We present an estimation method for agricultural crop yield functions, when unobserved productivity depends on water availability that is only partially observed. Using the setting of Bayesian non-linear filtering for estimating Hidden Markov Models, we discuss joint estimation of state variables and parameters in a structural production model with potentially endogenous regressors. An extension to particle filtering with resampling, convolution filter based on kernel regularization, is then discussed. We apply this non-parametric method to estimate a system of structural equations for rice crop yield and unobserved productivity on panel data for 10 districts in Punjab, India. Results based on computer-intensive resampling steps illustrate the interest of convolution particle filtering techniques, with low interquartile range of time-varying estimates. We compare fertilizer elasticity estimates with and without accounting for unobserved productivity, and we find a significant relationship between unobserved productivity and nitrogen fertilizer input, when the former is conditioned on district-level climate variables (summer rainfall, potential evapotranspiration).