NamWoong Kong

Scheduled-Stepsize NLMS Algorithm

This paper presents a method of scheduling stepsizes for the normalized least-mean-squares (SS-NLMS) algorithm. Geometrically interpreting the mean square deviation (MSD) learning curve leads to establishing an objective curve and to constructing a lookup table of stepsizes in order for the MSD to follow the curve. The SS-NLMS shows not only good performance but also robustness with respect to different signal-to-noise ratio (SNR) in measurement noise and different correlation in input signals with a very small number of online computations. Moreover, the scalability of the tabled stepsize with respect to the number of taps is described. For the efficient memory usage in practice, a modified version replaces the tabled stepsizes by down-sampled stepsizes with no performance degradation.

An Affine Projection Algorithm Based on Reuse Time of Input Vectors

This letter proposes an affine projection algorithm (APA) based on the concept of reuse time of the current input vector. Reuse time is defined as the survival period of an input vector, during which the input vector is continuously reused in the subsequent update equations. The algorithm consists of two key procedures: assignment and reduction. The assignment procedure assigns a fundamental reuse-time or zero to the individual reuse time of each current input vector only once by checking whether the current input vector has enough information for update, which eliminates the repetitive selection procedure for input vectors. The reduction procedure gradually decreases the fundamental reuse time by examining, from a stochastic point of view, whether the current error reaches the steady-state value, which indirectly controls the number of input vectors; this leads to fast convergence and small estimation errors. Through these two procedures, the proposed algorithm achieves not only improved performance but also extremely low computational complexity.

A two-stage affine projection algorithm with mean-square-error-matching step-sizes

This paper proposes a two-stage affine projection algorithm (APA) with different projection orders and step-sizes. The proposed algorithm has a high projection order and a fixed step-size to achieve fast convergence rate at the first stage and a low projection order and a variable step-size to achieve small steady-state estimation errors at the second stage. The stage transition moment from the first to the second stage is determined by examining, from a stochastic point of view, whether the current error reaches the steady-state value. Moreover, in order to prevent the sudden drop of convergence rate on switching from a high projection order to a low projection order, a matching step-size method has been introduced to determine the initial step-size of the second stage by matching the mean-square errors (MSEs) before and after the transition moment. In order to continuously reduce steady-state estimation errors, the proposed algorithm adjusts the step-size of the second stage by employing a simple algorithm. Because of the reduced projection orders and variable step-size in the steady-state, the algorithm achieves improved performance as well as extremely low computational complexity as compared to the existing APAs with selective input vectors and APAs with variable step-size.

Variable matrix-type step-size affine projection algorithm with orthogonalized input vectors

In this paper, we propose a variable matrix-type step-size affine projection algorithm (APA) with orthogonalized input vectors. We generate orthogonalized input vectors using the Gram-Schmidt process to implement the weight update equation of the APA using the sum of normalized least mean squares (NLMS)-like updating equations. This method allows us to use individual step sizes corresponding to each NLMS-like equation, which is equivalent to adopting the step size in the form of a diagonal matrix in the APA. We adopt a variable step-size scheme, in which the individual step sizes are determined to minimize the mean square deviation of the APA in order to achieve the fastest convergence on every iteration. Furthermore, because of the weight vector updated successively only along each innovative one among the reused inputs and effect of the regularization absorbed into the derived step size, the algorithm works well even for badly excited input signals. Experimental results show that our proposed algorithm has almost optimal performance in terms of convergence rate and steady-state estimation error, and these results are remarkable especially for badly excited input signals.

Variable regularized least-squares algorithm

This paper proposes a new variable regularized least-squares (VR-LS) algorithm by recursively constructing a weighting scalar of the regularized least-squares (LS) cost function. Since the recursive LS (RLS) algorithm provides the best performances by all of VR-LS algorithms, the design objective of the weighting scalar is chosen such that equivalent optimality is ensured between one-step-ahead cost functions of the RLS and of the VR-LS algorithm. The proposed VR-LS algorithm functions similarly as the RLS with uncorrelated inputs; however, this is not the case with colored (correlated) inputs. Therefore, a conventional filtering technique is applied to both on the inputs and on the desired signals so as to obtain whitened inputs. This enables the proposed algorithm handle the case of correlated inputs.

