Enhancing the SNR of the Fiber Optic Rotation Sensor using the LMS Algorithm


 Annis Blankenship
 2 years ago
 Views:
Transcription
1 1 Enhancing the SNR of the Fiber Optic Rotation Sensor using the LMS Algorithm Hani Mehrpouyan, Student Member, IEEE, Department of Electrical and Computer Engineering Queen s University, Kingston, Ontario, Canada Abstract This paper investigates the application of forward linear prediction based on the least mean square (LMS) algorithm in the design of a finite impulse response (FIR) filter for the purpose of improving the signal to noise ratio (SNR) of the measurements acquired from a fiber optic gyroscope (FOG) The proposed approach determines the optimum filter tap weights and eliminates the noise and other high frequency disturbances without the need for a training sequence, specific model, or statespace formulation The designed traversal tapdelay line filter is validated by processing raw sensor measurements of the KVH fiber optic gyroscope acquired using a National Instrument 12 bit data acquisition system Simulation results demonstrate significant SNR gain when the LMS filter is applied to the measurements results Moreover, the convergence rate of the LMS algorithm for small, large, and variable step sizes and the effect of the filter order on the cut off frequency and SNR gain is analyzed and compared Index Terms fiber optic gyroscope, measurement signal to noise ratio, forward linear prediction, least mean square, and transversal tap delay line filter I INTRODUCTION FIBER optic gyroscopes (FOGs) have become a well established navigational and guidance tool due to their long life, ruggedness, small size, low cost, and environmental insensitivity [1] However, the performance characteristics of FOGs are highly affected by the bias drift and angle random walk (ARW) Bias drift is defined as the deviation in rotation measurements due to temperature (increases with the temperature), affecting the long term performance of the FOGs [2], [3] On the other hand, ARW affects the short term performance of the system and is the broad noise component of the FOG output [3] ARW can be modeled as a random process which is the result of the combined effect of the noise introduced by the photodetector and the light source intensity noise [4], [5] During the alignment process, FOGs are used to monitor the components of Earth rotation rate along the sensitive axis to determine the initial movements of the platform [6] The accuracy by which Earth s rotation can be determined is significantly affected by the signal to noise ratio (SNR) and the magnitude of the ARW, where the higher the SNR the lower the variance of the rotational measurements Therefore, many different schemes based on hardware modifications or signal processing implementations have been proposed to try to reduce the ARW level and increase the SNR In this paper we focus on the latter Forward linear prediction (FLP) techniques have been used successfully to reduce the noise level in many applications In [7] the FLP algorithm is applied as a channel equalizer, compensating the negative effect of the channel fluctuations and significantly improving the average bit error rate and performance of the communication system FLP uses a set of past samples from a stationary process to predict future sample values [8] and subsequently reduce the noise The most common and practical predictor is the single timeunit predictor which is implemented using a tapdelay line filter with a predetermined order To simplify the filter implementation a finite impulse response (FIR) filter structure as presented in Fig 1 is used for the design of the filter The LMS algorithm is used to determine the optimum tap weights for the FIR filter based on fixed and variable step sizes [9] Fig 1 The structure of the tapdelay FIR filter that uses the past samples {d(n 1), d(n), d(n M)} to provide and estimate of the current sample value, ˆd(n) In this paper we investigate the use of FLP, based on the LMS algorithm to improve the SNR for the measurements data collected using FOGs As one of its main advantages the proposed strategy does not require any assumption on the distribution of the noise or a specific statespace model to perform the prediction and reduce the noise level Moreover, the optimum tap weights of the FIR filter are determined without the need for a training sequence, achieving the proposed performance gains with significantly lower complexity To validate the algorithm
2 2 outlined here, the designed filter is used to process the raw sensor measurements of a KVH fiber optic gyroscope at 128 Hz and the simulation results demonstrate significant SNR gain Moreover, we have investigated the convergence rate and the SNR for the LMS algorithm based on fixed and variable step sizes Finally, the effect of filter order on the cut off frequency and the achievable SNR gain for the overall system are reported and simulation results are presented to support the findings of the paper This paper is organized as follows: Section II outlines the system model and establishes the algorithms under consideration to determine the optimum filter coefficients with respect to a minimum mean square () design criteria for the LMS algorithm Section III discusses the extensive simulation results and examines the effect of filter order and the step size on the performance and convergence rate of the proposed algorithm, respectively This following notation is used throughout this report: italic letters (x) represent scalar quantities, bold lower case letters (x) represent vectors, bold upper case letters (X) represent matrices, and () T denotes transpose II SYSTEM AND FILTER MODEL In this section we define the system model for the proposed project Eq (1) defines the relationship between the raw sensor measurements r(n) and the desired signal d(n) r(n) = d(n) + ν(n), (1) where ν(n) is the additive noise representing ARW, with mean zero and variance σ 2 n The LMS algorithm is used to to extract the desired signal and improve the signal to noise ratio Fig 2 represents the block diagram for the FLP system setup Fig 2 The block diagram representing the two filter designs used to remove the disturbances from the received signal An FIR filter, illustrated in Fig 1, is used to estimate the desired signal, d(n) Based on the design criteria the input and output relationship for the filter can be illustrated as M ˆd(n) = w k r(n k), (2) k= where {w, w 1,, w M } represent the filter coefficients and M is the order of the FIR filter Eq (2) in vector form is represented as ˆd(n) = w T r, (3) where w T is transpose of the M 1 vector of the filter coefficients and r is the M 1 vector of the input parameters (r = {r(n), r(n 1),, r(n M)} T Based on the above system model the mean square error () for the above estimation problem can be defined as j(n) = E [(d(n) ˆd(n)) 2] = E[(d(n) w T r)(d(n) r T w)], (4) where j(n) is the cost function and can be rewritten as j(n) = E [ (d 2 (n)] 2w T E[rd(n)] + w T E[rr T ]w ] (5) Assuming that the input and the desired sequence are stationary zeromean random processes, Eq (5) can be modified as follows j(n) = σ 2 d 2w T p + w T Rw, (6) where σd 2 is the variance of d(n), p is the cross correlation vector between the input sequence and the desired sequence and is expressed as E[r(n)d(n)] E[r(n 1)d(n)] p = E[rd(n)] = E[r(n 2)d(n)], (7) E[r(n M)d(n)] and matrix R is the autocorrelation matrix of the input sequence and is defined in Eq (8) on the next page The objective of this design is to determine the filter coefficients, w, such that the cost function expressed in Eq (6) is minimized j(n) which has been derived based on the in its quadratic form can be presented as j(n) = j min + (w w o ) T R(w w o ), (9) where j min represents the minimum mean square error (M) corresponding to the optimal filter weights, w o By taking the gradient of j(n) in Eq (9) with respect to the filter weights and moving in small steps in the opposite direction of the gradient vector, the following relationship between the filter coefficients can be found as w n+1 = w n µ 2 j(n) w(n), (1) where the negative sign guarantees that the movement is in the negative direction of the gradient and the parameter µ is the step size The choice of µ dictates the convergence speed of the algorithm and also the value of the M The smaller the value of µ the lower the M, however the slower the algorithm converges to the optimum filter
3 3 R = E [ rr T ] = E[r 2 (n)] E[r(n)r(n 1)] E[r(n)r(n M)] E[r(n 1)r(n)] E[r 2 (n 1)] E[r(n 1)r(n M)] E[r(n M)r(n)] E[r(n M)r(n 1)] E[r 2 (n M)] (8) weights After further algebraic manipulation Eq (1) can be represented as [9] w n+1 = w n + µ e(n)r(n), (11) 2 where e(n) is the error function, defined as d(n) ˆd(n) and can be further expressed as e(n) = d(n) w T (n)r(n) (12) w(n) 35 x Filter impulse response III SIMULATION RESULTS In this section we investigate the performance of the FLP algorithm based on LMS, in terms of improving the SNR for the measurement data obtained using the KVH FOG The LMS algorithm presented in the previous section is used to find the optimum tapweights for the FIR filter and subsequently the filter is applied to the measurement data acquired using a National Instrument 12 bit data acquisition system at a 128 Hz The effect of filter order and the choice of the step size on the performance of the filter are also examined and the simulation results are presented Fig 3 represents the impulse response of the LMS filter Based on the results presented in Fig 3 the designed FIR filter is a moving average filter that removes the effect of the additive white noise by averaging over the samples This is an interesting development and demonstrates that the application of a simple averaging filter could significantly improve the SNR ratio for the measurements results performed using a FOG Fig 4 represents the magnitude and phase response of the LMS FIR filter One desired property of the filter is its linear phase characteristics Thus, the output of the filter does not suffer from variable group delay and is not distorted Based on the magnitude response we can deduce that the filter is a low pass filter with an approximate cut off frequency of 1 Hz as illustrated more clearly in Fig 5 The low cut off frequency of the filter removes the effect of high frequency disturbances, thus increasing the overall SNR Fig 6 represents the mean square error () for the FIR filter derived in Eq (12) with the step size µ = 1 As noted in Fig 6 approximately 1 samples are required for the filter to reach the minimum min square error (M) with µ = 1 This is a reasonably fast response considering that on a average it takes 1 to 15 minutes for the gyroscope to perform its measurements and demonstrates that the proposed algorithm does not suffer from significant delays and is applicable to real n Fig 3 Filter impulse response with filter order set to 3 and the step size µ = 1 world scenarios The following results examine the effect of variable step sizes on the achievable M Fig 7 represents the input output relationship for the LMS filter As noted in Fig 7, the digital input to the filter suffers from considerable distortion caused by ARW additive noise However, the output of the LMS filter is capable of removing a significant portion of the distortions and improve the SNR Quantitatively the SNR for the input to the system is measured to be 3397dB and after applying the FIR filter the SNR improves to 544dB The step size parameter plays an important role in the overall M for the LMS algorithm and how quickly the M is reached The maximum value for the step size, µ is calculated as 1 µ max =, (13) λ min + λ max where λ min and λ max are the minimum and maximum eigen values for autocorrelation matrix of the input signal, defined in Eq (8) For the data used throughout this paper and a filter order of, M = 3, λ min = and λ max = 7819 making µ max = 1278 based on Eq (13) One of the main goals of this project is to investigate the effect of the step size, µ, on the M of the LMS algorithm As stated previously a larger step size results in a faster convergence rate, however it also results in a larger M Fig 8 represents the derived in Eq (12) for different values of µ and also provides a comparison for the case of
4 4 1 x Fig 4 The magnitude and phase response of the FIR filter with M = 3 and µ = Fig 6 The for the the FIR filter with M = 3 and µ = Fig 5 The magnitude of the FIR filter with M = 3 and µ = 1 variable µ, ranging from the upper limit to the chosen lower limit for the step size At µ = 1278 the LMS algorithm converges very quickly and the M is reached At µ = 4, even though a lower overall M can be reached compared to µ max, close to 2 samples are required to for the LMS to converge, making µ = 4 an unattractive choice for the step size due to this significant delay Fig 8 also represents the plot for the case of variable step size, when 4 µ 1278 It is interesting to note that the by varying the step size from one iteration to another, one can achieve both fast convergence and low M Table I quantifies the SNR gain associated with different step sizes and demonstrates by choosing a variable step size, the LMS algorithm both converges very quickly and also results in the best SNR gain Fig 9 compares the linear phase characteristics of FIR filters with different step sizes It is important to note that as the step size increases