Sensitivity Functions for Linear Discrete Systems with Applications

z-transform techniques are employed to establish general symmetry and simultaneity properties of the first sensitivity functions of the phase-canonical form of single-input, nth-order, linear, constant, discrete-time, controllable systems. It is demonstrated that computation of the first sensitivity function requires one nth-order model in addition to the system model. This simultaneity property is extended to arbitrary single-input, nth-order, linear, constant, discrete systems. In complete analogy with results presented for continuous systems, symmetry and simultaneity properties may be established for the computation of the /th sensitivity function begin{equation*}^{l}beta^{y} triangleq frac{partial^{l}y_{i}}{partialalpha_{Jl}partialalpha_{Jl-1}cdotspartialalpha_{J2}partialalpha_{J1}}|_{alpha=alpha_{0}} {rm for} substack{i = 1,2,ldots,n\ J_{k} = 1,2,ldots,n\ k = 1,2,ldots,l.}end{equation*} Extension of these results to multi-input systems is also mentioned. The usefulness of the simultaneity property is illustrated by applying the results to the design of a low-sensitivity optimal control law.     

Output Probability Density Functions for Cross Correlators Utilizing Sampling Techniques

Sampling techniques provide a practical means of obtaining cross-correlation functions. In this paper, the correlation function is described by sums of the form Z = begin{equation*}Z = Sigma^{N}_{j=1}X_{j}Y_{j}end{equation*}. A general expression is derived for the probability density function of the random variable Z under the condition that Xj and Yj are stationary, jointly Gaussian random processes with nonzero means and unit variances.     

A Semicoherent Detection and Doppler Estimation Statistic

Consider a uniform train of M coherent short pulses transmitted by a radar and received with a Doppler shift. When thermal noise is present, let the mth sample of the return at the video be represented by the complex process Zm. A novel detection and Doppler estimation criterion is analyzed which depends on the semicoherent statistic begin{equation*}{Z_{K}}^prime = sum_{m=k+1}^{M} {^{z}m^{z}m-k}^{ *}end{equation*} where the asterisk stands for complex conjugate. Its characteristics are also studied when the real and imaginary parts of Zm are digitized to one bit.     

The Effect of Satellite Spin on Two-Way Doppler Rangerate Measurements

The rotation of a spin-stabilized satellite employing a turnstile antenna for reception and retransmission affects two-way Doppler range-rate measurements. Two different types of tracking systems are considered and, in both systems, the range-rate measurement is changed by the amount begin{equation*} |Delta dot{r}| = frac{|1 pm 1/k|}{2} lambda_{t}f_{s} end{equation*} where k is the turn-around ratio of the satellite transponder, Xt is the wavelength of the ground-based transmitter, and fs is the spin rate of the satellite. The positive sign is used if the turnstile antenna elements are connected to give the same polarization for both reception and transmission. If the antenna connections result in different polarizations, the minus sign is used and the magnitude of the effect is reduced.     

Comments on "The Psi-Angle Error Equation in Straplown Inertial Navigation Systems"

The negative sign on the psi-angle differential equation for strapdow inertial navigation error analysis discussed by Weinreb and Bar-ltzhack is not due to differences in error propagation between gimbaled and strapdown systems, but to the definition of strapdown gyro drift rate given by them. If a consistent definition of gyro drift rate for gimbaled and strapdown systems error analysis is used, the sign change does not occur.     

Real-Time Motion Desmearing of Airborne Imagery

This paper considers the real-time ?desmearing? of motion- ?smeared? imagery telemetered from an airborne platform. The specific configuration considered is the direct raster scan readout of a satellite-mounted vidicon. Three types of smearing are considered: 1) linear uniform smearing, 2) linear nonuniform smearing, and 3) nonlinear smearing. The simplest type of smearing, linear uniform, has as its desmearing or inverse filter a circulating delay line (CDL) cascaded with a differentiator. An error analysis of this filter is presented along with an experimental simulation. Linear, non-uniform smearing characterized by the operator begin{equation*}int^{t}_{t-delta(t)}I(tau){ }{dtau}end{equation*} is considered next. Two possible realizations for the inverse filter are discussed as to accuracy and practicality. Finally, an error analysis is performed for the nonlinear smearing that results from a skewing of the raster scan.     

