Effect of embedded unbiasedness on discrete-time optimal FIR filtering estimates

Unbiased estimation is an efficient alternative to optimal estimation when the noise statistics are not fully known and/or the model undergoes temporary uncertainties. In this paper, we investigate the effect of embedded unbiasedness (EU) on optimal finite impulse response (OFIR) filtering estimates of linear discrete time-invariant state-space models. A new OFIR-EU filter is derived by minimizing the mean square error (MSE) subject to the unbiasedness constraint. We show that the OFIR-UE filter is equivalent to the minimum variance unbiased FIR (UFIR) filter. Unlike the OFIR filter, the OFIR-EU filter does not require the initial conditions. In terms of accuracy, the OFIR-EU filter occupies an intermediate place between the UFIR and OFIR filters. Contrary to the UFIR filter which MSE is minimized by the optimal horizon of N opt points, the MSEs in the OFIR-EU and OFIR filters diminish with N and these filters are thus full-horizon. Based upon several examples, we show that the OFIR-UE filter has higher immunity against errors in the noise statistics and better robustness against temporary model uncertainties than the OFIR and Kalman filters

General Unbiased FIR Filter With Applications to GPS-Based Steering of Oscillator Frequency

The general unbiased finite-impulse response (UFIR) filter proposed in this brief has important structural advantages against its basic predecessor. It can be applied to systems with or without the control input. We derive this filter in a batch form and then design its fast iterative Kalman-like algorithm using recursions. The iterative UFIR algorithm proposed is applied to the three-state polynomial model which is basic in clock synchronization. We test it by the global positioning system-based frequency steering of an oven-controlled crystal oscillator. Better robustness and higher accuracy of the UFIR filter against the Kalman filter are shown experimentally

Automatic Curve Fitting Based on Radial Basis Functions and a Hierarchical Genetic Algorithm

Curve fitting is a very challenging problem that arises in a wide variety of scientific and engineering applications. Given a set of data points, possibly noisy, the goal is to build a compact representation of the curve that corresponds to the best estimate of the unknown underlying relationship between two variables. Despite the large number of methods available to tackle this problem, it remains challenging and elusive. In this paper, a new method to tackle such problem using strictly a linear combination of radial basis functions (RBFs) is proposed. To be more specific, we divide the parameter search space into linear and nonlinear parameter subspaces. We use a hierarchical genetic algorithm (HGA) to minimize a model selection criterion, which allows us to automatically and simultaneously determine the nonlinear parameters and then, by the least-squares method through Singular Value Decomposition method, to compute the linear parameters. The method is fully automatic and does not require subjective parameters, for example, smooth factor or centre locations, to perform the solution. In order to validate the efficacy of our approach, we perform an experimental study with several tests on benchmarks smooth functions. A comparative analysis with two successful methods based on RBF networks has been included

36th Annual Precise Time and Time Interval (PTTI) Meeting STUDIES OF THE UNBIASED FIR FILTER FOR THE TIME ERROR MODEL IN APPLICATIONS TO GPS-BASED TIMEKEEPING 1

The unbiased FIR filter is investigated to estimate the time interval error (TIE) K-D polynomial model of a local clock in GPS-based timekeeping in the presence of uniformly distributed sawtooth noise. An estimation algorithm is proposed and applied to the GPS-based TIE measurements of a crystal clock without using the sawtooth correction. Based upon this, we show that the TIE estimates fit actual values with an uncertainty of the GPS time. It is also demonstrated that estimates of the fractional frequency offset fit the measurements with the frequency shifts present in the reference rubidium source and the 1 PPS signal of a GPS receiver used

Nano-Droplet Formation In Polymer Dispersed Liquid Crystals

Motivational interviewing (MI) is an empirically based practice that provides counselors with methods for working with resistant and ambivalent clients. Whereas previous research has demonstrated the effectiveness of training current clinicians in this evidenced-based practice, no research has investigated the efficacy of teaching MI to counselors-in-training who work with clients from the general population. The authors examined the effect of a student-based training in MI for 43 graduate-level counselor trainees using a quasi-experimental controlled design. Statistical analyses based on pretest and posttest assessments revealed participants\u27 knowledge and skill in MI significantly improved in the treatment group. Implications for training future counselors and suggestions for additional research are explored. © 2012 by the American Counseling Association. All rights reserved