A new FIR filter for state estimation and its application

This paper proposes a new FIR （finite impulse response） filter under a least squares criterion using a forgetting factor. The proposed FIR filter does not require information of the noise covariances as well as the initial state, and has some inherent properties such as time-invariance, unbiasedness and deadbeat. The proposed FIR filter is represented in a batch form and then a recursive form as an alternative form. Prom discussions about the choice of a forgetting factor and a window length, it is shown that they can be considered as useful parameters to make the estimation performance of the proposed FIR filter as good as possible. It is shown that the proposed FIR filter can outperform the existing FIR filter with incorrect noise covariances via computer simulations. Finally, as a useful application, an image sequence stabilization problem is considered. Through this application, the FIR filtering based approach is shown to be superior to the Kalman filtering based approach.     

Best Linear Unbiased Fir Filters For Continuous‐Time State Space Models

This paper proposes a new linear finite impulse response (FIR) filter called the best linear unbiased FIR (BLUF) filter for the state estimation in continuous‐time state space models. The proposed BLUF filter for continuous‐time state space models is obtained by a formal limiting procedure of discretized systems. The BLUF filter is represented in an iterative form and then in a standard FIR form. It is shown that the proposed BLUF filter has deadbeat and unbiasedness properties. It is also shown that the BLUF filter is equivalent to the existing receding horizon Kalman FIR (RHKF) filter whose optimality is not clear to understand. The former is more systematic and logical while the latter is heuristic due to handling of infinite covariance of the initial state.     

A receding horizon unbiased FIR filter for discrete-time state space models

This paper concerns with a new linear finite impulse response (FIR) filter called the receding horizon unbiased FIR (RHUF) filter for the state estimation in discrete-time state space models. To obtain the RHUF filter, linearity, unbiasedness and FIR structure will be required beforehand in addition to a performance criteria of minimum variance. The RHUF filter is obtained by directly solving an optimization problem with the unbiasedness constraint. The RHUF filter has time-invariance and deadbeat properties. The RHUF filter is represented in both a batch form and an iterative form. It is shown that the RHUF filter is equivalent to the existing receding horizon Kalman FIR (RHKF) filter whose optimality is not clear to understand. The former is more systematic and logical, while the latter is heuristic due to handling of infinite covariance of the initial state information.     

Unbiased FIR Filtering with Incomplete Measurement Information

This paper proposes an unbiased filter with finite impulse response (FIR) structure for linear discrete time systems in state space form with incomplete measurement information. The measurements are transmitted from the plant to the FIR filter imperfectly due to random packet loss or sensor faults. The Bernoulli random process is used to describe the missing measurement details, and the missing data is replaced with recently transmitted data on the missing horizon. The missing horizon can hold the assumption for finite measurement of the FIR filter. Two examples are provided to demonstrate the proposed unbiased FIR (UFIR) filter robustness against temporary model uncertainty and consecutive missing measurement data compared with existing filters considering missing measurement.     

Cascaded warped-FIR and FIR filter structure for loudspeaker equalization with low computational cost requirements

This paper proposes an improved filter structure and methodology for the equalization of loudspeakers and other audio systems. It employs a cascaded structure of a finite impulse response (FIR) filter and a warped-FIR filter in order to obtain the best performance of both types of filters. In the task of loudspeaker equalization, FIR filters achieve excellent resolution and equalization at high frequencies, but at low frequencies the resolution obtained is too poor when evaluated in a logarithmic frequency axis, that could only be improved using high order filters. To solve this lack of resolution at low frequencies, warped-FIR filters have been employed, but at the expense of decreasing the resolution of the filter at high frequencies and increasing the complexity of the filter structure and its computational cost. The proposed combination of both types of filters, combined with the correct selection of their orders, and the λ value for the warped-FIR filter, allows the FIR filter to maintain its good resolution at high frequencies and achieve enough resolution at low frequencies with the warped-FIR filter. In this way, lower order filters with lower computational cost could be obtained than when using FIR or warped-FIR only. This approximation attains a more uniform resolution of the filter when evaluated in octaves, behaving much more like human hearing, than the linear frequency resolution obtained when employing only FIR filters.     

Receding-horizon unbiased FIR filters for continuous-timestate-space models without a priori initial state information

A receding horizon unbiased finite-impulse response filter (RHUFF) is proposed for continuous-time state space models. Linearity, unbiasedness, finite-impulse response (FIR) structure, and independence of the initial state information will be required in advance, in addition to a performance index of minimum variance. The proposed RHUFF is obtained by directly minimizing the performance index with the unbiasedness constraint. The proposed RHUFF is represented first in a standard FIR form and then in an iterative form. It is shown that the RHUFF is equivalent to the existing receding horizon (RH) Kalman FIR filter. The former is more systematic and logical, while the latter is heuristic due to the handling of infinite covariance of the initial state information     

Laguerre discrete-time filter design

The design of discrete-time ideal filters by finite impulse response (FIR) method requires long FIR filter structures.This is due to the infinite impulse response characteristics of the ideal filters. Optimum Laguerre filter structures with smaller length can be used instead of FIR filters to reduce the order of the filters.In this paper the method of designing optimum Laguerre ideal low-pass, band-pass, high-pass, and band-reject filters is introduced. The optimization is performed by evaluating the Laguerre parameter and coefficients when the mean-square-error between the frequency response of the desired filter and its corresponding Laguerre network frequency response is minimum. The problem with the Laguerre filter design is the complexity of computations for evaluating the optimum Laguerre parameter. This complexity is reduced to one half by introducing a lemma.Both, analytical and numerical solutions are presented and the results are illustrated via some examples. The corresponding results yield a reduced filter order, and appropriate linear phase, with lower ripples in stop-band and pass-band compared to the conventional FIR filters.     

