The effect of the clutter-to-noise ratio on Doppler filterperformance

The effect of the clutter-to-noise ratio on the performance of a Doppler filter is considered. Clutter is assumed to have a power level which is unknown and varies in range. The assessment of the performance of a Doppler filter is based on the gain of the filter, which is the normalized output signal-to-interference ratio improvement at a given Doppler. The gain is generally a complex function of the statistics of the clutter. New upper and lower bounds on the gain differential between the expected design point clutter-to-noise ratio and the actual clutter-to-noise ratio are found. These bounds are independent of the clutter covariance matrix and are only a function of the unknown clutter-to-noise ratio. The bounds are valid for both Gaussian and non-Gaussian noise and for arbitrary linear filters. The upper and lower bounds differ by the theoretical coherent integration gain, 10 logN dB, where N is the number of pulses. A tighter lower bound is found for the case when the filters are matched filters. A simple exact expression is found for matched filters assuming a Gaussian Markov clutter model as the clutter spectral width approaches zero. An easily implementable adaptive procedure is given which improves performance due to the unknown clutter-to-noise ratio. This work extends a previous result, valid for the Emerson filter, that shows the effect of clutter-to-noise ratio on performance in terms of an average quantity, the improvement factor     

A minimax approach to the design of Doppler filters

The detection of a target in correlated clutter, thermal noise, and extraneous interference is considered. The amplitude, phase and Doppler frequency of the signal are not known a priori. A general criterion is presented which measures the performance of a suboptimal test relative to an optimal test. The criterion is encompassed into a design procedure used to design Doppler filters. The procedure allows many design considerations to be taken into account, and results in a design which attempts to minimize the number of filters required. For low dimensionality the procedure results in single filter designs; for higher dimensionality multiple filters are designed. The performances of these systems are compared with the results obtained by Emerson (1978) and Andrews (1974). It is found that the procedure yields good filter designs under general conditions and may reduce the number of filters required compared with classical designs     

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。      

Kalman Filter Compensation for a Special Class of Systems

Filter compensation techniques for several special but practical cases are discussed. A general set of bias and covariance equations for linear filters with modeling errors is first summarized. A method for relating the modeling errors to the selection of the covariance of "process noise" for model error compensation is suggested. A performance ordering for cases when the true system becomes a subsystem of the model used for the filter construction is given. A bias correcting filter is derived for the case when the filter is matched only to a subsystem of the actual system.     

Suboptimal filter design with pseudomeasurements for targettracking

A suboptimal Kalman filter design method is presented for the problem of tracking a maneuvering target. The design method is essentially based on linear target dynamics and linear-like structured measurements called pseudomeasurements. The pseudomeasurements are obtained by manipulating the original nonlinear measurements algebraically. The resulting filter has computational advantages over other filters with similar performance. Also, a variant of the Berg model is proposed as a target acceleration model under the assumption of a coordinated turn maneuver. The proposed model is consistent with the underlying assumption. Monte Carlo computer simulation results are included to demonstrate the effectiveness of the proposed suboptimal filter associated with the target acceleration model     

A Tracking Filter in Spherical Coordinates Enhanced by De-noising of Converted Doppler Measurements

Tracking problem in spherical coordinates with range rate (Doppler) measurements, which would have errors correlated to the range measurement errors, is investigated in this paper. The converted Doppler measurements, constructed by the product of the Doppler measurements and range measurements, are used to replace the original Doppler measurements. A de-noising method based on an unbiased Kalman filter (KF) is proposed to reduce the converted Doppler measurement errors before updating the target states for the constant velocity (CV) model. The states from the de-noising filter are then combined with the Cartesian states from the converted measurement Kalman filter (CMKF) to produce final state estimates. The nonlinearity of the de-noising filter states are handled by expanding them around the Cartesian states from the CMKF in a Taylor series up to the second order term. In the mean time, the correlation between the two filters caused by the common range measurements is handled by a minimum mean squared error (MMSE) estimation-based method. These result in a new tracking filter, CMDN-EKF2. Monte Carlo simulations demonstrate that the proposed tracking filter can provide efficient and robust performance with a modest computational cost.     

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.     

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.     

Square root parallel Kalman filtering using reduced-order localfilters

The basic parallel Kalman filtering algorithms derived by H.R. Hashemipour et al. (IEEE Trans. Autom. Control. vol.33, p.88-94, 1988) are summarized and generalized to the case of reduced-order local filters. Measurement-update and time-update equations are provided for four implementations: the conventional covariance filter, the conventional information filter, the square-foot covariance filter, and the square-foot information filter. A special feature of the suggested architecture is the ability to accommodate parallel local filters that have a smaller state dimension than the global filter. The estimates and covariance or information matrices (or their square roots) from these reduced-order filters are collated at a central filter at each step to generate the full-size, globally optimal estimates and their associated error covariance or information matrices (or their square roots). Aspects of computational complexity and the ensuing tradeoff with communication are discussed     

The effects of IF bandpass mismatch errors on adaptive cancellation

The effects of IF bandpass mismatch errors on adaptive cancellers are investigated. Frequency mismatch errors occur because of errors in the synthesis process of the bandpass filters which are designed to be identical and are in each input channel. Tapped-delay line transversal filters can be used to compensate for these frequency mismatches and thus improve cancellation performance. A pole/zero error model of the filters is developed whereby closed-form solutions of the maximum achievable average cancellation are obtained. This cancellation is a function of the order of the ideally matched frequency filters, the number of time-delay taps in the compensating transversal filter, the bandwidth-tapped time-delay product, and the constraints on these parameters. A design procedure is outlined for optimizing the canceller with respect to these parameters and their constraints; specifically, results are presented for Butterworth-type input filters. It is shown that an arbitrarily low output noise residue cannot be achieved by arbitrarily increasing the number of time-delay taps     