the FIR filter loses its linear phase d(t) The filtered measurments Raw meas Filtered meas t (sec) Fig 7 The input/output relationship for the FIR filter with M = 3 and µ = 1 characteristics which negatively affects the overall system performance Thus, when choosing the step size it is also important to analyze the both the magnitude and phase response of the filter to ensure that designed filter does not distort the signal negatively Although, in this specific application, since the signal from the FOGs only consists of low frequency components the nonlinear phase property of the FIR filter does not affect the system performance The filter order is another important design parameter that affects the performance of the system in terms of SNR gain and cut off frequency Figs 1 and 11 represent the frequency response of the FIR filter when M = 1 and M = 2, respectively Comparing the results in Figs 1, 11, and 5, one can conclude that as the filter order is increased the cut off frequency for the FIR filter decreases, eliminating a larger portion of the high frequency
5 µ=12788 µ=4 µ=variable x 14 1 Max step size Fig 8 The for the the FIR filter with M = 3 and µ = 1278, µ = 4, and 4 µ 1278 TABLE I A COMPARISON OF THE EFFECT OF THE STEP SIZE, µ AND THE FILTER ORDER, M, ON THE SNR GAIN OF THE FLP ALGORITHM SNR gain Normalized Cut off frequency (f s = 2kHz) M = 3 µ = dB Hz µ = 4 165dB Hz 4 µ dB Hz M = 2 µ = dB Hz µ = dB Hz 4 µ dB Hz M = 1 µ = dB Hz µ = 4 969dB Hz 4 µ dB Hz disturbances caused by ARW noise Table I quantitatively represents the normalized cut off frequency for the FIR filters of order 1, 2, and 3 Moreover, Table I also demonstrates that the filter order plays a more significant role in noise reduction compared to that of the step size Therefore, the choice of filter order is an important design parameter since it affects, the cut off frequency, the SNR gain, and the operating delay of the filter, because the higher the filter order, the larger the overall delay Figs 12 and 13 represents the curves for the FIR filters of order M = 1, and M = 2, respectively The following observations can be made based on the simulation results: 1) The maximum step size, µ max, is different for different filter orders as pointed out in Figs 12, 13, 8, and Table I 3 4 x x 14 Min step size Variable step size 4 Fig 9 The Phase response for the FIR filter with M = 3 and µ = 1278, µ = 4, and 4 µ ) The minimum step size, µ min, needs to be adjusted according to the filter order, since as shown in Fig 12, µ min = 4 is too small for a filter order of 1, where close to 5 samples are required before the LMS algorithm converges, resulting in considerable delay 3) The M is not affected by the filter order since for filters of order M = 1, M = 2, and M = 3, the M ) The variable step size approach, where µ max is used in the first iteration and is then replaced by µ min in the following iterations can be applied to any filter order and is even more effective for smaller filter orders IV CONCLUSION In this paper noise reduction for the fiber optic gyroscopes using the forward linear prediction based on the least mean square error algorithm was investigated and developed The signal received from a FOG is affected by many different sources of noise, which greatly affects the accuracy of rotational measurements performed by such
6 µ=3835 µ=4 µ=variable Fig 1 The magnitude of the FIR filter with M = 1 and µ = 1 Fig 12 The for the the FIR filter with M = 1 and µ = 3835, µ = 4, and 4 µ µ=191 µ=4 µ=variable Fig 11 The magnitude of the FIR filter with M = 2 and µ = 1 devices Using forward linear prediction we have demonstrated that the previous samples received by the system can be used to estimate the current samples and subsequently reduce the amount of noise and improve signal to noise ratio The LMS algorithm is affected by the filter order and also the step size parameter The effect of filter order on the cut off frequency of the filter was investigated and it was demonstrated that the higher the filter order the lower the cut off frequency and the higher the overall SNR gain for the system Moreover, we investigated the use of a variable step size strategy to reduce the convergence delay associated with the LMS algorithm when keeping the M the same By applying the largest possible step size in the first iteration and subsequently applying the lower limit for the step size, we were able to reach the M Fig 13 The for the the FIR filter with M = 2 and µ = 191, µ = 4, and 4 µ 191 as fast as when the maximum value for the step size is applied Finally, it is important to note that the approach outlined in this paper can be applied to other applications to significantly reduce the effect of the noise REFERENCES [1] W K Burns, Optical Fiber Rotation Sensing Academic Press, Boston, 1994 [2] M Bowser M J Hammond, M Perlmutter, and R Christopher, Broad fiber optic gyroscopes for a broad range of applications, in IEEE Position Location and Navigation Symp, 1996, pp [3] H Lefevre, The Fiber Optic Gyroscope ArtechHouse, Norwood, MA, 1993
7 [4] A Noureldin, M Mintchev, D IrvineHalliday, and H Tabler, Computer modeling of microelectronic closed loop fiber optic gyroscope, in IEEE Canadian Conf on Electrical and Computer Engineering, 1999, pp [5] A Gelb, Applied Optimal Estimation MIT Press, Cambridge, England, 1974 [6] D H Titterton and J L Weston, Strapdown Inertial Navigation Technology Peter Peregrinus Ltd, London, 1997 [7] H Mehrpouyan, Channel equalizer design based on wiener filter and least mean square algorithms, in Submitted to EE517 at RMC, 29, pp 1 7 [8] S Haykin, Adaptive Filter Theory, 3rd ed Prentice Hall, Upper Saddle River, NJ, 1996 [9] B Widrow and S D Stearns, Adaptive Signal Processing Prentice Hall Signal Processing Series,
Adaptive Equalization of binary encoded signals Using LMS Algorithm
SSRG International Journal of Electronics and Communication Engineering (SSRGIJECE) volume issue7 Sep Adaptive Equalization of binary encoded signals Using LMS Algorithm Dr.K.Nagi Reddy Professor of ECE,NBKR
More informationLecture 5: Variants of the LMS algorithm
1 Standard LMS Algorithm FIR filters: Lecture 5: Variants of the LMS algorithm y(n) = w 0 (n)u(n)+w 1 (n)u(n 1) +...+ w M 1 (n)u(n M +1) = M 1 k=0 w k (n)u(n k) =w(n) T u(n), Error between filter output
More informationThe Filteredx LMS Algorithm
The Filteredx LMS Algorithm L. Håkansson Department of Telecommunications and Signal Processing, University of Karlskrona/Ronneby 372 25 Ronneby Sweden Adaptive filters are normally defined for problems
More information4F7 Adaptive Filters (and Spectrum Estimation) Least Mean Square (LMS) Algorithm Sumeetpal Singh Engineering Department Email : sss40@eng.cam.ac.
