A filter for on-line estimation of spectral content

Mallory, Gregory J. W.; Doraiswami, R.

doi:10.1109/19.816112

Cited by 10 publications

(6 citation statements)

References 9 publications

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“…(b) Piecewise linear Box-Jenkins model: As the analysis, design, estimation, identification, and control of a nonlinear system are not mathematically intractable; a linear parameter-varying (LPV) model is used to approximate the nonlinear system [8][9][10][11][12]. Its output is a sum of the signal (true output), the unknown stochastic, disturbance and measurement noise.…”

Section: Main Contributions Of This Papermentioning

confidence: 99%

Kalman-filter-based Accurate Trajectory Tracking and Fault-Tolerant Control of Quadrotor

Doraiswami¹,

Cheded²,

Brinkmann³

2021

International Conference of Control, Dynamic Systems, and Robotics

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A Kalman filter(KF)-based feedforward-feedback controller is proposed using the internal model(IM)-principle for accurate tracking of a desired trajectory, and fault-tolerant control of a quadrotor, despite input and output sensor measurements being affected by unknown disturbances, measurement noise and model perturbations. The quadrotor model is unstable and nonlinear. Its input is a nonlinear function of the roll, pitch and yaw, and its output is its position in the ground-fixed coordinates. The quadrotor is subject to model uncertainties, disturbances including wind gusts, aerodynamic drags, gravitational load, and Coriolis forces, and the inputs and the outputs are affected by unknown stochastic disturbances and measurement noise. Predictive analytics is used to estimate the true input by exploiting its smoothness and the randomness of the noisy input. The nonlinear system is better approximated using the linear parameter-varying (LPV) model described by piecewise-linear Box-Jenkins model at each operating point, than by conventional approximation techniques. The system and the associated Kalman filter (KF) are identified using novel emulator-generated data by minimizing the KF residual so that identified models are accurate, consistent and reliable. The proposed tracking, fault-tolerant control, and design of the KF residuals-based design of soft sensor were successfully evaluated on a simulated laboratory-scale quadrotor.

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Section: Main Contributions Of This Papermentioning

confidence: 99%

Kalman-filter-based Accurate Trajectory Tracking and Fault-Tolerant Control of Quadrotor

Doraiswami¹,

Cheded²,

Brinkmann³

2021

International Conference of Control, Dynamic Systems, and Robotics

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“…The inaccessible input

u_{0} false(k false)

is assumed to be a smooth input such as a sum of sinusoids, relatively to

u_{v} false(k false)

which exhibits random fluctuations, and

u_{0} false(k false)

, is extracted from

u false(k false)

using the frequency‐domain approach by exploiting their spectral characteristics such as the smooth waveform

u_{0} false(k false)

having a smooth line‐spectra, while the noisy input

u_{v} false(k false)

having a wildly‐varying spectra. The estimated true input, denoted by

u_{est}

, is derived from the accessible input

u false(k false)

using a predictive analytics approach, involving an artificial intelligence or machine learning algorithm [12–14 ]. The estimated input

u_{est}

then replaces the corrupted input

u false(t false)

in the rest of this Letter.…”

Section: Predictive Analytics Approachmentioning

confidence: 99%

“…The augmented state‐space model

()(, A, B, {bold-italicE}_{w}, C)

termed as Box–Jenkins model [8, 14 ] is given by

\begin{matrix} right leftthickmathspace.5em \\ bold-italicx (k + 1) & = bold-italicA bold-italicx (k) + bold-italicB u_{normalest} (k) + E_{w} u_{w} (k) \\ y (k) & = bold-italicC bold-italicx (k) + v (k) \end{matrix}

where

x = (][, \begin{matrix} 1em4pt \\ {bold-italicx}_{normals} \\ {bold-italicx}_{w} \end{matrix}) \in R^{n}

A = (][, \begin{matrix} 1em4pt \\ {bold-italicA}_{normals} & 0 \\ 0 & {bold-italicA}_{w} \end{matrix}) \in R^{n \times n}

is a transition matrix;

