Efficient Approximation of Kalman Filter for Target Tracking

A Kalman filter in the Cartesian coordinates is described for a maneuvering target when the radar sensor measures range, bearing, and elevation angles in the polar coordinates at high data rates. An approximate gain computation algorithm is developed to determine the filter gains for on-line microprocessor implementation. In this approach, gains are computed for three uncoupled filters and multiplied by a Jacobian transformation determined from the measured target position and orientation. The algorithm is compared with the extended Kalman filter for a typical target trajectory in a naval gun fire control system. The filter gains and the tracking errors for the proposed algorithm are nearly identical to the extended Kalman filter, while the computation requirements are reduced by a factor of four.     

Synthesis of Computationally Efficient Sequential Linear Estimators

The Kalman sequential linear estimation theory, although not always utilized because the number of computations required for many systems of practical importance becomes prohibitive, allows straight-forward synthesis of optimal estimators for many complex systems. Some systems designers have chosen to ignore variables and by such a reduction in system dimension have been able to economize with regard to the number of computations. The purpose of this paper is to demonstrate a method which allows economy of computation by partitioning the system state vector; the variables to be eliminated are placed in one subsystem and the remaining variables in one or more additional subsystems. The resultant system is computationally more efficient if some variables are eliminated. This is so because the remaining states have been partitioned into two or more subsystems. The number of computations for a subsystem varies approximately as the cube of the dimension of its state vector. By operating on several subsystems of lesser dimension than that of the unpartitioned system, the number of computations is decreased; performance will deteriorate. The method for determining the partitioning tends to keep this deterioration under control; it is illustrated by application to a marine-type inertial navigation system.     

Computationally Efficient Bank of Rectangular Digital Filters

A computationally efficient scheme for forming a bank of identical contiguous rectangular digital filters is described. The data processing is organized in a sequential form allowing use of the FFT algorithm as the first stage. An example is given in which a bank of 256 rectangular filters is formed using only a few percent of the number of complex multiplies required by straightforward procedures. The steepness of cutoff is unaltered and the inband ripple is only slightly affected, but the sidelobe level suffers some degradation.     

Generalized Response of a Linear FM Pulse Compression Matched Filter

A pulse compression matched filter is analyzed so that the response may be computed when the pulse width, FM rate, and center frequency simultaneously differ from design conditions. Unilateral and bilateral time domain amplitude weighting for sidelobe reduction is included. A general cross-ambiguity function is defined to include these effects and some basic computed results are presented for the peak envelope response with various degrees of Hamming weighting. Computer evaluation of this cross-ambiguity function allows one to choose a combination of mismatches for signal design trade-off between resolution and detection performance. Since no restrictions are placed upon the mismatch parameters, this analysis may also be used to evaluate the filter discrimination against various interfering signals.     

Some Matched Filter Configurations for Infrared Systems

An analysis of the output of three alternative matched filter configurations in an infrared scanning system model is presented. The sensor is corrupted by thermal noise, generation-recombination noise, photon noise, and modulation noise, the latter providing an extreme discoloration in the signal passband. Expressions for the signal voltage density spectrum, signal pulse shape, noise power spectrum, and average noise power at the matched filter output are derived where the integral evaluations attendant to these derivations do not appear elsewhere in the literature. The paper also provides graphical displays of the signal-to-noise power ratio at the filter output versus various system parameters, noise power spectrum out of the matched filter versus ?, and the signal pulse shape out of the filter versus time. Also included are discussions of practically realizable approximations to the matched filters and curve fitting techniques for the signal pulse shape function.     

Statistical Analysis of Wide-Band Pseudorandom Matched Filter Sonars

A stochastic model of pseudorandom (PR) signals is adopted and a statistical analysis carried out of the velocity (i. e., Doppler) and acceleration tolerances of wide-band PR matched filter sonar systems. The reference functions for these correlation detection systems are considered to be time-compressed or time-expanded replicas of the transmitted signal. Results are derived for the case of a PR signal having a flat power spectral density over a finite bandwidth. It is shown that the velocity and acceleration tolerances are essentially independent of the signal bandwidth and that therefore the radar-derived expressions for the narrow-band tolerances can be extended to the wide-band sonar case. An interesting result is that the derived acceleration tolerance is approximately three times the widely used estimate that is based on the target remaining in the same Doppler channel over the integration time.     

A Self Bit Synchronizer Matched to the Signal Shape

A suboptimum self bit synchronizer is considered that matches the signal shape, i. e., operates making a clever use of the knowledge of the signaling waveform. The noise performance of this system is analyzed for high signal-to-noise ratios, and an expression is obtained for the variance of the timing errors. This variance is compared with that of systems proposed by other authors on the basis of equal closed-loop noise bandwidth and equal signal shape. It is found that the use of this matched synchronizer enables appreciable timing jitter reductions.     

Bayesian Quickest Signal Detection in a Discrete-Time Observation

This paper deals with the problem of quickest detection of a signal in discrete-time observations where the noise is not necessarily additive. By introducing a new cost function, penalizing the decision delay, in addition to penalizing wrong decisions as in the classical case, a global risk function is derived for use in a Bayesian framework. The minimization of the average risk leads to the optimum Bayesian decision regions, giving the structure of the optimum receiver. Some simplifications for elementary costs and some applications are investigated. The optimum receiver is shown to be a parallel bank of classical optimum filters, each one matched to a particular delay of the signal to be detected. Our approach is shown to apply to the detection of certain changes in a stochastic process.     