4F7 Adaptive Filters (and Spectrum Estimation) Least Mean Square (LMS) Algorithm Sumeetpal Singh Engineering Department Email : sss40@eng.cam.ac.uk 1 1 Outline The LMS algorithm Overview of LMS issues
More informationIMU Components An IMU is typically composed of the following components:
APN064 IMU Errors and Their Effects Rev A Introduction An Inertial Navigation System (INS) uses the output from an Inertial Measurement Unit (IMU), and combines the information on acceleration and rotation
More informationBackground 2. Lecture 2 1. The Least Mean Square (LMS) algorithm 4. The Least Mean Square (LMS) algorithm 3. br(n) = u(n)u H (n) bp(n) = u(n)d (n)
Lecture 2 1 During this lecture you will learn about The Least Mean Squares algorithm (LMS) Convergence analysis of the LMS Equalizer (Kanalutjämnare) Background 2 The method of the Steepest descent that
More informationComputer exercise 2: Least Mean Square (LMS)
1 Computer exercise 2: Least Mean Square (LMS) This computer exercise deals with the LMS algorithm, which is derived from the method of steepest descent by replacing R = E{u(n)u H (n)} and p = E{u(n)d
More informationStability of the LMS Adaptive Filter by Means of a State Equation
Stability of the LMS Adaptive Filter by Means of a State Equation Vítor H. Nascimento and Ali H. Sayed Electrical Engineering Department University of California Los Angeles, CA 90095 Abstract This work
More informationAnalysis of Filter Coefficient Precision on LMS Algorithm Performance for G.165/G.168 Echo Cancellation
Application Report SPRA561  February 2 Analysis of Filter Coefficient Precision on LMS Algorithm Performance for G.165/G.168 Echo Cancellation Zhaohong Zhang Gunter Schmer C6 Applications ABSTRACT This
More informationALLAN VARIANCE ANALYSIS ON ERROR CHARACTERS OF LOW COST MEMS ACCELEROMETER MMA8451Q
HENRI COANDA AIR FORCE ACADEMY ROMANIA INTERNATIONAL CONFERENCE of SCIENTIFIC PAPER AFASES 04 Brasov, 4 May 04 GENERAL M.R. STEFANIK ARMED FORCES ACADEMY SLOVAK REPUBLIC ALLAN VARIANCE ANALYSIS ON ERROR
More informationFinal Year Project Progress Report. FrequencyDomain Adaptive Filtering. Myles Friel. Supervisor: Dr.Edward Jones
Final Year Project Progress Report FrequencyDomain Adaptive Filtering Myles Friel 01510401 Supervisor: Dr.Edward Jones Abstract The Final Year Project is an important part of the final year of the Electronic
More informationA STUDY OF ECHO IN VOIP SYSTEMS AND SYNCHRONOUS CONVERGENCE OF
A STUDY OF ECHO IN VOIP SYSTEMS AND SYNCHRONOUS CONVERGENCE OF THE µlaw PNLMS ALGORITHM Laura Mintandjian and Patrick A. Naylor 2 TSS Departement, Nortel Parc d activites de Chateaufort, 78 ChateaufortFrance
More informationLMS is a simple but powerful algorithm and can be implemented to take advantage of the Lattice FPGA architecture.
February 2012 Introduction Reference Design RD1031 Adaptive algorithms have become a mainstay in DSP. They are used in wide ranging applications including wireless channel estimation, radar guidance systems,
More informationISSN: 23195967 ISO 9001:2008 Certified International Journal of Engineering Science and Innovative Technology (IJESIT) Volume 3, Issue 3, May 2014
Nonlinear Adaptive Equalization Based on Least Mean Square (LMS) in Digital Communication 1 Manoj, 2 Mohit Kumar, 3 Kirti Rohilla 1 MTech Scholar, SGT Institute of Engineering and Technology, Gurgaon,
More informationPHASE ESTIMATION ALGORITHM FOR FREQUENCY HOPPED BINARY PSK AND DPSK WAVEFORMS WITH SMALL NUMBER OF REFERENCE SYMBOLS
PHASE ESTIMATION ALGORITHM FOR FREQUENCY HOPPED BINARY PSK AND DPSK WAVEFORMS WITH SMALL NUM OF REFERENCE SYMBOLS Benjamin R. Wiederholt The MITRE Corporation Bedford, MA and Mario A. Blanco The MITRE
More informationTitle Feedback Active Noise Control. Author(s) SingKiong. Conference: Issue Date DOI. Doc URLhttp://hdl.handle.
Title All Pass Filtered Reference LMS Alg Feedback Active Noise Control Author(s) Tabatabaei Ardekani, Iman; Abdulla, SingKiong Proceedings : APSIPA ASC 29 : Asi Citation Information Processing Association,
More informationComparative Performance Analysis of Adaptive Algorithms for Simulation & Hardware Implementation of an ECG Signal
International Journal of Electronics and Computer Science Engineering 2184 Available Online at www.ijecse.org ISSN 22771956 Comparative Performance Analysis of Adaptive Algorithms for Simulation & Hardware
More informationADAPTIVE ALGORITHMS FOR ACOUSTIC ECHO CANCELLATION IN SPEECH PROCESSING
www.arpapress.com/volumes/vol7issue1/ijrras_7_1_05.pdf ADAPTIVE ALGORITHMS FOR ACOUSTIC ECHO CANCELLATION IN SPEECH PROCESSING 1,* Radhika Chinaboina, 1 D.S.Ramkiran, 2 Habibulla Khan, 1 M.Usha, 1 B.T.P.Madhav,
More informationTechnical Report. An introduction to inertial navigation. Oliver J. Woodman. Number 696. August 2007. Computer Laboratory
Technical Report UCAMCLTR696 ISSN 14762986 Number 696 Computer Laboratory An introduction to inertial navigation Oliver J. Woodman August 27 15 JJ Thomson Avenue Cambridge CB3 FD United Kingdom phone
More informationHFAN Rev.1; 04/08
Application Note: HFAN9.1.0 Rev.1; 04/08 Impact of Transmitter RIN on Optical Link Performance AVAILABLE Impact of Transmitter RIN on Optical Link Performance 1 Overview Semiconductor laser relative intensity
More informationSENSOR FUSION FOR LINEAR MOTORS, AN APPROACH FOR LOWCOST MEASUREMENTS
Proc. of Mechatronics 22, University of Twente, 2426 June 22 SENSOR FUSION FOR LINEAR MOTORS, AN APPROACH FOR LOWCOST MEASUREMENTS Bas J. de Kruif, Bastiaan van Wermeskerken, Theo J. A. de Vries and
More informationAn Introduction to the Kalman Filter
An Introduction to the Kalman Filter Greg Welch 1 and Gary Bishop 2 TR 95041 Department of Computer Science University of North Carolina at Chapel Hill Chapel Hill, NC 275993175 Updated: Monday, July 24,
More informationSystem Identification for Acoustic Comms.:
System Identification for Acoustic Comms.: New Insights and Approaches for Tracking Sparse and Rapidly Fluctuating Channels Weichang Li and James Preisig Woods Hole Oceanographic Institution The demodulation
More informationA Spectral Clustering Approach to Validating Sensors via Their Peers in Distributed Sensor Networks
A Spectral Clustering Approach to Validating Sensors via Their Peers in Distributed Sensor Networks H. T. Kung Dario Vlah {htk, dario}@eecs.harvard.edu Harvard School of Engineering and Applied Sciences
More informationFormulations of Model Predictive Control. Dipartimento di Elettronica e Informazione
Formulations of Model Predictive Control Riccardo Scattolini Riccardo Scattolini Dipartimento di Elettronica e Informazione Impulse and step response models 2 At the beginning of the 80, the early formulations
More informationSynchronization of sampling in distributed signal processing systems
Synchronization of sampling in distributed signal processing systems Károly Molnár, László Sujbert, Gábor Péceli Department of Measurement and Information Systems, Budapest University of Technology and
More informationBy choosing to view this document, you agree to all provisions of the copyright laws protecting it.
