A game theory approach to constrained minimax state estimation

Simon, Daniel J.

doi:10.1109/tsp.2005.861732

Cited by 102 publications

(80 citation statements)

References 27 publications

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“…If the state constraints are nonlinear they can be linearized as discussed in [19]. Further work could explore the incorporation of state constraints for optimal smoothing, or the use of constraint switching in H ∞ filtering [21].…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Kalman Filter Constraint Switching for Turbofan Engine Health Estimation

Simon

2006

European Journal of Control

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Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. Recently published work has shown a new method for incorporating state variable inequality constraints in the Kalman filter. The resultant filter is a combination of a standard Kalman filter and a quadratic programming problem. The incorporation of state variable constraints has been shown to generally improve the filter's estimation accuracy. However, the incorporation of inequality constraints poses some risk to the estimation accuracy.After all, the Kalman filter is theoretically optimal, so the incorporation of heuristic constraints may degrade the optimality of the filter. This paper proposes a way to switch the filter constraints so that the state estimates follow the unconstrained (theoretically optimal) filter when the confidence in the unconstrained filter is high. * Corresponding author. Email address d.j.simon@csuohio.edu. This work was supported by the NASA Aviation Safety and Security Program at NASA Glenn Research Center. 1When confidence in the unconstrained filter is not so high, then we use our heuristic knowledge to constrain the state estimates. The confidence measure is based on the agreement of measurement residuals with their theoretical values. If some measurement residuals are low, and those residuals are highly sensitive to a given state, then we are confident that the unconstrained estimate of that state is correct.Otherwise, we incorporate our heuristic knowledge as state constraints. The algorithm is demonstrated on a linearized simulation of a turbofan engine to estimate engine health.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Kalman Filter Constraint Switching for Turbofan Engine Health Estimation

Simon

2006

European Journal of Control

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“…The H ∞ filters (see e.g. papers by Simon [22,23]) are a family of (robust) linear filters developed based on a min-max approach, like WEMM, and analyzed in the worst case setting. These filters are reminiscent of the celebrated Kalman filter [18], which was motivated and analyzed in a stochastic setting with Gaussian noise.…”

Section: Related Workmentioning

confidence: 99%

Weighted Last-Step Min-Max Algorithm with Improved Sub-logarithmic Regret

Moroshko

Crammer

2012

Lecture Notes in Computer Science

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In online learning the performance of an algorithm is typically compared to the performance of a fixed function from some class, with a quantity called regret. Forster [12] proposed a last-step min-max algorithm which was somewhat simpler than the algorithm of Vovk [26], yet with the same regret. In fact the algorithm he analyzed assumed that the choices of the adversary are bounded, yielding artificially only the two extreme cases. We fix this problem by weighing the examples in such a way that the min-max problem will be well defined, and provide analysis with logarithmic regret that may have better multiplicative factor than both bounds of Forster [12] and Vovk [26]. We also derive a new bound that may be sub-logarithmic, as a recent bound of Orabona et.al [21], but may have better multiplicative factor. Finally, we analyze the algorithm in a weak-type of non-stationary setting, and show a bound that is sublinear if the non-stationarity is sub-linear as well.

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“…Jamming 17,19 and estimation [22][23][24] have recently received more and more attention in adversarial PE situations due to the increasing availability of portable signal processing instruments. Here, jamming is defined as follows: Definition 1.1 Jamming is a soft kill action that attempts to dilute the effectiveness of an enemy weapon system through confusion, distraction, or deception.…”

Section: Challenge 3: How To Analyze Possible Jamming Influences In Pmentioning

confidence: 99%

“…In addition to problems caused by multiple superior evaders, there might exist jamming-estimation confrontation 17,19 between the players in complex PE games. In this section, we consider a min-max jammingestimation confrontation between pursuers and evaders.…”

Section: Jamming Confrontationmentioning

confidence: 99%

“…Similar to 17 and, 19 which built up unilateral min-max jamming models, we consider the following doublesided coupled time-variant system (assume all matrices have appropriate dimensions-which is based on Kalman Filter estimation)ẋ (18) Note that at first sight the cost function might not look intuitive. However, in jamming-estimating problems, 17 it is a common setting and can be explained as representing the case that both players are trying to maximally interfere with the enemy's estimation at some penalty such as energy cost or computation cost.…”

Section: Jamming Confrontationmentioning

confidence: 99%

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Multi-Pursuer Multi-Evader Pursuit-Evasion Games with Jamming Confrontation

Wei¹,

Chen²,

Cruz³

et al. 2007

Journal of Aerospace Computing, Information, and Communication

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Existing pursuer-evader (PE) game algorithms do not provide good real-time solutions for situations with the following complexities: (1) multi-pursuer multi-evader, (2) multiple evaders with superior control resources such as higher speeds, and (3) jamming confrontation between pursuers and evaders. This paper introduces a real-time decentralized approach, in which decentralization strategy reduces computational complexity in multi-pursuer multievader situations, cooperative chasing strategy guarantees capture of some superior evaders, and min-max double-sided jamming confrontation provides optimal jamming-estimation strategies under adversarial noisy environments. Extensive simulations confirm the efficiency of this approach.

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A game theory approach to constrained minimax state estimation

Cited by 102 publications

References 27 publications

Kalman Filter Constraint Switching for Turbofan Engine Health Estimation

Kalman Filter Constraint Switching for Turbofan Engine Health Estimation

Weighted Last-Step Min-Max Algorithm with Improved Sub-logarithmic Regret

Multi-Pursuer Multi-Evader Pursuit-Evasion Games with Jamming Confrontation

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