Title: Cooperative Estimation via Altruism,
Abstract: A novel approach, based on the notion of altruism, is presented to
cooperative estimation in a system comprising two information-sharing
estimators. The underlying assumption is that the system's global mission can
be accomplished even if only one of the estimators achieves satisfactory
performance. The notion of altruism motivates a new definition of cooperative
estimation optimality that generalizes the common definition of minimum mean
square error optimality. Fundamental equations are derived for two types of
altruistic cooperative estimation problems, corresponding to heterarchical and
hierarchical setups. Although these equations are hard to solve in the general
case, their solution in the Gaussian case is straightforward and only entails
the largest eigenvalue of the conditional covariance matrix and its
corresponding eigenvector. Moreover, in that case the performance improvement
of the two altruistic cooperative estimation techniques over the conventional
(egoistic) estimation approach is shown to depend on the problem's
dimensionality and statistical distribution. In particular, the performance
improvement grows with the dispersion of the spectrum of the conditional
covariance matrix, rendering the new estimation approach especially appealing
in ill-conditioned problems. The performance of the new approach is
demonstrated using a numerical simulation study.