连续时间系统的定常状态估计器

 对于线性定常的连续时间系统,当系统和测量噪声为平稳白噪声过程时,研究了定常的状态估计器的设计方法。为了改进传统的Kalman-Bucy滤波器的瞬态性能,提出了两种新的性能函数的定义,从而给出了两种便于工程应用的修正的Kalman-Bucy滤波器。     

增广误差模型算法在目标跟踪中的应用

针对目标机动运行过程中,滤波模型与机动状态模型失配的问题,提出了一种新的增广状态误差滤波模型。不同于现有增广方案,该模型从模型失配所致状态滤波误差的角度出发,将状态估计误差增广为一状态量,通过滤波估计后用其校正原状态量。算法分析表明,该增广滤波模型具有自适应调节多重渐消因子的等效特性,增强了对目标的跟踪能力。基于该增广状态误差滤波模型,给出了滤波算法设计并进行了仿真实验。实验结果表明,基于该模型的滤波算法在对机动目标进行跟踪时具有更强的鲁棒性。     

Kalman filtering with state equality constraints

Kalman filters are commonly used to estimate the states of a dynamic system. However, in the application of Kalman filters there is often known model or signal information that is either ignored or dealt with heuristically. For instance, constraints on state values (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. A rigorous analytic method of incorporating state equality constraints in the Kalman filter is developed. The constraints may be time varying. At each time step the unconstrained Kalman filter solution is projected onto the state constraint surface. This significantly improves the prediction accuracy of the filter. The use of this algorithm is demonstrated on a simple nonlinear vehicle tracking problem     

Interrelationship of single-filter and multiple-model adaptivealgorithms

An equivalent filter bank structure for multiple model adaptive estimation (MMAE) is developed that uses the residual and state estimates from a single Kalman filter and linear transforms to produce equivalent residuals of a complete Kalman filter bank. The linear transforms, which are a function of the differences between the system models used by the various Kalman filters, are developed for modeling differences in the system input matrix, the output matrix, and the state transition matrix. The computational cost of this new structure is compared with the cost of the standard Kalman filter bank (SKFB) for each of these modeling differences. This structure is quite similar to the generalized likelihood ratio (GLR) structure, where the linear transforms can be used to compute the matched filters used in the GLR approach. This approach produces the best matched filters in the sense that they truly represent the time history of the residuals caused by a physically motivated failure model     

A new adaptive Kalman filter for navigation systems of carrier-based aircraft

The features of carrier-based aircraft’s navigation systems during the approach and landing phases are investigated. A new adaptive Kalman filter with unknown state noise statistics is proposed to improve the accuracy of the INS/GNSS integrated navigation system. The adaptive filtering algorithm aims to estimate and adapt the unknown state noise covariance Q in high dynamic conditions, when the measurement noise covariance R is assumed to be known empirically in advance. The new adaptive Kalman ...     

Decentralized reduced-order filters

Continuous and discrete methods of designing simple reduced-order local filters within a large-scale network are suggested. The filters are designed to estimate only the local variables of interest and not the entire state vector. The method has the advantage that one need not know the mathematical models of the subsystems generating the interconnection variables. The order of the filter can be small enough so that there is no computational burden associated with the filter. The disadvantage of the method is that performance is lost by using a reduced-order filter instead of a full-order filter. An example that demonstrates one application in the aerospace industry is presented     

Interlaced Kalman filtering of 3D angular motion based on Euler'snonlinear equations

A novel Kalman filtering technique is presented that reduces the mean-square-error (MSE) between three-dimensional (3D) actual angular velocity values and estimated ones by an order of magnitude (when compared with the MSE resulting from direct measurements) even under extremely low signal-to-noise ratio conditions. The filtering problem is nonlinear in nature because the dynamics of 3D angular motion are described by Euler's equations. This nonlinear set of differential equations state that the angular acceleration in one axis is proportional to the torque applied to that axis, and to the products of angular velocity components in the other two axes of rotation. Instead of using extended Kalman filtering techniques to solve this complex problem, the authors developed a new approach where the nonlinear Euler's model is decomposed into two pseudolinear models (primary and secondary). The first model describes the time progression of the state vector containing the linear terms, while the other characterizes the propagation of the state vector containing the nonlinearities. This makes it possible to run two interlaced discrete-linear Kalman filters simultaneously. One filter estimates the values of the state vector containing the linear terms, while the other estimates the values of the state vector containing the nonlinear terms in the system. These estimates are then recombined, solving the nonlinear estimation process without linearizing the system. Thus, the new approach takes advantage of the simplicity, computational efficiency and higher convergence speed of the linear Kalman filter form and it overcomes many of the drawbacks typical of conventional extended Kalman filtering techniques. The high performance and effectiveness of this method is demonstrated through a computer simulation case study     

