In this paper, we propose a general robust subband adaptive filtering (GR-SAF) scheme against impulsive noise by minimizing the mean square deviation under the random-walk model with individual weight uncertainty. Specifically, by choosing different scaling factors such as from the M-estimate and maximum correntropy robust criteria in the GR-SAF scheme, we can easily obtain different GR-SAF algorithms. Importantly, the proposed GR-SAF algorithm can be reduced to a variable regularization robust normalized SAF algorithm, thus having fast convergence rate and low steady-state error. Simulations in the contexts of system identification with impulsive noise and echo cancellation with double-talk have verified that the proposed GR-SAF algorithms outperforms its counterparts.
Southwest University of Science and Technology（西南科技大学）；Southwest Jiaotong University（西南交通大学）；PUC-Rio（里约热内卢天主教大学）；University of York（约克大学）；Sichuan University（四川大学）
We propose two sparsity-aware normalized subband adaptive filter (NSAF) algorithms by using the gradient descent method to minimize a combination of the original NSAF cost function and the l1-norm penalty function on the filter coefficients. This l1-norm penalty exploits the sparsity of a system in the coefficients update formulation, thus improving the performance when identifying sparse systems. Compared with prior work, the proposed algorithms have lower computational complexity with comparable performance. We study and devise statistical models for these sparsity-aware NSAF algorithms in t…
Southwest University of Science and Technology（西南科技大学）；Zhejiang Lab（之江实验室）；PUC-Rio（里约热内卢天主教大学）；University of York（约克大学）；Harbin Engineering University（哈尔滨工程大学）
In this paper, we propose and analyze the sparsity-aware sign subband adaptive filtering with individual weighting factors (S-IWF-SSAF) algorithm, and consider its application in acoustic echo cancellation (AEC). Furthermore, we design a joint optimization scheme of the step-size and the sparsity penalty parameter to enhance the S-IWF-SSAF performance in terms of convergence rate and steady-state error. A theoretical analysis shows that the S-IWF-SSAF algorithm outperforms the previous sign subband adaptive filtering with individual weighting factors (IWF-SSAF) algorithm in sparse scenarios. I…
Southwest University of Science and Technology（西南科技大学）；University of York（约克大学）；PUC-Rio（里约热内卢天主教大学）
This paper proposes a unified sparsity-aware robust normalized subband adaptive filtering (SA-RNSAF) algorithm for identification of sparse systems under impulsive noise. The proposed SA-RNSAF algorithm generalizes different algorithms by defining the robust criterion and sparsity-aware penalty. Furthermore, by alternating optimization of the parameters (AOP) of the algorithm, including the step-size and the sparsity penalty weight, we develop the AOP-SA-RNSAF algorithm, which not only exhibits fast convergence but also obtains low steady-state misadjustment for sparse systems. Simulations in …
Differentiable Adaptive Kalman Filtering via Optimal Transport
Shanghai Research Institute for Intelligent Autonomous Systems（上海智能自主系统研究所）；Tongji University（同济大学）；School of Computer Science and Technology（计算机科学与技术学院）；Shanghai Jiaotong University（上海交通大学）；Shanghai Zhangjiang Institute of Mathematics（上海张江数学研究所）；East China Normal University（华东师范大学）
Online convex optimization is a sequential prediction framework with the goal to track and adapt to the environment through evaluating proper convex loss functions. We study efficient particle filtering methods from the perspective of such a framework. We formulate an efficient particle filtering methods for the non-stationary environment by making connections with the online mirror descent algorithm which is known to be a universal online convex optimization algorithm. As a result of this connection, our proposed particle filtering algorithm proves to achieve optimal particle efficiency.
