Random interference signal adaptive filtering method based on LMS algorithm For periodically disturbing magnetic signals with statistical regularity, filtering or shielding can be done by means of wavelet, high-order statistics, empirical mode decomposition (EMD) and linear impedance stabilization network [20-22]. However, in addition to the above mentioned EMI signals, random EMI signals are difficult to be eliminated by the above methods. Adaptive filtering algorithms are widely used in noise cancellation, narrow-band interference suppression in wideband signals, random echo cancellation and other aspects of communication. The commonly used adaptive filtering algorithms include Least mean square (LMS) algorithm, Recursive Least square (RLS) algorithm etc. Both of the above algorithms have better adaptive filtering ability, while LMS algorithm is low in complexity and easy to implement in hardware [23]. Considering the requirements of real-time measurement and the limitation of volume and power consumption, based on LMS adaptive filtering theory [24], an adaptive filter is designed to filter out random EMI. One input of the adaptive filter is the mixed signal x(n) of the actual scanning magnetic signal d(n) and the interference signal s(n) and the other input is the estimated reference input d(n) to the scanning magnetic signal. The adaptive filtering of input x(n) is used to match the output of the filter with y(n) and d(n), and the first stage output error e(n) is the best estimate of the jamming signal. The best estimate is fed to the mixed signal x(n), and the final output is the actual scanning magnetic signal d(n). Let the length of the mixed signal x(n) and the reference signal d(n) be N, the number of filter taps is M, and let n be from M to N, repeat the following iterative process:
X n [ x (n ), x (n 1), , x ( n M 1)] y (n) W T (n) X (n) e( n ) d ( n ) y ( n ) W (n 1) W ( n) 2 X ( n )e(n )
（17）
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The initialization parameter of the algorithm is W (n)=0 , y(n)=0、e(n)=0、M=8. Using the error e(n), the filter weight vector is updated in real time to realize the adaptive filtering of complex background signals. However, the convergence rate and the steady-state error of the traditional LMS algorithm depend on the iteration step size μ [25]. In response to the above problems, researchers proposed a variable step size LMS adaptive filtering algorithm [26,27]. When canceling the random EMI, smaller iterative steps can obtain smaller steady-state errors. As the target appears, the difference between d(n) and x(n) rapidly increases. In this case, a larger iteration step can quickly track the local trend of the non-stationary signal. Therefore, we propose a variable step size least mean square algorithm which is suitable for the characteristics of random EMI signals and has the step memory effect. The variation of the step size is expressed as:
p(n ) a1[1 cos(a2 e(n ) 3 )]
U
a
N
(n) a4 (n-1)+a5 p(n)
（18）
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The trend of the iteration step μ(n) is determined by the parameters a1～a5. The signal characteristics are analyzed through the experimental conditions, taking a1=0.8、 a2=0.85、a3=0.9、a4=0.75、a5=0.6. It can be seen from the above deduction that after increasing the variable step size, the number of multiplications of the algorithm is increased by 4 times than the LMS method with fixed step size. Therefore, the complexity of VSS-LMS algorithm is less than the fixed-step LMS algorithm, and still has better real-time performance. 3.1 The influence of random EMI signal pulse width on filtering effect Firstly, the influence of the pulse width of the random EMI signal on the filtering effect is discussed. The amplitude of the random EMI signal is set to 0.75V, the emergence moment is 0.15ms, and the pulse width is 10ns, 20ns, 30ns and 40ns respectively. For the above interference signal, the signal processed by the VSS-LMS filtering method is as shown in FIG.3, and the filtered signals are respectively shifted to the right by 0.01 ms. The amplitude of the interference signals with different pulse widths is compressed to 0.086V, The signal jitter decreases and the signal smoothness increases. Therefore, the VSS-LMS filter proposed in this paper can effectively eliminate the random EMI signals of different pulse widths without losing the effective measurement magnetic signal. The variation of the step size in the VSS-LMS algorithm is shown in FIG.4. When the interfering signal appears, the iterative step size rapidly changes. The peak value of the step size factor appears at the moment when the interference occurs. As the pulse width increases, the peak value of the step size is slightly reduction. The rapidly increasing iteration step can quickly track the random EMI signal, and the rest of the iteration steps are small, which is beneficial to smoothing the demagnetization signal and extracting the random EMI signal.