FIR filters and recursive forms for continuous time-invariant state-space models

An FIR (finite impulse response) filter and an FIR smoother are introduced for continuous time-invariant state-space models. It is shown in this note that finite impulse responses of the FIR filter and smoother can be easily determined by solving a simple Riccati-type matrix differential equation on a finite interval. Especially for systems with stationary processes, finite impulse responses of the FIR filter and smoother become time-invariant and can be computed from simpler equations. For fast computational purposes, recursive forms of the FIR filter and smoother are derived by using adjoint variables. In this case all gains for recursive forms are shown to be constant.     

A receding horizon Kalman FIR filter for discrete time-invariantsystems

A receding horizon Kalman FIR filter is presented that combines the Kalman filter and the receding horizon strategy when the horizon initial state is assumed to be unknown. The suggested filter is a FIR filter form which has many good inherent properties. It can always be defined irrespective of singularity problems caused by unknown information about the horizon initial state. The suggested filter can be represented in either an iterative form or a standard FIR form. It is also shown that the suggested filter possesses the unbiasedness property and the remarkable deadbeat property irrespective of any horizon initial condition. The validity of the suggested filter is illustrated by numerical examples     

A Fusion Kalman Filter and UFIR Estimator Using the Influence Function Method

In this paper,the Kalman filter(KF)and the unbiased finite impulse response(UFIR)filter are fused in the discrete-time state-space to improve robustness against uncertainties.To avoid the problem where fusion filters may give up some advantages of UFIR filters by fusing based on noise statistics,we attempt to find a way to fuse without using noise statistics.The fusion filtering algorithm is derived using the influence function that provides a quantified measure for disturbances on the resulting filtering outputs and is termed as an influence finite impulse response(IFIR)filter.The main advantage of the proposed method is that the noise statistics of process noise and measurement noise are no longer required in the fusion process,showing that a critical feature of the UFIR filter is inherited.One numerical example and a practice-oriented case are given to illustrate the effectiveness of the proposed method.It is shown that the IFIR filter has adaptive performance and can automatically switch from the Kalman estimate to the UFIR estimates according to operating conditions.Moreover,the proposed method can reduce the effects of optimal horizon length on the UFIR estimate and can give the state estimates of best accuracy among all the compared methods.     

基于支持向量机的滤波器设计与硬件实现

针对传统有限脉冲响应(FIR)滤波器设计方法和神经网络设计方法的不足,在改进使用支持向量机(SVM)设计FIR滤波器方法的基础上,提出了SVM设计FIR滤波器的硬件实现方法.使用理想滤波器的幅值响应训练SVM,得到训练参数,据此构建基于SVM的FIR滤波器的嵌入式系统.软件实现FIR滤波器的训练部分,硬件实现FIR滤波器的测试部分.单次判定测试向量的时间约为3500 ns,滤波准确率可达到98.41%.设计的滤波器具有良好的幅频特性,边界控制精确,逼近理想滤波器.     

The design of multi-dimensional acoustic beamformers via window functions

The design of broadband beamformers can be formulated as a semi-infinite programming optimization problem, where the coefficients of the filters are determined such that the actual response of the microphone array is near a given desired response. This problem can be solved by existing optimization solvers after the discretization of the infinite constraints. However, this problem will become large-scale and it's expensive to find the optimal solution, as the discretization points grow and the filter length increases. In this paper, we propose a fast method based on the window functions. First, we formulate a simplified optimization problem to find the limit of the cost function values as the filter length is sufficiently long. Hence, the optimal frequency response vector is obtained and the corresponding filter coefficients can be calculated. Second, we apply the window method to truncate the limiting filter to obtain a finite FIR filters. The performance as well as the computational complexity are investigated to demonstrate the effectiveness and efficiency of the proposed method.     

