Clutter suppression using recursive and nonrecursive MTI filters

The author calculates the effectiveness of clutter suppression of a moving-target-indicator (MTI) filter in tandem with a fast-Fourier-transform (FFT) Doppler filter bank, taking into account the transient response of the MTI filter. Both recursive and nonrecursive filters are considered. The analysis is extended to the high-pulse-repetition-frequency (PRF) case with clutter fold over. The results can be used to select key design parameters, including the MTI filter, the window size, and the initial transient segment to be discarded. Numerical examples are included     

Analytical steady-state solution for a three-state Kalman filter

A closed-form steady-state solution is presented for the discrete Kalman-Buch filter when only position is measured. The procedure is based on a comparison between the Wiener and Kalman approaches. The solution obtained is more straightforward than the one given by S.N. Gupta (see ibid., vol.AES-20, p.839-49, Nov. 1984), which is difficult to handle when the eigenvalues are complex. The results agree perfectly with those obtained by simulation of Kalman's recursive equations extended until the steady-state is reached. The results supply apriori tracking performances and are therefore useful for preliminary design. This approach is also applied to the Singer and Fitzgerald model, because of the latter's physical importance     

Effect of timing jitter on performance of MTI filters

The effect of transmitting timing jitter and sampling jitter on a multipulse clutter cancellation system is analyzed, and explicit expressions are obtained for the net increase in the residue clutter power due to timing jitter. The increase in mean-square error is found to be proportional to the jitter variance, with the two jitters contributing almost equally. The system analyzed can have either a recursive or nonrecursive MTI filter, and the latter includes the familiar two- and three-pulse canceller as special cases. The increase in residue clutter power for a three-pulse canceller is about 4.8 dB worse than that for a two-pulse canceller     

Analytical solution for continuous-time Kalman tracking filterswith colored measurement noise in frequency domain

New expressions are given for analytical solutions to the steady-state Kalman gains of the two-state exponentially correlated velocity (ECV) and the three-state exponentially correlated acceleration (ECA) tracking filters with position measurements by using spectral factorization method. The measurement colored noise model is characterized by a correlation time 1/λ. The vehicle oscillations such as wind-induced-bending is also considered in the modeling of the system which leads to the most generalized state transition matrix     

Continuous-time ECV and ECA track filters with colored measurementnoise

Analytical solutions are presented for two continuous-time track filters with correlation in both the measurement errors and the target maneuvers. The measurement error model is a first-order Markov process, characterized by a correlation time (γ) and a position error variance (r). The target motion is described by one of two dynamic models: the exponentially correlated velocity (ECV) model, and the exponentially correlated acceleration (ECA) model. For both models, the steady-state velocity variance exhibits resonant behavior. The analytical solutions include as special cases several previously published results     

CTD MTI Radar Filter with Charge-Transfer Inefficiency Compensation

The design and implementation of a second-order nonrecursive moving target indication (MTI) radar filter using commercially available charge-transfer devices as delay lines are described. A simple technique is included to compensate for the device charge-transfer in-efficiency and its sensitivity is analyzed. Experimental laboratory tests and results in an operating radar system are reported showing the good performance of the realized MTI radar filter.     

A Discrete Method for Parameter Identification in Linear Systems with Transport Lags

Linear dynamical systems with transport lags are characterized by linear differential-difference equations. The task of identifying unknown parameters in such systems from the input-output data is difficult due to mathematical complications associated with differentialdifference equations. This paper presents a method which solves the identification problem. The method is digitally oriented and shows how a continuous-time system can be identified by discrete techniques. The solution is based on Kalman's least square method. The identification procedure essentially involves two steps: 1) discretizing the continuous system via finite difference approximation, and 2) estimating the parameters through the identification of the resulting discrete model. Experimental results have verified the validity of the proposed method.     

Detection performance in K-distributed and correlatedRayleigh clutters

Performance prediction for a detection system employing noncoherent integration is carried out for a chi-square family of fluctuating targets in K-distributed clutter plus noise. The detection performance for Swerling 11 targets in the K-distributed clutter plus noise is compared with that in exponentially correlated Rayleigh clutter. The results show that the performance prediction based on N pulses integrated in clutter plus noise using the K-distributed clutter model may be approximately equivalent to that using the exponentially correlated Rayleigh-distributed clutter model     

New Clutter Rejection Waveforms for Long-Range Radar

A frequent compromise in the design of long-range search radars has to be made between the maximum unambiguous detection range and the achievable coherent clutter rejection performance. A new class of waveforms is introduced which offers the designer a previously unavailable flexibility in arriving at radar designs with improved clutter rejection without seriously affecting the maximum unambiguous search range. The key to these new waveforms is the recognition that a class of useful N-pulse, nonrecursive, moving target indicator (MTI) canceler designs exists which only requires the radar to transmit a total of N -1 (nonuniformly spaced) pulses.     

Simple Tracking Filters: Steady-State Filtering and Smoothing Performance

Computed data is presented, in normalized form, showing steady-state filtering and smoothing performance for optimum three-state estimators which assume exponentially correlated acceleration of the tracked object. The data are useful for preliminary design, gain selection, and performance prediction.     

