Self‐tuning fusion Kalman filter weighted by scalars and its convergence analysis for multi‐channel autoregressive moving average signals

For the multi‐sensor multi‐channel autoregressive (AR) moving average signals with white measurement noises and an AR‐colored measurement noise, a multi‐stage information fusion identification method is presented when model parameters and noise variances are partially unknown. The local estimators of model parameters and noise variances are obtained by the multidimensional recursive instrumental variable algorithm and correlation method, and the fused estimators are obtained by taking the average of the local estimators. They have the strong consistency. Substituting them into the optimal information fusion Kalman filter weighted by scalars, a self‐tuning fusion Kalman filter for multi‐channel AR moving average signals is presented. Applying the dynamic error system analysis method, it is proved that the proposed self‐tuning fusion Kalman filter converges to the optimal fusion Kalman filter in a realization, so that it has asymptotic optimality. A simulation example for a target tracking system with three sensors shows its effectiveness. Copyright © 2014 John Wiley & Sons, Ltd.     

Optimal and self‐tuning weighted measurement fusion Kalman filters and their asymptotic global optimality

For the multisensor linear discrete time‐invariant stochastic systems with unknown noise variances, using the correlation method, the information fusion noise variance estimators with consistency are given by taking the average of the local noise variance estimators. Substituting them into two optimal weighted measurement fusion steady‐state Kalman filters, two new self‐tuning weighted measurement fusion Kalman filters with a self‐tuning Riccati equation are presented. By the dynamic variance error system analysis (DVESA) method, it is rigorously proved that the self‐tuning Riccati equation converges to the steady‐state optimal Riccati equation. Further, by the dynamic error system analysis (DESA) method, it is proved that the steady‐state optimal and self‐tuning Kalman fusers converge to the global optimal centralized Kalman fuser, so that they have the asymptotic global optimality. Compared with the centralized Kalman fuser, they can significantly reduce the computational burden. A simulation example for the target tracking systems shows their effectiveness. Copyright © 2010 John Wiley & Sons, Ltd.     

Optimal and self‐tuning fusion Kalman filters for discrete‐time stochastic singular systems

Based on the optimal fusion estimation algorithm weighted by scalars in the linear minimum variance sense, a distributed optimal fusion Kalman filter weighted by scalars is presented for discrete‐time stochastic singular systems with multiple sensors and correlated noises. A cross‐covariance matrix of filtering errors between any two sensors is derived. When the noise statistical information is unknown, a distributed identification approach is presented based on correlation functions and the weighted average method. Further, a distributed self‐tuning fusion filter is given, which includes two stage fusions where the first‐stage fusion is used to identify the noise covariance and the second‐stage fusion is used to obtain the fusion state filter. A simulation verifies the effectiveness of the proposed algorithm. Copyright © 2008 John Wiley & Sons, Ltd.     

Hierarchical fusion robust Kalman filter for clustering sensor network time‐varying systems with uncertain noise variances

For the clustering time‐varying sensor network systems with uncertain noise variances, according to the minimax robust estimation principle, based on the worst‐case conservative system with conservative upper bounds of noise variances, applying the optimal Kalman filtering, the two‐level hierarchical fusion time‐varying robust Kalman filter is presented, where the first‐level fusers consist of the local decentralized robust fusers for the clusters, and the second‐level fuser is a global decentralized robust fuser for the cluster heads. It can reduce the communication load and save energy resources of sensors. Its robustness is proved by the proposed Lyapunov equation method. The concept of robust accuracy is presented, and the robust accuracy relations of the local, decentralized, and centralized fused robust Kalman filters are proved. Specially, the corresponding steady‐state robust local and fused Kalman filters are also presented, and the convergence in a realization between the time‐varying and steady‐state robust Kalman filters is proved by the dynamic error system analysis method. A simulation example shows correctness and effectiveness. Copyright © 2013 John Wiley & Sons, Ltd.     

