Generalised proportional–integral–derivative filter

Zhang, Junfeng; He, Xiao; Zhou, Donghua

doi:10.1049/iet-cta.2015.0610

Cited by 7 publications

(10 citation statements)

References 32 publications

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“…Simulation results in this paper show that the mean square error is reduced about six times. Results in show that the errors are reduced by the integral term, but the steady‐state error is not removed effectively. These methods, try to reduce the performance index (variance of error) but not the steady‐state error.…”

Section: Augmented Integral Kalman Filter (Aikf)mentioning

confidence: 99%

“…and using the following new augmented parameters

{\overset{K}{true}}_{k} = {bold-italicP}_{k}^{f} {\overset{H}{true}}^{T} {((), \overset{H}{true} P_{k}^{f} {\overset{H}{true}}^{T} + {\overset{R}{true}}_{k})}^{- 1}

{\overset{P}{true}}_{k}^{f} = {\overset{A}{true}}_{k - 1} {\overset{P}{true}}_{k - 1} {\overset{A}{true}}_{k - 1}^{T} + {\overset{Q}{true}}_{k - 1}

where

\overset{A}{true} = ([], \begin{matrix} array \\ array A & array {bold-italicD}_{i} \\ array 0 & array {bold-italicD}_{f} \end{matrix}), δ \overset{\overset{x}{true}}{true} ((), k) = ([], \begin{matrix} array \\ array δ \hat{bold-italicx} (k) \\ array δ \hat{bold-italicd} (k) \end{matrix}), \overset{H}{true} = ([], \begin{matrix} array \\ array H & array 0 \end{matrix})

Simulation results in show that the RMS error of the PIKF is about three times less than the RMS error in the conventional KF. In another method called Generalized Proportional Integral Derivative Filter (GPIDF) is presented and optimal gains K P , K I , and K D are computed by making the partial derivation of the trace of covariance matrix equal to zero. Simulation results in this paper show that the mean square error is reduced about six times.…”

Section: Augmented Integral Kalman Filter (Aikf)mentioning

confidence: 99%

“…There exist some literatures [12,[16][17][18]20] on proportional-integral KF. Apparently, their methods are different, but actually they act in the same way.…”

Section: Augmented Integral Kalman Filter (Aikf)mentioning

confidence: 99%

“…Simulation results in [16] show that the RMS error of the PIKF is about three times less than the RMS error in the conventional KF. In [20] another method called Generalized Proportional Integral Derivative Filter (GPIDF) is presented and optimal gains K P , K I , and K D are computed by making the partial derivation of the trace of covariance matrix equal to zero. Simulation results in this paper show that the mean square error is reduced about six times.…”

Section: Augmented Integral Kalman Filter (Aikf)mentioning

confidence: 99%

“…This benefit comes from the additional degrees of freedom in the observer or estimator design. All of these literature use a similar method [11][12][13][14][15][16][17][18][19][20][21][22]. They augment an integral state to the main system and compute a new observer or estimator gain for the augmented system.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Improving GPS/INS Integration Using FIKF‐Filtered Innovation Kalman Filter

Shaghaghian

Karimaghaee

2018

Asian Journal of Control

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The Kalman Filter (KF) is the most popular approach in sensor fusion and navigation applications. Improving the accuracy of estimation may increase the navigation accuracy. KF is the best choice for minimum variance optimal estimation, but it is not the best approach to improve some of the main and classic features such as steady-state error reduction. These features are more important than optimality for applications like accuracy improvement in navigation. Also, these features and their solutions have been addressed in classic control techniques as a widely known subject. Therefore, some similar improvements in the estimation problem are discussed in the literature. These studies try to conserve the optimality in the covariance of the error, but classic and optimal features cannot be achieved simultaneously. Hence, these methods are not as efficient as expected. This paper intends to improve the estimation of position and velocity in navigation problems by integrating classic and modern control techniques. Beside the classic features and advantages, it may be seen that the resulted covariance of error is not minimum anymore, but it is comparable with the optimal methods.

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Section: Augmented Integral Kalman Filter (Aikf)mentioning

confidence: 99%

“…and using the following new augmented parameters

{\overset{K}{true}}_{k} = {bold-italicP}_{k}^{f} {\overset{H}{true}}^{T} {((), \overset{H}{true} P_{k}^{f} {\overset{H}{true}}^{T} + {\overset{R}{true}}_{k})}^{- 1}

{\overset{P}{true}}_{k}^{f} = {\overset{A}{true}}_{k - 1} {\overset{P}{true}}_{k - 1} {\overset{A}{true}}_{k - 1}^{T} + {\overset{Q}{true}}_{k - 1}

where

\overset{A}{true} = ([], \begin{matrix} array \\ array A & array {bold-italicD}_{i} \\ array 0 & array {bold-italicD}_{f} \end{matrix}), δ \overset{\overset{x}{true}}{true} ((), k) = ([], \begin{matrix} array \\ array δ \hat{bold-italicx} (k) \\ array δ \hat{bold-italicd} (k) \end{matrix}), \overset{H}{true} = ([], \begin{matrix} array \\ array H & array 0 \end{matrix})

Section: Augmented Integral Kalman Filter (Aikf)mentioning

confidence: 99%

“…There exist some literatures [12,[16][17][18]20] on proportional-integral KF. Apparently, their methods are different, but actually they act in the same way.…”

Section: Augmented Integral Kalman Filter (Aikf)mentioning

confidence: 99%

Section: Augmented Integral Kalman Filter (Aikf)mentioning

confidence: 99%