Simple Tracking Filters: Closed-Form Solutions

A closed-form steady-state solution is presented for a three-state tracking filter with continuous position measurements and exponentially correlated target acceleration. Some other related closed-form solutions are discussed, and some comparative performance data is presented for the discrete measurement case.     

Fusion of distributed extended forgetting factor RLS state estimators

For single-target multisensor systems, two fusion methods are presented for distributed recursive state estimation of dynamic systems without knowledge of noise covariances. The estimator at every local sensor embeds the dynamics and the forgetting factor into the recursive least squares (RLS) method to remedy the lack of knowledge of noise statistics, developed before as the extended forgetting factor recursive least squares (EFRLS) estimator. It is proved that the two fusion methods are equivalent to the centralized EFRLS that uses all measurements from local sensors directly and their good performance is shown by simulation examples.     

ARMAX模型参数估计的新两步法

 本文提出了一种ARMAX模型参数估计的新两步法。这种方法与其它递推估计方法（如增广矩阵法,极大似然法,Durbin两步法、三步法等）比较,具有较好的收敛特性,对参数的估计,特别是对C参数的估计比较精确,这是利用其它方法,一直未能很好解决的一个难题。     

Analytical solution of discrete colored noise ECA tracking filter

New analytical solutions of steady-state Kalman gains are presented for a discrete-time tracking filter with correlation in both the measurement noise and the target maneuver. The measurement noise model is a first-order discrete Markov process characterized by a correlation coefficient ρ. The target motion is examined for an exponentially correlated acceleration maneuver type in which the vehicle oscillation such as wind-induced-bending is also considered. The present solution method is based on factorizing the observed spectral density matrix Ψ(z) in frequency domain. The algorithm proposed here gives the Kalman gain matrix directly. For a case when the steady-state error covariance matrix is desired, such gains can be incorporated with the algebraic Riccati equation     

A recursive moving-target-indication algorithm for optical imagesequences

A recursive track-before-detect algorithm, producing potentially large signal-to-noise ratio (SNR) gains under realizable conditions, is described. The basic relation has the form of a linear, constant-coefficient difference equation with a unity magnitude damping factor. Known as recursive moving-target-indication (RMTI), this procedure adapts easily to digital processing and achieves SNR gains comparable to those from other robust track-before-detect algorithms. Examples are given to demonstrate the performance of the moving target indicator (MTI) procedure     

石英加速度计误差模型系数的递推最小二乘辨识方法研究

为探索在线辨识的测试方法,满足实时辨识的需要,本文提出采用递推最小二乘法辨识石英加速度计模型系数,并对其在重力场测试中的应用进行了研究.介绍了递推最小二乘系数估计法原理,为便于实际应用,根据测试领域的习惯,对递推最小二乘方法进行了梳理.以加速度计分度头试验为例,将该方法应用于加速度计重力场试验的误差模型系数辨识.仿真分...     

Feedback Realization of a Continuous-Time Optimal Filter

Another derivation of a continuous-time optimal linear filter is presented. Using this result as a point of departure, a feedback version of this continuous filter is postulated and shown to be optimal in the limit as the ``feedback gain' becomes infinite. It is then demonstrated that the need for this infinite feedback gain can frequently be eliminated. This feedback realization of the continuous optimal filter has application to the problem of optimally mixing two or more redundant signals, each contaminated by random noise. The feedback configuration has the advantages of simplicity and the bounding of otherwise troublesome very large errors. A simple example is given of the mixing of two (velocity) references each having exponentially correlated error.     

Comments on `Tracking a maneuvering target using input estimation''

P.L. Boglar (see ibid., vol.AES-23, no.3, p.298-310, May 1987) developed a recursive formulation of the Chan, Hu, and Plant (CHP) algorithm, and the results of the simulation verified the performance improvements. The commenter claims that Bogler obtained an incorrect recursive formulation of input estimation because he incorrectly used the formulation of the Kalman filter. The commenter presents calculations that aim to demonstrate this claim     

Efficient recursive state estimator for dynamic systems withoutknowledge of noise covariances

An efficient recursive state estimator for dynamic systems without knowledge of noise covariances is suggested. The basic idea for this estimator is to incorporate the dynamic matrix and the forgetting factor into the least squares (LS) method to remedy the lack of knowledge of noises. We call it the extended forgetting factor recursive least squares (EFRLS) estimator. This estimator is shown to have similar asymptotic properties to a completely specified Kalman filter state estimator. More importantly, the performance of EFRLS greatly exceeds that of existing filtering techniques when the noise variance is misspecified. In addition, EFRLS also performs well when there is cross-correlation between the process and measurement noise streams or temporal dependencies within those streams. Some discussions and a number of simulations are made to provide practical guidance on the choice of an optimal forgetting factor and evaluate the performance of the EFRLS algorithms, which strongly dominates that of the standard forgetting factor recursive least squares (FRLS) and some misspecified Kalman filtering     

Comparison of motion and stereo methods in passive ranging systems

The authors compare the estimates in passive ranging systems using motion and stereo approaches. It is shown that an integrated approach is necessary to provide better range estimates over a field-of-view (FOV) of interest in helicopter flight. The recursive approach for processing a sequence of stereo images, described together with a recursive motion algorithm (RMA), provides the basis for an integrated method to provide more accurate range information. Results based on motion sequences of stereo images are presented