Characterization of Kalman filter residuals in the presence ofmismodeling

The mean and covariance of a Kalman filter residual are computed for specific cases in which the Kalman filter model differs from a linear model that accurately represents the true system (the truth model). Multiple model adaptive estimation (MMAE) uses a bank of Kalman filters, each with a different internal model, and a hypothesis testing algorithm that uses the residuals from this bank of Kalman filters to estimate the true system model. At most, only one Kalman filter model will exactly match the truth model and will produce a residual whose mean and standard deviation have already been analyzed. All of the other filters use internal models that mismodel the true system. We compute the effects of a mismodeled input matrix, output matrix, and state transition matrix on these residuals. The computed mean and covariance are compared with simulation results of flight control failures that correspond to mismodeled input matrices and output matrices     

An MMAE failure detection system for the F-16

A multiple model adaptive estimation (MMAE) algorithm is implemented with the fully nonlinear six-degree-of-motion, Simulation Rapid-Prototyping facility (SRF) VISTA F-16 software simulation tool. The algorithm is composed of a bank of Kalman filters modeled to match particular hypotheses of the real world. Each presumes a single failure in one of the flight-critical actuators, or sensors, and one presumes no failure. For dual failures, a hierarchical structure is used to keep the number of on-line filters to a minimum. The algorithm is demonstrated to be capable of identifying flight-critical aircraft actuator and sensor failures at a low dynamic pressure (20,000 ft, 0.4 Mach). Research includes single and dual complete failures. Tuning methods for accommodating model mismatch, including addition of discrete dynamics pseudonoise and measurement pseudonoise, are discussed and demonstrated. Scalar residuals within each filter are also examined and characterized for possible use as an additional failure declaration voter. An investigation of algorithm performance off the nominal design conditions is accomplished as a first step towards full flight envelope coverage     

Multiple model adaptive estimation with filter spawning

Multiple model adaptive estimation (MMAE) with filter spawning is used to detect and estimate partial actuator failures on the VISTA F-16. The truth model is a full six-degree-of-freedom simulation provided by Calspan and General Dynamics. The design models are chosen as 13-state linearized models, including first order actuator models. Actuator failures are incorporated into the truth model and design model assuming a "failure to free stream." Filter spawning is used to include additional filters with partial actuator failure hypotheses into the MMAE bank. The spawned filters are based on varying degrees of partial failures (in terms of effectiveness) associated with the complete-actuaton-failure hypothesis with the highest conditional probability of correctness at the current time. Thus, a blended estimate of the failure effectiveness is found using the filters' estimates based upon a no-failure hypothesis, a complete actuator failure hypothesis, and the spawned filters' partial-failure hypotheses. This yields substantial precision in effectiveness estimation, compared with what is possible without spawning additional filters, making partial failure adaptation a viable methodology.     

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     

Performance enhancement of a multiple model adaptive estimator

We describe performance improvement techniques for a multiple model adaptive estimator (MMAE) used to detect and identify control surface and sensor failures on an unmanned flight vehicle. Initially failure identification was accomplished within 4 s of onset, but by removing the “β dominance” effects, bounding the hypothesis conditional probabilities, retuning the Kalman filters, increasing the penalty for measurement residuals, decreasing the probability smoothing, and increasing residual propagation, the identification time was reduced to 2 s     

Enhanced motion and sizing of bank in moving-bank MMAE

The focus of this research is to provide methods for generating precise parameter estimates in the face of potentially significant parameter variations such as system component failures. The standard multiple model adaptive estimation (MMAE) algorithm uses a bank of Kalman filters, each based on a different model of the system. Parameter discretization within the MMAE refers to selection of the parameter values assumed by the elemental Kalman filters, and dynamically redeclaring such discretization yields a moving-bank MMAE. A new online parameter discretization method is developed based on the probabilities associated with the generalized chi-squared random variables formed by residual information from the elemental Kalman filters within the MMAE. This new algorithm is validated through computer simulation of an aircraft navigation system subjected to interference/jamming while attempting a successful precision landing of the aircraft.     

