form kalman filtering and smoothing
Tài liệu Kalman Filtering and Neural Networks - Chapter 1: KALMAN FILTERS doc
... Wiley, 1986 [3] M.S Grewal and A.P Andrews, Kalman Filtering: Theory and Practice Englewood Cliffs, NJ: Prentice-Hall, 1993 [4] H.L Van Trees, Detection, Estimation, and Modulation Theory, Part ... and time updates of Eqs (1.37)–(1.41) is the information formulation of the Kalman filter The information filter is distinguished from the basic Kalman filter in that it propagates the inverse of ... forward filtering, backward filtering, and smoothing matrix Pkf produced by the Kalman filter, which is naturally due to the fact that smoothing uses additional information contained in the future...
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Tài liệu Kalman Filtering and Neural Networks P2 doc
... PARAMETER-BASED KALMAN FILTER TRAINING methods that are claimed to exhibit superior capabilities in terms of training speed, mapping accuracy, generalization, and overall performance relative to standard ... second-order methods, weight updates using standard backpropagation can either be performed in batch or instance-by-instance mode The extended Kalman filter (EKF) forms the basis of a second-order neural ... second-order information about the training problem is also maintained and evolved The global EKF (GEKF) training algorithm was introduced by Singhal and Wu [2] in the late 1980s, and has served...
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Tài liệu Kalman Filtering and Neural Networks P3 doc
... moving right and up; square moving right and down; triangle moving right and up; circle moving right and down; square moving right and up; triangle moving right and down Training was performed in ... Cortex, 1, 1–47 (1991) [2] J.S Lund, Q Wu and J.B Levitt, ‘‘Visual cortex cell types and connections’’, in M.A Arbib, Ed., Handbook of Brain Theory and Neural Networks, Cambridge, MA: MIT Press, ... Lomber, P Girard and J Bullier, ´ ‘‘Cortical feedback improves discrimination between figure and background by V1, V2 and V3 neurons’’, Nature, 394, 784–787 (1998) [4] M.W Oram and D.I Perrett,...
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Tài liệu Kalman Filtering and Neural Networks P4 doc
... in D.A Rand and L.S Young, Eds Dynamical Systems and Turbulence, Warwick 1980, Lecture Notes in Mathematics Vol 898 1981, p 230 Berlin: Springer-Verlag [6] A.M Fraser, ‘‘Information and entropy ... used for performance evaluation, and Figure 4.6a shows one-step performance of the network on a short portion of the test data It is indeed difficult to distinguish between the actual and predicted ... x2 ðk þ 1Þ ¼ 1:0 þ mfx1 ðkÞ þ x2 ðkÞ cos½mðkÞg; ð4:6Þ where x1 and x2 are the real and imaginary components, respectively, of x and the parameter m is carefully chosen to be 0.7 so that the produced...
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Tài liệu Kalman Filtering and Neural Networks P5 pdf
... @x xk ^ D ð5:9Þ and where Rv and Rn are the covariances of vk and nk , respectively 5.2.2 EKF–Weight Estimation As proposed initially in [30], and further developed in [31] and [32], the EKF ... ð5:63Þ ^ where xkjN and pkjN are defined as the conditional mean and variance of xk ^ ^ kjN given w and all the data, fyk gN The terms xÀ and pÀ are the conditional kjN mean and variance of xÀ ... kjk 2sv 148 DUAL EXTENDED KALMAN FILTER METHODS The state Kalman filter is then modified by adding a final zero element to the vectors B and C (see Eqs (5.38) and (5.39)), and the linearized state...
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Tài liệu Kalman Filtering and Neural Networks P6 pdf
... normal (linear) Kalman smoother, in the EKS, the error covariances for the state estimates and the Kalman gain matrices Figure 6.3 Illustration of the information used in extended Kalman smoothing ... of f and g and the noise covariances Given observations of the (no longer hidden) states and outputs, f and g can be obtained as the solution to a possibly nonlinear regression problem, and the ... engineering and the other in statistics – form the basis of modern techniques in state estimation and model learning The Kalman filter, introduced by Kalman and Bucy in 1961 [1], was developed in...
