Matched-field based methods always involve the comparison of the output of a physical model and the actual data. The method of comparison and the nature of the data varies according to the problem at hand, but the result becomes always largely conditioned by the accurateness of the physical model and the amount of data available. The usage of broadband methods has become a widely used approach to increase the amount of data and to stabilize the estimation process. Due to the difficulties to accurately predict the phase of the acoustic field the problem whether the information should be coherently or incoherently combined across frequency has been an open debate in the last years. This paper provides a data consistent model for the observed signal, formed by a deterministic channel structure multiplied by a perturbation random factor plus noise. The cross-frequency channel structure and the decorrelation of the perturbation random factor are shown to be the main causes of processor performance degradation. Different Bartlett processors, such as the incoherent processor [Baggeroer et al., J. Acoust. Soc. Am. 80, 571-587 (1988)], the coherent normalized processor [Z.-H. Michalopoulou, IEEE J. Ocean Eng. 21, 384-392 (1996)] and the matched-phase processor [Orris et al., J. Acoust. Soc. Am. 107, 2563-2375 (2000)], are reviewed and compared to the proposed cross-frequency incoherent processor. It is analytically shown that the proposed processor has the same performance as the matched-phase processor at the maximum of the ambiguity surface, without the need for estimating the phase terms and thus having an extremely low computational cost.