Using the climate model of intermediate complexity LOVECLIM in an idealised framework, we assess three data-assimilation methods for reconstructing the climate state. The methods are a nudging, a particle filter with sequential importance resampling, and a nudging proposal particle filter and the test case corresponds to the climate of the high latitudes of the Southern Hemisphere during the past 150 yr. The data-assimilation methods constrain the model by pseudo-observations of surface air temperature anomalies obtained from the same model, but different initial conditions. All three data-assimilation methods provide with good estimations of surface air temperature and of sea ice concentration, with the nudging proposal particle filter obtaining the highest correlations with the pseudo-observations. When reconstructing variables that are not directly linked to the pseudo-observations such as atmospheric circulation and sea surface salinity, the particle filters have equivalent performance and their correlations are smaller than for surface air temperature reconstructions but still satisfactory for many applications. The nudging, on the contrary, obtains sea surface salinity patterns that are opposite to the pseudo-observations, which is due to a spurious impact of the nudging on vertical exchanges in the ocean.