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Tài liệu Kalman Filtering and Neural Networks P7 pptx
... ð7:29Þ n and where Rv and Rn are the covariances of vk and nk , respectively The noise means are denoted by n ¼ E½n and v ¼ E½v, and are usually assumed to equal zero 228 THE UNSCENTED KALMAN ... position and velocity, and top and _ _ _ bottom pendulum angle and angular velocity, x ¼ ½x; x; y1 ; y1 ; y2 ; y2 The system parameters correspond to the length and mass of each pendulum, and the ... unscented transformation Unscented Transformation The unscented transformation (UT) is a method for calculating the statistics of a random variable which undergoes a nonlinear transformation [3]...
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Tài liệu Kalman Filtering and Neural Networks - Chapter 4: CHAOTIC DYNAMICS pdf
... in D.A Rand and L.S Young, Eds Dynamical Systems and Turbulence, Warwick 1980, Lecture Notes in Mathematics Vol 898 1981, p 230 Berlin: Springer-Verlag [6] A.M Fraser, ‘‘Information and entropy ... used for performance evaluation, and Figure 4.6a shows one-step performance of the network on a short portion of the test data It is indeed difficult to distinguish between the actual and predicted ... x2 ðk þ 1Þ ¼ 1:0 þ mfx1 ðkÞ þ x2 ðkÞ cos½mðkÞg; ð4:6Þ where x1 and x2 are the real and imaginary components, respectively, of x and the parameter m is carefully chosen to be 0.7 so that the produced...
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Tài liệu Kalman Filtering and Neural Networks - Chapter 5: DUAL EXTENDED KALMAN FILTER METHODS docx
... @x xk ^ D ð5:9Þ and where Rv and Rn are the covariances of vk and nk , respectively 5.2.2 EKF–Weight Estimation As proposed initially in [30], and further developed in [31] and [32], the EKF ... ð5:63Þ ^ where xkjN and pkjN are defined as the conditional mean and variance of xk ^ ^ kjN given w and all the data, fyk gN The terms xÀ and pÀ are the conditional kjN mean and variance of xÀ ... kjk 2sv 148 DUAL EXTENDED KALMAN FILTER METHODS The state Kalman filter is then modified by adding a final zero element to the vectors B and C (see Eqs (5.38) and (5.39)), and the linearized state...
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Tài liệu Kalman Filtering and Neural Networks - Chapter 6: LEARNING NONLINEAR DYNAMICAL SYSTEMS USING THE EXPECTATION– MAXIMIZATION ALGORITHM doc
... normal (linear) Kalman smoother, in the EKS, the error covariances for the state estimates and the Kalman gain matrices Figure 6.3 Illustration of the information used in extended Kalman smoothing ... of f and g and the noise covariances Given observations of the (no longer hidden) states and outputs, f and g can be obtained as the solution to a possibly nonlinear regression problem, and the ... engineering and the other in statistics – form the basis of modern techniques in state estimation and model learning The Kalman filter, introduced by Kalman and Bucy in 1961 [1], was developed in...
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Tài liệu Kalman Filtering and Neural Networks - Chapter VII: THE UNSCENTED KALMAN FILTER pdf
... ð7:29Þ n and where Rv and Rn are the covariances of vk and nk , respectively The noise means are denoted by n ¼ E½n and v ¼ E½v, and are usually assumed to equal zero 228 THE UNSCENTED KALMAN ... position and velocity, and top and _ _ _ bottom pendulum angle and angular velocity, x ¼ ½x; x; y1 ; y1 ; y2 ; y2 The system parameters correspond to the length and mass of each pendulum, and the ... unscented transformation Unscented Transformation The unscented transformation (UT) is a method for calculating the statistics of a random variable which undergoes a nonlinear transformation [3]...
