单轴旋转惯性导航系统的水平姿态角误差修正方法

在单轴旋转惯性导航系统中,旋转轴不正交误差对于水平方向上的姿态角会产生一定的影响。针对传统最小二乘拟合估计旋转轴不正交角存在拟合近似误差大、未考虑到数据的统计特性等缺陷,提出一种基于Kalman滤波的水平姿态角误差修正方法。在传统方案的基础上,增加以加速度计的输出作为观测量,并采用带有确定性控制项的Kalman滤波方法估计旋转轴不正交角,进而修正转轴不正交误差。仿真实验结果表明,转轴不正交角较大时,该方案将水平姿态角误差峰峰值从传统的最小二乘拟合修正方案的50'进一步降低至10'以内,精度提升了约80%。实际试验结果表明该方案相比于传统的最小二乘拟合修正方案,提升了水平姿态角精度。     

基于导弹舵面信息的惯导姿态角速率滤波方法

针对导弹武器中低精度惯导系统陀螺所测量的弹体姿态角速率误差较大的问题,提出了利用导弹控制舵面信息与弹体姿态角的动力学关系构建滤波方程的方法,其相对于常用的低通滤波器能够更加精确地反映出姿态角的变化趋势.此外为降低采用EKF和UKF等非线性滤波方法所带来的计算复杂度,仿真中通过构造交错卡尔曼滤波器实现了对非线性系统的伪线性化.最后通过对某型低精度惯组在三轴姿态转台上的半实物仿真实验,该滤波算法将实测的惯导姿态角速率误差降低了40%以上.     

MEMS-IMU/GPS组合导航中的多模态Kalman滤波器设计

一般的Kalman滤波器要求有准确的动态和统计模型,而低成本的MEMS-IMU性能随着温度急剧变化,故在MEMS-IMU/GPS组合导航系统中使用一般的Kalman滤波器存在很多的局限性。针对低成本的MEMS-IMU/GPS组合导航系统,提出了多模态自适应滤波算法在MEMS-IMU/GPS组合导航系统中的应用;针对普通的多模态算法中的问题,采用修正的多模态自适应滤波算法来提高MEMS-IMU/GPS组合导航系统的性能。使用静态实时测试数据,验证了所提出的算法。测试结果表明,与普通Kalman滤波器相比,修正的多模态滤波算法提高了MEMS-IMU/GPS组合导航系统的性能;采用所提出的算法,MEMS-IMU/GPS组合导航系统的短时间静态位置精度小于5m(标准差),速度精度小于0.1m/s(标准差),姿态角精度小于0.5°(标准差)。     

基于正弦函数拟合的高动态捷联惯导姿态更新算法

为提高捷联惯导在高动态条件下的姿态解算精度,基于等效旋转矢量泰勒级数展开法,提出一种基于正弦函数拟合的高动态捷联惯导姿态更新算法。以正弦函数拟合载体运动角速度,考虑Bortz方程高阶项的影响,对陀螺角增量表示的旋转矢量进行泰勒六阶展开,对比旋转矢量不同形式表达式求得误差补偿系数。在MATLAB平台上,以圆锥运动与大角速率转动并存环境作为仿真条件,对所提算法与传统算法进行对比仿真分析。仿真结果表明,在小半锥角低频圆锥运动伴随高速角速率转动情况下,所提算法性能较好,当半锥角为0.5°、角频率为2.26πrad/s、常值角速率为5.30 rad/s、姿态解算周期为0.02 s时,所提正弦函数拟合三子样旋转矢量算法与传统扩展形式频率级数/显示频率三子样圆锥算法相比误差降低了2个数量级。     

一种小型无人倾转旋翼机全包线飞行的参数估计方法(英文)

小型无人倾转旋翼机的核心是飞行控制系统与捷联惯性导航系统(SINS)。针对小型无人倾转旋翼机的不同飞行模式设计了一套线性、计算效率高的捷联导航算法,为控制系统提供真实可靠的反馈参数。在直升机悬停与小速度飞行模式,利用加速度计与磁强计的输出计算测量姿态角并根据角度与角速率的关系设计低阶线性姿态估计算法,递推解算出MEMS陀螺的漂移特性,并实时补偿测量的角速率。在倾转与飞机飞行模式飞行器具有持续加速与高速的飞行特性,利用磁强计解算当前航向并引入GPS的速度与位置参数,设计了基于误差的线性Kalman滤波器,提高持续加速飞行状态的姿态估计精度。数值仿真表明在全包线飞行过程中设计的捷联导航算法具有良好的测量精度,并利用小型无人倾转旋翼机的飞行试验,验证了算法的估计性能与可靠性。     

