Unlike the conventional kernel adaptive filtering (KAF) approach of using a fixed kernel to define the Reproducing Kernel Hilbert Space (RKHS), this paper embeds the statistics of the input data in the kernel definition, obtaining a closed-form solution for nonlinear adaptive filtering. We call this solution the Functional Wiener Filter (FWF), and it is formally an extension of Parzen's work on the autocorrelation RKHS to nonlinear functional spaces. We present a method for approximating the FWF in an explicit, finite-dimensional RKHS to model time series directly from realizations, which is less computationally demanding at test time than other KAF methods. We show that FWF outperforms KAF on a synthetic dataset that meets the conditions of the theory, and is comparable to other KAF algorithms for both a chaotic and real-world time series. We demonstrate how the difference equation learned by the FWF can be extracted, leading to possible applications in system identification.
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).
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.
Efficient clutter filtering for pulsed radar systems remains an open issue when employing pulse-to-pulse modulation and irregular pulse interval waveforms within the coherent processing interval. The range and Doppler domain should be jointly processed for effective filtering leading to a large computational overhead. In this paper, the joint domain filtering is performed by constructing a clutter projection matrix, also known as the projected non-identical multiple pulse compression (NIMPC) method. The paper extends the projected NIMPC filter to irregular pulse interval waveforms. Additionall…
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…
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 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…
We propose the adaptive random Fourier features Gaussian kernel LMS (ARFF-GKLMS). Like most kernel adaptive filters based on stochastic gradient descent, this algorithm uses a preset number of random Fourier features to save computation cost. However, as an extra flexibility, it can adapt the inherent kernel bandwidth in the random Fourier features in an online manner. This adaptation mechanism allows to alleviate the problem of selecting the kernel bandwidth beforehand for the benefit of an improved tracking in non-stationary circumstances. Simulation results confirm that the proposed algorit…
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. …
Inference of space-time varying signals on graphs emerges naturally in a plethora of network science related applications. A frequently encountered challenge pertains to reconstructing such dynamic processes, given their values over a subset of vertices and time instants. The present paper develops a graph-aware kernel-based kriged Kalman filter that accounts for the spatio-temporal variations, and offers efficient online reconstruction, even for dynamically evolving network topologies. The kernel-based learning framework bypasses the need for statistical information by capitalizing on the smo…
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 …
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…
Southwest University of Science and Technology（西南科技大学）；PUC-Rio（里约热内卢天主教大学）；Xi’an Jiaotong University（西安交通大学）
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 …
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）
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…
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…
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-…
A hybrid estimator of the log-spectral density of a stationary time series is proposed. First, a multiple taper estimate is performed, followed by kernel smoothing the log-multitaper estimate. This procedure reduces the expected mean square error by $({π^2 \over 4})^{.8}$ over simply smoothing the log tapered periodogram. The optimal number of tapers is $O(N^{8/15})$. A data adaptive implementation of a variable bandwidth kernel smoother is given. When the spectral density is discontinuous, one sided smoothing estimates are used.
