This　paper　considers　modeling　for　tracking　of　extended　objects　using　measurements　of　down-range　and　cross-range　extent.　Modeling　smooth/non-smooth　objects　of　complex　geometric　shapes　using　support　functions　and　extended　Gaussian　images,　although　efficient,　may　not　be　easily　obtained.　In　view　of　this,　the　approaches　based　on　support　functions　and　extended　Gaussian　images　are　extended　and　further　developed.　In　this　paper,　we　attempt　to　model　a　complex　extended　object　as　a　Minkowski　addition　of　multiple　simple　sub-objects,　each　represented　by　a　support　function　or　extended　Gaussian　image.　Due　to　favorable　properties　of　the　Minkowski　addition,　the　new　approach　can　make　full　use　of　common　and　individual　properties　of　sub-objects　and　capture　more　detailed　shape　information.　This　facilitates　not　only　object　modeling,　but　also　derivation　of　tracking　algorithms.　Thus　the　proposed　approach　can　be　extended　to　the　case　with　a　variety　of　complex　objects.　Simulation　results　demonstrated　the　benefits　of　the　proposed　approach.