基于磁/惯性传感器旋转弹体定姿的Kalman滤波器设计

微惯性传感器精度较低,其漂移会引起很大的姿态误差,不能提供长时间稳定姿态;磁传感器组合的姿态角误差不随时间累积但姿态角更新速度慢。针对这一问题提出了利用磁/惯性传感器构建低成本姿态探测系统的方案,设计了Kalman滤波器融合二者信息——以磁传感器解算的姿态角和等效旋转矢量法解算的姿态角之差作为观测量,以惯性传感器的漂移和姿态误差角作为状态变量,整个解算过程无需使用地磁场强度。仿真结果表明了该算法的有效性,二者组合定姿可实现高精度的姿态测量。     

经纬仪测星评估惯导系统姿态角误差方法

针对动态条件航天测量船惯导系统姿态角精度鉴定和评估这个困扰多年的难题,提出一种利用经纬仪观测恒星对惯导姿态角误差进行解算的方法:用短时间(每颗星记录2 s)观测方位角大致均匀分布的多颗恒星数据解算惯导姿态角误差的稳态分量;用较长时间(每颗星记录200 s以上)观测特殊方位角单颗恒星的数据,观察惯导姿态角误差的动态特性,详细介绍了该方法数学模型的推导过程,从理论上分析了该方法各种数据误差源对解算精度的影响,并利用实际观测数据对惯导姿态角误差稳态分量和动态特性进行了解算和观察,结果与航天测量船惯导系统的设计指标基本吻合,表明该方法可以作为评估航天测量船惯导系统姿态角动态精度的一种有效手段.     

初始装订姿态误差对Kalman滤波器陀螺漂移估计的影响分析

探讨了动基座对准中的一个新的问题，初始装订姿态误差对Kalman滤波器估计陀螺漂移的影响，对该问题进行了试验和仿真。结果表明，利用速度匹配进行初始对准，初始装订姿态误差对两个水平陀螺漂移的估计值产生的影响，主要来自于系统初始装订姿态的精度和Kalman滤波器系统模型的精度，如果要保证滤波器足够的估计精度，应该首先从系统模型上解决。     

时间延迟对姿态角匹配传递对准的影响

姿态角匹配传递对准要求匹配信息在时间上统一。主子惯导之间存在传输延迟以及由于启动时间点随机性导致的解算点不匹配,造成信息在时间上不统一。分析了时间延迟对姿态角匹配传递对准的影响,并提出了一种将时间延迟分离并加以补偿处理的方法。采用滞后子惯导信息的方式预先补偿常值时延,而后采用状态增强的方式估计补偿随机启动时间点造成的随机时延,从而达到匹配信息时间统一的要求。试验结果表明,当主子惯导时间不同步,若不对时间延迟补偿,姿态角估计误差较大甚至不收敛;存在100 ms时间延迟时,相比于直接采用状态增强的方式估计补偿时间延迟,采用常值与随机时延分别补偿的方式卡尔曼滤波器收敛时间从28 s缩短至10 s,东向与北向水平估计精度分别提升至0.5'、0.3',航向估计精度相同。     

大方位失准角的舰载武器INS对准

研究了舰载武器惯导系统（INS）大方位失准角的传递对准问题。首先,给出了适用于大方位失准角的INS姿态误差和速度误差传播模型。然后,提出了一种改进的利用速度＋角速率匹配的传递对准算法,该算法能够借助海浪引起的舰船运动进行传递对准。通过基于奇异值分解的卡尔曼滤波器（SVD-KF）的引入,给出了非线性滤波算法的实现方案,并对SVD-KF和EKF在大方位失准角的舰载武器INS对准就姿态失准角的估计精度和收敛速度进行了比较。仿真结果验证了所提大方位失准角传递对准算法的可行性。     