This material is posted here with permission of the IEEE Such permission of the IEEE does not in any way imply IEEE endorsement of any of Helsinki University of Technology's products or services Internal
More informationLeast Squares Estimation
Least Squares Estimation SARA A VAN DE GEER Volume 2, pp 1041 1045 in Encyclopedia of Statistics in Behavioral Science ISBN13: 9780470860809 ISBN10: 0470860804 Editors Brian S Everitt & David
More informationTCOM 370 NOTES 994 BANDWIDTH, FREQUENCY RESPONSE, AND CAPACITY OF COMMUNICATION LINKS
TCOM 370 NOTES 994 BANDWIDTH, FREQUENCY RESPONSE, AND CAPACITY OF COMMUNICATION LINKS 1. Bandwidth: The bandwidth of a communication link, or in general any system, was loosely defined as the width of
More informationECE438  Laboratory 9: Speech Processing (Week 2)
Purdue University: ECE438  Digital Signal Processing with Applications 1 ECE438  Laboratory 9: Speech Processing (Week 2) October 6, 2010 1 Introduction This is the second part of a two week experiment.
More informationMeasuring the Earth s Rotation Rate Using a LowCost MEMS Gyroscope
Measuring the Earth s Rotation Rate Using a LowCost MEMS Gyroscope L. I. Iozan 1, J. Collin 2, O. Pekkalin 2, J. Hautamäki 2, J. Takala 2, C. Rusu 1 1 Technical University of ClujNapoca Baritiu 2628
More informationSolutions to Exam in Speech Signal Processing EN2300
Solutions to Exam in Speech Signal Processing EN23 Date: Thursday, Dec 2, 8: 3: Place: Allowed: Grades: Language: Solutions: Q34, Q36 Beta Math Handbook (or corresponding), calculator with empty memory.
More informationMATRIX TECHNICAL NOTES
200 WOOD AVENUE, MIDDLESEX, NJ 08846 PHONE (732) 4699510 FAX (732) 4690418 MATRIX TECHNICAL NOTES MTN107 TEST SETUP FOR THE MEASUREMENT OF XMOD, CTB, AND CSO USING A MEAN SQUARE CIRCUIT AS A DETECTOR
More informationTime Domain and Frequency Domain Techniques For Multi Shaker Time Waveform Replication
Time Domain and Frequency Domain Techniques For Multi Shaker Time Waveform Replication Thomas Reilly Data Physics Corporation 1741 Technology Drive, Suite 260 San Jose, CA 95110 (408) 2168440 This paper
More informationImproved Residual Analysis in ADC Testing. István Kollár
Improved Residual Analysis in ADC Testing István Kollár Dept. of Measurement and Information Systems Budapest University of Technology and Economics H1521 Budapest, Magyar tudósok krt. 2., HUNGARY Tel.:
More informationLecture 3: Quantization Effects
Lecture 3: Quantization Effects Reading: 6.76.8. We have so far discussed the design of discretetime filters, not digital filters. To understand the characteristics of digital filters, we need first
More information15.062 Data Mining: Algorithms and Applications Matrix Math Review
.6 Data Mining: Algorithms and Applications Matrix Math Review The purpose of this document is to give a brief review of selected linear algebra concepts that will be useful for the course and to develop
More informationPOTENTIAL OF STATEFEEDBACK CONTROL FOR MACHINE TOOLS DRIVES
POTENTIAL OF STATEFEEDBACK CONTROL FOR MACHINE TOOLS DRIVES L. Novotny 1, P. Strakos 1, J. Vesely 1, A. Dietmair 2 1 Research Center of Manufacturing Technology, CTU in Prague, Czech Republic 2 SW, Universität
More informationSignal Detection C H A P T E R 14 14.1 SIGNAL DETECTION AS HYPOTHESIS TESTING
C H A P T E R 4 Signal Detection 4. SIGNAL DETECTION AS HYPOTHESIS TESTING In Chapter 3 we considered hypothesis testing in the context of random variables. The detector resulting in the minimum probability
More informationCANCELLATION OF WHITE AND COLOR NOISE WITH ADAPTIVE FILTER USING LMS ALGORITHM
CANCELLATION OF WHITE AND COLOR NOISE WITH ADAPTIVE FILTER USING LMS ALGORITHM 1 Solaiman Ahmed, 2 Farhana Afroz, 1 Ahmad Tawsif and 1 Asadul Huq 1 Department of Electrical and Electronic Engineering,
More informationAP Series Autopilot System. AP202 Data Sheet. March,2015. Chengdu Jouav Automation Tech Co.,L.t.d
AP Series Autopilot System AP202 Data Sheet March,2015 Chengdu Jouav Automation Tech Co.,L.t.d AP202 autopilot,from Chengdu Jouav Automation Tech Co., Ltd, provides complete professionallevel flight
More informationDepartment of Electrical and Computer Engineering BenGurion University of the Negev. LAB 1  Introduction to USRP
Department of Electrical and Computer Engineering BenGurion University of the Negev LAB 1  Introduction to USRP  11 Introduction In this lab you will use software reconfigurable RF hardware from National
More informationCCNY. BME I5100: Biomedical Signal Processing. Linear Discrimination. Lucas C. Parra Biomedical Engineering Department City College of New York
BME I5100: Biomedical Signal Processing Linear Discrimination Lucas C. Parra Biomedical Engineering Department CCNY 1 Schedule Week 1: Introduction Linear, stationary, normal  the stuff biology is not
More informationSignal Detection. Outline. Detection Theory. Example Applications of Detection Theory
Outline Signal Detection M. Sami Fadali Professor of lectrical ngineering University of Nevada, Reno Hypothesis testing. NeymanPearson (NP) detector for a known signal in white Gaussian noise (WGN). Matched
More informationUNDERSTANDING NOISE PARAMETER MEASUREMENTS (AN60040)
