• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.2 no.2
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• pp.67-80
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• 1998

In this paper the linear algebraic system obtained from a singular integral equation with variable coeffcients by a quadrature-collocation method is considered. We study this underdetermined system by means of the Moore Penrose generalized inverse. Convergence in compact subsets of [-1, 1] can be shown under some assumptions on the coeffcients of the equation.

• ETRI Journal
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• v.41 no.5
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• pp.658-669
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• 2019

For dual-channel time-frequency (TF) overlapped signals with low sparsity in underdetermined blind source separation (UBSS), this paper proposes an effective method based on interval probability to estimate and expand the types of mixing matrices. First, the detection of TF single-source points (TF-SSP) is used to improve the TF sparsity of each source. For more distinguishability, as the ratios of the coefficients from different columns of the mixing matrix are close, a local peak-detection mechanism based on interval probability (LPIP) is proposed. LPIP utilizes uniform subintervals to optimize and classify the TF coefficient ratios of the detected TF-SSP effectively in the case of a high level of TF overlap among sources and reduces the TF interference points and redundant signal features greatly to enhance the estimation accuracy. The simulation results show that under both noiseless and noisy cases, the proposed method performs better than the selected mainstream traditional methods, has good robustness, and has low algorithm complexity.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.13 no.5
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• pp.2454-2468
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• 2019

The existing direct position determinations(DPD) for coherently distributed(CD) sources are mostly applicable for uniform linear array(ULA), which result in a low degree of freedom(DOF), and it is difficult for them to realize the effective positioning in underdetermined condition. In this paper, a novel DPD algorithm for coherently distributed sources based on compressed sensing with a moving nested array is present. In this algorithm, the nested array is introduced to DPD firstly, and a positioning model of signal moving station based on nested array is constructed. Owing to the features of coherently distributed sources, the cost function of compressed sensing is established based on vectorization. For the sake of convenience, unconstrained transformation and convex transformation of cost functions are carried out. Finally, the position coordinates of the distribution source signals are obtained according to the theory of optimization. At the same time, the complexity is analyzed, and the simulation results show that, in comparison with two-step positioning algorithms and subspace-based algorithms, the proposed algorithm effectively solves the positioning problem in underdetermined condition with the same physical element number.

• Journal of Broadcast Engineering
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• v.17 no.6
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• pp.954-963
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• 2012

As a greedy algorithm reconstructing the sparse signal from underdetermined system, orthogonal matching pursuit (OMP) algorithm has received much attention. In this paper, we multiple candidate matching pursuit (MuCaMP), which builds up candidate support set in every iteration and uses the minimum residual at last iteration. Using the restricted isometry property (RIP), we derive the sufficient condition for MuCaMP to recover the sparse signal exactly. The MuCaMP guarantees to reconstruct the K-sparse signal when the sensing matrix satisfies the RIP constant ${\delta}_{N+K}<\frac{\sqrt{N}}{\sqrt{K}+3\sqrt{N}}$. In addition, we show a recovery performance both noiseless and noisy measurements.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.49 no.2
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• pp.122-129
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• 2012

As a greedy algorithm reconstructing the sparse signal from underdetermined system, orthogonal matching pursuit (OMP) algorithm has received much attention in recent years. In this paper, we present an extension of OMP for pursuing efficiency of the index selection. Our approach, referred to as generalized OMP (gOMP), is literally a generalization of the OMP in the sense that multiple (N) columns are identified per step. Using the restricted isometry property (RIP), we derive the condition for gOMP to recover the sparse signal exactly. The gOMP guarantees to reconstruct sparse signal when the sensing matrix satisfies the RIP constant ${\delta}_{NK}$ < $\frac{\sqrt{N}}{\sqrt{K}+2\sqrt{N}}$. In addition, we show recovery performance and the reduced number of iteration required to recover the sparse signal.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2012.11a
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• pp.114-116
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• 2012