Spectral Analysis of Optimal and Suboptimal Gyro Monitoring Filters

Gyro monitoring filters are used to estimate and correct gyro drift rates of local-level inertial navigation systems. Conventional gyro monitoring filters are usually designed based on a simplified model of gyro drift rate. Furthermore, the effectiveness of these filters-and of many filters of the "Kalman" type-is often measured in terms of the root mean square (rms) criterion in contrast to the spectral content criterion typical of classical Wiener filtering theory. This paper has two objectives: to propose a gyro monitoring filter which is based on a more detailed model of gyro drift rate; and to propose a method of filter performance evaluation which uses as criterion a measure of the spectral content of the error process. The proposed gyro monitoring filter is shown to have improved spectral contents resulting in superior navigation performance for the gyro error models used in the calculations (comparable to commercial-grade aircraft gyros).     

某型方位旋转平台惯导系统转速模型分析与验证

某型平台惯导系统采用方位旋转调制技术,通过对台体匀速转动的控制调制陀螺的漂移。台体的转速不是固定值,是随惯导系统所在地区而改变的,且台体转速异常必伴随方位陀螺故障。为了正确判断台体转速的理论是否正常,文章推导了转速的理论计算公式,不同地区惯导系统的实测数据表明实测值与理论计算值一致,验证了转速计算公式的正确性,为监控方位陀螺状态提供了技术途径。     

捷联惯性导航系统动静态误差特性分析研究

捷联惯性导航系统动静态误差特性是基于惯性的组合导航系统的主要误差来源。为此,根据捷联惯性导航系统的误差状态方程,本文分析了不同动静态情况下的捷联惯导系统的误差漂移特性。针对静基座和动基座的不同特点,分别采用了特征根和基于数值仿真分析的方法,并建立了相应的误差特性分析模型。重点研究了陀螺常值漂移、加速度计零位偏置和随机性误差对惯性导航系统误差漂移特性的影响;全面分析验证了惯性导航系统的动静态误差特性。本文的研究工作将为惯性组合导航系统误差分析建模提供了有益的参考。     

Inertial System Platform Rotation

Differential error equations are derived for the navigation errors of a local level undamped pure inertial platform that continuously rotates in azimuth. From these, the time response equations for the vector position error produced by a constant level gyro drift error, as a function of platform rotation rate, are computed and evaluated. It is shown that platform rotation attenuates the system position error due to level gyro bias and that this attenuation is a nonlinear function of rotation rate.     

D-最优试验设计在动力调谐陀螺测试中的应用

 为了提高动力调谐陀螺的静态漂移误差测试精度,针对简化静态漂移误差模型,并且考虑陀螺安装角误差的影响,依据D-最优试验设计理论以及正交设计的均匀分散性试验设计思路,设计了一种满足D-最优性质的正交八位置试验方案,并在整个正交空间内采用全局搜索的方法验证了其D-最优性。在相同试验环境下,采用力反馈位置试验法,以全正交空间预测误差平方和最小为评价准则,对该八位置试验方案和国军标GJB1183—91中的八位置试验方案进行比较与评价,试验结果表明该八位置试验方案优于国军标GJB1183—91中八位置试验方案。     

Accurate INS Transfer Alignment Using a Monitor Gyro and External Navigation Measurements

A particular alignment mechanization for a nonmaneuvering vehicle is described which uses a monitor gyro to estimate the slave inertial navigation system (INS) equivalent east gyro drift rate and thus improves azimuth alignment. A state-space model of the dynamic system with measurements is developed. Results of covariance simulations employing Kalman filter estimation are presented for two master INS position update scenarios, one involving frequent and very accurate updates and the other including infrequent and coarse updates. The ef fects of position updates and the monitor gyro on the quality of transfer alignment are demonstrated and analyzed.     

The Improvement of a Low-Cost Inertial Navigator Through Conditional Feedback

A concept for providing an accurate low-cost inertial reference was presented in a previous paper. Low-cost platform gyros, poor in terms of their drift rates, furnish the space-fixed reference frame. A single high-accuracy gyro, mounted on the platform, monitors the performance of the platform gyros. Consequently, drift rates are estimated, predicted, and applied as signals to correct the platform for gyro uncertainties. This paper features new estimation and predictive techniques.     

