A multivariate score-driven filter is developed to extract signals from noisy vector processes. By assuming that the conditional location vector from a multivariate Student’s t distribution changes over time, we construct a robust filter which is able to overcome several issues that naturally arise when modeling heavy-tailed phenomena and, more in general, vectors of dependent non-Gaussian time series. We derive conditions for stationarity and invertibility and estimate the unknown parameters by maximum likelihood. Strong consistency and asymptotic normality of the estimator are derived. Analytical formulae are derived which consent to develop estimation procedures based on a fast and reliable Fisher scoring method. An extensive Monte–Carlo study is designed to assess the finite samples properties of the estimator, the impact of initial conditions on the filtered sequence, the performance when some of the underlying assumptions are violated, such as symmetry of the underlying distribution and homogeneity of the degrees of freedom parameter across marginals. The theory is supported by a novel empirical illustration that shows how the model can be effectively applied to estimate consumer prices from home scanner data.