Afsar Saranli

Complexity reduction in radial basis function (RBF) networks by using radial B-spline functions

Abstract In this paper, new basis consisting of radial cubic and quadratic B-spline functions are introduced together with the CORDIC algorithm, within the context of RBF networks as a means of reducing computational complexity in real-time signal-processing applications. The new basis are compared with two other existing and popularly used basis families, namely the Gaussian functions and the inverse multiquadratic functions (IVMQ) in terms of approximation performance and computational requirements. The new basis are shown to achieve approximation performance very similar to the Gaussian basis functions and are better than the IVMQ functions with less computational load and without any need for approximation methods such as table-lookup.

A statistical unified framework for rank-based multiple classifier decision combination

Abstract This study presents a theoretical investigation of the rank-based multiple classifier decision combination problem, with the aim of providing a unified framework to understand a variety of such systems. The combination of the decisions of more than one classifiers with the aim of improving overall system performance is a concept of general interest in pattern recognition, as a viable alternative to designing a single sophisticated classifier. The problem of combining the classifier decisions in the raw form of candidate class rankings is formulated as a discrete optimization problem. The objective function to be maximized is selected as the overall probability of correct decision. This formulation introduces a set of observation statistics about the joint behavior of the classifiers which are to be estimated by observing the classifiers operated on a cross-validation test set. The resulting binary programming problem is shown to have a simple and global optimum solution but which also necessitates a prohibitive number of observation statistics. From the objective function expansion, the problem observation space is defined and a method based on partitioning is introduced to reduce its prohibitive dimensionality. Within this partitioning formalism called as the Partitioned Observation Space (POS) theory, the number of behavior observation statistics can be reduced to levels which are feasible to estimate from the available cross-validation test data. It is shown by examples that such specific partitionings can be defined when reasonable assumptions or prior knowledge about the classifiers are incorporated into the problem domain. It is also demonstrated that certain specific partitionings of the classifier observation space effectively lead to the highest rank, Borda count and logistic regression rank-based decision combination methods from the literature. The analysis presented is general and promises to lead to a class of algorithms for rank-based decision combination. The potential of the theory and practical issues in implementation are illustrated by applying it in a real-life phonetic discrimination problem from speech pattern classification with encouraging results.

Tracker-aware adaptive detection: An efficient closed-form solution for the Neyman--Pearson case

A promising line of research for radar systems attempts to optimize the detector thresholds so as to maximize the overall performance of a radar detector-tracker pair. In the present work, we attempt to move in a direction to fulfill this promise by considering a particular dynamic optimization scheme which relies on a non-simulation performance prediction (NSPP) methodology for the probabilistic data association filter (PDAF), namely, the modified Riccati equation (MRE). By using a suitable functional approximation, we propose a closed-form solution for the special case of a Neyman-Pearson (NP) detector. The proposed solution replaces previously proposed iterative solution formulations and results in dramatic improvement in computational complexity without sacrificed system performance. Moreover, it provides a theoretical lower bound on the detection signal-to-noise ratio (SNR) concerning when the whole tracking system should be switched to the track before detect (TBD) mode.

Threshold Optimization for Tracking a Nonmaneuvering Target

A promising line of research attempts to bridge the gap between radar detector and radar tracker by means of considering jointly optimal parameter settings for both of these subsystems. We consider the problem of detection threshold optimization in a tracker-aware manner so that a feedback from the tracker to the detector is formed to maximize the overall system performance. We explore the research space for tracker-aware detector threshold optimization schemes and compare various approaches in a theoretical and experimental framework. In particular, we consider the optimization schemes which rely on two nonsimulation performance prediction (NSPP) algorithms for the probabilistic data association filter (PDAF), namely, the modified Riccati equation (MRE) and hybrid conditional averaging (HYCA). The study identifies a number of algorithmic and experimental evaluation gaps in this space and we propose to fill these gaps. Simulation results on relevant tracking scenarios demonstrate and discuss the behavior of the existing and proposed methods in terms of steady-state and transient tracking performance.

On output independence and complementariness in rank-based multiple classifier decision systems

This study presents a theoretical analysis of output independence and complementariness between classifiers in a rank-based multiple classifier decision system in the context of the partitioned observation space theory. To enable such an analysis, an information theoretic interpretation of a rank-based multiple classifier system is developed and basic concepts from information theory are applied to develop measures for output independence and complementariness. It is shown that output independence of classifiers is not a requirement for achieving complementariness between these classifiers. Namely, output independence does not imply a performance improvement by combining multiple classifiers. A condition called dominance is shown to be important instead. The information theoretic measures proposed for output independence and complementariness are justified by simulated examples.

