Comments on "On the identification of variances and adaptive Kalman filtering"

Alspach, Daniel L.

doi:10.1109/tac.1972.1100153

Cited by 11 publications

(9 citation statements)

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“…The noise properties, namely, the noise CMs, have to be found on the basis of the measured data. Therefore, during the past 5 decades, various methods for the noise CM estimation have been proposed in the literature . The development of the noise CM estimation methods is thus closely tied with the advent of the SS models of dynamical systems being used in optimal and adaptive state estimation and control .…”

Section: Motivation Principal Classification and Goal Of The Papermentioning

confidence: 99%

“…The feedback‐free noise CM estimation methods cover the correlation methods and the MLMs . The correlation methods are based on an analysis of the innovation sequence properties of a suboptimal linear filter in a way similar to the illustration in this subsection. The MLMs are based on optimisation techniques from the system identification designed for input‐output models …”

Section: Motivation Principal Classification and Goal Of The Papermentioning

confidence: 99%

“…The methods differ in assumptions related to the considered model, underlying ideas and principles, properties of the estimates, and number and essence of the design parameters. Traditionally, CM estimation methods are divided into 4 groups: the correlation methods , the maximum‐likelihood methods (MLMs) , the covariance matching methods (CMMs) , and the Bayesian methods …”

Section: Introductionmentioning

confidence: 99%

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Noise covariance matrices in state‐space models: A survey and comparison of estimation methods—Part I

Duník

Straka

Kost

et al. 2017

Adaptive Control & Signal

118

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This paper deals with the estimation of the noise covariance matrices of systems described by state-space models. Stress is laid on the systematic survey and classification of both the recursive and batch processing methods proposed in the literature with a special focus on the correlation methods. Besides the correlation methods, representatives of other groups are introduced also with respect to their basic idea, estimate properties, assumptions and possible extensions, and user-defined parameters. Common and dual properties of the methods are highlighted, and a simulation comparison using exemplary MATLAB implementations of the methods is provided. KEYWORDSadaptive systems, noise covariance matrix, state estimation, state-space model, system identification INTRODUCTIONKnowledge of a system model is a key prerequisite for many state estimation, signal processing, fault detection, and optimal control problems. The model is often designed to be consistent with random behaviour of the system quantities and properties of the measurements. While the deterministic part of the model often arises from mathematical modelling on the basis of physical, chemical, or biological laws governing the behaviour of the system, the statistics of the stochastic part are often difficult to find by the modelling and have to be identified using the measured data. Incorrect description of the noise statistics may result in significant worsening of estimation, signal processing, detection, or control quality or even in a failure of the underlying algorithms.In the last 5 decades, therefore, a significant research interest has been focused on a design of the methods for the estimation of the properties of the stochastic part of the model. The attention has been devoted to both the input-output models 1-5 and the state-space (SS) models 6-14 and both recursive and batch processing methods. This paper focuses on the methods estimating the properties of the stochastic part of the system described by an SS model discrete in time. In particular, the methods estimating the covariance matrices (CMs) † of noises in the state and measurement equation from a sequence of measured data are of interest. The methods are further denoted as the noise CM estimation methods.

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Section: Motivation Principal Classification and Goal Of The Papermentioning

confidence: 99%

Section: Motivation Principal Classification and Goal Of The Papermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Noise covariance matrices in state‐space models: A survey and comparison of estimation methods—Part I

Duník

Straka

Kost

et al. 2017

Adaptive Control & Signal

118

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“…In reality, the process noise is not known. Algorithms for process noise estimation have long existed [3,41,200].…”

Section: Crousementioning

confidence: 99%

“…In the United States, the broadcast power of a digital television station in the ultrahigh frequency band is limited to a maximum of 1 MW [297] quasi-omnidirectionally, with many stations broadcasting at a lower power. 3 The topic has aroused significant criticism that there is a possible loss in gain because different parts of the array broadcast different waveforms and broadcasting some theoretical MIMO waveforms would cause the antennas on a real system to melt [78].…”

Section: Introductionmentioning

confidence: 99%

Basic tracking using nonlinear 3D monostatic and bistatic measurements

Crouse¹

2014

IEEE Aerosp. Electron. Syst. Mag.

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Monostatic and bistatic position and Doppler measurements used in radar and sonar systems are nonlinear transformations of a Cartesian state. These nonlinearities pose a challenge for many target tracking algorithms, causing the so-called contact lens problem, which describes the nonlinear appearance of the measurement probability density function in Cartesian coordinates. This tutorial considers methods for measurement filtering (tracking without considering data association) using a single-Gaussian approximation when monostatic and bistatic position and Doppler measurements are available. The connection between the cubature Kalman filter and numerous other filtering algorithms is shown, and the accuracy and consistency of different algorithms are compared through simulation. An effort is made to express the geometric relationships associated with multistatic tracking in a simple vectorial manner. This tutorial focuses on basic tracking, and the companion tutorials "Tracking Using 3D Monostatic and Bistatic Measurements in Refractive Environments" and "Basic Tracking Using Nonlinear Continuous-Time Dynamic Models" extend the results to more sophisticated physical models.

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The Discrete-Time Kalman Filter Under Uncertainty in Noise Covariances

Sangsuk-Iam¹

1996

Control and Dynamic Systems

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Comments on "On the identification of variances and adaptive Kalman filtering"

Cited by 11 publications

References 1 publication

Noise covariance matrices in state‐space models: A survey and comparison of estimation methods—Part I

Noise covariance matrices in state‐space models: A survey and comparison of estimation methods—Part I

Basic tracking using nonlinear 3D monostatic and bistatic measurements

The Discrete-Time Kalman Filter Under Uncertainty in Noise Covariances

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