Federated square root filter for decentralized parallel processors

An efficient, federated Kalman filter is developed for use in distributed multisensor systems. The design accommodates sensor-dedicated local filters, some of which use data from a common reference subsystem. The local filters run in parallel, and provide sensor data compression via prefiltering. The master filter runs at a selectable reduced rate, fusing local filter outputs via efficient square root algorithms. Common local process noise correlations are handled by use of a conservative matrix upper bound. The federated filter yields estimates that are globally optimal or conservatively suboptimal, depending upon the master filter processing rate. This design achieves a major improvement in throughput (speed), is well suited to real-time system implementation, and enhances fault detection, isolation, and recovery capability     

Performance Bounds for Continuous-time Filters in the Presence of Modeling Errors

We are concerned with obtaining bounds on the performance of Kalman-type, linear, continuous-time filters susceptible to modeling errors. Limiting the discussion to stationary performance, we obtain bounds on the performance index, the mean square error of estimates for suboptimal and optimal (Kalman) filters. The bounds are expressed in terms of the model matrices and the range of errors of the matrices. The results are useful to a designer in comparing the performance of a suboptimal filter with that of the optimal filter when he has information on the range of modeling errors. The tightness of the bounds is shown by an application of the results in the estimation of the motion of an aircraft carrier at sea.     

组合导航系统中一种基于特征值分解的自适应信息融合滤波算法

基于分散滤波理论的联合滤波算法,可以有效地降低组合导航系统的计算负担,并且增强系统的容错性能。给出了一种联合滤波算法中信息分配系数的自适应计算方法,能够使联合系统根据导航过程中各传感器的信息质量的变化合理地反馈全局信息。仿真结果表明,该算法可以有效地降低由于导航子系统降级带来的滤波误差。     

Applications of Mininum Variance Reduced-State Estimators

This paper presents an algorithm for a class of suitably constrained reduced-order filters which minimize the variance of the estimated variables. The algorithm generates both the filter gain history and the true estimation error covariance. The algorithm provides a quantitative criterion which can be used to measure the performance of any reduced-order estimator. Both continuous and discrete estimators are considered. Several examples are treated including an application of the technique to a hybrid navigation system of high order.     

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     

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 optimal reduced-order stochastic observer-estimator

An optimal reduced-order observer-estimator (filter) is developed which can provide a full-dimensional vector of state estimates for systems where the dimension of the measurement vector is smaller than that of the state vector and none of the measurements are noise free. The reduced-order filter consists of two subfilters each of which provides a subset of the optimal estimate. A two-step L-K transformation is employed to minimize the estimate error variance of each subfilter. The optimal reduced-order filter developed is computationally efficient     

A quantization architecture for track fusion

Many practical multi-sensor tracking systems are based on some form of track fusion, in which local track estimates and their associated covariances are shared among sensors. Communication load is a significant concern, and the goal of this paper is to propose an architecture for low-bandwidth track fusion. The scheme involves intelligent scalar and vector quantization of the local state estimates and of the associated estimation error covariance matrices. Simulation studies indicate that the communication saving can be quite significant, with only minor degradation of track accuracy.     

Kalman filtering for matrix estimation

A general discrete-time Kalman filter (KF) for state matrix estimation using matrix measurements is presented. The new algorithm evaluates the state matrix estimate and the estimation error covariance matrix in terms of the original system matrices. The proposed algorithm naturally fits systems which are most conveniently described by matrix process and measurement equations. Its formulation uses a compact notation for aiding both intuition and mathematical manipulation. It is a straightforward extension of the classical KF, and includes as special cases other matrix filters that were developed in the past. Beyond the analytical value of the matrix filter, it is shown through various examples arising in engineering problems that this filter can be computationally more efficient than its vectorized version.     

