R. Kirlin

Robust adaptive Kalman filtering with unknown inputs

The conventional sequential adaptive procedure for estimating noise covariances and input forcing function has suboptimal performance and potential instability. In this work we present a robust procedure for optimally estimating a polynomial-form input forcing function, its time of occurrence and the measurement error covariance matrix, R. This procedure is based on a running window robust regression analysis. In addition a general robust procedure for estimating the process noise covariance matrix, Q, is derived. This procedure is based on the optimal filters residual characteristics and stochastic approximation.

Robust adapative Kalman filtering for systems with unknown step inputs and non-Gaussian measurement errors

Target tracking with Kalman filters is hampered by target maneuvering and unknown process and measurement noises. We show that moving data windows may be used to analyze state and measurement error sequences, determining robust estimates of bias and covariance. For steps in the system forcing functions and non-Gaussian measurement errors, the robust estimators yield improvements over linear bias and covariance estimators. Extensive simulations compare conventional, linear adaptive, and robust adaptive average step responses of a first-order system filter. Quantities examined are state estimate, state error, process and measurement covariance estimates, Kalman gain, and input step estimate.

Delay estimation simulations and a normalized comparison of published results

Three recent publications have reported delay-estimate variances from simulations using the generalized cross-correlator method on both stationary random signals with noise and deterministic signals with noise. Further simulations with finite energy signals are reported here. A method of comparing the three reported data sets is developed, and a remarkable consistency is observed even though the simulation parameters have varied widely.

A robust running-window detector and estimator for step-signals in contaminated Gaussian noise

An N-point window is applied to noisy data to recover stepped signals in non-Gaussian noise. Robust measures of signal step level and noise distribution spread are used to detect sequential clusters of data points which are statistically significantly different, thereby detecting the step. Using conventional analysis-of-variance methods, but with robust parameter estimates, false alarm probabilities are set reasonably accurately, and miss probabilities and signal level estimates are shown by simulation to yield good results. Applications to Kalman filtering, seismic and well-log data, and image processing are indicated.

Optimal delay estimation in a multiple sensor array having spatially correlated noise

The maximal likelihood (ML) estimation of time-of-arrival differences for signals from a single source or target arriving at M \geq 2 sensors has been the subject of a large number of papers in recent years. These time differences or delays enable target location. Nearly all previous work has assumed noises which are independent among all sensors. Herein, noises are taken to have complex correlation between sensors. A set of nonlinear equations in the unknown delays is derived and the Fisher information matrix (FIM) for the estimates is also derived. The Cramer-Rao matrix bound (CRMB), which is the inverse of FIM, shows optimal estimator covariances. Computer evaluations are plotted for CRMB elements with varied SNR and noise covariance values typical of turbulent boundary layer noise in towed arrays and signal sources at infinite range (plane-wave fronts). Maximum changes in the bound are within ±3 dB for complex noise correlations with magnitudes up to 0.4, which we tested.

A posteriori estimation of vocal tract length

Various estimators of vocal tract length, both iterative and noniterative, have been proposed and used for various speech processing and speech pathological purposes. The results of the accuracy of these methods are compared with an a posteriori estimator and others. The a posteriori estimator is shown to provide nearly the same accuracy as the more complex and computation-time costly iterative algorithms.

Two-dimensional coherent noise suppression in seismic data using eigendecomposition

A method for the suppression of coherent noise in seismic data based on the eigendecomposition of a data covariance matrix is demonstrated. Based on the Karhunen-Loeve transform, the proposed procedure is useful against noise energy exhibiting both two-dimensional space and time coherencies or coherent two-dimensional patterns which are not necessarily linear and therefore cannot generally be velocity-filtered. This method trains on a region containing the undesired coherent noise; the dominant eigenvectors determined from the covariance matrix of that noise are used to reconstruct the noise in the region of interest. Subtracting the reconstruction from the original data leaves a residual in which the coherent noise has been suppressed. In the example considered, this method effectively suppresses the noise in a record of marine seismic data containing backscattered source energy. >

Augmenting the maximum likelihood delay estimator to give maximum likelihood direction

The maximum likelihood (ML) estimator was developed by Knapp and Carter [1] for determining time delay between two signals received at two spatially separated sensors in the presence of uncorrelated noise. This brief note shows that that estimator is readily extended to ML estimation of arrival angle even though the medium causes a non-linear phase-versus-frequency difference (in general, a filtering) between the two received signals.

Robust adaptive Kalman filtering for systems with unknown step inputs and non-Gaussian measurement errors

Target tracking with Kalman filters is hampered by target maneuvering and unknown process and measurement noises. We show that moving data windows may be used to analyze state and measurement error sequences, determining robust estimates of bias and covariance. For unknown large steps in the system forcing functions and non-Gaussian measurement errors the robust estimators yield improvements over linear bias and covariance estimators. Extensive simulations compare conventional, linear adaptive and robust adaptive average step responses of a first-order system filter.

Analysis of delay estimation improvement factors due to multiple measurements and A priori information

Signals from distant sources produce intersensor delays in towed arrays which may have their measurement variances improved when all possible sensor-pair measurements and a priori knowledge of range are taken into account. Improvement factors are defined and plotted versus signal-to-noise ratio and versus number of sensors in the arrays. Clustered versus equally spaced sensors is another aspect investigated. Analytical results are obtained for three sensors.