Sparse한 신호 복원 방법으로 underdetermined system에서 greed 알고리듬은 간결함과 낮은 복잡도로 인해 활발히 연구되고 있다. 이에 본 논문은 기존 greed 알고리듬 기법에서 iteration 마다 다중 경로를 이용하여 스파스 신호를 복원하는 개선된 알고리듬을 제안한다. 모의 실험을 통해 제안된 알고리듬이 기존의 greedy 알고리듬보다 좋은 복원 성능을 가짐을 확인할 수 있다.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2012.07a
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• pp.473-474
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• 2012

Sparse한 신호 복원 방법으로 underdetermined system에서 ll-minimization을 이용한 compressive sensing의 연구와 함께, ll-minimization비에 간단한 greed 알고리듬도 활발히 연구되고 있다. 이에 본 논문은 greed 알고리듬의 대표적인 orthogonal matching pursuit기법에서 iteration 마다 후보 support를 유지하는 알고리듬을 연구한다. 모의 실험을 통해 OMP의 iteration 단계에서 하나의 support만 선택하는 것보다 후보 support를 유지하는 것이 sparse 신호를 복원하는 경우는 OMP와 비슷한 성능을 보이지만 덜 sparse한 신호복원에서는 더 좋은 성능을 보임을 확인 할 수 있다.

• Structural Engineering and Mechanics
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• v.16 no.1
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• pp.17-34
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• 2003

This paper presents a damage assessment procedure applied to periodic spring mass systems using an eigenvalue sensitivity-based method. The damage is directly related to the stiffness reduction of the damage element. The natural frequencies of periodic structures with one single disorder are found by adopting the transfer matrix approach, consequently, the first order approximation of the natural frequencies with respect to the disordered stiffness in different elements is used to form the sensitivity matrix. The analysis shows that the sensitivity of natural frequencies to damage in different locations depends only on the mode number and the location of damage. The stiffness changes due to damage can be identified by solving a set of underdetermined equations based on the sensitivity matrix. The issues associated with many possible damage locations in large structural systems are addressed, and a means of improving the computational efficiency of damage detection while maintaining the accuracy for large periodic structures with limited available measured natural frequencies, is also introduced in this paper. The incomplete measurements and the effect of random error in terms of measurement noise in the natural frequencies are considered. Numerical results of a periodic spring-mass system of 20 degrees of freedom illustrate that the proposed method is simple and robust in locating single or multiple damages in a large periodic structure with a high computational efficiency.

• Proceedings of the KIEE Conference
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• 1995.07b
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• pp.874-876
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• 1995

Force and compliance control has been used in the control of legged walking vehicles to achieve superior terrain adaptability on rough terrains. The compliance control requires distribution of the vehicle load over the supporting legs. However, the constraint equations for ground reaction forces of supporting legs are generally underdetermined, allowing an infinite number of solutions. Thus, it is possible to apply an optimization criteria in solving the force setpoint problem. It has been observed that the previous force setpoint optimization methods sometimes cause a system stability problem and/or the load distribution among supporting legs is not well balanced due to a memory effect on the solution trajectory, This paper presents an iterative force setpoint method to solve this problem using an interpolation technique. By simulation it was shown that an excessive load unbalance among supporting legs and the memory effect in the force trajectory are alleviated much with the proposed method.

• ETRI Journal
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• v.43 no.5
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• pp.869-880
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• 2021

Herein, we estimate the direction of arrival (DOA) of non-Gaussian signals for nested arrays (NAs) by implementing the fourth-order difference co-array (FODC) and successive methods. In particular, considering the property of the fourth-order cumulant (FOC), we first construct the FODC of the NA, which can obtain O(N⁴) virtual elements using N physical sensors, whereas conventional FOC methods can only obtain O(N²) virtual elements. In addition, the closed-form expression of FODC is presented to verify the enhanced degrees of freedom (DOFs). Subsequently, we exploit the vectorized FOC (VFOC) matrix to match the FODC of the NA. Notably, the VFOC matrix is a single snapshot vector, and the initial DOA estimates can be obtained via the discrete Fourier transform method under the underdetermined correlation matrix condition, which utilizes the complete DOFs of the FODC. Finally, fine estimates are obtained through the spatial smoothing-Capon method with partial spectrum searching. Numerical simulation verifies the effectiveness and superiority of the proposed method.