Presence Of Noisy Inputs Research Articles

Bias-compensated augmented complex-valued NSAF algorithm and its low-complexity implementation

The performance of traditional adaptive filtering algorithms will be degraded when the input signal contains noise. To handle colored noisy input and output measurements in the complex domain, this paper proposes an augmented complex-valued estimation-input NSAF (ACEI-NSAF) algorithm, derived by using estimated noiseless input, which is obtained by the minimization of an instantaneous perturbation with both input and output data, to update the weight vectors. Benefiting from this, the proposed algorithm can achieve unbiased estimation of the unknown system in the presence of noisy inputs, thereby surpassing the augmented complex-valued NSAF (ACNSAF) algorithm. The mean stability, excess mean-square error, and computational complexity are investigated, and the unbiasedness condition of the proposed algorithm is presented. Subsequently, a low-complexity ACEI-NSAF (SACEI-NSAF) algorithm is introduced by using the subband selection approach. Experimental results in system identification demonstrate the effectiveness of the proposed algorithms and analysis.

Diffusion Average-Estimate Bias-Compensated LMS Algorithms Over Adaptive Networks Using Noisy Measurements

In this paper, we consider the problem of distributed estimation over adaptive networks in the presence of noisy input, output and communication links. First, a diffusion average-estimate bias-compensated LMS (D-ABC-LMS) algorithm is devised for processing these noisy measurements. Different from the existing diffusion schemes, it consists of three steps: (i) bias-compensated weight update, (ii) average estimation and (iii) weight combination, where the second step utilizes a moving average technique to process imprecise exchange weights caused by communication link noise. Then, we analyze the stability and convergence of the D-ABC-LMS algorithm, and derive closed-form expressions to predict its steady-state mean-square deviation (MSD) and network MSD (NMSD). In addition, by introducing one more step via the adaptive mixture of the noisy exchange weight vectors and their denoised estimates, we propose a diffusion mixed average-estimate bias-compensated LMS (D-MABC-LMS) method for increasing the convergence rate of the D-ABC-LMS scheme. Finally, computer simulation results show the superiority of the proposed algorithms over previously reported techniques using noisy measurements over adaptive networks.

Influence of input noises on the mean-square performance of the normalized subband adaptive filter algorithm

The normalized subband adaptive filter (NSAF) algorithm has gained a large amount of attention owning to its fast convergence rate for correlated inputs. However, the convergence analysis of the NSAF algorithm has not been researched extensively, especially in the presence of noisy inputs which is frequently encountered in the applications of system identification and channel estimation. In this paper, we perform the performance analysis of the NSAF algorithm under noisy inputs. According to several reasonable assumptions and approximations, the expressions of the transient-state and steady-state mean-square deviation (MSD) are derived. Simulations under different kinds of environments confirm the accuracy of our theoretical expressions.

Widely Linear Complex-Valued Estimated-Input LMS Algorithm for Bias-Compensated Adaptive Filtering With Noisy Measurements

In this paper, a novel widely linear complex-valued estimated-input adaptive filter (WLC-EIAF) is first proposed for processing noisy input and output data in the complex domain. The WLC-EIAF consists of two steps: (i) estimation of noise-free input and (ii) update of the weight vector, which is realized by alternating the minimization of an instantaneous perturbation with both input and output data. Based on the WLC-EIAF method and adopting the least mean-square (LMS) scheme, a widely linear complex-valued estimated-input LMS (WLC-EILMS) algorithm is developed. It is able to achieve an unbiased parameter estimation and, thus, outperforms the widely linear complex-valued LMS (WL-CLMS) algorithm in the presence of noisy input and output. In particular, for Gaussian signals, closed-form expressions are derived for its steady-state excess mean-square error performance. Furthermore, the linear complex-valued estimated-input LMS and linear real-valued estimated-input LMS algorithms are presented, which are two simplified versions of the WLC-EILMS for circular and real-valued signals, respectively. Simulation results demonstrate that the proposed methods achieve significantly improved performance in terms of mean-square deviation and mean-square error when compared to the WL-CLMS and CLMS algorithms.

Latticed-LTL synthesis in the presence of noisy inputs

Latticed-LTL synthesis in the presence of noisy inputs

Fast learning of robot trajectories via unsupervised neural networks

This paper proposes an unsupervised neural network for trajectory learning of a robotic arm. The neural network encodes trajectories by using competitive and temporal Hebbian learning rules and operates by producing the current and the next position for the robotic arm. Different types of trajectories can be learned independently of their complexity. Tests will focus on trajectories with one crossing point. The algorithm is able to reproduce the trajectories accurately and unambiguously due to context units used together with the input. Also, the proposed model is shown to be fault-tolerant and can respond well in the presence of noisy inputs.

Perceptron-like learning in time-summating neural networks

This paper investigates the ability of a single-layer, time-summating neural network to associate and store temporal sequences. In particular, the associative learning of temporal sequences is reformulated as an equivalent classification task involving static patterns. This leads to a generalization of the perceptron learning rule and convergence theorem to the case of temporal sequences. Using geometrical arguments based on linear separability it is shown how a time-summating network can handle temporal features such as ordering and coarticulation effects. Such an ability is a consequence of the fact that the time-summating network develops an activity trace consisting of a decaying sum of all previous inputs to the network. On the other hand, such an activity trace may also lead to an accumulation of errors in the presence of noisy inputs. This motivates a modification of the perceptron learning rule involving the introduction of a stability parameter that guarantees a certain level of robustness to noise. The performance of the network in the presence of random input sequences is then analysed using statistical-mechanical techniques. Finally, it is shown how, with small modifications, the time-summating network can be trained to store and recall complex sequences.

Connectionist hashed associative memory

This paper proposes the use of simple connectionist networks as hashing functions for sparse associative or content addressable memory. The robustness of such networks in the presence of noisy inputs, and the property that “similar inputs lead to similar outputs” permits (in a probabilistic sense) faster-than-linear retrieval of data which best fits the input. The input may be noisy or have partially specified feature vectors. Mathematical analysis is presented for the Boolean feature case using a network with randomly selected connection strengths.

The feasibility of motion and structure from noisy time-varying image velocity information

This research addresses the problem of noise sensitivity inherent in motion and structure algorithms. The motion and structure paradigm is a two-step process. First, we measure image velocities and, perhaps, their spatial and temporal derivatives, are obtained from time-varying image intensity data and second, we use these data to compute the motion of a moving monocular observer in a stationary environment under perspective projection, relative to a single 3-D planar surface. The first contribution of this article is an algorithm that uses time-varying image velocity information to compute the observer's translation and rotation and the normalized surface gradient of the 3-D planar surface. The use of time-varying image velocity information is an important tool in obtaining a more robust motion and structure calculation. The second contribution of this article is an extensive error analysis of the motion and structure problem. Any motion and structure algorithm that uses image velocity information as its input should exhibit error sensitivity behavior compatible with the results reported here. We perform an average and worst case error analysis for four types of image velocity information: full and normal image velocities and full and normal sets of image velocity and its derivatives. (These derivatives are simply the coefficients of a truncated Taylor series expansion about some point in space and time.) The main issues we address here are: just how sensitive is a motion and structure computation in the presence of noisy input, or alternately, how accurate must our image velocity information be, how much and what type of input data is needed, and under what circumstances is motion and structure feasible? That is, when can we be sure that a motion and structure computation will produce usable results? We base our answers on a numerical error analysis we conduct for a large number of motions.