智能抛物面天线多目标最优控制

大型天线必须保持非常精确的形状。由于载荷变化及各种随机干扰,为了保持精确的形状,这类结构宜采用主动控制。针对智能抛物面天线结构,建立了对天线反射面的最佳吻合抛物面的RMS精度和作动器能耗为综合目标的多目标优化模型。优化模型以结构强度和作动器性能作为约束条件,模型转化为二次规划问题进行求解,实现智能抛物面天线的准静态最优控制。算例表明,可以用较少的作动器,实现大型天线结构的精密控制。     

Simulation of mass transfer during osmotic dehydration of apple: a power law approximation method

In this study, unsteady one-dimensional mass transfer during osmotic dehydration of apple was modeled using an approximate mathematical model. The mathematical model has been developed based on a power law profile approximation for moisture and solute concentrations in the spatial direction. The proposed model was validated by the experimental water loss and solute gain data, obtained from osmotic dehydration of infinite slab and cylindrical shape samples of apple in sucrose solutions (30, 40 and 50 % w/w), at different temperatures (30, 40 and 50 °C). The proposed model’s predictions were also compared with the exact analytical and also a parabolic approximation model’s predictions. The values of mean relative errors respect to the experimental data were estimated between 4.5 and 8.1 %, 6.5 and 10.2 %, and 15.0 and 19.1 %, for exact analytical, power law and parabolic approximation methods, respectively. Although the parabolic approximation leads to simpler relations, the power law approximation method results in higher accuracy of average concentrations over the whole domain of dehydration time. Considering both simplicity and precision of the mathematical models, the power law model for short dehydration times and the simplified exact analytical model for long dehydration times could be used for explanation of the variations of the average water loss and solute gain in the whole domain of dimensionless times.     

Instability in the higher modes of a nonlinear equation

The linear approximation is used to study the stability of two- and three-dimensional higher-order modes of a nonlinear wave equation against exponentially increasing perturbations. For all the nonlinear models considered the higher modes are unstable; the number of exponentially increasing perturbations and their growth rate are determined by the mode number and the form of the nonlinear relationship. Numerical tests are described in the parabolic approximation on the stability of the first axially symmetric mode against small amplitude perturbations and the conditions are determined under which higher-order modes can be observed.     

NONLINEAR FLUID FORCES IN CYLINDRICAL SQUEEZE FILMS. PART I: SHORT AND LONG LENGTHS

Using three approximation methods, nonlinear models have been derived for short and long cylindrical squeeze films with arbitrary inner cylinder motions. Elliptical and parabolic velocity profiles are employed in the derivation in order to determine the effects of the choice of velocity profile. The only differences in the final squeeze film equations, due to the three approximation methods and the two velocity profiles, are in the four constant coefficients. Each term in the squeeze film equations is a nonlinear function of cylinder position. Comparing the present nonlinear expressions with existing models for short cylindrical squeeze films shows that the force terms are either exactly the same or have the same trends with instantaneous eccentricity values. For long cylindrical squeeze films, the present expressions have some force terms which are essentially the same as in other studies, while other force terms show variations with position which are very different from a previously published study.     

A parabolic approximation for elastic waves

A parabolic approximation is developed for elastic waves, which depends on the variations in elastic properties being small and taking place slowly within a wavelength. The equations describe a wave which is, in a zeroth approximation, plane and which is diffracted by the heterogeneity by small angles only.The parabolic equation has well-known advantages over the original wave equations for numerical integration. In addition, the quantities to be calculated vary slowly over a wave length and numerical step sizes can be relatively large. The results are comparable with those of ray theory but, since they include diffraction effects, they are valid to a much greater range.     

