## Abstract

A game theory approach is introduced which provides a simple solution to the problem of finite-time optimal estimation. In this game a measurement record is given and the first player looks for the best estimate of a prespecified combination of the system states in the presence of “hostile” noise signals and system initial condition that are applied by his adversary (say nature). It turns out that the game possesses a saddle-point solution which leads to an optimal smoothed estimate that is identical to the corresponding L_{2}-optimal estimate. A similar game is formulated and solved where the estimate is restricted to be causal. This game provides a saddle-point equilibrium interpretation to the finite-time H_{∞}-optimal filtered estimation. The two games are very closely related. It is shown that in the first game the first player's strategy, which is the optimal smoothed estimate, is a linear-fractional transformation of the H_{∞}-optimal filter which applies a nonzero free contracting Y parameter. It, therefore, achieves a unity H_{∞}-norm bound for the operator that relates the exogenous signals to the estimation error.

Original language | English |
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Pages (from-to) | 957-963 |

Number of pages | 7 |

Journal | IEEE Transactions on Automatic Control |

Volume | 38 |

Issue number | 6 |

DOIs | |

State | Published - Jun 1993 |