半球谐振陀螺仪谐振子品质因数不均匀引起的误差分析

 半球谐振子的品质因数不均匀性是造成陀螺仪输出误差的一个主要误差源,所以研究在参数激励以及位置激励两种模式下,谐振子品质因数不均匀对于陀螺仪输出误差的影响具有一定的理论意义。在引入半球谐振子的环形振动模型的基础上,首先考虑参数激励方式下,品质因数不均匀引起的进动角速率误差的表达式,仿真分析了不均匀性四次谐波对陀螺仪漂移角度的贡献,结果表明漂移角度为具有趋势项的振动曲线。然后在位置激励方式下,通过开环和闭环两种模式分别研究了品质因数不均匀的四次谐波对于输入角速率解算的影响,得出了当位置激励对准固有韧性轴时,解算的误差能够得到抑制的结论。总之,在两种激励方式下,品质因数的四次谐波分量都会导致陀螺仪出现输出误差。     

激光陀螺四位置寻北仪提高精度方法

为消除激光陀螺零偏和常值漂移的影响,采用四位置方案来实现高精度寻北。本文简述了单轴激光陀螺四位置寻北方案,给出了陀螺敏感轴与机体系前向偏差角标定方法,研究了寻北仪在倾斜基座下数据补偿算法。本文研究了由于在四个位置上电机转动不到位所引起的误差补偿算法。通过对寻北仪系统测试,采用电机转动不到位补偿后数据标准差降低了0.02º,激光陀螺寻北仪系统达到了高精度快速寻北的要求。     

Fast alignment and calibration algorithms for inertial navigation system

Algorithms for fast estimating the azimuth misalignment angle and calibrating gyro drift rates are approached from the point of view of control theory. By introducing the Lyapunov transformation, the equivalence of Strapdown Inertial Navigation System (SINS) and Gimbaled Inertial Navigation System (GINS) is discussed, and it shows that the analysis results of GINS can be applied to SINS directly by using such kind of equivalence. A similar transformation that based on physical essence is introduced, so that the true states can be replaced by the so-called pseudo-states, and then the observable states of INS can be dynamically decoupled with the unobservable states. Consequently, the best completely observable subsystem model of INS can be obtained. Based on the simplified subsystem model of INS, the algorithms for fast estimating the azimuth misalignment angle and calibrating gyro drift rates are proposed. The proposed algorithms show that the azimuth misalignment angle and gyro drift rates can be estimated from the rates of leveling misalignment angles without using the gyro output signals.     

微硅陀螺静态漂移自回归模型辨识研究

利用微硅陀螺测量的数据，运用过程辨识理论和时间序列分析方法，建立了陀螺静态漂移的自回归（AR）模型，进而得到连续微分方程。     

半球谐振陀螺惯性系统设计探讨

研究了速率积分半球谐振陀螺及其惯性系统的技术特点和应用,并与光学陀螺惯性系统进行了比较。介绍了半球谐振陀螺短期断电工作和小体积低功耗的特点,探讨了自校准技术,并分析了环境适应性设计和对配套部件的要求,为半球谐振陀螺惯性系统工程化设计提供了开放性观点。     

Optimum Alignment of an Inertial Autonavigator

The performance of an inertial autonavigator can only be as good as the accuracy to which the system is initially aligned. Optical methods of alignment can be performed with high precision; however, this technique requires external equipment and is subject to some physical constraints, such as land-based operation. The general problem discussed here is the use of an automatic azimuth alignment technique known as gyrocompassing. In the use of the gyrocompassing technique to obtain azimuth alignment, accuracies are degraded considerably by two dominant error sources, the level axis controlling gyro drift rate and the imperfections of reference or independent velocity information. Consequently, an optimum performance controller is developed for driving the system in this mechanization and is based on a priori knowledge of the second-order statistics of the system error sources. The performance criteria will be to minimize the mean square azimuth error.     

适合航天飞机应用的星体跟踪器

本文推导了航天飞机采用新型探测器件——电荷耦合器件CCD（ChargeCoupled DeVices）组成的星体跟踪器进行姿态稳定的公式。并提供一种适合航天飞机应用的星体跟踪器原理样机。