A tracker-aware detector threshold optimization formulation for tracking maneuvering targets in clutter

In this paper, we consider a tracker-aware radar detector threshold optimization formulation for tracking maneuvering targets in clutter. The formulation results in an online method with improved transient performance. In our earlier works, the problem was considered in the context of the probabilistic data association filter (PDAF) for non-maneuvering targets. In the present study, we extend the ideas in the PDAF formulation to the multiple model (MM) filtering structures which use PDAFs as modules. Although our results are general for the MM filters, our simulation experiments apply the proposed solution in particular for the interacting multiple model PDAF (IMM-PDAF) case. It is demonstrated that the suggested formulation and the resulting optimization method exhibits notable improvement in transient performance in the form of track loss immunity. We believe the method is promising as a detector-tracker jointly-optimal filter for the IMM-PDAF structure for tracking maneuvering targets in clutter.

Task oriented kinematic analysis for a legged robot with half-circular leg morphology

In this paper, we study the kinematics of a legged robot with half-circular leg morphology. In particular, our focus is on the RHex hexapod platform. A new kinematic model for RHex is developed considering the leg shape and its consequences, which was over simplified in the previous models seen in literature. The formulation is an accurate kinematic representation of the robot in the sagittal plane that is based on a four-link mechanism analogy. When only pure rolling motion of the legs are considered, it is found that when front and rear pairs of legs are in contact with the ground, the robot becomes a one degree-offreedom mechanism and position of the middle pair of legs are redundant. The problem is solved in two steps; the first one being the determination of the initial configuration of the leg angular positions which defines the initial value of the variable distance of the front and rear leg and ground contact ponts. After the initial configuration of the system is set, pitch angle of the robot body can be manipulated by controlling one of the leg angular positions and the results are presented on an example case; positioning a body fixed unactuated sensor by controlling robot body pitch angle through the actuation of one of the legs. The results are a good display of the multi-functional aspect of the legs in addition to their use for locomotion.

Control of underactuated planar hexapedal pronking through a dynamically embedded SLIP monopod

Pronking (aka. stotting) is a gait in which all legs are used in synchrony, resulting in long flight phases and large jumping heights that may potentially be useful for mobile robots on rough terrain. Robotic instantiations of this gait suffer from severe pitch instability either due to underactuation, or the lack of sufficient feedback. Nevertheless, the dynamic nature of this gait suggests that the Spring-Loaded Inverted Pendulum Model (SLIP), a very successful predictive model for both natural and robotic runners, would be a good basis for more robust and maneuverable robotic pronking. In this paper, we describe how “template-based control”, a controller structure based on the embedding of a simple dynamical “template” within a more complex “anchor” system, can be used to achieve stable and controllable pronking for a planar, underactuated hexapod model. In this context, high-level control of the gait is regulated through speed and height commands to the SLIP template, while the embedding controller based on approximate inverse-dynamics and carefully designed passive dynamics ensures the stability of the remaining degrees of freedom. We show through extensive simulation experiments that unlike existing open-loop alternatives, the resulting control structure provides stability, explicit maneuverability and significant robustness against sensor and actuator noise.

On optimal resource allocation in multifunction radar systems

Recent studies have focused on the problem of resource allocation in systems in which multiple applications contend for multiple resources in order to satisfy their application level requirements. Multifunction radar system is an example of such a system in which multiple targets are tracked by the radar system simultaneously requiring processor and energy resources of the radar system. Lee et al. (2003) studied the problem of maximizing the overall tracking quality of the multifunction radar system by applying optimization procedures offline. The optimization methods employed in this work first considered the sampling frequency alone as a resource and optimized this resource by using the approach of Seto et al. (1996). Later in the same study, sampling frequency and computation time are attempted to be optimized together by using the Q-RAM approach. However, the method presented failed to be extendable to accommodate additional resource variables. In the present study, two improvements over the solution approach are presented. Firstly, the optimization problem for a tracking radar system is extended so as to enable the consideration of the average power of the transmitted signal as a resource which can be optimized besides sampling frequency and computation time. By this extension, a novel optimization algorithm is proposed to optimize the average power together with the sampling frequency and computation time. Secondly, it is also shown that the extendible method presented can also be applied for the two variable case and produce comparatively more favorable results as compared with the Q-RAM based solution.

Rank-Based Multiple Classifier Decision Combination: A Theoretical Study

This study presents a theoretical investigation of the rankbased multiple classifier decision problem for closed-set pattern identification. The problem of combining the decisions of more than one classifiers with raw outputs in the form of candidate class rankings is considered and formulated as a general discrete optimization problem with an objective function based on the total probability of correct decision. This formulation uses certain performance statistics about the joint behavior of the ensemble of classifiers, which need to be estimated from the cross-validation data. An initial approach leads to an integer (binary) programming problem with a simple and global optimum solution but of prohibitive dimensionality. Therefore, we present a partitioning formalism under which this dimensionality can be reduced by incorporating our prior knowledge about the problem domain and the structure of the training data. It is also shown that the formalism can effectively explain a number of successfully used combination approaches in the literature.