  This paper presents distributed conjugate gradient algorithms for distributed
parameter estimation and spectrum estimation over wireless sensor networks. In
particular, distributed conventional conjugate gradient (CCG) and modified
conjugate gradient (MCG) are considered, together with incremental and
diffusion adaptive solutions. The distributed CCG and MCG algorithms have an
improved performance in terms of mean square error as compared with least--mean
square (LMS)--based algorithms and a performance that is close to recursive
least--squares (RLS) algorithms. In comparison with existing centralized or
distributed estimation strategies, key features of the proposed algorithms are:
1) more accurate estimates and faster convergence speed can be obtained; 2) the
design of preconditioners for CG algorithms, which have the ability to improve
the performance of the proposed CG algorithms is presented and 3) the proposed
algorithms are implemented in the area of distributed parameter estimation and
spectrum estimation. The performance of the proposed algorithms for distributed
estimation is illustrated via simulations and the resulting algorithms are
distributed, cooperative and able to respond in real time to change in the
environment.