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Tài liệu Kalman Filtering and Neural Networks - Contents pptx
... Cherkassky and Mulier = LEARNING FROM DATA: Concepts, Theory, and Methods Diamantaras and Kung = PRINCIPAL COMPONENT NEURAL NETWORKS: Theory and Applications Haykin = KALMAN FILTERING AND NEURAL ... 137 Joint extended Kalman filter, 125 ‘‘Joseph’’ version of the covariance update equation, Kalman filter, 1, 5, 177 Kalman filter, information formulation of, 13 Kalman gain, Kalman gain matrix, ... ALPHA-STABLE DISTRIBUTIONS AND APPLICATIONS Passino and Burgess = STABILITY ANALYSIS OF DISCRETE EVENT SYSTEMS Sanchez-Pena and Sznaler = ROBUST SYSTEMS THEORY AND ´ ˜ APPLICATIONS Sandberg, Lo, Fancourt,...
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Tài liệu Tracking and Kalman filtering made easy P1 doc
... Company.) WHY TRACKING AND PREDICTION ARE NEEDED IN A RADAR Figure 1.1-3 Fan-beam track-while-scan S-band and X-band radar antennas emplaced on tower at Prince William Sound Alaska (S-band antenna on ... book for the determination of artillery and mortar launch sites are the Firefinder AN=TPQ-36 and AN=TPQ-37 radars of Figures 1.1-15 and 1.1-16 [1] An air and surface–ship surveillance radar that ... g and h as shall be seen later (Some actually are identical) For some of these filters g and h depend on n This is the case for the Kalman filter It is worthwhile emphasizing that (1.2-11a) and...
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Tài liệu Tracking and Kalman filtering made easy P2 docx
... Tracking Filters: Steady-State Filtering and Smoothing Performance,’’ IEEE Transactions on Aerospace and Electronic Systems, Vol AES-16, No 6, November 1980 # 1980 IEEE.) 96 KALMAN FILTER Figure 2.10-2 ... for h for Singer g–h–k Kalman filter (After Fitzgerald, R J., ‘‘Simple Tracking Filters: Steady-State Filtering and Smoothing Performance,’’ IEEE Transactions on Aerospace and Electronic Systems, ... steady-state Singer g–h–k Kalman filter (After Fitzgerald, R J, ‘‘Simple Tracking Filters: Steady-State Filtering and Smoothing Performance,’’ IEEE Transactions on Aerospace and Electronic Systems,...
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Tài liệu Tracking and Kalman filtering made easy P3 pdf
... CHIRP WAVEFORM The chirp waveform is one of the most extensively used waveforms for rader systems [57, 58, 70] We shall first describe chirp waveform, pulse compression, and match filtering and then ... such a waveform on tracking accuracy 3.5.1 Chirp Waveform, Pulse Compression, Match Filtering of Chirp Waveform, and Pulse Compression Figure 3.5-1 shows the typical chirp pulse waveform It consists ... 12, and 14 form the returns from such a constant-velocity target, the target having a velocity in the band between 28 and 35 knots The rule used for declaring a target present in a Doppler band...
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Tài liệu Tracking and Kalman filtering made easy P4 docx
... transformation F in general and on two other forms of this transformation, the Givens and Householder, are given in respectively Chapters 10 and 12 4.4 ADAPTIVE NULLING, THE ORTHONORMAL TRANSFORMATION, ... this case M, T, and È all become a function of time (or equivalently n) and are replaced by M n and T n and Èðt n ; t nÀ1 Þ, respectively; see pages 172, 173, and 182 of reference and Chapter 15 ... x and x As a result our à determination of X n;n degenerates into finding the x and x that minimize " 01 and " ; specifically the x1 and x2 that minimizes ð" 01 Þ þ ð" 02 Þ ORTHONORMAL TRANSFORMATION...
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Tài liệu Tracking and Kalman filtering made easy P5 ppt
... SYSTEMATIC AND RANDOM ESTIMATION ERRORS magnitude as was done in Section 1.2.4.5; see (1.2-22) and (1.2-23) One way of doing this is described in the next section 5.10 BALANCING SYSTEMATIC AND RANDOM ... measured and not its derivatives, then Y n ¼ MX n þ N n ð5:4-3Þ where because range is the only measurement M ¼ ½1 0 0 ð5:4-3aÞ and Y n and N n are  matrices given by Yn ¼ ½ yn and N n ¼ ... used on the matrices T and X n above because we shall shortly develop an alternate, more standard form for the process state vector that uses different expressions for T and X n :) It is now a...
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