B = (][, \begin{matrix} 1em4pt \\ {bold-italicB}_{s} \\ 0 \end{matrix}) \in R^{n x 1}

is the input vector,

{bold-italicE}_{w} = (][, \begin{matrix} 1em4pt \\ 0 \\ {bold-italicB}_{w} \end{matrix}) \in R^{n \times 1}

is the disturbance entry vector and

C = (][, \begin{matrix} 1em4pt \\ {bold-italicC}_{s} & bold-i... \end{matrix})

…”

Section: Disturbance Modelmentioning

confidence: 99%

New approach to model‐order selection

Doraiswami

Cheded

2020

Electron. lett.

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A new, direct and practical scheme is proposed for determining the model orders of a system, its signal and disturbance using key properties of Kalman filter (KF). Unlike conventional methods, it enjoys the unique property of being both necessary and sufficient. The system is described by the Box–Jenkins model, whose accessible input and output are corrupted by unknown zero‐mean white Gaussian‐distributed disturbances and measurement noise. The signal and disturbance are outputs of asymptotically‐stable linear time‐invariant systems driven by an inaccessible input and a zero‐mean white Gaussian noise process, respectively. Predictive analytics is used to estimate the input by exploiting its smoothness and the randomness of the noisy input. The system, signal, and disturbance models and their associated KFs are identified for various selected model orders by minimising the KF residuals so that these become zero‐mean white noise processes. The selected model‐order corresponds to the minimum‐variance residual. Equivalently, the minimum order is selected when the number of poles or the output estimates of the identified models are all identical for all orders equal to, or exceeding the minimal order. The scheme is successfully evaluated and shown to outperform the commonly‐used but only sufficient Akaike Information Criterion.

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“…However, in practice the white noise assumption may not hold and the estimates generally suffer from bias. Further as the spectrum of the signal and the corrupting noise is generally unknown and may have their spectra practically coincident, a twostep approach given by Mallory and Doraiswami [15] was used to estimate the LPC, h. It should be emphasized that through this two-step approach, the estimate of h captures only the information pertaining to the signal and not the noise. Using the direct approach, it may be complicated to include both filtering while estimating the parameter recursively, especially when the spectra of the signal and the noise are unknown.…”

Section: Estimation Of the Circuit Parametersmentioning

confidence: 99%

Factors affecting the stimulus artifact tail in surface-recorded somatosensory-evoked potentials

2006

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Surface-recorded somatosensory-evoked potentials (SEPs) are neural signals elicited by an external stimulus. In the case of electrically induced SEPs, the artifact generated by the stimulation process can severely distort the signal. In some cases, the artifact tail often lasts well into the initiation of the SEP making the determination of absolute latency very difficult. In this work, a new approach was taken to identify factors that affect the tail of the artifact. The methodology adopted was the development of a lumped electrical circuit model of the artifact generation process. While the modeling of the instrumentation hardware is relatively simple, this is not the case with tissue and electrode/skin interface effects. Consequently, this paper describes a novel tissue modeling approach that uses an autoregressive moving average (ARMA) parametric technique and an artificial neural network (ANN) to estimate tissue parameters from experimental data. This coupled with an estimation of the stimulation electrode-skin impedance completes the lumped circuit model. Simulink (The Mathworks Inc.) was used to evaluate the model under several different conditions. These results show that both the stimulation electrode-skin interface impedance and nature of the body tissue directly under the recording electrodes have a profound effect on the appearance of the stimulus artifact tail. This was verified by experimentally recorded data obtained from the median nerve using surface electrodes. Conclusions drawn from this work include that stimulation electrodes with low series capacitance should be used whenever possible to minimize the duration of the artifact tail.

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A filter for on-line estimation of spectral content

Cited by 10 publications

References 9 publications

Kalman-filter-based Accurate Trajectory Tracking and Fault-Tolerant Control of Quadrotor

Kalman-filter-based Accurate Trajectory Tracking and Fault-Tolerant Control of Quadrotor

New approach to model‐order selection

Factors affecting the stimulus artifact tail in surface-recorded somatosensory-evoked potentials

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