We formulate the problem of neural network optimization as Bayesian filtering, where the observations are the backpropagated gradients. While neural network optimization has previously been studied using natural gradient methods which are closely related to Bayesian inference, they were unable to recover standard optimizers such as Adam and RMSprop with a root-mean-square gradient normalizer, instead getting a mean-square normalizer. To recover the root-mean-square normalizer, we find it necessary to account for the temporal dynamics of all the other parameters as they are geing optimized. The…
Southwest University of Science and Technology（西南科技大学）；JingWei HiRain（经纬恒润）；PUC-Rio（里约热内卢天主教大学）；University of York（约克大学）；Sichuan University（四川大学）
In this paper, we propose a novel normalized subband adaptive filter algorithm suited for sparse scenarios, which combines the proportionate and sparsity-aware mechanisms. The proposed algorithm is derived based on the proximal forward-backward splitting and the soft-thresholding methods. We analyze the mean and mean square behaviors of the algorithm, which is supported by simulations. In addition, an adaptive approach for the choice of the thresholding parameter in the proximal step is also proposed based on the minimization of the mean square deviation. Simulations in the contexts of system …
Key Laboratory of Magnetic Suspension Technology and Maglev Vehicle, Ministry of Education（磁悬浮技术与磁浮车辆教育部重点实验室）；School of Electrical Engineering, Southwest Jiaotong University（西南交通大学电气工程学院）
In recent years, the multitask diffusion least mean square (MD-LMS) algorithm has been extensively applied in the distributed parameter estimation and target tracking of multitask network. However, its performance is mainly limited by two aspects, i.e, the correlated input signal and impulsive noise interference. To overcome these two limitations simultaneously, this paper firstly introduces the subband adaptive filter (SAF) into the multitask network. Then, a robust multitask diffusion normalized M-estimate subband adaptive filtering (MD-NMSAF) algorithm is proposed by solving the modified Hu…
This paper studies the statistical models of the noise-robust normalized subband adaptive filter (NR-NSAF) algorithm in the mean and mean square deviation senses involving transient-state and steady-state behavior by resorting to the method of the vectorization operation and the Kronecker product. The analysis method does not require the Gaussian input signal. Moreover, the proposed analysis removes the paraunitary assumption imposed on the analysis filter banks as in the existing analyses of subband adaptive algorithms. Simulation results in various conditions demonstrate the effectiveness of…
We show that a new design criterion, i.e., the least squares on subband errors regularized by a weighted norm, can be used to generalize the proportionate-type normalized subband adaptive filtering (PtNSAF) framework. The new criterion directly penalizes subband errors and includes a sparsity penalty term which is minimized using the damped regularized Newton's method. The impact of the proposed generalized PtNSAF (GPtNSAF) is studied for the system identification problem via computer simulations. Specifically, we study the effects of using different numbers of subbands and various sparsity pe…
This paper introduces a solution to the problem of selecting dynamically (online) the ``optimal'' p-norm to combat outliers in linear adaptive filtering without any knowledge on the probability density function of the outliers. The proposed online and data-driven framework is built on kernel-based reinforcement learning (KBRL). To this end, novel Bellman mappings on reproducing kernel Hilbert spaces (RKHSs) are introduced. These mappings do not require any knowledge on transition probabilities of Markov decision processes, and are nonexpansive with respect to the underlying Hilbertian norm. Th…
This study addresses the problem of selecting dynamically, at each time instance, the ``optimal'' p-norm to combat outliers in linear adaptive filtering without any knowledge on the potentially time-varying probability distribution function of the outliers. To this end, an online and data-driven framework is designed via kernel-based reinforcement learning (KBRL). Novel Bellman mappings on reproducing kernel Hilbert spaces (RKHSs) are introduced that need no knowledge on transition probabilities of Markov decision processes, and are nonexpansive with respect to the underlying Hilbertian norm. …
Tokyo University of Agriculture and Technology（东京农工大学）；Università Politecnica delle Marche（马尔凯理工大学）
The present paper proposes generalized Gaussian kernel adaptive filtering, where the kernel parameters are adaptive and data-driven. The Gaussian kernel is parametrized by a center vector and a symmetric positive definite (SPD) precision matrix, which is regarded as a generalization of the scalar width parameter. These parameters are adaptively updated on the basis of a proposed least-square-type rule to minimize the estimation error. The main contribution of this paper is to establish update rules for precision matrices on the SPD manifold in order to keep their symmetric positive-definitenes…
In this paper the use of adaptive filtering techniques to obtain better peak sidelobe suppression and integrated sidelobe energy will be discussed with regard to weather radars and obtaining better sensitivity with this technique. The performance of these new coefficient sets obtained with adaptive filter (using RLS optimization) will be discussed and presented. They will also be compared with the existing techniques and their peak sidelobe levels.