Numerical instabilities and convergence control for convex approximation methods

Convex approximation methods could produce iterative oscillation of solutions for solving some problems in structural optimization. This paper firstly analyzes the reason for numerical instabilities of iterative oscillation of the popular convex approximation methods, such as CONLIN (Convex Linearization), MMA (Method of Moving Asymptotes), GCMMA (Global Convergence of MMA) and SQP (Sequential Quadratic Programming), from the perspective of chaotic dynamics of a discrete dynamical system. Then, the usual four methods to improve the convergence of optimization algorithms are reviewed, namely, the relaxation method, move limits, moving asymptotes and trust region management. Furthermore, the stability transformation method (STM) based on the chaos control principle is suggested, which is a general, simple and effective method for convergence control of iterative algorithms. Moreover, the relationships among the former four methods and STM are exposed. The connection between convergence control of iterative algorithms and chaotic dynamics is established. Finally, the STM is applied to the convergence control of convex approximation methods for optimizing several highly nonlinear examples. Numerical tests of convergence comparison and control of convex approximation methods illustrate that STM can stabilize the oscillating solutions for CONLIN and accelerate the slow convergence for MMA and SQP.     

A comparison of parabolic wave theories for linearly elastic solids

The Schrödinger equation describes a theory for propagating scalar waves which is frequently termed a parabolic theory. This theory has been demonstrated to provide a paraxial, or narrow-angled, approximation to the theory of acoustic wave propagation, described by the Helmholtz equation, by a variety of seemingly different procedures. Several authors have considered the question of an approximation to the time harmonic equations of linear elastodynamics, which is parabolic in the above described sense. Since none of the deivation procedures employed can be termed rigorous, and since the results of these procedures are different, the validity of each of the theories is suspect and all should be considered further. In this paper we consider three parabolic theories of elastodynamics; by Hudson, by Landers and Claerbout, and by McCoy; and apply them in turn to a computational experiment that can be solved in the perturbation limit using the exact equations of elastodynamics. The principal conclusion achieved is that an approximate theory for propagating vector waves must be based on a representation of the vector wave field, that explicitly incorporates different wave speeds for the dilitational and rotational components, if predictions of the approximate theory are to approach those of the exact formulation for narrow angles.     

Precursors for waves in random media

We consider scattering of a pulse propagating through a three-dimensional random media and study the shape of the pulse in the parabolic approximation. We show that, similarly to the one-dimensional O’Doherty–Anstey theory, the pulse undergoes a deterministic broadening. Its amplitude decays only algebraically and not exponentially in time, due to the signal low/midrange frequency component. We also argue that the parabolic approximation captures the front evolution (but not the signal away from the front) correctly even in the fully three-dimensional situation.     

Describing the soil physical characteristics of soil samples with cubical splines

The Mualem-Van Genuchten equations have become very popular in recent decades. Problems were encountered fitting the equations’ parameters through sets of data measured in the laboratory: parameters were found which yielded results that were not monotonic increasing or decreasing. Due to the interaction between the soil moisture retention and the hydraulic conductivity relationship, some data sets yield a fit that seems not to be optimal. So the search for alternatives started. We ended with the cubical spline approximation of the soil physical characteristics. Software was developed to fit the spline-based curves to sets of measured data. Five different objective functions are tested and their results are compared for four different data sets. It is shown that the well-known least-square approximation does not always perform best. The distance between the measured points and the fitted curve, as can be evaluated numerically in a simple way, appears to yield good fits when applied as a criterion in the optimization procedure. Despite an increase in computational effort, this method is recommended over the least square method.     

Solitons in viscous films flowing down a vertical wall

Periodic wave solutions in a film of viscous liquid near optimal regimes have been investigated in the boundary layer approximation by Shkadov et al. [1]. Urintsev [2] has found nonlinear steady solutions near the upper neutral stability curve on the basis of the Navier-Stokes equations. In the present paper, equations are derived that can be used either to make the boundary-layer solution more accurate or estimate its applicability. Soliton type solutions are considered for parameter of the problem in the range δ ε (0, ∞). Asymptotic expansions are considered in the limits δ → 0 and δ → ∞. For finite δ, two numerical algorithms are proposed for solving the problem; one of them is for equations in von Mises variables. The numerical solutions revealed the existence of “singular” sections, at which the velocity profile differs strongly from parabolic. The integral characteristics of the soliton — the phase velocity, amplitude, etc. — are found to be close to the corresponding characteristics obtained earlier by the present author [3] by assuming that the velocity profile is parabolic. The first determination is made of the critical value δ = δ_** of the onset of boundary layer separation in the vertically flowing viscous film. It is interesting that the separation does not occur on the rigid wall but at an interface near the crest of the soliton.