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3.2 The influence of random EMI signal energy on filter effect Secondly, the effect of random EMI signal energy on the filtering effect is studied. The pulse width of random EMI signal is set as 20ns and the emergence time is 0.15ms. The amplitudes are 0.6V, 0.8V, 1.0V and 1.2V respectively. The results of signal processing using the VSS-LMS filtering method are shown in FIG.5. The filtered signals are respectively shifted to the right by 0.01ms. The amplitude of the filtered interference signal increases with the original peak value. When the original peak value is 1.2V, the filtered peak value is 0.106V, when the original peak value is 0.6V, the filtered peak value is 0.059V. Therefore, the VSS-LMS filtering algorithm proposed in this paper can effectively eliminate random electromagnetic interference signals of different power. The variation of the step size in VSS-LMS algorithm is shown in FIG.6. Similarly, when the interference signal appears, the iterative step size changes rapidly. The peak value of the step size factor appears at the moment when the interference occurs, and the iteration steps are small in the rest of the time. Interfering with the increase of the signal peak, the peak value of the step factor slightly increases. 3.3 The influence of random EMI signal occurrence time on filter effect Due to the randomness of the interference, the influence of different random EMI moments on the filtering effect is investigated finally. The random EMI signal pulse width is 20ns, the amplitude is 0.8V, the occurrence time of random EMI are 0.11ms, 0.16ms, 0.21ms, 0.26ms and 0.31ms. The results of signal processing using the VSS-LMS filtering method are shown in FIG.7, it can be seen that the amplitude of the interference signal is suppressed to about 0.083V, and the signal smoothness of the position where the interference signal is located is improved. Therefore, the VSS-LMS filtering algorithm proposed in this paper can effectively eliminate the random EMI signals at different times. The variation of the step size in the VSS-LMS algorithm is shown in FIG.8. At different times when the interfering signal appears, the iterative step size rapidly changes. The peak value of the step size factor appears at the moment when the interference occurs, and the rest time steps are small. 4. Experimental Results and Discussions In order to further verify the performance of the above VSS-LMS filtering algorithm, the experimental measurement system is built. By adjusting the pulse width, power and occurrence time of interference signals, the experimental filter parameters are recorded under different state parameters. Monte Carlo method is used to carry out experiments. Each experiment is repeated 200 times to obtain the amplitude probability density distribution of the measured filtered interference signal. The filtering effect of the VSS-LMS method proposed in this paper is tested. Firstly, the interference signal pulse width was adjusted, and the amplitude of random electromagnetic interference was set at 0.8V, and the occurrence time was 0.15ms. When the pulse width was 10ns, 20ns, 30ns and 40ns, the filtered interference signals are measured. It can be seen that the amplitude distribution of the signal amplitude becomes more and more dispersed as the pulse width increases. Secondly, the pulse width of the random EMI signal is adjusted to 20ns, and the moment of emergence is 0.15ms. When the random disturbance amplitude is 1.2V,
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1.0V, 0.8V and 0.6V, the interference signal after VSS-LMS filtering is measured. It can be seen that with the increase of the amplitude of the interference signal, the amplitude-probability density curve of the filtered signal moves to the right and the distribution becomes divergent. Finally, the random electromagnetic interference signal pulse width is adjusted to 20ns, the signal amplitude is 0.8V, when the target azimuth are 0.11ms, 0.16ms, 0.21ms, 0.26ms and 0.31ms, the interference signal after VSS-LMS filtering is measured. With the increase of the slope of the curve at the moment when the interference signal appears, the distribution of the probability density curve of the filtered signal becomes concentrated. 5. Conclusion In this study, a VSS-LMS random EMI filtering method with step memory effect is designed for WCE magnetic localization system. Simulation and experiment are conducted respectively for three kinds of random disturbance factors such as different interference pulse width, peak power and occurrence time. Using Monte Carlo experimental method to get the statistical distribution of filtering signal. The results show that the VSS-LMS filtering algorithm proposed in this paper can effectively reduce the random electromagnetic interference signals with different pulse widths, different powers and different moments, it can effectively keep the measuring magnetic signals and improve the positioning accuracy.
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Acknowledgements: This study was supported by National Natural Science Foundation of China (51605227) and the Fundamental Research Funds for the central universities(NUST30915011303).
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References 1 Than T D, Alici G, Zhou H, et al. A review of localization systems for robotic endoscopic capsules[J]. IEEE Transactions on Biomedical Engineering, 2012, 59(9): 2387-2399. 2 Iddan G, Meron G, Glukhovsky A, et al. Wireless capsule endoscopy[J]. Nature, 2000, 405(6785): 417. 3 Than T D, Alici G, Zhou H, et al. Enhanced Localization of Robotic Capsule Endoscopes Using Positron Emission Markers and Rigid-Body Transformation[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2017. 4 Hu C, Li M, Song S, et al. A cubic 3-axis magnetic sensor array for wirelessly tracking magnet position and orientation[J]. IEEE Sensors Journal, 2010, 10(5): 903-913. 5 Weitschies W, Blume H, Mönnikes H. Magnetic marker monitoring: high resolution real-time tracking of oral solid dosage forms in the gastrointestinal tract[J]. European Journal of Pharmaceutics and Biopharmaceutics, 2010, 74(1): 93-101. 6 Carpi F, Shaheed H. Grand challenges in magnetic capsule endoscopy[J]. Expert review of medical devices, 2013, 10(4): 433-436. 7 Keller J, Fibbe C, Rosien U, et al. Recent advances in capsule endoscopy: development of maneuverable capsules[J]. Expert review of gastroenterology &
