On the Complexity and Approximability of Optimal Sensor Selection and Attack for Kalman Filtering

Given a linear dynamical system affected by stochastic noise, we consider the problem of selecting an optimal set of sensors (at design time) to minimize the trace of the steady-state a priori or a posteriori error covariance of the Kalman filter, subject to certain selection budget constraints. We...

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Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 66; no. 5; pp. 2146 - 2161
Main Authors: Ye, Lintao, Woodford, Nathaniel, Roy, Sandip, Sundaram, Shreyas
Format: Journal Article
Language:English
Published: New York IEEE 01.05.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Approximation
Approximation algorithms
Budgets
Computational complexity
Cost function
Covariance
Covariance matrices
Estimation error
Greedy algorithms
Kalman filters
Mathematical analysis
Noise measurement
optimization
Polynomials
sensor systems
Sensors
state estimation
Steady state
Time constant
ISSN:0018-9286, 1558-2523
Online Access:Get full text
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Summary:Given a linear dynamical system affected by stochastic noise, we consider the problem of selecting an optimal set of sensors (at design time) to minimize the trace of the steady-state a priori or a posteriori error covariance of the Kalman filter, subject to certain selection budget constraints. We show the fundamental result that there is no polynomial-time constant-factor approximation algorithm for this problem. This contrasts with other classes of sensor selection problems studied in the literature, which typically pursue constant-factor approximations by leveraging greedy algorithms and submodularity (or supermodularity) of the cost function. Here, we provide a specific example showing that greedy algorithms can perform arbitrarily poorly for the problem of design-time sensor selection for Kalman filtering. We then study the problem of attacking (i.e., removing) a set of installed sensors, under predefined attack budget constraints, to maximize the trace of the steady-state a priori or a posteriori error covariance of the Kalman filter. Again, we show that there is no polynomial-time constant-factor approximation algorithm for this problem and show specifically that greedy algorithms can perform arbitrarily poorly.
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2020.3007383