A Novel Family of Adaptive Filtering Algorithms Based on The Logarithmic Cost

We introduce a novel family of adaptive filtering algorithms based on a relative logarithmic cost. The new family intrinsically combines the higher and lower order measures of the error into a single continuous update based on the error amount. We introduce important members of this family of algorithms such as the least mean logarithmic square (LMLS) and least logarithmic absolute difference (LLAD) algorithms that improve the convergence performance of the conventional algorithms. However, our approach and analysis are generic such that they cover other well-known cost functions as described in the paper. The LMLS algorithm achieves comparable convergence performance with the least mean fourth (LMF) algorithm and extends the stability bound on the step size. The LLAD and least mean square (LMS) algorithms demonstrate similar convergence performance in impulse-free noise environments while the LLAD algorithm is robust against impulsive interferences and outperforms the sign algorithm (SA). We analyze the transient, steady state and tracking performance of the introduced algorithms and demonstrate the match of the theoretical analyzes and simulation results. We show the extended stability bound of the LMLS algorithm and analyze the robustness of the LLAD algorithm against impulsive interferences. Finally, we demonstrate the performance of our algorithms in different scenarios through numerical examples.Comment: Submitted to IEEE Transactions on Signal Processin

Improved convergence performance of adaptive algorithms through logarithmic cost

We present a novel family of adaptive filtering algorithms based on a relative logarithmic cost. The new family intrinsically combines the higher and lower order measures of the error into a single continuous update based on the error amount. We introduce the least mean logarithmic square (LMLS) algorithm that achieves comparable convergence performance with the least mean fourth (LMF) algorithm and overcomes the stability issues of the LMF algorithm. In addition, we introduce the least logarithmic absolute difference (LLAD) algorithm. The LLAD and least mean square (LMS) algorithms demonstrate similar convergence performance in impulse-free noise environments while the LLAD algorithm is robust against impulsive interference and outperforms the sign algorithm (SA). © 2014 IEEE

Robust Adaptive Filtering Algorithm Design for Improving the Performance in Impulsive-noise Environment

DoctorThis thesis proposes the various methods to improve the robustness against impulsive measurement noise of various adaptive filtering algorithms, which are the normalized least-mean-square (NLMS) algorithm, the affine projection (AP) algorithm (APA), the normalized subband adaptive filter (SAF), and the robust recursive least-squares (RLS) algorithm.First, we introduce the concept of the step-size scaler by investigating and modifying the tanh-type cost function for adaptive filtering with impulsive measurement noise. The step-size scaler instantly scales down the step size of gradient-based adaptive algorithms whenever impulsive measurement noise appears, which eliminates a possibility of updating weight vector estimates based on wrong information due to impulsive noise. The most attractive feature of the step-size scaler is that this is easily applicable to various gradient-based adaptive algorithms. To reduce the computational complexity, the simplified version of the step-size scaler, which is obtained by investigating and modifying the ln-type cost function, also is proposed. We perform several representative NLMS-type algorithms without or with the step-size scaler in impulsive-noise environments. The simulation results show that the step-size scaler improves the robustness against impulsive measurement whether the cost functions of the NLMS-type algorithms are adapted in impulsive-noise environments or not.Second, we propose a variable step-size (VSS) APA associated with a step-size scaler, which is suitable for application in the APA, to improve the robustness of APA against impulsive measurement noise. In the proposed VSS APA, the step-size scaler is applied to the equations for updating the step size, which are developed by interpreting the behavior of the mean square deviation (MSD) of the conventional APA. To reduce the computational complexity of the step-size scaler, a simplified version of the step-size scaler is introduced. By simulations in impulsive-noise environments, we confirm the proposed VSS APA leads to an excellent transient and steady-state behavior with in colored inputs.Third, we propose a variable step-size (VSS) normalized SAF (NSAF) using a step-size scaler, which is suitable for application in the NSAF. In the NSAF, since impulsive-type noise contains all frequencies in equal amounts, theoretically, every subbnad output errors can be influenced by impulsive measurement noise. Therefore the step-size scalers use the sum of the normalized subband output errors with respect to the subband input vectors. In the proposed VSS NSAF, the equations for updating the step size are constructed by interpreting the behavior of the MSD of the NSAF and applying the step-size scalers. Simulations using the proposed VSS NSAF show an excellent transient and steady-state behavior with colored input in impulsive-noise environments.Finally, we proposed a robust recursive least-squares (RLS) algorithm using the gain scaler which is developed by the step-size scaler. When impulsive measurement noise occurs, the gain vector of the proposed RLS algorithm is scaled down by the gain scaler. This suppresses the updating weight estimates using undesirable the output error due to impulsive measurement noise. Simulation results show the convergence and steady-state performance the proposed RLS algorithm and the compared robust RLS-type algorithms in impulsive-noise environments

Flight Mechanics/Estimation Theory Symposium, 1990

This conference publication includes 32 papers and abstracts presented at the Flight Mechanics/Estimation Theory Symposium on May 22-25, 1990. Sponsored by the Flight Dynamics Division of Goddard Space Flight Center, this symposium features technical papers on a wide range of issues related to orbit-attitude prediction, determination and control; attitude sensor calibration; attitude determination error analysis; attitude dynamics; and orbit decay and maneuver strategy. Government, industry, and the academic community participated in the preparation and presentation of these papers

Mission Analysis Program for Solar Electric Propulsion (MAPSEP). Volume 1: Analytical manual for earth orbital MAPSEP

An introduction to the MAPSEP organization and a detailed analytical description of all models and algorithms are given. These include trajectory and error covariance propagation methods, orbit determination processes, thrust modeling, and trajectory correction (guidance) schemes. Earth orbital MAPSEP contains the capability of analyzing almost any currently projected low thrust mission from low earth orbit to super synchronous altitudes. Furthermore, MAPSEP is sufficiently flexible to incorporate extended dynamic models, alternate mission strategies, and almost any other system requirement imposed by the user. As in the interplanetary version, earth orbital MAPSEP represents a trade-off between precision modeling and computational speed consistent with defining necessary system requirements. It can be used in feasibility studies as well as in flight operational support. Pertinent operational constraints are available both implicitly and explicitly. However, the reader should be warned that because of program complexity, MAPSEP is only as good as the user and will quickly succumb to faulty user inputs