Optimal linear estimation for systems with multiple packet dropouts

Sun, Shuli; Xie, Lihua; Xiao, Wendong; Soh, Yeng Chai

doi:10.1016/j.automatica.2007.09.023

Cited by 295 publications

(187 citation statements)

References 25 publications

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“…Proof: It can be shown that (22) follows directly from (5)- (6) and (18), and therefore the proof is omitted for conciseness.…”

Section: Resultsmentioning

confidence: 99%

“…Note that the linearization is enforced to tackle the nonlinearities f (·) and h(·). As such, (22) and (23) involve ℵ 1,k and ℵ 2,k+1 which add extra computational difficulty for the design of filter gain. Actually, due to the consideration of the linearization errors, it is literally impossible to obtain the accurate value of the filtering error covariance P k+1|k+1 , and a seemingly natural way is to design appropriate filter gain K k+1 in order to guarantee an upper bound for the filtering error covariance that can then be minimized at each sampling instant.…”

Section: Remarkmentioning

confidence: 99%

“…Theorem 3 Consider the covariance matrices of the one-step prediction error and the filtering error in (22) and (23). Assume that (17) and (20) are true.…”

Section: Remarkmentioning

confidence: 99%

“…[3, 8-10, 22, 34]. To be more specific, the optimal estimation problems have been investigated in [8,22] for linear systems with multiple packet dropouts and the random sensor delays have been taken into account in [9,34]. It is worth mentioning that, in most reported results, the measurement signal has been assumed to be either completely lost or successfully transferred, and a typical way is to model the missing measurements by the Bernoulli distribution.…”

Section: Introductionmentioning

confidence: 99%

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Extended Kalman filtering with stochastic nonlinearities and multiple missing measurements

et al. 2012

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In this paper, the extended Kalman filtering problem is investigated for a class of nonlinear systems with multiple missing measurements over a finite horizon. Both deterministic and stochastic nonlinearities are included in the system model, where the stochastic nonlinearities are described by statistical means that could reflect the multiplicative stochastic disturbances. The phenomenon of measurement missing occurs in a random way and the missing probability for each sensor is governed by an individual random variable satisfying a certain probability distribution over the interval [0,1]. Such a probability distribution is allowed to be any commonly used distribution over the interval [0, 1] with known conditional probability. The aim of the addressed filtering problem is to design a filter such that, in the presence of both the stochastic nonlinearities and multiple missing measurements, there exists an upper bound for the filtering error covariance. Subsequently, such an upper bound is minimized by properly designing the filter gain at each sampling instant. It is shown that the desired filter can be obtained in terms of the solutions to two Riccati-like difference equations that are of a form suitable for recursive computation in online applications. An illustrative example is given to demonstrate the effectiveness of the proposed filter design scheme.

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“…Proof: It can be shown that (22) follows directly from (5)- (6) and (18), and therefore the proof is omitted for conciseness.…”

Section: Resultsmentioning

confidence: 99%

Section: Remarkmentioning

confidence: 99%

“…Theorem 3 Consider the covariance matrices of the one-step prediction error and the filtering error in (22) and (23). Assume that (17) and (20) are true.…”

Section: Remarkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Extended Kalman filtering with stochastic nonlinearities and multiple missing measurements

et al. 2012

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“…However, perfect communication is not always possible in many engineering systems especially in a networked environment. For example, due to sensor temporal failure or network transmission delay/loss [6,18,19], at certain time points, the system measurement may contain noise only, which means the real signal is missing. Filtering problem with missing measurements has gained considerable research attention and many results have been reported in the literature, see [12,19].…”

Section: Introductionmentioning

confidence: 99%

H∞ filtering with randomly occurring sensor saturations and missing measurements

2012

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In this paper, the H∞ filtering problem is investigated for a class of nonlinear systems with randomly occurring incomplete information. The considered incomplete information includes both the sensor saturations and the missing measurements. A new phenomenon of sensor saturation, namely, randomly occurring sensor saturation (ROSS), is put forward in order to better reflect the reality in a networked environment such as sensor networks. A novel sensor model is then established to account for both the ROSS and missing measurement in a unified representation by using two sets of Bernoulli distributed white sequences with known conditional probabilities. Based on this sensor model, a regional H∞ filter with a certain ellipsoid constraint is designed such that the filtering error dynamics is locally mean-square asymptotically stable and the H∞-norm requirement is satisfied. Note that the regional l2 gain filtering feature is specifically developed for the random saturation nonlinearity. The characterization of the desired filter gains is derived in terms of the solution to a convex optimization problem that can be easily solved by using the semi-definite programme method. Finally, a simulation example is employed to show the effectiveness of the filtering scheme proposed in this paper.

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