高性能子字并行运算单元的设计与实现

通过硬件共享的方式实现一套高性能子字并行运算单元,运算单元采用流水线设计,可以一个周期进行1个64-bit、2个32-bit、4个16-bit或8个8-bit定点运算,1个双精度或2个单精度浮点运算。运算单元采用Verilog HDL设计,在0.18 μm 标准CMOS工艺库下实现,并针对实际多媒体应用程序基于ESCA系统进行性能评测。实验结果表明,该运算单元可以在硬件开销和性能上获得较好的平衡。     

提高定点精度的FPGA信号处理算法

为了满足速度、功耗等诸多限制的要求,数字信号处理算法常使用FPGA实现。而实现时由于硬件特点,通常将浮点运算转换成定点运算,但定点转换设计流程复杂、周期长,且存在数据范围和精度之间的矛盾。利用浮点数的优点,本文改进了基于FPGA的定点数的基本运算规则,有效解决了上述矛盾。本文详细论述了实现移位、加/减、乘、除基本运算模块的方法和步骤,最后以FIR数字滤波器为设计实例。仿真结果表明:改进的定点数算法比定点运算误差小、精度高、数据范围宽,能有效地防止溢出。     

Fast transformation of three-dimensional graphics structures via mixed-point arithmetic

Real-time animation of three-dimensional structures on refreshed tube interactive graphics processors usually requires floating-point arithmetic hardware for matrix manipulation and object transformation by the resultant matrix. An algorithm is described which uses fixed-point hardware to effect the required transformations at speeds surpassing that possible with floating-point hardware with no effective loss in accuracy. The algorithm involves ‘mixed-point arithmetic’—limited precision floating-point multiplication, conversion to an integer-fraction doubleword, and fixed-point addition.     

基于定点DSP的浮点开平方算法的实现

本文提出了基于TMS320C2XX定点DSP的浮点开平方算法，给出了实现方法及程序清单，实践证明该方法具有精度高，运算速度快、程序简单等特点。     

TEC-XP16教学机浮点运算指令快速设计方法

为解决TEC-XP16教学机缺少浮点运算指令的问题,设计32 bit浮点加法、32 bit浮点减法、32 bit浮点乘法、32 bit浮点除法指令以及实现浮点运算的算法。为解决人工方式设计微程序和修改微程序控制器源程序效率低且容易出错等问题,提出一种能够由汇编语言程序自动生成微程序以及能够由微程序自动修改控制器ABEL语言源程序的方法。实验结果表明,所设计的32 bit浮点运算指令的功能是正确的,平均5 s之内就能根据汇编语言源程序自动生成微程序,平均2 s之内就能根据微程序等自动修改并生成控制器ABEL语言源程序。该方法也可推广到其他复杂指令的设计。     

自校正对角阵加权信息融合Kalman预报器

For the multisensor systems with unknown noise statistics, using the modern time series analysis method, based on on-line identification of the moving average (MA) innovation models, and based on the solution of the matrix equations for correlation function, estimators of the noise variances are obtained, and under the linear minimum variance optimal information fusion criterion weighted by diagonal matrices, a self-tuning information fusion Kalman predictor is presented, which realizes the self-tuning decoupled fusion Kalman predictors for the state components. Based on the dynamic error system, a new convergence analysis method is presented for self-tuning fuser. A new concept of convergence in a realization is presented, which is weaker than the convergence with probability one. It is strictly proved that if the parameter estimation of the MA innovation models is consistent, then the self-tuning fusion Kalman predictor will converge to the optimal fusion Kalman predictor in a realization, or with probability one, so that it has asymptotic optimality. It can reduce the computational burden, and is suitable for real time applications. A simulation example for a target tracking system shows its effectiveness.     

The TigerSHARC DSP architecture

This highly parallel DSP architecture based on a short-vector memory system incorporates techniques found in general-purpose computing. It promises sustained performance close to its peak computational rates of 900 MFLOPS (32-bit floating-point) or 3.6 BOPS (16-bit fixed-point)     

Recursive Noise Adaptive Kalman Filtering by Variational Bayesian Approximations

This article considers the application of variational Bayesian methods to joint recursive estimation of the dynamic state and the time-varying measurement noise parameters in linear state space models. The proposed adaptive Kalman filtering method is based on forming a separable variational approximation to the joint posterior distribution of states and noise parameters on each time step separately. The result is a recursive algorithm, where on each step the state is estimated with Kalman filter and the sufficient statistics of the noise variances are estimated with a fixed-point iteration. The performance of the algorithm is demonstrated with simulated data.      

