  This paper proposes a consensus-based distributed nonlinear filter with
kernel mean embedding (KME). This fills with gap of posterior density
approximation with KME for distributed nonlinear dynamic systems. To
approximate the posterior density, the system state is embedded into a
higher-dimensional reproducing kernel Hilbert space (RKHS), and then the
nonlinear measurement function is linearly converted. As a result, an update
rule of KME of posterior distribution is established in the RKHS. To show the
proposed distributed filter being capable of achieving the centralized
estimation accuracy, a centralized filter, serving as an extension of the
standard Kalman filter in the state space to the RKHS, is developed first.
Benefited from the KME, the proposed distributed filter converges to the
centralized one while maintaining the distributed pattern. Two examples are
introduced to demonstrate the effectiveness of the developed filters in target
tracking scenarios including nearly constantly moving target and turning
target, respectively, with bearing-only, range and bearing measurements.