UNDERSTANDING NOISE PARAMETER MEASUREMENTS (AN60040 Overview This application note reviews noise theory & measurements and Sparameter measurements used to characterize transistors and amplifiers at
More informationAdvanced Signal Processing and Digital Noise Reduction
Advanced Signal Processing and Digital Noise Reduction Saeed V. Vaseghi Queen's University of Belfast UK WILEY HTEUBNER A Partnership between John Wiley & Sons and B. G. Teubner Publishers Chichester New
More informationLogLikelihood Ratiobased Relay Selection Algorithm in Wireless Network
Recent Advances in Electrical Engineering and Electronic Devices LogLikelihood Ratiobased Relay Selection Algorithm in Wireless Network Ahmed ElMahdy and Ahmed Walid Faculty of Information Engineering
More informationLuigi Piroddi Active Noise Control course notes (January 2015)
Active Noise Control course notes (January 2015) 9. Online secondary path modeling techniques Luigi Piroddi piroddi@elet.polimi.it Introduction In the feedforward ANC scheme the primary noise is canceled
More informationADAPTIVE EQUALIZATION. Prepared by Deepa.T, Asst.Prof. /TCE
ADAPTIVE EQUALIZATION Prepared by Deepa.T, Asst.Prof. /TCE INTRODUCTION TO EQUALIZATION Equalization is a technique used to combat inter symbol interference(isi). An Equalizer within a receiver compensates
More informationAdaptive Online Gradient Descent
Adaptive Online Gradient Descent Peter L Bartlett Division of Computer Science Department of Statistics UC Berkeley Berkeley, CA 94709 bartlett@csberkeleyedu Elad Hazan IBM Almaden Research Center 650
More informationAcoustic Echo Cancellation For Speech And Random Signal Using Estimated Impulse Responses
Adaptive Filter International Journal of Recent Development in Engineering and Technology Acoustic Echo Cancellation For Speech And Random Signal Using Estimated Impulse Responses S. I. M. M. Raton Mondol
More informationSIMPLIFIED PERFORMANCE MODEL FOR HYBRID WIND DIESEL SYSTEMS. J. F. MANWELL, J. G. McGOWAN and U. ABDULWAHID
SIMPLIFIED PERFORMANCE MODEL FOR HYBRID WIND DIESEL SYSTEMS J. F. MANWELL, J. G. McGOWAN and U. ABDULWAHID Renewable Energy Laboratory Department of Mechanical and Industrial Engineering University of
More informationUnderstanding and Applying Kalman Filtering
Understanding and Applying Kalman Filtering Lindsay Kleeman Department of Electrical and Computer Systems Engineering Monash University, Clayton 1 Introduction Objectives: 1. Provide a basic understanding
More informationDigital Communication Fundamentals
Chapter 2 Digital Communication Fundamentals 2.1 Introduction As we said at the end of Chapter 1, CDMA is applicable to digital (as opposed to analog) communication. This chapter is therefore devoted to
More informationInterference Cancelation in Ultrasonic Sensor Arrays by Stochastic Coding and Adaptive Filtering
Interference Cancelation in Ultrasonic Sensor Arrays by Stochastic Coding and Adaptive Filtering Bernhard Wirnitzer FHMannheim Institut für Digitale Signalverarbeitung Windeckstr. 11, D68163 Mannheim,
More informationADAPTIVE CHANNEL EQUALIZER FOR WIRELESS COMMUNICATION SYSTEMS
International Journal of Electronics and Communication Engineering (IJECE) ISSN(P): 22789901; ISSN(E): 2278991X Vol. 2, Issue 5, Nov 2013, 159166 IASET ADAPTIVE CHANNEL EQUALIZER FOR WIRELESS COMMUNICATION
More informationNonData Aided Carrier Offset Compensation for SDR Implementation
NonData Aided Carrier Offset Compensation for SDR Implementation Anders Riis Jensen 1, Niels Terp Kjeldgaard Jørgensen 1 Kim Laugesen 1, Yannick Le Moullec 1,2 1 Department of Electronic Systems, 2 Center
More informationFundamental to determining
GNSS Solutions: CarriertoNoise Algorithms GNSS Solutions is a regular column featuring questions and answers about technical aspects of GNSS. Readers are invited to send their questions to the columnist,
More informationCHAPTER 8 FACTOR EXTRACTION BY MATRIX FACTORING TECHNIQUES. From Exploratory Factor Analysis Ledyard R Tucker and Robert C.
CHAPTER 8 FACTOR EXTRACTION BY MATRIX FACTORING TECHNIQUES From Exploratory Factor Analysis Ledyard R Tucker and Robert C MacCallum 1997 180 CHAPTER 8 FACTOR EXTRACTION BY MATRIX FACTORING TECHNIQUES In
More informationMaking Accurate Voltage Noise and Current Noise Measurements on Operational Amplifiers Down to 0.1Hz
Author: Don LaFontaine Making Accurate Voltage Noise and Current Noise Measurements on Operational Amplifiers Down to 0.1Hz Abstract Making accurate voltage and current noise measurements on op amps in
More informationEqualisation Algorithms in Fixed Point Arithmetic by A.T. Markettos (CAI)
Equalisation Algorithms in Fixed Point Arithmetic by A.T. Markettos (CAI) Fourthyear project in Group E, / Cambridge University Engineering Department Abstract The conversion from floating point to fixed
More informationDesigning interface electronics for zirconium dioxide oxygen sensors of the XYA series
1 CIRCUIT DESIGN If not using one of First Sensors ZBXYA interface boards for sensor control and conditioning, this section describes the basic building blocks required to create an interface circuit Before
More informationKristine L. Bell and Harry L. Van Trees. Center of Excellence in C 3 I George Mason University Fairfax, VA 220304444, USA kbell@gmu.edu, hlv@gmu.