按对角阵加权自校正信息融合Kalman预报器及其收敛性分析

对于带未知噪声统计的多传感器系统，应用现代时间序列分析方法，基于滑动平均(MA)新息模型的在线辨识和相关函数矩阵方程的解，得到了噪声方差估值器，且在按对角阵加权线性最小方差最优信息融合准则下，提出了自校正信息融合Kalman预报器.它实现了状态分量的自校正解耦融合Kalman预报器.基于动态误差系统，提出了自校正融合器的一种新的收敛性分析方法.提出了按实现收敛新概念，它比以概率1收敛弱.严格证明了:假如MA新息模型参数估计是一致的，则自校正融合Kalman预报器将按实现或按概率1收敛到最优融合Kalman预报器，因而它具有渐近最优性.它可减小计算负担，且便于实时应用. 一个3传感器跟踪系统的仿真例子证明了其有效性.     

一类新的固定点和固定区间KALMAN平滑器1)

Using the modern time series analysis method,based on the autoregressive moving average (ARMA)innovation model and white noise estimators,this paper presents two new fixed-point Kalman smoothers and two new forward fixed-interval Kalman smoothers for linear discrete time-invariant stochastic systems.Their advantages are that the solution of the Riccati equation is avoided,and that the algorithms are simple and can be implemented on line.The optimal initial estimate formulas are given in order to ensure the optimality of the proposed smoothers.A simulation example shows their usefulness.     

Trade-offs of certified fixed-point code synthesis for linear algebra basic blocks

In embedded systems, efficient implementations of numerical algorithms typically use the fixed-point arithmetic rather than the standardized and costly floating-point arithmetic. But, fixed-point developers face two difficulties: First, writing fixed-point codes is tedious and error prone. Second, the low dynamic range of fixed-point numbers leads to the persistent belief that fixed-point computations are inherently inaccurate. In this article, we address these two limitations by introducing a methodology to design and implement tools that synthesize fixed-point programs. To strengthen the user’s confidence in the synthesized code, analytic methods are presented to automatically assert its numerical quality. Furthermore, we use this framework to generate fixed-point code for linear algebra basic blocks such as matrix multiplication and inversion. For example, the former task involves trade-offs such as choosing to maximize the code’s accuracy or minimize its size. For the two cases of matrix multiplication and inversion, we describe, implement, and experiment with several algorithms to find trade-offs between the conflicting goals.     

基于IQmath库的定点DSP算法设计

基于TI公司提供的IQmath库实现在定点DSP芯片TMS320F28xx上进行精确的浮点运算,方便开发人员采用C/C＋＋编写浮点运算程序,可以节省设计和调试时间。IQmath库主要应用于高速度和高精度的实时计算,与直接采用ANSIC语言相比效率更高,这对设计实时性要求很高的控制系统尤其重要。     

Robust weighted state fusion Kalman estimators for networked systems with mixed uncertainties

This paper is concerned with robust weighted state fusion estimation problem for a class of time-varying multisensor networked systems with mixed uncertainties including uncertain-variance multiplicative and linearly correlated additive white noises, and packet dropouts. By augmented state method and fictitious noise technique, the original system is converted into one with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst-case system with the conservative upper bounds of uncertain noise variances, four weighted state fusion robust Kalman estimators (filter, predictor and smoother) are presented in a unified form that the robust filter and smoother are designed based on the robust Kalman predictor. Their robustness is proved by the Lyapunov equation approach in the sense that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. Their accuracy relations are proved. The corresponding robust local and fused steady-state Kalman estimators are also presented, and the convergence in a realization between the time-varying and steady-state robust Kalman estimators is proved by the dynamic error system analysis (DESA) method. Finally, a simulation example applied to uninterruptible power system (UPS) shows the correctness and effectiveness of the proposed results.     

基于改进4-2压缩结构的32位浮点乘法器设计

本文介绍一种用于高性能DSP的32位浮点乘法器设计,通过采用改进Booth编码的树状4-2压缩器结构,提高了速度,降低了功耗,该乘法器结构规则且适合于VLSI实现,单个周期内完成一次24位整数乘或者32位浮点乘。整个设计采用Verilog HDL语言结构级描述,用0.25um单元库进行逻辑综合.完成一次乘法运算时间为24.30ns.     

A unified closed-loop stability measure for finite-precision digital controller realizations implemented in different representation schemes

A computationally tractable unified finite word length closed-loop stability measure is derived which is applicable to fixed-point, floating-point and block-floating-point representation schemes. Both the dynamic range and precision of an arithmetic scheme are considered in this new unified measure. For each arithmetic scheme, the optimal controller realization problem is defined and a numerical optimization approach is adopted to solve it. Numerical examples are used to illustrate the design procedure and to compare the optimal controller realizations in different representation schemes.     

