A difficult aspect of multimodal estimation is the possible discrepancybetween the sampling rates and/or the noise levels of theconsidered data. Many algorithms cope with these dissimilaritiesempirically. In this paper, we propose a conceptual analysis ofmultimodality where we try to find the “optimal” way of combiningmodalities. More specifically, we consider a simple Kalman filteringframework where several noisy sensors with different samplingfrequences and noise variances regularly observe a hidden state.We experimentally underline some relationships between the samplinggrids and the asymptotic variance of the maximum a posteriori(MAP) estimator. However, the explicit study of the asymptoticvariance seems intractable even in the simplest cases. We describe apromising idea to circumvent this difficulty: exploiting a stochasticmeasurement model for which one can more easily study the averageasymptotic behavior.