POSERIOR CRAMÉRRAO BOUND FOR RACKING ARGE BEARING Kristine L. Bell and Harry L. Van rees Center of Excellence in C 3 I George Mason University Fairfax, VA 220304444, USA bell@gmu.edu, hlv@gmu.edu ABSRAC
More informationCascaded Estimation Architecture for Integration of FootMounted Inertial Sensors
Cascaded Estimation Architecture for Integration of FootMounted Inertial Sensors Bernhard Krach and Patrick Robertson German Aerospace Center (DLR) Institute of Communications and Navigation Folie 1 Sensor
More informationRoundoff Noise in IIR Digital Filters
Chapter 16 Roundoff Noise in IIR Digital Filters It will not be possible in this brief chapter to discuss all forms of IIR (infinite impulse response) digital filters and how quantization takes place in
More informationNuclear Magnetic Resonance
Nuclear Magnetic Resonance Introduction Atomic magnetism Nuclear magnetic resonance refers to the behaviour of atomic nuclei in the presence of a magnetic field. The first principle required to understand
More informationTTT4120 Digital Signal Processing Suggested Solution to Exam Fall 2008
Norwegian University of Science and Technology Department of Electronics and Telecommunications TTT40 Digital Signal Processing Suggested Solution to Exam Fall 008 Problem (a) The input and the inputoutput
More informationMaximum likelihood estimation of mean reverting processes
Maximum likelihood estimation of mean reverting processes José Carlos García Franco Onward, Inc. jcpollo@onwardinc.com Abstract Mean reverting processes are frequently used models in real options. For
More informationGyroscope Angular Rate Sensor Three main types
Gyroscopes Gyroscope Angular Rate Sensor Three main types Spinning Mass Optical Ring Laser Gyros Fiber Optic Gyros Vibratory Coriolis Effect devices MEMS 4 March 2011 EE 570: Location and Navigation: Theory
More informationAUTOCORRELATED RESIDUALS OF ROBUST REGRESSION
AUTOCORRELATED RESIDUALS OF ROBUST REGRESSION Jan Kalina Abstract The work is devoted to the DurbinWatson test for robust linear regression methods. First we explain consequences of the autocorrelation
More informationDigital Modulation. David Tipper. Department of Information Science and Telecommunications University of Pittsburgh. Typical Communication System
Digital Modulation David Tipper Associate Professor Department of Information Science and Telecommunications University of Pittsburgh http://www.tele.pitt.edu/tipper.html Typical Communication System Source
More informationEDUMECH Mechatronic Instructional Systems. Ball on Beam System
EDUMECH Mechatronic Instructional Systems Ball on Beam System Product of Shandor Motion Systems Written by Robert Hirsch Ph.D. 9989 All Rights Reserved. 999 Shandor Motion Systems, Ball on Beam Instructional
More informationEqualization/Compensation of Transmission Media. Channel (copper or fiber)
Equalization/Compensation of Transmission Media Channel (copper or fiber) 1 Optical Receiver Block Diagram O E TIA LA EQ CDR DMUX 18 dbm 10 µa 10 mv pp 400 mv pp 2 Copper Cable Model Copper Cable 4foot
More informationJPEG compression of monochrome 2Dbarcode images using DCT coefficient distributions
Edith Cowan University Research Online ECU Publications Pre. JPEG compression of monochrome Dbarcode images using DCT coefficient distributions Keng Teong Tan Hong Kong Baptist University Douglas Chai
More informationMath 7 Elementary Linear Algebra MARKOV CHAINS. Definition of Experiment An experiment is an activity with a definite, observable outcome.
T. Henson I. Basic Concepts from Probability Examples of experiments: Math 7 Elementary Linear Algebra MARKOV CHAINS Definition of Experiment An experiment is an activity with a definite, observable outcome.
More informationEpipolar Geometry. Readings: See Sections 10.1 and 15.6 of Forsyth and Ponce. Right Image. Left Image. e(p ) Epipolar Lines. e(q ) q R.
Epipolar Geometry We consider two perspective images of a scene as taken from a stereo pair of cameras (or equivalently, assume the scene is rigid and imaged with a single camera from two different locations).
More informationFixedPoint Arithmetic
FixedPoint Arithmetic FixedPoint Notation A Kbit fixedpoint number can be interpreted as either: an integer (i.e., 20645) a fractional number (i.e., 0.75) 2 1 Integer FixedPoint Representation Nbit
More informationSpectrum Characteristics of Ternary PSK Signals Amplified with NonLinear Amplifiers
Spectrum Characteristics of Ternary PSK Signals Amplified with NonLinear Amplifiers HIDEYUKI TORII and MAKOTO NAKAMURA Department of Network Engineering Kanagawa Institute of Technology 100 Shimoogino,
More informationAdaptive DemandForecasting Approach based on Principal Components Timeseries an application of datamining technique to detection of market movement
Adaptive DemandForecasting Approach based on Principal Components Timeseries an application of datamining technique to detection of market movement Toshio Sugihara Abstract In this study, an adaptive
More informationAdaptive Variable Step Size in LMS Algorithm Using Evolutionary Programming: VSSLMSEV
Adaptive Variable Step Size in LMS Algorithm Using Evolutionary Programming: VSSLMSEV Ajjaiah H.B.M Research scholar Jyothi institute of Technology Bangalore, 560006, India Prabhakar V Hunagund Dept.of
More informationAn Evolutionary Computation Embedded IIR LMS Algorithm
An Evolutionary Computation Embedded IIR LMS Algorithm Deependra Talla 1, Sathyanarayan S. Rao 2 and Lizy K. John 1 deepu@ece.utexas.edu, rao@ece.vill.edu, ljohn@ece.utexas.edu 1 Department of Electrical
More informationA SIMULATION STUDY ON SPACETIME EQUALIZATION FOR MOBILE BROADBAND COMMUNICATION IN AN INDUSTRIAL INDOOR ENVIRONMENT
A SIMULATION STUDY ON SPACETIME EQUALIZATION FOR MOBILE BROADBAND COMMUNICATION IN AN INDUSTRIAL INDOOR ENVIRONMENT U. Trautwein, G. Sommerkorn, R. S. Thomä FG EMT, Ilmenau University of Technology P.O.B.