基于联合卡尔曼滤波的多传感器信息融合算法及其应用

针对常见卡尔曼滤波器在处理多传感器组合系统的数据时,存在计算量大和故障数据相互污染的问题,提出了一种应用联合卡尔曼滤波技术进行多传感器信息融合,以求得参数最优估计的方法。文中首先对联合卡尔曼滤波的基本原理和4种主要结构方式进行了论述和分析,然后给出了融合算法的实现,最后以多传感器组合导航系统为例,对其进行计算机仿真。结果表明,该方法可有效提高计算的精度和可靠性,具有较好的容错性和环境适应性,有效高的工程实用价值。     

The modified extended Kalman filter based recursive estimation for Wiener nonlinear systems with process noise and measurement noise

This article develops the modified extended Kalman filter based recursive estimation algorithms for Wiener nonlinear systems with process noise and measurement noise. The prior estimate of the linear block output is computed based on the auxiliary model, and the posterior estimate is updated by designing a modified extended Kalman filter. A multi-innovation gradient algorithm and a recursive least squares algorithm are derived to estimate the parameters of the linear subsystem, respectively. The simulation examples are provided to demonstrate the effectiveness of the proposed algorithms.     

Unscented Kalman Filtering for Self‐Sensing Magnetic Levitation against Magnetic Saturation

This paper investigates the magnetic saturation problem of self‐sensing electromagnetic levitation system and presents a novel self‐sensing scheme. The proposed approach employs a demodulation technique. By superimposing a high‐frequency voltage, the resulting electromagnet coil currents have ripples that can be used for gap sensing. This paper shows that the gap length is not uniquely estimated when using only the relation between the ripple, the control currents, and the gap. The constraint conditions are to be determined to solve the problem. The proposed approach utilizes the dynamical motion model of the electromagnetic levitation system to uniquely identify the gap. Introducing the system behavior dynamics, the gap can be exactly estimated. To incorporate the system model with the gap sensing algorithm, a nonlinear filtering methodology is employed. The proposed estimator is demonstrated by the experiments. The results show that it is possible to address magnetic saturation with the proposed gap sensing scheme. The estimator has a good accuracy in a wider gap range compared to the conventional methods.     

Design of a near‐optimal adaptive filter in digital signal processor for active noise control

Adaptive filter has been applied in adaptive feedback and feedforward control systems, where the filter dimension is often determined by trial‐and‐error. The controller design based on a near‐optimal adaptive filter in digital signal processor (DSP) is developed in this paper for real‐time applications. The design integrates the adaptive filter and the experimental design such that their advantages in stability and robustness can be combined. The near‐optimal set of controller parameters, including the sampling rate, the dimension of system identification model, the dimension (order) of adaptive controller in the form of an FIR filter, and the convergence rate of adaptation is shown to achieve the best possible system performance. In addition, the sensitivity of each design parameter can be determined by analysis of means and analysis of variance. Effectiveness of the adaptive controller on a DSP is validated by an active noise control experiment. Copyright © 2007 John Wiley & Sons, Ltd.     

Self‐tuning control for polynomial systems using a receding horizon observer and control strategy

A receding horizon observer and control scheme is introduced for non‐linear systems described by polynomial maps. This control scheme has a natural interpretation as a two‐stage adaptive or self‐tuning control algorithm. The non‐linear feedback that results is defined only on the basis of past input and output measurements. The computational complexity aspects of this approach to adaptive or self‐tuning control are briefly discussed. A linear system and a Hénon map example are used to illustrate the ideas. Copyright © 2004 John Wiley & Sons, Ltd.     

Average information‐weighted consensus filter for target tracking in distributed sensor networks with naivety issues

In the consensus‐based state estimation, multiple neighboring nodes iteratively exchange their local information with each other and the goal is to get more accurate and more convergent state estimation on each node. In order to improve network scalability and fault tolerance, the distributed sensor networks are desirable because the requirements of the fusion node are eliminated. However, the state estimation becomes challenging in the case of limited sensing regions and/or distinct measurement‐noise covariances. A novel distributed average information‐weighted consensus filter (AICF) is proposed, which does not require the knowledge of the total number of sensor nodes. Based on the weighted average consensus, AICF effectively addresses the naivety issues caused by unequal measurement‐noise covariances. Theoretical analysis and experimental verification show that AICF can approach the optimal centralized state estimation.     