A fast algorithm for color space conversion and rounding error analysis based on fixed-point digital signal processors

The YCbCr (luminance, chrominance-blue, and chrominance-red) color space is adopted in video codecs or transmission, while the HSV (hue, saturation and value) color space is used in some video analysis algorithms. In this paper, a fast algorithm based on fixed-point digital signal processors (DSPs) is proposed for YCbCr to HSV conversion. Floating-point multiplications are replaced with fixed-point shifts, 16-bit fixed-point multiplications, and additions. To compensate for rounding error and convert floating-point multiplication into 16-bit fixed-point multiplication in the calculation, tables occupying 225 bytes and 256 bytes are established, respectively. According to the experimental results, the error caused by the proposal is within the acceptable range. At the same time, the proposed algorithm is about 10 times faster than traditional YCbCr to HSV conversion algorithm on a fixed-point digital signal processor (DSP) platform and about 1.41 times faster on a personal computer (PC) platform.     

Robust centralized and weighted measurement fusion Kalman estimators for uncertain multisensor systems with linearly correlated white noises

This paper addresses the design of robust centralized fusion (CF) and weighted measurement fusion (WMF) Kalman estimators for a class of uncertain multisensor systems with linearly correlated white noises. The uncertainties of the systems include multiplicative noises, missing measurements, and uncertain noise variances. By introducing the fictitious noises, the considered system is converted into one with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst-case system with the conservative upper bounds of uncertain noise variances, the robust CF and WMF time-varying Kalman estimators (predictor, filter, and smoother) are presented in a unified framework. Applying the Lyapunov equation approach, their robustness is proved in the sense that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. Using the information filter, their equivalence is proved. Their accuracy relations are proved. The computational complexities of their algorithms are analyzed and compared. Compared with CF algorithm, the WMF algorithm can significantly reduce the computational burden when the number of sensors is larger. A robust weighted least squares (WLS) measurement fusion filter is also presented only based on the measurement equation, and it is proved that the robust accuracy of the robust CF or WMF Kalman filter is higher than that of robust WLS filter. The corresponding robust fused steady-state estimators are also presented, and the convergence in a realization between the time-varying and steady-state robust fused estimators is proved by the dynamic error system analysis (DESA) method. A simulation example shows the effectiveness and correctness of the proposed results.     

一种低成本128位高精度浮点SIMD乘加单元的设计与实现

SIMD单元集成已经成为提高处理器性能的重要途径之一。虽然定点SIMD单元的硬件复用低成本设计技术已经较为成熟,但是,大部分浮点SIMD单元的硬件设计还停留在简单的硬件复制方法上。本文针对日益增长的128位高精度浮点操作的计算需求,提出了其相应的SIMD低成本硬件结构方案。综合实验结果表明,所提出的SIMD浮点乘加单元比传统128位高精度浮点乘加单元具有更加优化的性能与面积参数。     

Self-tuning weighted measurement fusion Kalman filter and its convergence

For multisensor systems, when the model parameters and the noise variances are unknown, the consistent fused estimators of the model parameters and noise variances are obtained, based on the system identification algorithm, correlation method and least squares fusion criterion. Substituting these consistent estimators into the optimal weighted measurement fusion Kalman filter, a self-tuning weighted measurement fusion Kalman filter is presented. Using the dynamic error system analysis (DESA) method, the convergence of the self-tuning weighted measurement fusion Kalman filter is proved, i.e., the self-tuning Kalman filter converges to the corresponding optimal Kalman filter in a realization. Therefore, the self-tuning weighted measurement fusion Kalman filter has asymptotic global optimality. One simulation example for a 4-sensor target tracking system verifies its effectiveness.     

Program-based dynamic precision selection framework with a dual-mode unified shader for mobile GPUs

To extend the life of battery-driven mobile devices while maintaining image quality, this work proposes a Program-based Dynamic Precision Selection (PDPS) framework with a dual-mode unified shader. Since fixed-point arithmetic can be performed faster and more energy-efficiently than floating-point arithmetic on power-limited devices, the use of fixed-point rather than floating-point rendering is a critical concern. The proposed PDPS framework is composed of a runtime profile-based mechanism for automatically determining the precision of each shading program in fixed-point arithmetic. Additionally, a scene change detection mechanism is developed to recalculate the rendering precision whenever a 3D scene changes. The results reveal an average 18% reduction in energy and 35% faster performance under fixed-point rendering. The degradation in rendered image quality under the proposed PDPS cannot be detected by the naked eye, and the PSNR is an average of 15% better than that achieved using related approach.