A Useful Approximation to Binary FSK Probability of Error

A technique for calculating a simple approximation to the probability of error for binary frequency-shift keying (FSK) systems when the predetection bandwidth-bit duration product is large enough so that the signal portion of the detector output is relatively undistorted is described. The results are mathematically simple and avoid the calculation of the density function of the nonclick noise part of the output phase noise.     

基于小波变换的色谱数据平滑滤噪和高效压缩

根据色谱信号及色谱分析的特征和小波变换能精细刻划信号奇异性的特点,本文提出了一种基于多分辨小波分析的色谱伏安信号的平滑滤噪和高效压缩算法.该算法压缩比高(平均大于100倍),滤波效果好,广泛适用于高效液相色谱、气相色谱和红外光谱的滤波和压缩.该算法尤其适用于被强噪声污染的信号处理.     

Limitations of a Variance Approximation

A common approximation for the variance of a function of two random variables is obtained via a series expansion. It is shown that for some cases the error in the approximation is quite large. This approximation is sometimes used to compare the relative merits of two alternate systems. The comparison might be erroneous if the system differences are comparable to the approximation errors.     

多率滤波器组消除混迭的一种方法

通过大量抽取均匀滤波器组中产生的混迭分量并对之进行分析,提出了适当设定综合滤波器与分析滤波器的关系以使混迭相互抵消的方法。理论分析表明,在频率交界点可将混迭完全消除,如果相邻滤波器的频率特性对称性较好,可使总混迭很小。实验证明该方法有效。     

A Modification to Improve the Inverse Filter of Senmoto and Childers

An inverse filter, contained in a recently published paper by Senmoto and Childers, is improved by the application of a shaping function derived by Turin in an earlier paper.     

从数值逼近引出泰勒（Taylor）定理

用简单函数逼近（近似表示）复杂函数是数学中的一种基本思想方法。本文将要引出的Taylor定理就是用高阶多项式来逼近具有一定可微性的函数所得到的一个基本定理，它一理论研究和近似计算中有重要价值。     

A Stratified Statistical Filter with Nonlinear Application

This paper introduces a statistical filter (or, more strictly, a filtering algorithm) which has intended application in the area of nonlinear systems. Within this context, the filter enables one to investigate the convergence effects produced by varying the initial estimates associated with the respective state variables, together with the various system parameters. The present algorithm is not intended to replace the more powerful optimal statistical filters used in linear theory, but rather to provide a simulation tool which can readily be applied to a given nonlinear system. The application considered in this paper bears a similarity to a tracking problem which might be encountered by an optical device, where angular information is the primary observable quanity. In this particular application, angular observations are available, and statistical estimates are desired for a position variable, together with an unknown parameter. The application is introduced primarily for the purpose of demonstrating the behavior of the filter when applied to a relatively simple nonlinear system.     

Approximation to Probability of Detection for Log-Normal Target Fluctuation

A relatively simple expression for the approximation to the probability of detection of a log-normally fluctuating target is provided. Absolute errors normally have a magnitude less than 0.01.     

一种新的有效的群签名方案

介绍了一种有效的群签名方案。该方案的安全性是基于译码问题的难度和线性码的纠删特性和ElGamal签名方案的安全性。已知[n,k,d]码和相应的数字签名方案,则签名和群公钥的长度分别是n+5和n2+5。对于方案的计算代价,签名过程除O(n)算术运算外基本上与ElGamal方案相同;打开签名的过程非常有效,只需O(d2)运算量。方案允许新成员加入群时不修改群公钥。通过向某些成员分发新的成员资格证书,可以将成员从群中删除。     

A New Optimal Hatch Filter to Minimize the Effects of Ionosphere Gradients for GBAS

At present, the main problem faced by ground-based augment system （GBAS） is that though carder smoothing filter and local differential global positioning system （LDGPS） improve the accuracy of the pseudorange by reducing the noise in it and eliminating almost all the common errors between the user and the reference station, they also cause extra errors on account of the effects of the ionosphere temporal and spatial gradients. Based on the analysis of these errors as well as the smoothing noise, this article suggests a new algorithm to design the optimal Hatch filter, whose smoothing window width varies real-time with the satellite elevation, ionosphere variation, and distance from the user to the reference station. By conducting the positioning process in the GBAS emulation platform for several hours and after its comparison with the performances of traditional Hatch filters, it is found that the errors in the differential correction become smaller and the positioning accuracy gets heightened with this new method.     

Feedback Realization of a Continuous-Time Optimal Filter

Another derivation of a continuous-time optimal linear filter is presented. Using this result as a point of departure, a feedback version of this continuous filter is postulated and shown to be optimal in the limit as the ``feedback gain' becomes infinite. It is then demonstrated that the need for this infinite feedback gain can frequently be eliminated. This feedback realization of the continuous optimal filter has application to the problem of optimally mixing two or more redundant signals, each contaminated by random noise. The feedback configuration has the advantages of simplicity and the bounding of otherwise troublesome very large errors. A simple example is given of the mixing of two (velocity) references each having exponentially correlated error.     

用于非线性跟踪问题的一种新的粒子滤波器

机动目标跟踪系统通常是非线性而且不完全观测的 ,所以问题的关键在于每一时刻的目标机动性都是高度不确定的。提出了一种新的平滑粒子滤波算法 ,该算法在粒子滤波器中加入了对系统模型的概率分布密度的平滑处理 ,从而很好的解决了目标的机动性估计问题。在仿真研究中 ,与辅助粒子滤波器的比较验证了本文算法处理非线性跟踪问题的优越性