改进的粒子群优化算法设计FIR低通数字滤波器

粒子群优化算法(PSO)因具有参数少、易于实现等优点,在解决优化问题时表现出很好的性能。有限长单位脉冲响应(FIR)数字滤波器因具有稳定的结构、易于实现等优点,在实际中有着很广泛的应用。因此,将基于三角函数因子的改进PSO算法(TFPSO)用于对FIR低通数字滤波器性能的优化,并将其与基于折射原理反向学习(refrPSO)、基于反向学习(OPSO)的PSO算法所设计的FIR低通数字滤波器的性能进行比较。在实验中构造出一种性能较好的适应值函数,以验证这几种改进的PSO算法所设计的FIR低通数字滤波器的性能。实验结果表明,基于三角函数因子的PSO算法滤波性能较差,而基于折射原理反向学习的PSO算法性能最佳。     

Neural filtering method for stationary signal processes

In this paper a new method of neural filtering using artificial neural network systems is presented for the filtering problems of linear and nonlinear, stationary and nonstationary stochastic signals. The neural filter (denoted neurofilter) developed in this paper has either finite impulse response (FIR) structure or infinite impulse response (IIR) structure. The neurofilter differs from the conventional linear digital FIR and IIR filters because the artificial neural network system used in the neurofilter has a nonlinear structure due to the sigmoid function. Numerical studies for the estimation of a second-order Butterworth process are performed by changing the structures of the neurofilter in order to evaluate the performance indices under changes of the output noises or disturbances. The results obtained from these studies verified the capabilities which are essentially necessary for on-line filtering of various stochastic signals.     

Weighted average extended FIR filter bank to manage the horizon size in nonlinear FIR filtering

In this paper, we propose a novel approach to manage the horizon size in nonlinear finite impulse response (FIR) filtering. The proposed approach is to perform state estimation through a bank of FIR filters called a weighted average extended FIR filter bank (WAEFFB). In the WAEFFB, the state estimate is obtained by weighting the average of multiple estimates from a bank of extended FIR filters that uses different horizon sizes. The horizon sizes used for the WAEFFB are adjusted constantly by maximizing the likelihood function. We show through simulations that the WAEFFB yields better results than the conventional approach that uses a constant (i.e., fixed) horizon size.     

Novel Double Modular Redundancy Based Fault-Tolerant FIR Filter for Image Denoising

In signal processing and communication systems, digital filters are widely employed. In some circumstances, the reliability of those systems is crucial, necessitating the use of fault tolerant filter implementations. Many strategies have been presented throughout the years to achieve fault tolerance by utilising the structure and properties of the filters. As technology advances, more complicated systems with several filters become possible. Some of the filters in those complicated systems frequently function in parallel, for example, by applying the same filter to various input signals. Recently, a simple strategy for achieving fault tolerance that takes advantage of the availability of parallel filters was given. Many fault-tolerant ways that take advantage of the filter’s structure and properties have been proposed throughout the years. The primary idea is to use structured authentication scan chains to study the internal states of finite impulse response (FIR) components in order to detect and recover the exact state of faulty modules through the state of non-faulty modules. Finally, a simple solution of Double modular redundancy (DMR) based fault tolerance was developed that takes advantage of the availability of parallel filters for image denoising. This approach is expanded in this short to display how parallel filters can be protected using error correction codes (ECCs) in which each filter is comparable to a bit in a standard ECC. “Advanced error recovery for parallel systems,” the suggested technique, can find and eliminate hidden defects in FIR modules, and also restore the system from multiple failures impacting two FIR modules. From the implementation, Xilinx ISE 14.7 was found to have given significant error reduction capability in the fault calculations and reduction in the area which reduces the cost of implementation. Faults were introduced in all the outputs of the functional filters and found that the fault in every output is corrected.     

数字下变频中的FPGA高效滤波器设计

介绍了一种在FPGA上实现高效窄带有限冲击响应滤波器(FIR)的设计方法.该方法利用数字下变频抗混叠滤波器的多速率和窄带的特点,采用插值FIR滤波器(IFIR)和多相滤波器相结合的设计思路,实现了该滤波器的高效设计.     

含时延和丢失数据不确定系统的FIR滤波器

针对状态空间模型中存在服从伯努利分布的时延和随机观测丢失的情况,基于极大似然法则,分别设计有限脉冲响应(finite impulse response, FIR)滤波器的慢速率批处理形式和快速率迭代形式.首先,将时延和数据丢失情况下的模型表述为服从伯努利分布的概率线性函数;然后,通过极大似然处理从而得到所提出极大似然FIR算法;最后,将在相同条件下的极大似然FIR估计、改进型卡尔曼滤波以及无偏FIR估计3种滤波方法进行对比,从估计误差、均方根误差和不确定性影响等角度进行比较分析.实验部分通过3-DOF直升机模型仿真,可发现所提出极大似然FIR估计方法在处理时延和数据丢失问题时更加有效,鲁棒性更高.     

Direct data-driven filter design for uncertain LTI systems with bounded noise

This paper investigates the filter design problem for linear time-invariant dynamic systems when no mathematical model is available, but a set of initial experiments can be performed where also the variable to be estimated is measured. Instead of using the initial experimental data to identify a model on the basis of which a filter is designed, these data are used to directly design a filter. Assuming norm-bounded disturbances and noises, a Set Membership formulation is followed. For classes of filters with exponentially decaying impulse response, approximating sets are determined that guarantee to contain all the solutions to the optimal filtering problem, where the aim is the minimization of the induced norm from disturbances to the estimation error. A method is proposed for designing almost-optimal linear filters with finite impulse response, whose worst-case filtering error is at most twice the lowest achievable one. In the H_∞ SISO case, an efficient technique is presented, that allows the evaluation of bounds on the guaranteed worst-case filtering error of the designed filter. Numerical examples illustrate the effectiveness of the proposed solution.