A new recursive filter for systems with multiplicative noise

An optimal linear recursive minimum mean-square-error estimator was previously developed by the authors (see IEEE Trans. Autom. Control, vol.34, no.5, p.568-74, May 1989) for a zero-mean signal corrupted by multiplicative noise in its measurement model. This recursive filter cannot be obtained by the recursive structure of a conventional Kalman filter where the new estimate is a linear combination of the previous estimate and the new data. Instead, the recursive structure was achieved by combining the previous estimate with recursive innovation, a linear combination of the most recent two data samples and the previous estimate. In this work the signal is extended to be nonzero-mean. In the conventional Kalman filter, the superposition principle can be applied to both the signal and the measurement models for this nonzero-mean extension. However, when multiplicative noise exists, the measurement model becomes nonlinear. Therefore, a new recursive structure for the innovation process needs to be developed to achieve a recursive filter     

Stable recursive filters using gradient techniques (Corresp.)

In this correspondence the "well known" necessary and sufficient stability conditions for a recursive filter are derived, and a new gradient algorithm is presented that guarantees the stability of a recursive filter. Recent interest in recursive filters is given in [1]-[5].     

基于遗传算法的递归式MTI滤波器的设计

递归式MTI滤波器从理论上讲几乎可以合成任意形状的频率响应函数,因而具有很广的应用范围。为了能够灵活设计出满足系统要求的递归式MTI滤波器,提出了一种设计方法。该方法以遗传算法(GA)的基本思想为基础,利用滤波器的改善因子、通带宽度和通带波纹来构成适应函数,并用GA来加快参量搜索速度和获取全局近似最优解。实验仿真设计了两种典型的递归式MTI滤波器,结果证明该方法是一种有效的设计方法,它可以灵活而快速地设计出所需要的滤波器。     

基于强跟踪的平方根不敏卡尔曼滤波器

针对不敏卡尔曼滤波器在递推过程中的数值不稳定性以及系统发生突变时跟踪效果不佳的问题,提出一种新的机动目标自适应跟踪算法——基于强跟踪的平方根不敏卡尔曼滤波器(STF-SRUKF)。该算法一方面基于平方根滤波的思想,在递推过程中采用协方差矩阵的平方根代替协方差矩阵本身,以保证数值计算的稳定性;另一方面,基于强跟踪滤波的思想,在递推过程中引入时变渐消因子,实时调节增益矩阵,以增强目标运动发生突变时的跟踪能力。仿真结果表明,STF-SRUKF算法对于突发机动的目标运动模型具有良好的跟踪效果,而且具有较好的稳定性。     

Recursive fan filters for a broad-band partially adaptive antenna

This paper presents a technique for designing a broad-band partially adaptive antenna using a new recursive fan filter. Each beamformer is designed using recursive two-pole sections. This method reduces the number of taps of the fan filter considerably. Interferences occurring in the sidelobes as well as the mainlobe of the desired pattern and having the same frequency as the desired signal and overlap in bandwidths are cancelled effectively independent of frequency     

Suppression of transients in variable recursive digital filterswith a novel and efficient cancellation method

A new method for suppressing transients in recursive infinite impulse response (IIR) digital filters is proposed. The technique is based on modifying the state (delay) variables of the filter when coefficients are changed so that the filter enters a new state smoothly without transient attacks, as originally proposed by Zetterberg and Zhang (1988). In this correspondence, we modify the Zetterberg-Zhang algorithm to render it feasible for efficient implementation. We define a mean square error (MSE) measure for transients and determine the optimal transient suppressor to cancel the transients down to a desired level at the minimum complexity of implementation. The application of the method to all-pole and direct-form II (DF II) IIR filter sections is studied in detail. Time-varying recursive filtering with transient elimination is illustrated for tunable fractional delay filters and variable-bandwidth lowpass filters     

Recursive time-varying filter banks for subband image coding

Filter banks, subband/wavelets, and multiresolution decompositions that employ recursive filters have been considered previously and are recognized for their efficiency in partitioning the frequency spectrum. This paper presents an analysis of a new infinite impulse response (IIR) filter bank in which these computationally efficient filters may be changed adaptively in response to the input. The new filter bank framework is presented and discussed in the context of subband image coding. In the absence of quantization errors, exact reconstruction can be achieved. By the proper choice of an adaptation scheme, it is shown that recursive linear time-varying (LTV) filter banks can yield improvement over conventional ones.     

Efficient tunable IIR and allpass filter structures

A new recursive filter structure is proposed which can be controlled on-line using a single parameter. The structure can be used for interpolation in timing synchronisation of digital communications receivers. The technique is illustrated with an example of the implementation of a tunable fractional delay allpass filter using the Thiran design technique     

Design of recursive variable digital filters with theoretically guaranteed stability

Stability is one of the most concerned issues in designing a recursive variable digital filter (VDF). This is because the coefficients of a recursive VDF constantly vary in the tuning process, and updating the coefficients may incur instability. Thus, an appropriate measure needs to be taken for ensuring its stability. This paper presents a new coefficient transformation (CT) method for transforming the coefficients of a recursive transfer-function denominator into a set of new coefficients. From the viewpoint of conventional constant-coefficient filter (constant filter) design, the new coefficients can take arbitrary values without incurring instability. For designing a stable VDF, we apply this CT to the variable case and approximate each transformed coefficient as a distinct polynomial in the tuning parameter. Thus, we can change the filter coefficients by changing the value of the tuning parameter, and thus tune the magnitude response. Thanks to the proposed CT, updating the filter coefficients will never incur instability. This is the core part of the CT-based design approach. In this paper, we utilise a weighting function to ignore the transition-band errors and thus enhance the design accuracy of important frequency bands (passband and stopband). Moreover, the polynomials use different degrees so as to reduce the VDF complexity. Two design examples (lowpass VDF and bandpass VDF) are provided for verifying the design accuracy and checking the stability.     