More informationAnalog to Digital, A/D, Digital to Analog, D/A Converters. An electronic circuit to convert the analog voltage to a digital computer value
Analog to Digital, A/D, Digital to Analog, D/A Converters An electronic circuit to convert the analog voltage to a digital computer value Best understood by understanding Digital to Analog first. A fundamental
More informationMOBILE ROBOT TRACKING OF PREPLANNED PATHS. Department of Computer Science, York University, Heslington, York, Y010 5DD, UK (email:nep@cs.york.ac.
MOBILE ROBOT TRACKING OF PREPLANNED PATHS N. E. Pears Department of Computer Science, York University, Heslington, York, Y010 5DD, UK (email:nep@cs.york.ac.uk) 1 Abstract A method of mobile robot steering
More informationThe CUSUM algorithm a small review. Pierre Granjon
The CUSUM algorithm a small review Pierre Granjon June, 1 Contents 1 The CUSUM algorithm 1.1 Algorithm............................... 1.1.1 The problem......................... 1.1. The different steps......................
More informationBasics on Digital Signal Processing
Basics on Digital Signal Processing Introduction Vassilis Anastassopoulos Electronics Laboratory, Physics Department, University of Patras Outline of the Course 1. Introduction (sampling quantization)
More informationConditional guidance as a response to supply uncertainty
1 Conditional guidance as a response to supply uncertainty Appendix to the speech given by Ben Broadbent, External Member of the Monetary Policy Committee, Bank of England At the London Business School,
More informationLEASTMEANSQUARE ADAPTIVE FILTERS
LEASTMEANSQUARE ADAPTIVE FILTERS LEASTMEANSQUARE ADAPTIVE FILTERS Edited by S. Haykin and B. Widrow A JOHN WILEY & SONS, INC. PUBLICATION This book is printed on acidfree paper. Copyright q 2003 by
More informationComponent Ordering in Independent Component Analysis Based on Data Power
Component Ordering in Independent Component Analysis Based on Data Power Anne Hendrikse Raymond Veldhuis University of Twente University of Twente Fac. EEMCS, Signals and Systems Group Fac. EEMCS, Signals
More informationHFTA010.0: Physical Layer Performance: Testing the Bit Error Ratio (BER)
HFTA010.0: Physical Layer Performance: Testing the Bit Error Ratio (BER) This technical article first appeared in Lightwave Magazine, September, 2004, Explaining those BER testing mysteries. The ultimate
More informationGPSFREE TERRAINBASED VEHICLE TRACKING PERFORMANCE AS A FUNCTION OF INERTIAL SENSOR CHARACTERISTICS
GPSFREE TERRAINBASED VEHICLE TRACKING PERFORMANCE AS A FUNCTION OF INERTIAL SENSOR CHARACTERISTICS Kshitij Jerath and Sean N. Brennan Department of Mechanical and Nuclear Engineering The Pennsylvania
More informationA RegimeSwitching Model for Electricity Spot Prices. Gero Schindlmayr EnBW Trading GmbH g.schindlmayr@enbw.com
A RegimeSwitching Model for Electricity Spot Prices Gero Schindlmayr EnBW Trading GmbH g.schindlmayr@enbw.com May 31, 25 A RegimeSwitching Model for Electricity Spot Prices Abstract Electricity markets
More informationComparing Dual Microphone System with Different Algorithms and Distances between Microphones.
Master Thesis Electrical Engineering May 2013 Comparing Dual Microphone System with Different Algorithms and Distances between Microphones. Ariful Islam Shafinaz Shahjahan Nitu This thesis is presented
More informationNonlinear Iterative Partial Least Squares Method
Numerical Methods for Determining Principal Component Analysis Abstract Factors Béchu, S., RichardPlouet, M., Fernandez, V., Walton, J., and Fairley, N. (2016) Developments in numerical treatments for
More informationDesign and Development of Noise Cancellation System for Android Mobile Phones
Abstract Design and Development of Noise Cancellation System for Android Mobile Phones Ravikanth N. 1, Sanket Dessai 2 1M.Sc. [Engg.] Student, 2Assistant Professor Department of Computer Engineering,
More informationAdaptive Notch Filter for EEG Signals Based on the LMS Algorithm with Variable StepSize Parameter
5 Conference on Information Sciences and Systems, The Johns Hopkins University, March 16 18, 5 Adaptive Notch Filter for EEG Signals Based on the LMS Algorithm with Variable StepSize Parameter Daniel
More informationImage Compression through DCT and Huffman Coding Technique
International Journal of Current Engineering and Technology EISSN 2277 4106, PISSN 2347 5161 2015 INPRESSCO, All Rights Reserved Available at http://inpressco.com/category/ijcet Research Article Rahul
More informationImproving highend active speaker performance using digital active crossover filters
Improving highend active speaker performance using digital active crossover filters Dave Brotton  May 21, 2013 Consumer requirement for fewer wires connecting their home entertainment systems is driving
More informationA PCBASED TIME INTERVAL COUNTER WITH 200 PS RESOLUTION
35'th Annual Precise Time and Time Interval (PTTI) Systems and Applications Meeting San Diego, December 24, 2003 A PCBASED TIME INTERVAL COUNTER WITH 200 PS RESOLUTION Józef Kalisz and Ryszard Szplet
More informationThe QOOL Algorithm for fast Online Optimization of Multiple Degree of Freedom Robot Locomotion
The QOOL Algorithm for fast Online Optimization of Multiple Degree of Freedom Robot Locomotion Daniel Marbach January 31th, 2005 Swiss Federal Institute of Technology at Lausanne Daniel.Marbach@epfl.ch
More information