Sensor/actuator failure detection in the Vista F-16 by multiplemodel adaptive estimation

Multiple model adaptive estimation (MMAE) is applied to the Variable-In-flight Stability Test Aircraft (VISTA) F-16 flight control system at a low dynamic pressure flight condition (0.4 M at 20000 ft). Single actuator and sensor failures are addressed first, followed by dual actuator and sensor failures. The system is evaluated for complete or “hard” failures, partial or, “soft” failures, and combinations of hard and soft actuator and sensor failures. Residual monitoring is discussed for single and dual failure scenarios. Performance is enhanced by the application of a modified Bayesian form of MMAE, scalar residual monitoring to reduce ambiguities, automatic dithering where advantageous, and purposeful commands     

Detection of interference/jamming and spoofing in a DGPS-aidedinertial system

Previous research at the Air Force Institute of Technology (AFIT) has resulted in the design of a differential Global Positioning System (DGPS) aided INS-based (inertial navigation system) precision landing system (PLS) capable of meeting the FAA precision requirements for instrument landings. The susceptibility of DGPS transmissions to both intentional and nonintentional interference/jamming and spoofing must be addressed before DGPS may be safely used as a major component of such a critical navigational device. This research applies multiple model adaptive estimation (MMAE) techniques to the problem of detecting and identifying interference/jamming and spoofing in the DGPS signal. Such an MMAE is composed of a bank of parallel filters, each hypothesizing a different failure status, along with an evaluation of the current probability of each hypothesis being correct, to form a probability-weighted average state estimate as an output. For interference/jamming degradation represented as increased measurement noise variance, simulation results show that, because of the good failure detection and isolation (FDI) performance using MMAE, the blended navigation performance is essentially that of a single extended Kalman filter (EKF) artificially informed of the actual interference noise variance. However, a standard MMAE is completely unable to detect spoofing failures (modeled as a bias or ramp offset signal directly added to the measurement). This work describes a moving-bank pseudoresidual MMAE (PRMMAE) to detect and identify such spoofing. Using the PRMMAE algorithm, spoofing is very effectively detected and isolated; the resulting navigation performance is equivalent to that of an EKF operating in an environment without spoofing     

贝叶斯假设理论检测发动机传感器故障

贝叶斯多重假设检验是将被检测传感器的M个可能状态,作相应M个假设H_i,其先验概率分别为P(H_i)(i=1,2,…,M),故障决策就是从给定观测量M,寻求H_j为真,由贝叶斯风险函数H_i(i=1,2,…,M,i≠j)个假设中的最小值确定最可能发生的假设H_l。      

Reconfigurable flight control via multiple model adaptive controlmethods

An aircraft flight control system with reconfigurable capabilities is considered. A multiple model adaptive controller (MMAC) is shown to provide effective reconfigurability when subjected to single and double failures of sensors and/or actuators. A command generator tracker/proportional-plus-integral/Kalman filter (CGT/PI/KF) form of controller was chosen for each of the elemental controllers within the MMAC algorithm and each was designed via LQG synthesis to provide desirable vehicle behavior for a particular failure status of sensors and actuators. The MMAC performance is enhanced by an alternate computation of the MMAC hypothesis probabilities, use of maximum a posteriori probability (MAP) versus Bayesian form of the MAC (or a modified combination of both), and reduction of identification ambiguities through scalar residual monitoring for the case of sensor failures     

基于机载实时模型的发动机执行机构 故障状态参数估计

为了对发动机的主燃烧室供油量控制器、喷管喉部面积控制器、风扇进口可调导叶角度控制器、压气机进口可调导叶角度控制器进行故障诊断,建立了基于简化n+1残量方法的非线性机载实时模型,并结合常增益扩展卡尔曼滤波器建立执行机构控制参数估计器,利用非线性部件级模型模拟飞行包线内发动机执行机构的软故障.仿真结果表明:执行机构控制参数估计器在飞行包线内能实现较高精度估计,且具有较好的稳定性.     

