The optimal filter (minimum mean square error) of discrete bilinear stochastic systems with output feedback is studied here. The sequential filter of bilinear systems is derived for suboptimal adaptive estimation of the unknown aprioristate and observation-noise statistics simultaneously with the bilinear system state. The unbiased estimations of state-noise varianceQand observation-noise variance R are obtained under some usual conditions. For on-line operation, this paper gives the recursive form of this adaptive suboptimal filter (ASF). Computer simulations show that ASF approximates the minimum mean square error (MSE) filter very well, and ASF provides improved state estimates at little computing expense