Tensor Kalman Filter and Its Applications

Chang, Shih Yu; Wu, Hsiao-Chun

doi:10.1109/tkde.2022.3169129

Cited by 12 publications

(5 citation statements)

References 44 publications

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“…At this, point the igniting is at a high rate (FOSC), this rate is rather high (> 40 kHz) which is beyond the audio noise causation igniting. Pleasing Fpwm as sampling period d, to make a symmetric PWM arrangement at the center and total harmonic distortion (THD) will be smaller, d is taken as (9) [21], [22].…”

Section: Resultsmentioning

confidence: 99%

Igniting transistor to control three-phase alternating current motor servo

Rustam,

Ghea Mahardika,

Devira Ramady

et al. 2024

TELKOMNIKA

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The background of research try to use an open loop system, without feedback, by building torque in the target position. Theoretical basis manages the turning round of servo motor change direct currents to alternating currents by adjusting the rate input used. Methodology in simple terms, the flowchart of code processing from igniting transistors to managing the turning round of a three-phase alternating current (AC) servo motor. The result of the transistor ignition time with room phasor pulse width modulation (PWM) to set the ignition of a three-phase AC servo motor in the process of igniting as ordered, for manage position only igniting transistors in target position, and building torque at there. Discussion, igniting transistors to manage the turning round of servo motors, allows motion of servo motor, allows motion of servo motor to be added faster, accurately, soft, and steady. In conclusion, in this case the researcher uses it more specifically by turning on the transistor only at the target position, so that the torque generated is only at the target position, the servo motor motion from the start position immediately ends at the target position. Suggestions, this system igniting can be applied at a motion high-velocity system like a missile system controlled.

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Section: Resultsmentioning

confidence: 99%

Igniting transistor to control three-phase alternating current motor servo

Rustam,

Ghea Mahardika,

Devira Ramady

et al. 2024

TELKOMNIKA

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“…Tensors or multidimensional arrays are functions of three or more indices i, j, k,⋯ , which are mathematical objects generalized from matrices (two-dimensional arrays) and vectors (one-dimensional arrays). The development of new tensor theories and tensor-related algorithms has recently drawn the attention of the signal-processing society [1][2][3], big-data analytics [4][5][6], and system design [7,8] as multirelational characterization among different attributes and objects is crucial for applications of modern signal and system analysis. It is well-known that the z-transform has been applied as an indispensable tool for the analysis and design of discretetime signals and systems.…”

Section: Introductionmentioning

confidence: 99%

“…The existing z-transform is actually a scalar function. Recently, the multiinput multioutput (MIMO) systems involving multirelational signals have been emerging as the most generalized model in practice [1][2][3][4][5][6]. Our preceding work for characterizing such a MIMO system is to build a corresponding "transform tensor," each of whose entries turns out to be the individual z-transform of a discrete-time impulse response sequence [8].…”

Section: Introductionmentioning

confidence: 99%

Tensor z‐Transform

Chang,

2024

Journal of Applied Mathematics

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The multi-input multioutput (MIMO) systems involving multirelational signals generated from distributed sources have been emerging as the most generalized model in practice. The existing work for characterizing such a MIMO system is to build a corresponding transform tensor, each of whose entries turns out to be the individual z-transform of a discrete-time impulse response sequence. However, when a MIMO system has a global feedback mechanism, which also involves multirelational signals, the aforementioned individual z-transforms of the overall transfer tensor are quite difficult to formulate. Therefore, a new mathematical framework to govern both feedforward and feedback MIMO systems is in crucial demand. In this work, we define the tensor z-transform to characterize a MIMO system involving multirelational signals as a whole rather than the individual entries separately, which is a novel concept for system analysis. To do so, we extend Cauchy’s integral formula and Cauchy’s residue theorem from scalars to arbitrary-dimensional tensors, and then, to apply these new mathematical tools, we establish to undertake the inverse tensor z-transform and approximate the corresponding discrete-time tensor sequences. Our proposed new tensor z-transform in this work can be applied to design digital tensor filters including infinite-impulse-response (IIR) tensor filters (involving global feedback mechanisms) and finite-impulse-response (FIR) tensor filters. Finally, numerical evaluations are presented to demonstrate certain interesting phenomena of the new tensor z-transform.

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“…Kalman filtering is a very important estimation method to estimate the unknown variables from the measured values [1], and the standard discrete Kalman filtering model (SKF) was first proposed by Kalman and applied to the integrated its output; in other words, some information about the system model is likely to be implicit in the measurement output, which then naturally affects the filtering results when the system model parameters are not accurate enough [2]. Accurate noise parameters are essential for Kalman filters to obtain optimal estimates.…”

Section: Introductionmentioning

confidence: 99%

An adaptive Kalman filtering algorithm based on maximum likelihood estimation

Wang

Cheng

et al. 2023

Meas. Sci. Technol.

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Traditional adaptive Kalman filtering algorithms based on innovation are often used to solve the problem of reduced or even divergent filtering estimation accuracy under abnormal measurement noise. However, these algorithms are usually characterized by difficulties in selecting window width and window weight, which cannot simultaneously take into account the filtering tracking sensitivity and filtering accuracy.In this paper, an adaptive Kalman filtering algorithm based on maximum likelihood estimation is proposed, which determines the window size and window weight size under the kth moment by designing a window adaptive selection function and a weight function to change the innovation covariance at the kth moment, which in turn changes the measurement noise covariance at the kth moment, so that the measurement noise covariance is no longer a fixed single value, but can better adapt to the changes in the environment, reflecting good adaptive characteristics. The simulation results based on GPS/SINS integrated navigation system demonstrate that the new filtering algorithm of this paper reflects higher filtering accuracy and stronger robustness under the carrier in multiple motion states and accompanied by time-varying measurement noise interference. Compared with the traditional adaptive Kalman filtering algorithm based on innovation, the accuracy of attitude angle estimation error under this method is improved by 119.97%; the accuracy of velocity estimation error is improved by 264.42%; the accuracy of position estimation error is improved by 156.69%.

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Tensor Kalman Filter and Its Applications

Cited by 12 publications

References 44 publications

Igniting transistor to control three-phase alternating current motor servo

Igniting transistor to control three-phase alternating current motor servo

Tensor z‐Transform

An adaptive Kalman filtering algorithm based on maximum likelihood estimation

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