Control of a large space structure using MMAE/MMAC techniques

The application of moving-bank multiple model adaptive estimation and control (MMAE/MMAC) algorithms to an actual spade structure (Space Integrated Controls Experiment (SPICE)) being examined at Phillips Laboratory at Kirtland AFB, NM, is presented. The structure consists of a large platform and a smaller platform connected by three legs in a tripod fashion. Kalman filtering and LQG (linear system, quadratic cost, Gaussian noise) control techniques are utilized as the primary design tools for the components of the MMAE/MMAC. Implementing a bank of filters or controllers increases the robustness of the algorithms when uncertainties exist in the system model, whereas the moving bank is utilized to reduce the computational load. Several reduced-order models are developed from the truth model using modal analysis and modal cost analysis. The MMAE/MMAC design with a substantially reduced-order filter model provides an excellent method to estimate a wide range of parameter variations and to quell oscillations in the structure.     

Reducing lag in virtual displays using multiple model adaptiveestimation

A multiple model adaptive predictor is applied to a virtual environment flight simulator to remove the effect of computational and scene-rendering delay time. Angular orientation of the user's head is predicted a period of time into the future, so that the scene can be rendered appropriately by the time the user actually looks in that direction. Single nonadaptive predictors cannot adequately cover the dynamic range of head motion. By using three dissimilar models of head motion upon which to base the individual elemental filters within the multiple model adaptive estimator (MMAE) algorithm, an MMAE is designed which outperforms the nonadaptive Kalman predictor proposed by Liang (1991)     

Fault Detection and Diagnosis of Aircraft Actuators using Fuzzy-Tuning IMM Filter

This paper proposes a new interacting multiple model (IMM) filter for actuator fault detection. Since each individual filter of the IMM filter uses the combined information of the estimation values from all the operating filters, it can effectively estimate system parameter variations, thereby it can diagnose the actuator damage with an unknown magnitude. In this study, to diagnose the actuator failure fast and accurately, fuzzy logic is used to tune a transition probability among multiple models. This makes the fault detection process smooth and reduces the possibility of false fault detection. Also, a discrete fault tolerant command tracker is derived to cope with actuator damages. To validate the performance of the proposed fault detection and diagnosis (FDD) algorithm, numerical simulations are performed for a high performance aircraft system.     

非线性滤波方法及其在飞行状态及参数估计中的应用

基于非线性系统高阶近似的思想,提出一种比推广卡尔曼滤波（ＥＫＦ）更接近非线性系统本质的近似滤波方法,并应用于飞行状态的参数估计（或称为飞行轨迹重构）问题。仿真和实际飞行数据计算结果表明：提出的非线性近似滤波方法比ＥＫＦ有更高的估计精度和更好的鲁棒性,对飞机机动形状、数据长度要求不高,滤波收敛速度快。利用飞行状态估计数学模型的具体特点,使计算量和存储量大幅度减少。该方法应用于非线性较强的飞行状态及参数估计问题。可得到比ＥＫＦ更好的结果。     

基于Kalman滤波的空天飞行器再入制导算法

针对空天飞行器应用传统数值预测校正再入制导算法实时性不佳的问题,提出一种基于Kalman滤波的预测校正制导算法。该算法采取四阶多项式拟合速度-高度飞行剖面,利用Kalman滤波估计选定的速度点对应的高度,得到满足再入走廊及航程要求的拟合系数。在此基础上,减少一个终端约束,增加一个待估计剖面参数,可实现对再入过程飞行时间的调节。研究发现,再入过程中通过在线辨识修正不确定性参数能够提高制导指令的适应性;飞行末段利用跟踪参考剖面制导可有效避免飞行速度与终端速度接近时发生拟合系数求解发散的问题。多组不同再入条件下的算例仿真结果表明,基于Kalman滤波的空天飞行器再入制导算法实时性好,制导精度高,能够实现飞行时间可控,具有较强的鲁棒性和工程应用潜力。     

A Celestial Analytic Positioning Method by Stellar Horizon Atmospheric Refraction

