  Motivated by estimation problems arising in autonomous vehicles and
decentralized control of unmanned aerial vehicles, we consider multi-agent
estimation and filtering problems in which multiple agents generate state
estimates based on decentralized information and the objective is to minimize a
coupled mean-squared error which we call \emph{team mean-square error}. We call
the resulting estimates as minimum team mean-squared error (MTMSE) estimates.
We show that MTMSE estimates are different from minimum mean-squared error
(MMSE) estimates. We derive closed-form expressions for MTMSE estimates, which
are linear function of the observations where the corresponding gain depends on
the weight matrix that couples the estimation error. We then consider a
filtering problem where a linear stochastic process is monitored by multiple
agents which can share their observations (with delay) over a communication
graph. We derive expressions to recursively compute the MTMSE estimates. To
illustrate the effectiveness of the proposed scheme we consider an example of
estimating the distances between vehicles in a platoon and show that MTMSE
estimates significantly outperform MMSE estimates and consensus Kalman
filtering estimates.
