Nonlinear Filters and Operators and the Constant-Gain Extended Kalman Filter

Grimble, M.J.; Jukes, K. A.; Goodall, D.P.

doi:10.1093/imamci/1.4.359

Cited by 22 publications

(10 citation statements)

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“…is assumed to be finite gain stable. For stability analysis, the time sequences can be considered to be contained in extensions of the discrete Marcinkiewicz space [11]. This is the space of time-sequences with time-averaged square summable signals that have a finite power.…”

Section: (6)mentioning

confidence: 99%

“…A realization of can be obtained using the spectral factor defined above as (30) where satisfies (19). Also recall the weighted message signal is given from (17) (15) that the observations and substituting from (32) From (10), (12), (13), and (14) and obtain (33) Also using equations (11), (16), and (30) Under the assumption that and commute, then…”

Section: B Solutionmentioning

confidence: 99%

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Nonlinear Minimum Variance Estimation for Discrete-Time Multi-Channel Systems

Grimble

Naz

2009

IEEE Trans. Signal Process.

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A nonlinear operator approach to estimation in discrete-time systems is described. It involves inferential estimation of a signal which enters a communications channel involving both nonlinearities and transport delays. The measurements are assumed to be corrupted by a colored noise signal which is correlated with the signal to be estimated. The system model may also include a communications channel involving either static or dynamic nonlinearities. The signal channel is represented in a very general nonlinear operator form. The algorithm is relatively simple to derive and to implement.

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Section: (6)mentioning

confidence: 99%

Section: B Solutionmentioning

confidence: 99%

Nonlinear Minimum Variance Estimation for Discrete-Time Multi-Channel Systems

Grimble

Naz

2009

IEEE Trans. Signal Process.

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“…It was motivated by the successful developments in Nonlinear Generalized Minimum Variance Control which have provided simple solutions to difficult nonlinear industrial application problems ( [17], [18]). Simulation results to be presented 46th IEEE CDC, New Orleans, USA, Dec. [12][13][14]2007 ThC12.1…”

Section: F Significance Of the Parallel Path Dynamicsmentioning

confidence: 99%

NMV optimal estimation for nonlinear discrete-time multi-channel systems

Grimble

2007

2007 46th IEEE Conference on Decision and Control

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A nonlinear operator approach to estimation in discrete-time multivariable systems is described. It involves inferential estimation of a signal which enters a communications channel involving both nonlinearities and transport delays. The measurements are assumed to be corrupted by a colored noise signal which is correlated with the signal to be estimated. The system model also includes a communications channel involving hard or dynamic nonlinearities. The signal and noise channels are represented in a very general nonlinear operator form. The algorithm is relatively simple to derive and to implement. The optimal nonlinear estimator is derived in terms of the nonlinear operators that describe the system. The results are the dual of the nonlinear generalized minimum variance control problem that has been very successful in providing a practical simple algorithm for nonlinear processes

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“…Constant gain Kalman filters (CGKF) have been analyzed in [7][8][9]. However these do not completely circumvent the use of filter statistics P0, Q and R which may not be optimal or near optimal for deriving the constant Kalman gains.…”

Section: Introductionmentioning

confidence: 99%

A constant gain Kalman filter approach to track maneuvering targets

Yadav¹,

Awasthi

Naik

et al. 2013

2013 IEEE International Conference on Control Applications (CCA)

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Tracking of maneuvering targets is an important area of research with applications in both the military and civilian domains. One of the most fundamental and widely used approaches to target tracking is the Kalman filter. In presence of unknown noise statistics there are difficulties in the Kalman filter yielding acceptable results. In the Kalman filter operation for state variable models with near constant noise and system parameters, it is well known that after the initial transient the gain tends to a steady state value. Hence working directly with Kalman gains it is possible to obtain good tracking results dispensing with the use of the usual covariances. The present work applies an innovations based cost function minimization approach to the target tracking problem of maneuvering targets, in order to obtain the constant Kalman gain. Our numerical studies show that the constant gain Kalman filter gives good performance compared to the standard Kalman filter. This is a significant finding in that the constant gain Kalman filter circumvents or in other words trades the gains with the filter statistics which are more difficult to obtain. The problems associated with using a Kalman filter for tracking a maneuvering target with unknown system and measurement noise statistics can be circumvented by using the constant gain approach which seeks to work only with the gains instead of the state and measurement noise covariances. The approach is applied to a variety of standard maneuvering target models.

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Nonlinear Filters and Operators and the Constant-Gain Extended Kalman Filter

Cited by 22 publications

References 0 publications

Nonlinear Minimum Variance Estimation for Discrete-Time Multi-Channel Systems

Nonlinear Minimum Variance Estimation for Discrete-Time Multi-Channel Systems

NMV optimal estimation for nonlinear discrete-time multi-channel systems

A constant gain Kalman filter approach to track maneuvering targets

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