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hepatology, 2012, 6(5): 561-566. 8 Wang X, Meng M Q H. Perspective of active capsule endoscope: actuation and localisation[J]. International Journal of Mechatronics and Automation, 2011, 1(1): 38-45. 9 Pahlavan K, Bao G, Ye Y, et al. Rf localization for wireless video capsule endoscopy[J]. International Journal of Wireless Information Networks, 2012, 19(4): 326-340. 10 Salerno M, Ciuti G, Lucarini G, et al. A discrete-time localization method for capsule endoscopy based on on-board magnetic sensing[J]. Measurement Science and Technology, 2011, 23(1): 015701. 11 Yim S, Sitti M. 3-D localization method for a magnetically actuated soft capsule endoscope and its applications[J]. IEEE Transactions on Robotics, 2013, 29(5): 1139-1151. 12 Kim M G, Hong Y S, Lim E J. Position and orientation detection of capsule endoscopes in spiral motion[J]. International Journal of Precision Engineering and Manufacturing, 2010, 11(1): 31-37. 13 Di Natali C, Beccani M, Valdastri P. Real-time pose detection for magnetic medical devices[J]. IEEE Transactions on Magnetics, 2013, 49(7): 3524-3527. 14 Popek K M, Mahoney A W, Abbott J J. Localization method for a magnetic capsule endoscope propelled by a rotating magnetic dipole field[C]//Robotics and Automation (ICRA), 2013 IEEE International Conference on. IEEE, 2013: 5348-5353. 15 Basar M R, Malek F, Juni K M, et al. Ingestible wireless capsule technology: A review of development and future indication[J]. International Journal of Antennas and Propagation, 2012, 2012. 16 Spyrou E, Iakovidis D K. Video-based measurements for wireless capsule endoscope tracking[J]. Measurement Science and Technology, 2013, 25(1): 015002. 17 Nagy Z, Fluckiger M, Ergeneman O, et al. A wireless acoustic emitter for passive localization in liquids[C]//Robotics and Automation, 2009. ICRA'09. IEEE International Conference on. IEEE, 2009: 2593-2598. 18 Gumprecht J D J, Lueth T C, Khamesee M B. Navigation of a robotic capsule endoscope with a novel ultrasound tracking system[J]. Microsystem technologies, 2013, 19(9-10): 1415-1423. 19 Krieger A, Iordachita I I, Guion P, et al. An MRI-compatible robotic system with hybrid tracking for MRI-guided prostate intervention[J]. IEEE Transactions on Biomedical Engineering, 2011, 58(11): 3049-3060. 20 Aggarwal R, Singh J K, Gupta V K, et al. Noise reduction of speech signal using wavelet transform with modified universal threshold[J]. International Journal of Computer Applications, 2011, 20(5): 14-19. 21 Inoue T, Saruwatari H, Takahashi Y, et al. Theoretical analysis of musical noise in generalized spectral subtraction based on higher order statistics[J]. IEEE Transactions on Audio, Speech, and Language 22 Wu Z, Huang N E. Ensemble empirical mode decomposition: a noise-assisted data analysis method[J]. Advances in adaptive data analysis, 2009, 1(01): 1-41. 23 BoyanHuang,YeguiXiao,YapingMa, et al. Asimplifiedvariablestep-size
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LMSalgorithmfor Fourier analysis and its statistical properties[J]. Signal Processing, 2015, 117: 69-81. [24] Kwong R H, Johnston E W. A variable step size LMS algorithm[J]. IEEE Transactions on signal processing, 1992, 40(7): 1633-1642. [25] Zhang Y. Adaptive algorithms and structures with potential application in reverberation time estimation in occupied rooms[M]. Cardiff University (United Kingdom), 2007. [26]Mader A, Puder H, Schmidt G U. Step-size control for acoustic echo cancellation filters–an overview[J]. Signal Processing, 2000, 80(9): 1697-1719. [27] Shin H C, Sayed A H, Song W J. Variable step-size NLMS and affine projection algorithms[J]. IEEE signal processing letters, 2004, 11(2): 132-135.
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P(ζ,β,y)
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Figure 1. Mathematical model of rotating scanning magnetic signal
Figure 2. The y-axis direction magnetic field component in the MD model and EMM model: (a),(b),(c) and (d) are the distance between the core and the sensor is 10mm, 12mm, 14mm and 16mm
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Figure 3. Simulation of different EMI filters with different pulse widths
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Figure 4. Change of step factor in VSS-LMS algorithm
Figure 5. Simulation of different EMI filters with different power
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Figure 6. Change of step factor in VSS-LMS algorithm
Figure 7. Simulation of EMI filters with different occurrence time Figure 8. Change of step factor in VSS-LMS algorithm
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Figure 9. Probability density distribution of EMI signals with different pulse widths after filtering
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Figure 10. Probability density distribution of EMI signals with different energy after filtering
Figure 11. Probability density distribution of EMI signals with different occurrence time after
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filtering
Table 1.System parameters
Parameter
Value
Parameter
Value
Gain
200
5
8.72×10
Br/T
1.02
Threshold Level/mV
-150
r/mm
1
Magnetic resolution/μT
0.012
L/mm
12
Sensitivity/(mV/(V·Gauss))
1.18
σN/mV
45
Sensor bandwidth/MHz
5
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m/(A/m)