Precisely　measuring　the　rotor＇s　position　is　a　prerequisite　for　brushless　DC　motors　(BLDC)　to　start　quickly　and　commutate　accurately.　However,　it　is　impossible　to　exactly　detect　the　rotor＇s　position　because　the　signals　of　back　electromotive　force　(BEMF)　are　weak　when　the　BLDC　is　at　a　low　speed.　By　using　the　state-space　equation,　the　Luenberger　observer,　with　directly　detected　input　signals,　is　able　to　estimate　the　current　BEMF　signals.　But,　the　observational　error　increases　obviously　when　there　are　matching　errors　between　the　parameters　of　the　observer　and　the　actual　parameters　of　the　BLDC.　Sliding　mode　observer　(SMO),　relying　on　its　sliding　characteristic,　has　the　advantage　of　good　robustness　to　the　variation　of　system　parameters.　However,　the　observational　error　is　large.　Hence,　it　is　possible　that　there　exists　an　observer,　whose　robustness　is　superior　to　the　Luenberger　observer,　and　observational　error　is　smaller　than　the　SMO.　With　the　method　of　optimizing　parameter,　the　switch　function　can　be　optimized.　Simulation　results　prove　the　existence　of　the　observer.　By　contrasting　and　analyzing　the　simulation　results,　it　is　proved　that　the　robustness　of　the　designed　observer　is　superior　to　the　Luenberger　observer,　meantime　the　observational　error　is　smaller　than　the　SMO.