Stochastic stability of the continuous-time extended Kalman filter

Reif, Konrad; Günther, Stefan; Yaz, E.; Unbehauen, R.

doi:10.1049/ip-cta:20000125

Cited by 117 publications

(99 citation statements)

References 15 publications

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“…First, we revisit the traditional extended Kalman filter [28,29]. Over the past 40 years, EKF has been the most widely used nonlinear estimation technique for various industrial applications [30][31][32].…”

Section: Nonlinear Estimationmentioning

confidence: 99%

Sensorless Direct Torque Control of Surface-Mounted Permanent Magnet Synchronous Motors with Nonlinear Kalman Filtering

Park

Wang

2018

Energies

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Abstract:The demand for sensorless control of surface-mounted permanent magnet synchronous motor drives has grown rapidly. Among various sensorless control techniques developed, Matsui's current model-based approach and the extended Kalman filter approach have gained much attention. However, the performance of these control methods can be severely worsened or may even become unstable under strong disturbances or sensing failures. This paper presents a comparative study of the extended Kalman filter, the resilient extended Kalman filter, and the unscented Kalman filter-based sensorless direct torque and flux control approaches for the surface-mounted permanent magnet synchronous motor drives. Computer simulation studies and hardware implementation results have shown the efficiency and superior performance of the resilient extended Kalman filter and the unscented Kalman filter over the traditional extended Kalman filter for sensorless direct torque control applications.

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Section: Nonlinear Estimationmentioning

confidence: 99%

Sensorless Direct Torque Control of Surface-Mounted Permanent Magnet Synchronous Motors with Nonlinear Kalman Filtering

Park

Wang

2018

Energies

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“…The described filter is the simplest but successful state estimator that has been utilized by practitioners for decades [8,9,15,30,38]. Theoretical justifications of this method in both deterministic and stochastic settings can be found in [4,34].…”

Section: Dx(t) = F(x(t) U(t))dt + G(t)dw(t) T > 0 (11)mentioning

confidence: 99%

Practical implementation of extended Kalman filtering in chemical systems with sparse measurements

Kulikov

Kulikova

2018

Russian Journal of Numerical Analysis and Mathematical Modelling

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Chemical systems are often characterized by a number of peculiar properties that create serious challenges to state estimator algorithms. They may include hard nonlinear dynamics, states subject to some constraints arising from a physical nature of the process (for example, all chemical concentrations must be nonnegative), and so on. The classical Extended Kalman Filter (EKF), which is considered to be the most popular state estimator in practice, is shown to be ineffective in chemical systems with infrequent measurements. In this paper, we discuss a recently designed version of the EKF method, which is grounded in a high-order Ordinary Differential Equation (ODE) solver with automatic global error control. The implemented global error control boosts the quality of state estimation in chemical engineering and allows this newly built version of the EKF to be an accurate and efficient state estimator in chemical systems with both short and long waiting times (i.e., with frequent and infrequent measurements). So chemical systems with variable sampling periods are algorithmically admitted and can be treated as well.

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“…Theorem 1 is a significant contribution to the problem of robocentric mapping and is a fundamental result. It is important to note again that the algorithm considered in this paper is based on nothing more than an EKF-like architecture and a coordinate transform; see [20], [24], [25] for other EKF stability results.…”

Section: Theoremmentioning

confidence: 99%

A stochastically stable solution to the problem of robocentric mapping

Bishop¹

2009

2009 IEEE International Conference on Robotics and Automation

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Abstract-This paper provides a novel solution for robocentric mapping using an autonomous mobile robot. The robot dynamic model is the standard unicycle model and the robot is assumed to measure both the range and relative bearing to the landmarks. The algorithm introduced in this paper relies on a coordinate transformation and an extended Kalman filter like algorithm. The coordinate transformation considered in this paper has not been previously considered for robocentric mapping applications. Moreover, we provide a rigorous stochastic stability analysis of the filter employed and we examine the conditions under which the mean-square estimation error converges to a steady-state value.

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Stochastic stability of the continuous-time extended Kalman filter

Cited by 117 publications

References 15 publications

Sensorless Direct Torque Control of Surface-Mounted Permanent Magnet Synchronous Motors with Nonlinear Kalman Filtering

Sensorless Direct Torque Control of Surface-Mounted Permanent Magnet Synchronous Motors with Nonlinear Kalman Filtering

Practical implementation of extended Kalman filtering in chemical systems with sparse measurements

A stochastically stable solution to the problem of robocentric mapping

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