Error-free coefficient realisation of recursive part via input-partitioned filter structure

A new filter structure is developed which allows precise coefficient implementation in the recursive part of the system. This is achieved by partitioning the input sequence into sets of inputs and realising the recursive part of the system into parallel subfilters with precise pole realisation.     

平方根求积分卡尔曼滤波器

 针对具有加性噪声的非线性高斯动态系统的状态估计问题,本文提出一种近似递归的高斯滤波器:平方根求积分卡尔曼滤波器(SRQKF).该滤波器是在求积分卡尔曼滤波器(QKF)基础上的平方根实现形式,使用统计线性回归的方法,通过一套参数化高斯密度的高斯-厄米特积分点来线性化非线性函数的;滤波器采用平方根的实现方法,不仅增强了数值的鲁棒性,确保了状态协方差矩阵的半正定性,而且在一定程度上提高了滤波精度.仿真实验表明,SRQKF的滤波精度比QKF提高约12%,且均高于无味滤波器(UF)和扩展卡尔曼滤波器(EKF),但这二者的计算复杂度均比UF和EKF大.对滤波精度要求比较高的非线性场合,新滤波器是一种很有效的非线性滤波算法.     

A Recursive Digital Filter Using DPCM

A recursive digital filter using differential pulse-code modulation (DPCM) is proposed. The filter can realize any rational transfer function without the need for a new design. Results on roundoff error and limit cycle oscillations are presented. The implementation of these filters is also discussed.     

Approximation rationnelle de filtres

Considerable attention has been devoted to the design of recursive filters approximating the specifications of a given numerical filter. The authors consider here the approximation problem in the least square sense on the impulse response and, due to its physical basis, they work in the parametrical space of poles and residues. After a review of existing methods, a new one is described which, contrary to the previous ones, allows us to take into account the non linear aspect of the problem. Results are presented for three types of applications in signal processing : recursive approximation of a finite impulse response filter, order reduction, design of a whitening filter.     

Complex-Valued Recurrent Neural Network with IIR Neuron Model: Training and Applications

In this paper, based on the digital filter theory and approach, a new algorithm for training a complex-valued recurrent neural network, is proposed. Each recurrent neuron is modeled as an infinite impulse response (IIR) filter. The network weights are updated by optimizing the IIR filter coefficients, and the optimization is based on the layer-by-layer optimizing procedure as well as the recursive least-squares method. The performance of the proposed algorithm is demonstrated with application to a complex communication channel equalization. Our approach provides a new way to perform fast training of complex-valued recurrent neural networks.     

New charge transfer recursive filter

A new fully integrated recursive charge transfer filter is described using the concept of passive recirculation of charges. This is a novel solution for voice channel or data filters in digital communications.     

Inherent matrix identities on ARMA lattice filter realizationalgorithm and their application

Presents the matrix identities that are inherent in the solution of the normal equations for an ARMA lattice filter. This derivation also makes clear the relationship between the recursive least squares (RLS) method and the ARMA lattice filter realization algorithm. Further, as an application of the matrix identities, a new method for model identification with frequency weighting (MIFW) is presented     

动态系统基于时域与频域相结合的多尺度联合滤波器

针对基于小波变换与Kalman滤波相结合的多尺度联合估计方法中存在的问题,本文利用新的系统分块技术与多尺度变换方法相结合,建立一个动态系统基于时域与频域相结合的多尺度联合滤波器.首先,将时域中描述的状态方程和观测方程改写为块状态方程和块观测方程;利用多尺度变换技术在时域和频域中联合描述它们;结合Kalman滤波与顺序滤波的思想,建立了一类应用于动态系统的多尺度估计联合滤波器.新滤波器不仅保留了传统Kalman滤波器的实时性和递归性等优良性质,而且在滤波过程中还具有对随机状态信号进行多尺度分析的能力.计算机仿真实验验证了利用新估计器得到的估计精度可与利用传统Kalman滤波器得到的估计精度相媲美.     

Image detail-preserving filter for impulsive noise attenuation

A new nonlinear filter is proposed for attenuating impulsive noise while preserving image details. The filter truncates the grey value of a pixel to the maximal or minimal value of its enclosed surrounding band. Impulsive noise inside the band is thus attenuated while image details are preserved as long as they stretch to the band. The recursive form of the proposed filter leads to a simple architecture for fast implementation. Theoretical analysis and experimental results demonstrate the effectiveness of this new filter for both noise attenuation and detail preservation. For moderately contaminated images, as shown in the experiments, the proposed filter outperforms the standard median filter, the centre-weighted median filter and the unidirectional multistage median filter in terms of mean absolute error and filtering speed.     

A new recursive pseudo least squares algorithm for ARMA filteringand modeling. II

For pt.I see ibid., vol.40, no.11, p.2766-74 (Nov. 1992). A recursive algorithm for ARMA (autoregressive moving average) filtering has been developed in a companion paper. These recursions are seen to have a lattice-like filter structure. The ARMA parameters, however, are not directly available from the coefficients of this filter. The problem of identification of the ARMA model from the coefficients of this filter is addressed here. Two new update relations for certain pseudoinverses are derived and used to obtain a recursive least squares algorithm for AR parameter estimation. Two methods for the estimation of the MA parameters are also presented. Numerical results demonstrate the usefulness of the proposed algorithms