Xi’an Jiaotong University（西安交通大学）；Xi’an Microelectronic Technology Institute（西安微电子技术研究所）；Harbin Engineering University（哈尔滨工程大学）；National Space Science Center, Chinese Academy of Sciences（中国科学院国家空间科学中心）
In recent years, correntropy has been seccessfully applied to robust adaptive filtering to eliminate adverse effects of impulsive noises or outliers. Correntropy is generally defined as the expectation of a Gaussian kernel between two random variables. This definition is reasonable when the error between the two random variables is symmetrically distributed around zero. For the case of asymmetric error distribution, the symmetric Gaussian kernel is however inappropriate and cannot adapt to the error distribution well. To address this problem, in this brief we propose a new variant of correntro…
Kernel adaptive filtering (KAF) is proposed for nonlinearity-tolerant optical direct detection. For 7x128Gbit/s PAM4 transmission over 33.6km 7-core-fiber, KAF only needs 10 equalizer taps to reach KP4-FEC limit (BER@2.2e-4), whereas decision-feedback-equalizer needs 43 equalizer taps to reach HD-FEC limit (BER@3.8e-3).
This short note addresses the design of a partially adaptive filter to retrieve a signal of interest in the presence of strong low-rank interference and thermal noise. We consider a generalized sidelobe canceler implementation where the dimension-reducing transformation is build resorting to ideas borrowed from randomized matrix approximations. More precisely, the main subspace of the auxiliary data $Z$ is approximated by $ZΩ$ where $Ω$ is a random matrix or a matrix that picks at random columns of $Z$. These transformations do not require eigenvalue decomposition, yet they provide performance…
Computing the optimal solution to a spatial filtering problems in a Wireless Sensor Network can incur large bandwidth and computational requirements if an approach relying on data centralization is used. The so-called distributed adaptive signal fusion (DASF) algorithm solves this problem by having the nodes collaboratively solve low-dimensional versions of the original optimization problem, relying solely on the exchange of compressed views of the sensor data between the nodes. However, the DASF algorithm has only been shown to converge for filtering problems that can be expressed as smooth o…
This paper introduces two new algorithms to accurately estimate the process noise covariance of a discrete-time Kalman filter online for robust orbit determination in the presence of dynamics model uncertainties. Common orbit determination process noise techniques, such as state noise compensation and dynamic model compensation, require offline tuning and a priori knowledge of the dynamical environment. Alternatively, the process noise covariance can be estimated through adaptive filtering. However, many adaptive filtering techniques are not applicable to onboard orbit determination due to com…
Technical University of Munich（慕尼黑工业大学）；Costa Rica Institute of Technology（哥斯达黎加理工学院）
When signals are measured through physical sensors, they are perturbed by noise. To reduce noise, low-pass filters are commonly employed in order to attenuate high frequency components in the incoming signal, regardless if they come from noise or the actual signal. Therefore, low-pass filters must be carefully tuned in order to avoid significant deterioration of the signal. This tuning requires prior knowledge about the signal, which is often not available in applications such as reinforcement learning or learning-based control. In order to overcome this limitation, we propose an adaptive low-…
Suppose $L$ simultaneous independent stochastic systems generate observations, where the observations from each system depend on the underlying parameter of that system. The observations are unlabeled (anonymized), in the sense that an analyst does not know which observation came from which stochastic system. How can the analyst estimate the underlying parameters of the $L$ systems? Since the anonymized observations at each time are an unordered set of L measurements (rather than a vector), classical stochastic gradient algorithms cannot be directly used. By using symmetric polynomials, we for…
Concordia Institute for Information Systems Engineering, Concordia University（康考迪亚大学康考迪亚信息系统工程研究所）；University of Western Ontario（西安大略大学）
Pathological Hand Tremor (PHT) is among common symptoms of several neurological movement disorders, which can significantly degrade quality of life of affected individuals. Beside pharmaceutical and surgical therapies, mechatronic technologies have been utilized to control PHTs. Most of these technologies function based on estimation, extraction, and characterization of tremor movement signals. Real-time extraction of tremor signal is of paramount importance because of its application in assistive and rehabilitative devices. In this paper, we propose a novel on-line adaptive method which can a…
