The ongoing development of gain-scheduled filters is motivated by the estimation of the sideslip angle of ground vehicles. The present work proposes an approach based on finite-frequency specifications and an energy-to-peak (E2P) index for designing linear parameter-varying (LPV) filters. After reporting a new theoretical result, analysis and synthesis conditions are proposed for gain-scheduled and robust filters. Their properties are tested and illustrated using a simulated ground vehicle system via a comparative study, highlighting the advantages of the proposed approach.