On the Optimality of Linear Signaling to Deceive Kalman Filters over Finite/Infinite Horizons

Muhammed O. Sayin, Tamer Başar

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper, we address the problem of obtaining optimal deceptive signaling strategies between two agents, a sender and a receiver, over an ideal channel. Different from classical (cooperative) communication settings, here, the agents select their strategies under two different cost measures. For the case when these costs are quadratic, we analyze the Stackelberg equilibrium, where the sender leads the game by committing his/her strategies beforehand. This is an infinite-dimensional optimization problem, where the sender needs to anticipate the receiver’s reaction while selecting his/her policy within the general class of stochastic kernels. The specific model we adopt for the underlying information of interest is a discrete-time Markov process generated by a vector-valued linear dynamical system, and at each instant, the information is a realization of a square integrable multivariate random vector. Over both finite and infinite horizons, we show the optimality of memoryless, “linear” signaling rules when the receiver uses a Kalman filter to estimate its information of interest. We develop algorithms that deliver the optimal signaling strategies. Numerical analysis shows that the performance of the sender degrades slightly when the receiver uses the best nonlinear estimator even when the information of interest is a Rademacher random variable rather than Gaussian.

Original languageEnglish (US)
Title of host publicationDecision and Game Theory for Security - 10th International Conference, GameSec 2019, Proceedings
EditorsTansu Alpcan, Yevgeniy Vorobeychik, John S. Baras, György Dán
PublisherSpringer
Pages459-478
Number of pages20
ISBN (Print)9783030324292
DOIs
StatePublished - Jan 1 2019
Event10th International Conference on Decision and Game Theory for Security, GameSec 2019 - Stockholm, Sweden
Duration: Oct 30 2019Nov 1 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11836 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference10th International Conference on Decision and Game Theory for Security, GameSec 2019
CountrySweden
CityStockholm
Period10/30/1911/1/19

Keywords

  • Deception
  • Infinite-horizon
  • Security
  • Semi-definite programming
  • Signaling
  • Stackelberg games

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Sayin, M. O., & Başar, T. (2019). On the Optimality of Linear Signaling to Deceive Kalman Filters over Finite/Infinite Horizons. In T. Alpcan, Y. Vorobeychik, J. S. Baras, & G. Dán (Eds.), Decision and Game Theory for Security - 10th International Conference, GameSec 2019, Proceedings (pp. 459-478). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11836 LNCS). Springer. https://doi.org/10.1007/978-3-030-32430-8_27