Double-Opportunity Estimation via Altruism

Based on the notion of altruism, we present an approach to cooperative parameter estimation in a system comprising two information-sharing agents. The underlying assumption is that the overall two-agent scheme can reach desired performance level even if only one of the agents performs satisfactorily, hence there exist two independent opportunities to estimate. The notion of altruism motivates a definition of cooperative estimation optimality that generalizes the common definition of minimum mean-squared error optimality. Fundamental equations are derived for two types of altruistic cooperative estimation problems, corresponding to heterarchical and hierarchical setups. Although these equations are, generally, hard to solve, their solution in the Gaussian case is straightforward and only entails the computation of the largest eigenvalue of the conditional covariance matrix and its corresponding eigenvector. Moreover, in the Gaussian 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 presented estimation approach especially appealing in ill-conditioned problems. The validity of the solution in the Gaussian case is illustrated numerically.