Reduced Order Kalman Filtering Without Model Reduction

Simon, Daniel J.

doi:10.2316/journal.201.2007.2.201-1662

Cited by 22 publications

(15 citation statements)

References 22 publications

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“…Finally, another front of promising studies concerns the possibility of obtaining reduced-order Kalman filters for the SSAC problem by reducing the associated Riccati equation instead of reducing the dynamic error model. Similar ideas have been successfully employed in [37,82]. …”

Section: Discussionmentioning

confidence: 98%

On the Error State Selection for Stationary SINS Alignment and Calibration Kalman Filters—Part II: Observability/Estimability Analysis

Silva

Hemerly

Filho

2017

Sensors

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This paper presents the second part of a study aiming at the error state selection in Kalman filters applied to the stationary self-alignment and calibration (SSAC) problem of strapdown inertial navigation systems (SINS). The observability properties of the system are systematically investigated, and the number of unobservable modes is established. Through the analytical manipulation of the full SINS error model, the unobservable modes of the system are determined, and the SSAC error states (except the velocity errors) are proven to be individually unobservable. The estimability of the system is determined through the examination of the major diagonal terms of the covariance matrix and their eigenvalues/eigenvectors. Filter order reduction based on observability analysis is shown to be inadequate, and several misconceptions regarding SSAC observability and estimability deficiencies are removed. As the main contributions of this paper, we demonstrate that, except for the position errors, all error states can be minimally estimated in the SSAC problem and, hence, should not be removed from the filter. Corroborating the conclusions of the first part of this study, a 12-state Kalman filter is found to be the optimal error state selection for SSAC purposes. Results from simulated and experimental tests support the outlined conclusions.

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Section: Discussionmentioning

confidence: 98%

On the Error State Selection for Stationary SINS Alignment and Calibration Kalman Filters—Part II: Observability/Estimability Analysis

Silva

Hemerly

Filho

2017

Sensors

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“…• A first method is the reduced order Kalman filter (see Simon, 2007). In this approach the unobservable modes of the system are eliminated from the equations of motion by performing a projection on the observable space.…”

Section: What About Unobservable Systemsmentioning

confidence: 99%

State and Parameter Estimation for Vehicle Dynamics

Naets

2021

CISM International Centre for Mechanical Sciences

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An accurate knowledge of the vehicle state and parameters is essential for current and future active vehicle applications. However, many of these quantities cannot be measured directly in commercial vehicles through the use of cost effective sensors. Estimation methods allow one to combine a (simple) model for the vehicle with available measurement data in order to assimilate a wide range of quantities of interests, ranging from slip states to tire parameters. In this chapter we will review various basic estimation algorithms, and discuss how they can lead to valuable estimators for vehicle dynamics applications by considering gradually increasing model complexity. This should provide the reader with the basic insights required to set up their own vehicle dynamics estimators.F. Naets (B) DMMS,

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“…The general perception is that more measurements are better; however, when the cost of measurement, communication, and/or computation is considered, this may not be the case. One option is to develop a reduced order model Kalman filter, without resorting to model reduction [9]. If this is not possible, other trade-offs between performance and resource utilization are sought.…”

Section: Literature Overviewmentioning

confidence: 99%

Sensor Graphs for Guaranteed Cooperative Localization Performance

Yuan¹,

Tanner²

2010

Control and Intelligent Systems

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A group of mobile robots can localize cooperatively, using relative position and absolute orientation measurements, fused through an extended Kalman filter (ekf).The topology of the graph of relative measurements is known to affect the steady state value of the position error covariance matrix. Classes of sensor graphs are identified, for which tight bounds for the trace of the covariance matrix can be obtained based on the algebraic properties of the underlying relative measurement graph. The string and the star graph topologies are considered, and the explicit form of the eigenvalues of error covariance matrix is given. More general sensor graph topologies are considered as combinations of the string and star topologies, when additional edges are added. It is demonstrated how the addition of edges increases the trace of the steady state value of the position error covariance matrix, and the theoretical predictions are verified through simulation analysis.

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Reduced Order Kalman Filtering Without Model Reduction

Cited by 22 publications

References 22 publications

On the Error State Selection for Stationary SINS Alignment and Calibration Kalman Filters—Part II: Observability/Estimability Analysis

On the Error State Selection for Stationary SINS Alignment and Calibration Kalman Filters—Part II: Observability/Estimability Analysis

State and Parameter Estimation for Vehicle Dynamics

Sensor Graphs for Guaranteed Cooperative Localization Performance

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