A Study on Particle Filters for Single-Tone Frequency Tracking

In this paper, we present an online approach for frequency tracking of a noisy sinusoid using sequential Monte Carlo (SMC) methods, also known as particle filters (PFs). In addition, apart from employing the classical Cartesian formulation model, we also develop two alternative dynamical models, namely, nearly constant frequency (NCF) and Singer, which are adapted from the maneuvering target tracking discipline, to describe the evolution of time-varying frequencies, and investigate their fitness to the frequency tracking application. When compared with conventional techniques whose performance is restricted to linear Gaussian models and/or to slowly varying frequencies, PFs are more flexible to handle situations where these conditions are violated. Extensive evaluations on the proposed new models and PF tracking algorithms are conducted with different sets of frequency inputs and levels of signal-to-noise ratio (SNR). According to the computer simulation results, it is found that PFs under all investigated models consistently outperform and are less sensitive to SNR levels than the extended Kalman filter (EKF). Furthermore, the results suggest that while none of the models perfectly fits all types of frequency inputs, NCF model is more suitable for moderately varying frequencies, whereas the Singer is more suitable for rapidly changing frequencies.     

Nonlinear Estimation of Generalized Vector Shot Processes

A class of nonlinear filters for dynamical systems driven by generalized Poisson processes is developed. One of the filters, the maximum a posteriori (MAP) filter, is shown by a numerical example to be superior to other known predictors in getting the highest target hit probabilities, and it is relatively simple to implement. This filter has applications in both fire control and air traffic control of maneuvering piloted vehicles.     

传感器故障下的航空发动机机载自适应模型重构

利用航空发动机测量参数偏离正常工作情况下的变化量,可以估计发动机的非额定工作状况,并以此对机载模型进行校正,使其与真实发动机工作状况保持一致。建立了包含发动机性能蜕化因素的状态变量模型并对其进行了增广,设计了卡尔曼滤波器,根据可测输出偏离量对发动机性能蜕化值进行了估计,并将性能蜕化值用于修正发动机不可测输出参数。考虑了当某一传感器发生故障后,利用一簇卡尔曼滤波器对发生故障的传感器进行诊断并隔离,并依据剩余非故障传感器的信息对自适应模型进行重构。仿真结果表明,重构的自适应模型能够满足精度及实时性要求。      

A Novel PF-LSSVR-based Framework for Failure Prognosis of Nonlinear Systems with Time-varying Parameters

Particle filtering (PF) is being applied successfully in nonlinear and/or non-Gaussian system failure prognosis. However, for failure prediction of many complex systems whose dynamic state evolution models involve time-varying parameters, the traditional PF-based prognosis framework will probably generate serious deviations in results since it implements prediction through iterative calculation using the state models. To address the problem, this paper develops a novel integrated PF-LSSVR framework based on PF and least squares support vector regression (LSSVR) for nonlinear system failure prognosis. This approach employs LSSVR for long-term observation series prediction and applies PF-based dual estimation to collaboratively estimate the values of system states and parameters of the corresponding future time instances. Meantime, the propagation of prediction uncertainty is emphatically taken into account. Therefore, PF-LSSVR avoids over-dependency on system state models in prediction phase. With a two-sided failure definition, the probability distribution of system remaining useful life (RUL) is accessed and the corresponding methods of calculating performance evaluation metrics are put forward. The PF-LSSVR framework is applied to a three-vessel water tank system failure prognosis and it has much higher prediction accuracy and confidence level than traditional PF-based framework.     

基于双模型滤波算法的环控系统换热器故障诊断

 在建立飞机环控系统数学模型的基础上,提出采用双模型滤波方法进行参数估计、状态预测和故障诊断,提高飞机环控系统故障诊断的快速性和准确性。如果采用最小二乘算法,参数估计是静态的,故障诊断延迟一般较大;采用单模型扩展Kalman滤波算法,虽然能够实现动态估计,但不能同时兼顾稳态过程和过渡过程（突发故障）的参数估计,导致误差较大。为了解决上述难题,针对飞机环控系统换热器故障诊断,提出两模型滤波算法。该算法由两个滤波器组成,分别用于跟踪系统的稳态和过渡过程。由于采用了两滤波器模型分别匹配不同的系统特征,能够改善飞机环控系统不同状态下的参数估计和状态预测性能,从而提高系统故障诊断的精度和速度。仿真结果证实了该算法的有效性。     

Reduced state estimators for consistent tracking of maneuvering targets

Linear Kalman filters, using fewer states than required to completely specify target maneuvers, are commonly used to track maneuvering targets. Such reduced state Kalman filters have also been used as component filters of interacting multiple model (IMM) estimators. These reduced state Kalman filters rely on white plant noise to compensate for not knowing the maneuver - they are not necessarily optimal reduced state estimators nor are they necessarily consistent. To be consistent, the state estimation and innovation covariances must include the actual errors during a maneuver. Blair and Bar-Shalom have shown an example where a linear Kalman filter used as an inconsistent reduced state estimator paradoxically yields worse errors with multisensor tracking than with single sensor tracking. We provide examples showing multiple facets of Kalman filter and IMM inconsistency when tracking maneuvering targets with single and multiple sensors. An optimal reduced state estimator derived in previous work resolves the consistency issues of linear Kalman filters and IMM estimators.     

