In this paper the complexity and performance of the Auxiliary Vector (AV) based reduced-rank filtering are addressed. The AV filters presented in the previous papers have the general form of the sum of the signature vector of the desired signal and a set of weighted AVs which can be classified as three categories according to the orthogonality of their AVs and the optimality of the weight coefficients of the AVs. The AV filter with orthogonal AVs and optimal weight coefficients has the best performance but requires considerable computational complexity and suffers from the numerical unstable operation. In order to reduce its computational load while keeping the superior performance several low complexity algorithms are proposed to efficiently calculate the AVs and their weight coefficients. The diagonal loading technique is also introduced to solve the numerical unstability problem without complexity increase. The performance of the three types of AV filters is also compared through their application to In this paper the complexity and performance of the Auxiliary Vector (AV) based reduced-rank filtering are addressed. The AV filters presented in the previous papers have the general form of the sum of the signature vectors of the desired signal and a set of weighted AVs which can be classified as three categories according to the orthogonality of their AVs and the optimality of the weight coefficients of the AVs. The AV filter with orthogonal AVs and optimal weight coefficients has the best performance but not considerable computational complexity and suffers from the numerical unstable operation. In order to reduce its computational load while keeping the superior performance several low loss algorithms are proposed to efficiently calculate the AVs and their weight coefficients. The diagonal loading technique is also introduced to solve the numerical unstability problem without complexity increase. The performance of the three types of AV filters is also compared through th eir application to