自适应高阶容积卡尔曼滤波在目标跟踪中的应用

针对传统容积卡尔曼滤波(CKF)在系统状态发生突变时估计精度下降的问题,将强跟踪滤波(STF)算法与高阶容积卡尔曼滤波(HCKF)算法相结合,提出了一种自适应高阶容积卡尔曼滤波(AHCKF)方法。该算法采用高阶球面-相径容积规则,可获得高于传统CKF的估计精度,同时在HCKF算法中引入STF,通过渐消因子在线修正预测误差协方差阵,强迫残差序列正交,提高了算法的鲁棒性,增强了算法应对系统状态突变等不确定因素的能力。将提出的AHCKF算法应用于具有状态突变的机动目标跟踪问题并进行数值仿真,仿真结果表明,AHCKF算法在系统状态发生突变的情况下表现出良好的滤波性能,有效地避免了状态突变造成的滤波精度下降,较传统的CKF、HCKF、交互式多模型-容积滤波(IMM-CKF)和自适应容积卡尔曼滤波(ACKF)算法有更强的鲁棒性和系统自适应能力。     

On the Accuracy And Resolution of Radar Signals

Information matrices are derived for estimates of the range parameters of moving targets as obtained by combining a priori information (if available) with reflected radar signals observed in the presence of additive white Gaussian noise. The inverse of the information matrix provides a lower bound on the covariance matrix of any unbiased parameter estimates. This bound can be approached with a high signal-to-noise ratio and optimum data processing (matched filters). Arbitrary frequency modulation, amplitude modulation, and target motion as well as various assumptions on processing the RF phase are considered. The multiple-target case makes possible investigation of a signal's resolution ability, as well as its accuracy potentials. Results for a carrier frequency much greater than the effective signal bandwidth are obtained as a special case. A main purpose of the paper is the reduction of the original radar problem to a linear model which is equivalent in the sense of having the same information matrix. These models provide valuable insight into the relative effects of multiple targets, choice of modulation, a priori information, and assumptions regarding RF phase and bandwidth. The linear equivalent model also leads to a valuable computational algorithm for investigations using digital or hybrid computers. The various special cases of interest are obtained by simple modifications of the general case, and thus the algorithm can provide a very versatile tool for evaluating and designing radar signals.     

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.     

Exact multisensor dynamic bias estimation with local tracks

An exact solution is provided for the multiple sensor bias estimation problem based on local tracks. It is shown that the sensor bias estimates can be obtained dynamically using the outputs of the local (biased) state estimators. This is accomplished by manipulating the local state estimates such that they yield pseudomeasurements of the sensor biases with additive noises that are zero-mean, white, and with easily calculated covariances. These results allow evaluation of the Cramer-Rao lower bound (CRLB) on the covariance of the sensor bias estimates, i.e., a quantification of the available information about the sensor biases in any scenario. Monte Carlo simulations show that this method has significant improvement in performance with reduced rms errors of 70% compared with commonly used decoupled Kalman filter. Furthermore, the new method is shown to be statistically efficient, i.e., it meets the CRLB. The extension of the new technique for dynamically varying sensor biases is also presented.     

Noise subspace techniques in non-gaussian noise using cumulants

We consider noise subspace methods for narrowband direction-of-arrival or harmonic retrieval in colored linear non-gaussian noise of unknown covariance and unknown distribution. The non-gaussian noise covariance is estimated via higher order cumulants and combined with correlation information to solve a generalized eigenvalue problem. The estimated eigenvectors are used in a variety of noise subspace methods such as multiple signal classification (MUSIC), MVDR and eigenvector. The noise covariance estimates are obtained in the presence of the harmonic signals, obviating the need for noise-only training records. The covariance estimates may be obtained nonparametrically via cumulant projections, or parametrically using autoregressive moving average (ARMA) models. An information theoretic criterion using higher order cumulants is presented which may be used to simultaneously estimate the ARMA model order and parameters. Third- and fourth-order cumulants are employed for asymmetric and symmetric probability density function (pdf) cases, respectively. Simulation results show considerable improvement over conventional methods with no prewhitening. The effects of prewhitening are particularly evident in the dominant eigenvalues, as revealed by singular value decomposition (SVD) analysis     