Vision-based camber measurement system in the endless hot rolling process

In the endless hot rolling process, camber is a significant defect where camber is flatness asymmetries produced by nonuniform distribution of rolling pressure. This kind of defect may not only cause clogging of the finishing mill, but also visible defects, such as bar edge folds, edge cracks, holes, and scrapes. It is important to measure the exact camber values of the overall shape and head/tail part of steel bars to reduce camber for hot-rolled steel bars. We introduce a vision-based camber measurement system based on two-area-scan charge-coupled device (CCD) cameras and proposes a camber-detection algorithm to achieve the optimal cutting-line, the overall bar shape, and camber values from the obtained image. The proposed algorithm consists of three parts: optimal cutting-line detection, image-stitching, and camber detection. The optimal cutting-line detection part determines the cutting line of the head/tail part of the bar for continuous joining between steel bars. The image-stitching part obtains the overall shape of a hot-rolled steel bar with continuous image sequence obtained by two-area-scan CCD cameras. The camber-detection part measures head camber, tail camber, and whole camber of the steel bar. Through the proposed camber-detection algorithm, the system not only satisfies a time constraint for detecting the camber of the steel bar but also obtains the optimal cutting line, the overall bar shape, and the camber values.

An Affine Projection Algorithm With Update-Interval Selection

This paper presents a mean-square deviation (MSD) analysis of the periodic affine projection algorithm (P-APA) and two update-interval selection methods to achieve improved performance in terms of the convergence and the steady-state error. The MSD analysis of the P-APA considers the correlation between the weight error vector and the measurement noise vector. Using this analysis, it is verified that the update interval governs the trade-off between the convergence rate and the steady-state errors in the P-APA. To overcome this drawback, the proposed APAs increase the update interval when the adaptive filter reaches the steady state. Consequently, these algorithms can reduce the overall computational complexity. The simulation results show that the proposed APAs perform better than the previous algorithms.

An affine projection algorithm using the inner product of input vectors

This paper proposes an affine projection algorithm (APA) using the inner product between input vectors. The existing APAs have fast convergence rate but large steady-state estimation errors. In order to reduce the estimation errors, the proposed algorithm adjusts the number of the input vectors by grouping of the input vectors. The grouping process uses the angle between a current input vector and past input vectors. The proposed algorithm puts the input vectors with a similar angle size into the same group and replaces input vectors in the group with the representative input vector. The angle interval for the grouping adjusts the number of groups and is gradually increasing to reduce the number of input vector at the steady state. This leads to reduce the steady-state estimation errors. The experimental results show that the proposed algorithm has small steady-state estimation errors comparing to the existing algorithms.

Development of defect detection algorithm in cold rolling

In this paper, we propose the defect detection algorithm using the image processing in cold rolling. This algorithm consists of two separated parts: defect detection of the steel sheet in a rolling process and defect detection of the cutting plane in a side trimming process. The objective of the crack and hole detection is to find the position and diameter of holes and some information of cracks such as the depth, width, position, and type. Furthermore, the objective of the defect detection for the cutting plane is to find the position of defects on the cutting plane, the number of those, and the thickness ratio between the cutting plane and the cold rolled steel sheets. Experimental results show that the proposed algorithm finds the defect information of cold rolled steel sheets satisfying the processing-speed constraint of 30 frames/sec.

An Affine Projection Algorithm with Two Numbers of Input Vectors

This paper presents an affine projection algorithm (APA) with a large number of input vectors at the first stage and with a small number of input vectors at the second stage, where the transition is performed by using the criterion for computing the optimum number of input vectors in the dynamic selection APA (DS-APA). The proposed algorithm has fast convergence at the first stage and a small steady-state estimation error at the second stage, which performs like APAs with the selective input vectors including DS-APA. However, the proposed algorithm has only two fixed numbers of input vectors and low complexity, which is more applicable for hardware implementation comparing to APAs with the selective input vectors. Simulations illustrate the performance of the proposed algorithm.