Multiple‐constraint Adaptive Filtering

Abstract

An algorithm is derived for multichannel time‐series data processing, which maintains specified initial multiple filter constraints for known signal or noise sources while simultaneously adapting the filter to minimize the effect of the unknown noise field. Problems of implementing the technique such as convergence, determination of a starting filter, and comparison of results with conventional filters are discussed and illustrated with data from a vertical seismic array. The procedure is shown to be stable and obtains approximately 3–4 db gain in S/N improvement over conventional Wiener filtering in the band 1 to 3 hz.

Quadratically Constrained Beamforming Robust Against Direction-of-Arrival Mismatch

“…In [13]- [20], the linear constraint of the MVDR in (3) has been generalized to a set of linear constraints as subject to (7) where is an matrix and is an vector. The solution can be found by using the Lagrange multiplication method as This is called the LCMV beamformer.…”

“…We first loosen the constraint by choosing only two constraints and from the infinite constraints for . The corresponding optimization problem can be written as subject to and (13) Due to the fact that the constraint is loosened, the minimum to this problem is a lowerbound of the original problem in (11). Note that the constraint in (13) is a nonconvex quadratic constraint.…”

“…Therefore, this approach can be viewed as an LCMV beamformer with a further optimized in (7). However, this approach is reformulated from the nonconvex quadratic problem in (13). It is intrinsically different from a linearly constrained problem.…”

“…There are many methods developed for solving the DOA mismatch problem. In [13]- [20], linear constraints have been imposed when minimizing the output variance. The linear constraints can be designed to broaden the main beam of the beampattern.…”

Magnitude Constraint Minimum Variance Beamformer With Conjugate Symmetric Constraint and Norm Constraint

“…However, both the two methods require the error bound of steering vector which is hard to preset in some practical applications. The linear constraint minimum variance (LCMV) method uses equality linear constraints to force the responses near the DOA of SOI to be unity, which broadens the main lobe of the beampattern and improves the robustness of adaptive beamforming against DOA mismatch [20,21]. However, the LCMV beamformer could not achieve the best SINR performance due to the deviation between the optimal array responses and the preset unity-ones in the constrained directions.…”