Recursive Least Squares Identification With Variable-Direction Forgetting via Oblique Projection Decomposition

In this paper,a new recursive least squares(RLS)identification algorithm with variable-direction forgetting(VDF)is proposed for multi-output systems.The objective is to enhance parameter estimation performance under non-persistent excitation.The proposed algorithm performs oblique projection decomposition of the information matrix,such that forgetting is applied only to directions where new information is received.Theoretical proofs show that even without persistent excitation,the information matrix remains lower and upper bounded,and the estimation error variance converges to be within a finite bound.Moreover,detailed analysis is made to compare with a recently reported VDF algorithm that exploits eigenvalue decomposition(VDF-ED).It is revealed that under non-persistent excitation,part of the forgotten subspace in the VDF-ED algorithm could discount old information without receiving new data,which could produce a more ill-conditioned information matrix than our proposed algorithm.Numerical simulation results demonstrate the efficacy and advantage of our proposed algorithm over this recent VDF-ED algorithm.

Short-range clutter suppression method combining oblique projection and interpolation in airborne CFA radar

The airborne conformal array(CFA)radar's clutter ridges are range-modulated,which result in a bias in the estimation of the clutter covariance matrix(CCM)of the cell under test(CUT),further,reducing the clutter suppression performance of the airborne CFA radar.The clutter ridges can be effectively compensated by the space-time separation interpolation(STSINT)method,which costs less computation than the space-time interpolation(STINT)method,but the performance of interpolation algorithms is seriously affected by the short-range clutter,especially near the platform height.Location distributions of CFA are free,which yields serious impact that range spaces of steering vector matrices are non-orthogonal complement and even no longer disjoint.Further,a new method is proposed that the shortrange clutter is pre-processed by oblique projection with the intersected range spaces(OPIRS),and then clutter data after being pre-processed are compensated to the desired range bin through the STSINT method.The OPIRS also has good compatibility and can be used in combination with many existing methods.At the same time,oblique projectors of OPIRS can be obtained in advance,so the proposed method has almost the same computational load as the traditional compensation method.In addition,the proposed method can perform well when the channel error exists.Computer simulation results verify the effectiveness of the proposed method.

A Count Sketch Maximal Weighted Residual Kaczmarz Method with Oblique Projection for Highly Overdetermined Linear Systems

Motivated by the count sketch maximal weighted residual Kaczmarz (CS-MWRK) method presented by Zhang and Li (Appl. Math. Comput., 410, 126486), we combine the count sketch tech with the maximal weighted residual Kaczmarz Method with Oblique Projection (MWRKO) constructed by Wang, Li, Bao and Liu (arXiv: 2106.13606) to develop a new method for solving highly overdetermined linear systems. The convergence rate of the new method is analyzed. Numerical results demonstrate that our method performs better in computing time compared with the CS-MWRK and MWRKO methods.

Partial Oblique Projection Learning for Optimal Generalization

In practice, it is necessary to implement an incremental and active learning for a learning method. In terms of such implementation, this paper shows that the previously discussed S-L projection learning is inappropriate to constructing a family of projection learning, and proposes a new version called partial oblique projection (POP) learning. In POP learning, a function space is decomposed into two complementary subspaces, so that functions belonging to one of the subspaces can be completely estimated in noiseless case; while in noisy case, the dispersions are set to be the smallest. In addition, a general form of POP learning is presented and the results of a simulation are given.

Sparse recovery method for far-field and near-field sources localization using oblique projection

In this paper, we propose a novel source localization method to estimate parameters of arbitrary field sources, which may lie in near-field region or far-field region of array aperture. The proposed method primarily constructs two special spatial-temporal covariance matrixes which can avoid the array aperture loss, and then estimates the frequencies of signals to obtain the oblique projection matrixes. By using the oblique projection technique, the covariance matrixes can be transformed into several data matrixes which only contain single source information, respectively. At last, based on the sparse signal recovery method, these data matrixes are utilized to solve the source localization problem. Compared with the existing typical source localization algorithms, the proposed method improves the estimation accuracy, and provides higher angle resolution for closely spaced sources scenario. Simulation results are given to demonstrate the performance of the proposed algorithm.

Projection Improved SPAI Preconditioner for FGMRES

Krylov subspace methods are widely used for solving sparse linear algebraic equations,but they rely heavily on preconditioners,and it is difficult to find an effective preconditioner that is efficient and stable for all problems.In this paper,a novel projection strategy including the orthogonal and the oblique projection is proposed to improve the preconditioner,which can enhance the efficiency and stability of iteration.The proposed strategy can be considered as a minimization process,where the orthogonal projection minimizes the energy norm of error and the oblique projection minimizes the 2-norm of the residual,meanwhile they can be regarded as approaches to correct the approximation by solving low-rank inverse of the matrices.The strategy is a wide-ranging approach and provides a way to transform the constant preconditioner into a variable one.The paper discusses in detail the projection strategy for sparse approximate inverse(SPAI)preconditioner applied to flexible GMRES and conducts the numerical test for problems from different applications.The results show that the proposed projection strategy can significantly improve the solving process,especially for some non-converging and slowly convergence systems.

N4SID and MOESP Algorithms to Highlight the Ill-conditioning into Subspace Identification

In this paper,an analysis for ill conditioning problem in subspace identifcation method is provided.The subspace identifcation technique presents a satisfactory robustness in the parameter estimation of process model which performs control.As a frst step,the main geometric and mathematical tools used in subspace identifcation are briefly presented.In the second step,the problem of analyzing ill-conditioning matrices in the subspace identifcation method is considered.To illustrate this situation,a simulation study of an example is introduced to show the ill-conditioning in subspace identifcation.Algorithms numerical subspace state space system identifcation(N4SID)and multivariable output error state space model identifcation(MOESP)are considered to study,the parameters estimation while using the induction motor model,in simulation(Matlab environment).Finally,we show the inadequacy of the oblique projection and validate the efectiveness of the orthogonal projection approach which is needed in ill-conditioning;a real application dealing with induction motor parameters estimation has been experimented.The obtained results proved that the algorithm based on orthogonal projection MOESP,overcomes the situation of ill-conditioning in the Hankel s block,and thereby improving the estimation of parameters.

Robust linear receivers for STBC systems with unknown co-channel interference

Focusing on space-time block code （STBC） systems with unknown co-channel interference, an oblique projection-based robust linear receiver is proposed in this paper.Based on the oblique projection, the desired signal subspace and interference-plus-noise subspace are first identified from the received signal.Then the matched filter receiver is used to decode the STBC encoded signals in the desired signal subspace.Simulation results show that the proposed linear receiver obtains significant performance improvement over conventional Capon-type receivers under finite sample-size situations and in the presence of channel estimation errors.