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。      

Navigation system design using time-varying complementary filters

A new methodology for the design of navigation systems for autonomous vehicles is introduced. Using simple kinematic relationships, the problem of estimating the velocity and position of an autonomous vehicle is solved by resorting to special bilinear time-varying filters. These are the natural generalization of linear time-invariant complementary filters that are commonly used to properly merge sensor information available at low frequency with that available in the complementary region. Complementary filters lend themselves to frequency domain interpretations that provide valuable insight into the filtering design process. This work extends these properties to the time-varying setting by resorting to the theory of linear differential inclusions and by converting the problem of weighted filter performance analysis into that of determining the feasibility of a related set of linear matrix inequalities (LMIs). Using this set-up, the stability of the resulting filters as well as their "frequency-like" performance can be assessed using efficient numerical analysis tools that borrow from convex optimization techniques. The mathematical background that is required for complementary time-varying filter analysis and design is introduced. Its application to the design of a navigation system that estimates position and velocity of an autonomous vehicle by complementing position information available from GPS with the velocity information provided by a Doppler sonar system is described.     

A Novel Speckle Filter for SAR Images Based on Informationtheoretic Heterogeneity Measurements

Most adaptive speckle filters are based on the local coefficient of variation, which serves to measure the heterogeneity of synthetic aperture radar (SAR) images. However, the sensitivity of the measurements to speckle and noise of SAR images would greatly deteriorate the speckle reduction. This article, based upon the information theory, presents a novel parameter for the heterogeneity measurement as a general index to quantitate the SAR image heterogeneity. Further, as a new speckle reduction algorithm based on the aforesaid quantitative heterogeneity measurements, it puts forward a heterogeneity-based speckle reduction filter (HBSRF), which uses the information-theoretic heterogeneity measurements as a criterion to classify the SAR images as belonging to homogeneous or heterogeneous regions. Then the finite iteration procedure and edge detection algorithms are adopted to strike the best balance between speckle reduction and edge preservation. The results from the computer simulation have demonstrated that the proposed effective method is superior to the conventional speckle filters based on the local coefficient of variation both in textural preservation and speckle reduction.     

Novel quaternion Kalman filter

This paper presents a novel Kalman filter (KF) for estimating the attitude-quaternion as well as gyro random drifts from vector measurements. Employing a special manipulation on the measurement equation results in a linear pseudo-measurement equation whose error is state-dependent. Because the quaternion kinematics equation is linear, the combination of the two yields a linear KF that eliminates the usual linearization procedure and is less sensitive to initial estimation errors. General accurate expressions for the covariance matrices of the system state-dependent noises are developed. In addition, an analysis shows how to compute these covariance matrices efficiently. An adaptive version of the filter is also developed to handle modeling errors of the dynamic system noise statistics. Monte-Carlo simulations are carried out that demonstrate the efficiency of both versions of the filter. In the particular case of high initial estimation errors, a typical extended Kalman filter (EKF) fails to converge whereas the proposed filter succeeds.     

Discrete-time state estimation of analog double integrators

The problem of minimum variance discrete-time state estimation of a continuous-time double integrator via noisy continuous-time measurements is considered. The error covariance matrices of this estimation are calculated and analyzed. The relations between these covariance matrices and the error covariance matrix of the optimal continuous-time filter are obtained, and a way for determining the required sampling period is proposed. A commonly used approximated model is investigated; it is shown to be inappropriate unless a specific improvement is introduced in the model     

On a decoupled multitarget tracking algorithm

An analysis is conducted of the optimality of a decoupled tracking filtering algorithm for addressing the problem of tracking multiple targets with correlated measurements and maneuvers. It is proved that the decoupled filters are, in general, suboptimal and are not in fact Kalman filters. However, it is shown also that if the standard Kalman filter is asymptotically stable, the decoupled filters will converge asymptotically to the stable version of the standard Kalman filter. For the case of time-invariant measurement and process noise covariance, a simple sufficient condition guaranteeing the asymptotical stability of the decoupled filters are given