This article, in allusion to the limitation of conventional stellar horizon atmospheric refraction based on orbital dynamics model and nonlinear Kalman filter in practical applications, proposes a new celestial analytic positioning method by stellar horizon atmospheric refraction for high-altitude flight vehicles, such as spacecraft, airplanes and ballistic missiles. First, by setting up the geometric connexion among the flight vehicle, the Earth and the altitude of starlight refraction, an expression for the relationship of starlight refraction angle and atmospheric density is deduced. Second, there are produced a novel measurement model of starlight refraction in a continuous range of altitudes (CRA) from 20 km to 50 km on the basis of the standard atmospheric data in stratosphere, and an empirical formula of stellar horizon atmospheric refraction in the same altitudes against the tangent altitude. Third, there is introduced a celestial analytic positioning algorithm, which uses the least square differential correction instead of nonlinear Kalman filter. The information about positions of a flight vehicle can be obtained directly by solving a set of nonlinear measurement equations. The stellar positioning algorithm adopts the characteristics of stellar horizon atmospheric refraction thereby removing needs for orbit dynamics models and priori knowledge of flight vehicles. The simulation results evidence the validity of the proposed stellar positioning algorithm.     

Tracking a Maneuvering Target Using Input Estimation

The conventional Kalman tracking filter incurs mean tracking errors in the presence of a pilot-induced target maneuver. Chan,Hu, and Plant proposed a solution to this problem which used themean deviations of the residual innovation sequence to make corrections to the Kalman filter. This algorithm is further developedhere for the case of a one-dimensional Kalman filter, for which an Implementable closed-form recursive relation exists. Simulation results show that the Chan, Hu, and Plant method can accurately detect and correct an acceleration discontinuity under a variety of maneuver models and radar parameters. Also, the inclusion of thislogic into a multiple hypothesis tracking system is briefly outlined.     

MMAE/MMAC control for bending with multiple uncertain parameters

A moving-bank multiple model estimator/controller (MMAE/MMAC) based on linear system, quadratic cost, and Gaussian noise (LQG) assumptions is used to quell unwanted vibrations in a simulated large flexible space structure. The structure, known as the Space Integrated Controls Experiment (SPICE), exists at Phillips Laboratory, Kirtland Air Force Base, New Mexico. The structure consists of a large platform and a smaller platform connected by a tripod of flexible legs. The purpose of the control system is to maintain a very precise line-of-sight (LOS) vector through the center of the spacecraft. Kalman filtering, used to estimate the position and velocity of the bending modes of the structure, and LQG control techniques are the primary design tools used in the MMAE/MMAC algorithms. Implementing a parallel bank of filters increases robustness when uncertainties exist in the system model, here specifically allowing adaptation to uncertain and changing undamped natural frequencies of the bending modes of the structure. A moving-bank algorithm is utilized to reduce the computational loading. The MMAE/MMAC design provides a well-suited method of estimating variations in the vector of undamped natural frequencies and quelling vibrations in the structure. The MMAE/MMAC was able to track numerous parameter changes and jumps while providing adequate control for the structure.     

Sensor/actuator fault diagnosis based on statistical analysis of innovation sequence and Robust Kalman Filtering

In this paper, an approach to detect and isolate the aircraft sensor/actuator faults affecting the mean of the Kalman filter innovation sequence is presented. The effects of the sensor and actuator faults in the innovation process of the channels are investigated, and a decision approach to isolate the sensor and actuator faults is proposed. When a Kalman filter is used, the decision statistics change regardless of whether the fault is in the sensors or in the actuators, whilst when a Robust Kalman Filter (RKF) is used, it is easy to distinguish the sensor and actuator faults. A novel feature of this diagnostic method is that the innovation sequence based fault isolation algorithm has been presented and hence, the sensor/actuator fault detection and isolation problem has been solved. The categories (or classes) of the likely faults are not demanded. The statistical characteristics of the system are not required to be known after the fault has occurred. In the simulations, the longitudinal dynamics of an aircraft control system are considered, and the detection and isolation of pitch rate gyro faults and actuator faults affecting the mean of the innovation sequence are examined.