Unscented summation information‐weighted consensus filter for distributed sensor networks with incomplete information

In order to improve network scalability and fault tolerance, the distributed sensor networks are desirable. However, the distributed state estimation becomes challenging when some sensors have insufficient information due to restricted observability, and/or have imparity information due to unequal measurement‐noise covariances. Centralized summation information‐fusion (CSI) model is presented which performs weighted least‐squares estimation for all measurement information to achieve the optimal centralized state estimation. The CSI model revises the initialization and covariance propagation in the original information‐weighted consensus filter (ICF). Since centralized information fusion is a summation mode and is approached by the average consensus protocol, all the covariances involved in the CSI model contain the information regarding the total number of nodes. The artificially preset initial values are considered as measurement information and fused in accordance with the CSI model. By combining the CSI model with unscented transform, distributed unscented summation information‐weighted consensus filter (USICF) is proposed. USICF realizes the nonlinear estimation in the context of highly incomplete information. Theoretical analysis and experimental verification showed that USICF achieves better performance than UICF that is based on ICF.     

An adaptive noise reduction filter for discrete signal by use of sandglass‐type neural network

An adaptive noise reduction filter composed of a sandglass‐type neural network (SNN) noise reduction filter (RF) is proposed in this paper. SNN was originally devised to work effectively for information compression. It is a hierarchial network and is symmetrically structured. SNN consists of the same number of units in the input and output layers and a smaller number of units in the hidden layer. It is known that SNN has signal processing performance which is equivalent to Karhunen–Loeve expansion after learning. We proved the theoretical suitability of SNN for an adaptive noise reduction filter for discrete signals. The SNNRF behaves optimally when the number of units in the hidden layer is equal to the rank of the covariance matrix of the signal components included in the input signal. Further we show by applying the recursive least squares method to learning of the SNNRF that the filter can process signals for on‐line adaptive noise reduction. This is an extremely desirable feature for practical application. In order to verify the validity of SNNRF, we performed computer experiments examining how the noise reduction ability of SNNRF is affected by altering the properties of the input pattern, learning algorithm, and SNN. The results confirm that the SNNRF acquired appropriate characteristics for noise reduction from the input signals, and markedly improved the SNR of the signals. © 1999 Scripta Technica, Electr Eng Jpn, 127(4): 39–51, 1999     

Sparse leaky‐LMS algorithm for system identification and its convergence analysis

In this paper, a novel adaptive filter for sparse systems is proposed. The proposed algorithm incorporates a log‐sum penalty into the cost function of the standard leaky least mean square (LMS) algorithm, which results in a shrinkage in the update equation. This shrinkage, in turn, enhances the performance of the adaptive filter, especially, when the majority of unknown system coefficients are zero. Convergence analysis of the proposed algorithm is presented, and a stability criterion for the algorithm is derived. This algorithm is given a name of zero‐attracting leaky‐LMS (ZA‐LLMS) algorithm. The performance of the proposed ZA‐LLMS algorithm is compared to those of the standard leaky‐LMS and ZA‐LMS algorithms in sparse system identification settings, and it shows superior performance compared to the aforementioned algorithms. Copyright © 2013 John Wiley & Sons, Ltd.     

