On the parametrization and design of an extended Kalman filter frequency tracker

Bittanti, Sergio; Savaresi, Sergio M.

doi:10.1109/9.880631

Cited by 191 publications

(99 citation statements)

References 16 publications

(43 reference statements)

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“…The resulting model was used by, among others, Bittanti and Savaresi (2000) and La Scala and Bitmead (1996). At each time step, reparameterize so that φ k = 0 by rotating…”

Section: Instant Phasor Modelmentioning

confidence: 99%

“…These models can be used for frequency tracking in any nonlinear filtering algorithm. Approaches used in the literature include the ekf, pf, and rbpf (Bittanti and Savaresi, 2000;Kim et al, 2008;La Scala and Bitmead, 1996;Ng et al, 2009), see Section 2.4. The focus here, however, is on the Rao-Blackwellized point mass filter (rbpmf).…”

Section: The Rbpmf For Frequency Trackingmentioning

confidence: 99%

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Frequency Tracking for Speed Estimation

Lindfors¹

2018

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Estimating the frequency of a periodic signal, or tracking the time-varying frequency of an almost periodic signal, is an important problem that is well studied in literature. This thesis focuses on two subproblems where contributions can be made to the existing theory: frequency tracking methods and measurements containing outliers.Maximum-likelihood-based frequency estimation methods are studied, focusing on methods which can handle outliers in the measurements. Katkovnik's frequency estimation method is generalized to real and harmonic signals, and a new method based on expectation-maximization is proposed. The methods are compared in a simulation study in which the measurements contain outliers. The proposed methods are compared with the standard periodogram method.Recursive Bayesian methods for frequency tracking are studied, focusing on the Rao-Blackwellized point mass filter (rbpmf). Two reformulations of the rbpmf aiming to reduce computational costs are proposed. Furthermore, the technique of variational approximate Rao-Blackwellization is proposed, which allows usage of a Student's t distributed measurement noise model. This enables recursive frequency tracking methods to handle outliers using heavy-tailed noise models in Rao-Blackwellized filters such as the rbpmf. A simulation study illustrates the performance of the methods when outliers occur in the measurement noise.The framework above is applied to and studied in detail in two applications. The first application is on frequency tracking of engine sound. Microphone measurements are used to track the frequency of Doppler-shifted variants of the engine sound of a vehicle moving through an area. These estimates can be used to compute the speed of the vehicle. Periodogram-based methods and the rbpmf are evaluated on simulated and experimental data. The results indicate that the rbpmf has lower rmse than periodogram-based methods when tracking fast changes in the frequency.The second application relates to frequency tracking of wheel vibrations, where a car has been equipped with an accelerometer. The accelerometer measurements are used to track the frequency of the wheel axle vibrations, which relates to the wheel rotational speed. The velocity of the vehicle can then be estimated without any other sensors and without requiring integration of the accelerometer measurements. In situations with high signal-to-noise ratio (snr), the methods perform well. To remedy situations when the methods perform poorly, an accelerometer input is introduced to the formulation. This input is used to predict changes in the frequency for short time intervals.v Populärvetenskaplig sammanfattningPeriodiska signaler förekommer ofta i praktiken. I många tillämpningar är det intressant att försöka skatta frekvensen av dessa periodiska signaler, eller vibrationer, genom mätningar av dem. Detta kallas för frekvensskattning eller frekvensföljning beroende på om frekvensen är konstant eller varierar över tid. Två tillämpningar studeras i denna licentiatavhandling. Målet i...

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“…The resulting model was used by, among others, Bittanti and Savaresi (2000) and La Scala and Bitmead (1996). At each time step, reparameterize so that φ k = 0 by rotating…”

Section: Instant Phasor Modelmentioning

confidence: 99%

Section: The Rbpmf For Frequency Trackingmentioning

confidence: 99%

Frequency Tracking for Speed Estimation

Lindfors¹

2018

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“…(15), the frequency to be tracked must be considered in the Kalman gain update routine. In practice, the frequency of the swept sinusoid can also be estimated as proposed in (Bittanti and Savaresi, 2000) and the time-varying Kalman gain is updated with the estimated state instead of a priori known value.…”

Section: Chirp Excitation Signalmentioning

confidence: 99%

Online Identification of a Two-Mass System in Frequency Domain using a Kalman Filter

Nevaranta

Derammelaere

Parkkinen

et al. 2016

MIC

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Some of the most widely recognized online parameter estimation techniques used in different servomechanism are the extended Kalman filter (EKF) and recursive least squares (RLS) methods. Without loss of generality, these methods are based on a prior knowledge of the model structure of the system to be identified, and thus, they can be regarded as parametric identification methods. This paper proposes an on-line non-parametric frequency response identification routine that is based on a fixed-coefficient Kalman filter, which is configured to perform like a Fourier transform. The approach exploits the knowledge of the excitation signal by updating the Kalman filter gains with the known time-varying frequency of chirp signal. The experimental results demonstrate the effectiveness of the proposed online identification method to estimate a non-parametric model of the closed loop controlled servomechanism in a selected band of frequencies.

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“…This famous estimation problem was notably studied by Riche de Prony in his 1795 seminal paper [30] (see [21], [28] for more recent works). Several other resolution methods have been elaborated, such as linear or nonlinear regression, subspace methods [19], [32], [21], the extended Kalman filter [3], the notches filter [29], or techniques from adaptive nonlinear control [20], [26]. Nevertheless, the parameter estimation problem in a fraction of the time signal, from a biased and noisy signal has not been entirely solved.…”

Section: Introductionmentioning

confidence: 99%

An algebraic approach for human posture estimation in the sagittal plane using accelerometer noisy signal

Perruquetti

Bonnet

Mboup

et al. 2012

2012 IEEE 51st IEEE Conference on Decision and Control (CDC)

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Abstract-Our aim is to develop an algebraic approach to estimate human posture in the sagittal plane using Inertial Measurement Unit (IMU) providing accelerations and angular velocities. For this purpose, we address the issue of the estimation of the amplitude, frequency and phase of a biased and noisy sum of three sinusoidal waveform signals on a moving time horizon. The length of the time window being small, the estimation must be done within a fraction of the signal's period. The problem is solved via an algebraic method. The efficiency of our approach is illustrated by computer simulations.

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On the parametrization and design of an extended Kalman filter frequency tracker

Cited by 191 publications

References 16 publications

Frequency Tracking for Speed Estimation

Frequency Tracking for Speed Estimation

Online Identification of a Two-Mass System in Frequency Domain using a Kalman Filter

An algebraic approach for human posture estimation in the sagittal plane using accelerometer noisy signal

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