Input Design for System Identification via Convex Relaxation

This paper proposes a new framework for the optimization of excitation inputs for system identification. The optimization problem considered is to maximize a reduced Fisher information matrix in any of the classical D-, E-, or A-optimal senses. In contrast to the majority of published work on this topic, we consider the problem in the time domain and subject to constraints on the amplitude of the input signal. This optimization problem is nonconvex. The main result of the paper is a convex relaxation that gives an upper bound accurate to within $2/\pi$ of the true maximum. A randomized algorithm is presented for finding a feasible solution which, in a certain sense is expected to be at least $2/\pi$ as informative as the globally optimal input signal. In the case of a single constraint on input power, the proposed approach recovers the true global optimum exactly. Extensions to situations with both power and amplitude constraints on both inputs and outputs are given. A simple simulation example illustrates the technique.Comment: Preprint submitted for journal publication, extended version of a paper at 2010 IEEE Conference on Decision and Contro

Pulsar Timing Arrays and their Applications

Millisecond pulsars are intrinsically very stable clocks and precise measurement of their observed pulse periods can be used to study a wide variety of astrophysical phenomena. In particular, observations of a large sample of millisecond pulsars at regular intervals, constituting a Pulsar Timing Array (PTA), can be used as a detector of low-frequency gravitational waves and to establish a standard of time independent of terrestrial atomic timescales. Three major timing array projects have been established: The European Pulsar Timing Array (EPTA), the North American pulsar timing array (NANOGrav) and the Parkes Pulsar Timing Array (PPTA). Results from the PPTA project are described in some detail and future prospects for PTA projects are discussed.Comment: 8 pages, 3 figures, to appear in the AIP Conference Proceedings for the Pulsar Conference 2010, Sardinia, Italy, October 201