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     

Implementation and performance analysis of accurate localization of short-range targets based on multisensor systems

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Structures for radar detection in compound Gaussian clutter

The problem of coherent radar target detection in a background of non-Gaussian clutter modeled by a compound Gaussian distribution is studied here. We show how the likelihood ratio may be recast into an estimator-correlator form that shows that an essential feature of the optimal detector is to compute an optimum estimate of the reciprocal of the unknown random local power level. We then proceed to show that the optimal detector may be recast into yet another form, namely a matched filter compared with a data-dependent threshold. With these reformulations of the optimal detector, the problem of obtaining suboptimal detectors may be systematically studied by either approximating the likelihood ratio directly, utilizing a suboptimal estimate in the estimator-correlator structure or utilizing a suboptimal function to model the data-dependent threshold in the matched filter interpretation. Each of these approaches is studied to obtain suboptimal detectors. The results indicate that for processing small numbers of pulses, a suboptimal detector that utilizes information about the nature of the non-Gaussian clutter can be implemented to obtain quasi-optimal performance. As the number of pulses to be processed increases, a suboptimal detector that does not require information about the specific nature of the non-Gaussian clutter may be implemented to obtain quasi-optimal performance     

Nonlinear Filter Evaluation for Estimating Vehicle Position and Velocity Using Satellites

Approximate nonlinear filtering theory is applied to the estimation of vehicle position and velocity in three demensions using sequential range measurements to three known locations. The particular case studied is a satellite air traffic control system which utilizes range measurements to two geostationary satellites and an altitude measurement. Three approximate filters are examined as suboptimal realizations of the minimum-variance filter and simulation results are presented to show that simple first-order approximation is an adequate representation. The parametric relationship between state covariance, measurement noise, vehicle maneuver structure, data rate, and system geometry is presented.     

一种针对结构损伤的非线性容错飞行控制方法

飞机结构损伤会引起气动参数变化,进而影响系统的静稳定性和控制精度。针对具有多输入的非线性飞机模型,利用带有二阶命令滤波器的自适应反步控制方法在线估计飞机气动参数,补偿结构损伤导致的气动参数变化对控制系统的影响,以实现容错飞行控制功能;引入的命令滤波器可以避免反步控制中复杂的求导运算。从理论上分析证明了带有二阶命令滤波器的自适应反步控制的闭环系统稳定性,并给出了控制跟踪误差的理论上界和二阶命令滤波器频率参数选取的下界。通过一个大型客机垂直尾翼脱落场景的仿真实验,验证了所提容错控制方法的有效性。     

Effects of output filter on cross regulation in SRC

Cross regulation performance of multioutput series resonant converter (SRC) topologies using capacitive or inductive filters is analyzed. The steady state cross regulation characteristics are derived using the state-plane techniques and are illustrated by the examples of two-output SRCs with capacitive and inductive filters. The characteristic curves show that over some range of output currents, the cross regulation performance of an SRC with an inductive filter is much improved over the SRC with capacitance filter and less dependent on the tolerances in leakage inductances and the loading on unregulated outputs. It is shown that the converter control characteristics of an SRC with an inductive filter are relatively unaffected by the addition of the second output. The theoretical results are verified by simulation     

Improved Range Resolution Filters for Rectangular-Pulse Radar Systems

The performance of several new clutter-reduction filters suitable for rectangular-pulse radar systems is investigated. The new filters consist of various approximations and modifications of two filters known to be optimal for certain criteria: the well-known Urkowitz filter which optiizes the clutter improvement ratio, and the newer sidelobe reduction filter which minimizes output noise power subject to peak sidelobe constaints. The new filters are compared usig five basic criteria: clutter improvement ratio, signal-to-noise ratio, sidelobe peak ratio, pulse compression ratio, and filter complexity. The results are summarized in tabular and graphical form.     

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     

The effect of I,Q mismatch errors on adaptive cancellation

The effects of in-phase (I) and quadrature-phase (Q) amplitude errors and low-pass-filter (LPF) errors on adaptive cancellers are investigated. I,Q errors occur because of errors in the synthesis process of the mixers and LPFs designed to be identical for each input channel. These I,Q errors among the channels result in cancellation degradation. Tapped delay line transversal filters have been proposed as a way to compensate for these errors and thus improve cancellation performance. However, it is shown that if there is any LPF mismatch, then transversal filtering has a small effect on improving canceler performance. The use of individual I,Q adaptive transversal filter weighting is suggested as a means of completely eliminating the phase amplitude errors, and making the canceler performance responsive to transversal filter compensation     

Analysis of upgraded GPS internal Kalman filter

GPS receivers with provisions for inertial navigation system (INS) aiding are designed with internal Kalman filters that model generic INSs and process the basic GPS pseudorange and deltarange (range-rate) data to produce an output of inertially-smoothed, “GPS-derived” position and velocity. These Kalman filters model only the basic nine INS errors (position, velocity, and tilt) and do not model any INS gyro or accelerometer errors. It was found that a significant performance improvement could be achieved under conditions of degraded GPS satellite availability by augmenting this type of filter with the six INS gyro and accelerometer bias errors. It is, therefore, recommended that serious consideration be given to incorporating these states into the design of the GPS internal Kalman filter