Digital filter design with state space method for 1‐bit signal processing based on delta‐sigma modulation

One‐bit signal processing based on delta‐sigma modulation has been studied for hardware implementation of signal processing systems. In the 1‐bit signal processing, finite word‐length problems such as overflow and coefficient quantization error occur. To solve the problems, a new design method with state space is proposed in this paper. Digital filters are designed to show the feasibility of the method. First, the L₁/L₂‐sensitivity is shown to evaluate coefficient quantization error and L₂ scaling constraints to prevent overflow. Second, a state space equation is presented and the L₁/L₂‐sensitivity and L₂‐scaling constraints are extended to take the filter structure and oversampling effects into account. Finally, the proposed method is shown to attain a higher SNR than conventional ones. © 2011 Wiley Periodicals, Inc. Electr Eng Jpn, 175(4): 48–56, 2011; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/eej.21075     

Robust integrated covariance intersection fusion Kalman estimators for networked systems with random measurement delays,multiplicative noises,and uncertain noise variances

In this article, the robust distributed fusion Kalman filtering problems are addressed for the networked mixed uncertain multisensor systems with random one-step measurement delays, multiplicative noises, and uncertain noise variances. A new augmented state approach with fictitious measurement noises modeled by the first-order moving average models is presented, by which the original system is transformed into a standard uncertain system only with uncertain-variance fictitious white noises. Based on the minimax robust estimation principle and Kalman filtering theory, a universal integrated covariance intersection (ICI) fusion approach is presented in the sense that first of all the robust local estimators and their conservative error variances and crosscovariances are presented, and then integrating the local estimation information yields ICI fusers. An extended Lyapunov equation approach with two kinds of Lyapunov equations is presented in order to prove the robustness and to compute fictitious noise statistics. Applying these approaches, the minimax robust local, ICI, and fast ICI fused Kalman estimators (predictor, filter, and smoother) are presented, such that for all admissible uncertainties, their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds. Their robustness, accuracy relations, and convergence are also proved. The proposed ICI fusers improve the robust accuracies and overcome the drawbacks of the original covariance intersection fusers, such that the robust local estimators and their conservative variances are assumed to be known, and their conservative crosscovariances are ignored. Two simulation examples applied to the offshore platform system verify their correctness, effectiveness, and applicability.     

A hybrid noise canceller with a real‐time adaptive Wiener filter and a geometric‐based voice–activity detector for an automotive application

In real‐time environments a speech recognition system in a car has to receive the driver's voice only while suppressing the background noise. This paper presents a hybrid real‐time adaptive filter that operates within a geometrical zone defined around the head of the desired speaker. Any sound outside of this zone is considered to be noise and is suppressed. As this defined geometrical zone is small, it is assumed that only driver's speech is incoming from this zone. The technique uses three microphones to define a geometric‐based voice–activity detector (VAD) to cancel the unwanted speech coming from outside of the zone. However, when unwanted speech and desired speech are incoming at the same time, the VAD fails to identify the unwanted speech or desired speech. In such a situation an adaptive Wiener filter is switched on for noise reduction. In the case of sole unwanted speech incoming from outside of a desired zone, this speech is muted at the output of the hybrid noise canceller. In the case of desired and unwanted speeches incoming together, the SNR is improved by as much as 20 dB. Copyright © 2009 John Wiley & Sons, Ltd.     

Design and performance analysis of LMS algorithm based adaptive filter embedded with CFAR detector under non‐homogeneous clutter scenarios

The paper presents performance analysis of least‐mean‐square algorithm based adaptive filter embedded with constant false alarm rate (CFAR) detector for the purpose of better detection of target under non‐homogeneous clutter environment in radar application. The objective of this paper is to develop a method by redesigning the radar detector in such a way to emphasize the target response and de‐emphasize the clutter response. The hardware implementation using pipeline technique for the adaptive filter reveals its capability to support high sampling frequency, which is an ardent necessity for high performance radar. The moderate area‐delay‐product and low power consumption have made it suitable for hardware realization for such application. The extensive MATLAB simulation of proposed design shows remarkable improvement of detection performance in terms of signal‐to‐noise ratio of 17 dB considering probability of detection at 0.8 over the generic cell averaging CFAR (CA‐CFAR). Copyright © 2015 John Wiley & Sons, Ltd.