  This study proposes a coupled velocity model (CVM) that establishes the
relation between the orientation and velocity using their correlation, avoiding
that the existing extended object tracking (EOT) models treat them as two
independent quantities. As a result, CVM detects the mismatch between the prior
dynamic model and actual motion pattern to correct the filtering gain, and
simultaneously becomes a nonlinear and state-coupled model with multiplicative
noise. The study considers CVM to design a feasible distributed weighted least
squares (WLS) filter. The WLS criterion requires a linear state-space model
containing only additive noise about the estimated state. To meet the
requirement, we derive such two separate pseudo-linearized models by using the
first-order Taylor series expansion. The separation is merely in form, and the
estimates of interested states are embedded as parameters into each other's
model, which implies that their interdependency is still preserved in the
iterative operation of two linear filters. With the two models, we first
propose a centralized WLS filter by converting the measurements from all nodes
into a summation form. Then, a distributed consensus scheme, which directly
performs an inner iteration on the priors across different nodes, is proposed
to incorporate the cross-covariances between nodes. Under the consensus scheme,
a distributed WLS filter over a realistic network with ``naive'' node is
developed by proper weighting of the priors and measurements. Finally, the
performance of proposed filters in terms of accuracy, robustness, and
consistency is testified under different prior situations.
