  The work concerns the space-distribution dependent Zakai equations from
nonlinear filtering problems of McKean-Vlasov stochastic differential equations
with correlated noises. First of all, we establish the space-distribution
dependent Kushner-Stratonovich equations and the space-distribution dependent
Zakai equations. Then, the pathwise uniqueness of their strong solutions is
shown. Finally, we prove a superposition principle between the
space-distribution dependent Zakai equations and space-distribution dependent
Fokker-Planck equations. As a by-product, we give some conditions under which
space-distribution dependent Fokker-Planck equations have weak solutions.

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