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Aiming at the above problem, a novel multi-sensor marginalized particle filter based on average weight optimization in correlated noise is proposed.
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If r ¯ ≠ 0, then the above problem has at least one solution.
Therefore, from Theorem 3.1, the above problem has at least one positive solution.
Thus the above problem possesses at least one positive solution in K.
Therefore, by Theorem 2, we know that the above problem has at least one solution.
According to Theorem 1.1, the above problem has at least one weak solution.
Therefore, from Theorem 3.3, it is easy to see that the above problem has at least one positive solution.
By using Theorem 3.5, the above problem has at least one solution if b < ( κ N − 2 ) 1 + λ.
Thus,,,, and satisfy the conditions of Theorem 3.1, and there exists at least a positive solution of the above problem.
end{cases} Therefore, from Theorem 3.2, it is easy to see that the above problem has at least one positive solution.
And he got the existence of at least two positive solutions of the above problem by means of a fixed point theorem in a cone.
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