Satellite radar altimetry appears to be a highly promising method that could be used to complement in situ limnimetric station surveys in remote river basins. However, a major drawback of satellite altimetry is its poor temporal resolution. The sampling period ranges from 10 to 35 days, depending on the satellite. This paper proposes a methodology for obtaining time series with a one-day sampling period. The method is based on a linear model exploiting data at a limited number of in situ limnimetric stations. Three parameter estimation methods are proposed: the least square (LS) and weighted least square (WLS) methods, and an optimization method based on a multi-objective criterion (OPT). The model and parameter estimation methods are evaluated by means of simulated altimetric time series whose characteristics are as realistic as possible. The absolute precision of the interpolation and its sensitivity to model structures, missing values and random noise are investigated. The RMS of the interpolation residuals ranges from 0.6 to 40.9 cm. Results show that taking into account more than one in situ reference station significantly decreases the RMS errors. Taking into account time shifts between stations improves the results too, reducing the RMS error by 16.4 cm (32.7%) in one case. In the ideal case, i.e. with no missing values and random noise, the OPT technique provides slightly better absolute results than the LS method, and significantly better results than the WLS approach. The OPT method is the least sensitive to missing values and random noise, two artefacts that systematically affect radar altimetric data.