A dimension reduced INS/VNS integrated navigation method for planetary rovers

Inertial navigation system/visual navigation system (INS/VNS) integrated navigation is a commonly used autonomous navigation method for planetary rovers. Since visual measurements are related to the previous and current state vectors (position and attitude) of planetary rovers, the performance of the Kalman filter (KF) will be challenged by the time-correlation problem. A state augmentation method, which augments the previous state value to the state vector, is commonly used when dealing with this problem. However, the augmenting of state dimensions will result in an increase in computation load. In this paper, a state dimension reduced INS/VNS integrated nav-igation method based on coordinates of feature points is presented that utilizes the information obtained through INS/VNS integrated navigation at a previous moment to overcome the time rel-evance problem and reduce the dimensions of the state vector. Equations of extended Kalman filter (EKF) are used to demonstrate the equivalence of calculated results between the proposed method and traditional state augmented methods. Results of simulation and experimentation indicate that this method has less computational load but similar accuracy when compared with traditional methods.     

Paral lel VLSI Implementation of the Kalrman Filter

The problem of parallel implementation of the square-root Kalman filters is addressed. At the system level, our approach is to apply systolic-type VLSI processor arrays as basic building blocks to accelerate the matrix operations required in each iteration. To maximize the parallelism, we also exploit an inter-array pipelining scheme through the overlapping of execution between successive processor arrays. We estimate that with (5n2 + r2 + 8nr + n + 3r)/2 processors, it would take max[(4n + 2r, 2n + 4r-2)] time units to complete one Kalman filter iteration, where n is the dimension of the underlying state space model and r is the dimension of the input vector.     

A reduced-order model for integrated GPS/INS

The dominant factor in determining the computation time of the Kalman filter is the dimension n of the model state vector. The number of computations per iteration is on the order of n³. Any reduction in the number of states will benefit directly in terms of increased computation time. In this paper, a high order model in integrated GPS/INS is described first, then a reduced-order model based on the high-order model, is developed. Finally, a faster tracking approach for Kalman filters is discussed. A typical aircraft trajectory is designed for a complex high-dynamic aircraft flight experiment. A Monte Carlo analysis shows that the reduced order model presented in this paper provides satisfactory accuracy for aircraft navigation     

状态变量有源RC滤波器最大动态范围的研究

高阶有源RC滤波器存在着多种实现方法，而级联实现法在工程上得到广泛应用，因为级联滤波器的设计和调整相当方便。然而，在级联滤波器中．一个更关键的指标是它的动态范围。获得好的动态范围是指两个层面的问题：(1)确保级联内部信号电平不会对各运放产生过激励；(2)确保带内信号电平不会小到被噪声淹没。为了解决上述问题，在详细讨论了包括双二次型在内的状态变量有源RC滤波器最大动态范围的实现问题的基础上给出了实用的设计公式。     

Hierarchical adaptive Kalman filtering for interplanetary orbitdetermination

A modular and flexible approach to adaptive Kalman filtering has recently been introduced using the framework of a mixture-of-experts regulated by a gating network. Each expert is a Kalman filter modeled with a different realization of the unknown system parameters. The unknown or uncertain parameters can include elements of the state transition matrix, observation mapping matrix, process noise covariance matrix, and measurement noise covariance matrix. The gating network performs on-line adaptation of the weights given to individual filters based on performance. The mixture-of-experts approach is extended here to a hierarchical architecture which involves multiple levels of gating. The proposed architecture provides a multilevel hypothesis testing capability. The utility of the hierarchical architecture is illustrated via the problem of interplanetary navigation (Mars Pathfinder) using simulated radiometric data. It serves as a useful tool for assisting navigation teams in the process of selecting the parameters of the navigational filter over various operating regimes. It is shown that the scheme has the capability of detecting changes in the system parameters and switching filters appropriately for optimal performance. Furthermore, the expectation-maximization (EM) algorithm is shown to be applicable in the proposed framework     

基于改进混合卡尔曼滤波器的航空发动机机载自适应模型

提出了基于改进混合卡尔曼滤波器的航空发动机机载自适应模型方法,即以机载非线性模型的输出作为分段线性卡尔曼滤波器的稳态基准值,将性能蜕化因子作为该滤波器的增广状态量进行在线估计,并反馈给机载非线性模型使其完成在线更新.同时,根据工作模式切换机制使该模型获得有效输出.通过将该方法应用于某型涡扇发动机进行一系列仿真表明,在全飞行包线内、不同工作状态以及性能蜕化严重的情况下,该模型能够始终与实际发动机相匹配,满足实际应用需求.      

Target tracking in maneuver-centered coordinates

Aircraft targets normally maneuver on circular paths, which has led to tracking filters based on circular turns. A coordinate system to track circular maneuvers with a simple Kalman filter is introduced. This system is a polar coordinate system located at the center of the maneuver. It leads to a tracking filter with range, angle, and angular velocity in the state vector. Simulation results are presented, showing that the algorithm displays improved performance over methods based on constant x-y acceleration when tracking circular turns