John H. Painter

Reconciling steady-state Kalman and alpha-beta filter design

The deterministic design of the alpha-beta filter and the stochastic design of its Kalman counterpart are placed on a common basis. The first step is to find the continuous-time filter architecture which transforms into the alpha-beta discrete filter via the method of impulse invariance. This yields relations between filter bandwidth and damping ratio and the coefficients, alpha and beta . In the Kalman case, these same coefficients are related to a defined stochastic signal-to-noise ratio and to a defined normalized tracking error variance. These latter relations are obtained from a closed-form, unique, positive-definite solution to the matrix Riccati equation for the tracking error covariance. A nomograph is given that relates the stochastic and deterministic designs. >

Multipath Modeling for Aeronautical Communications

One of the fundamental technical problems in aeronautical digital communications is that of multipath propagation between aircraft and ground terminal. This paper examines in detail a model of the received multipath signal that is useful for application of modern detection and estimation theories. The model treats arbitrary modulation and covers the selective and nonselective cases. The necessarily nonstationary statistics of the received signal are determined from the link geometry and the surface roughness parameters via a Kirchhoff solution. Use of the model in solving detection and estimation problems is outlined. Results of a flight experiment are presented and compared to a digital simulation for verification of the model.

Hypertrapezoidal fuzzy membership functions

The authors present a method for representing N-dimensional fuzzy membership functions. The proposed method is a generalization of the one-dimensional trapezoidal membership function commonly used in fuzzy systems. The issue of correlation between input variables and a decrease in the rule base size is the motivation for extending the definition of membership functions into more than one domain. The approach outlined in this paper is focused by practical considerations and use of a Bayesian version of fuzzy logic which requires that set membership sum to one. The fuzzy partitioning which stems from the presented method is parameterized by M+1 values, yielding an efficient mechanism for designing complex fuzzy systems.

A fuzzy-tuned adaptive Kalman filter

In this paper, fuzzy processing is applied to the adaptive Kalman filter. The filter gain coefficients are adapted over a 50 dB range of unknown signal/noise dynamics, using fuzzy membership functions. Specific simulation results are shown for a dynamic system model which has position-velocity states, as in vehicle tracking applications such as the global positioning system (GPS). The filter is single-input single-output, driven by measurements of position, corrupted by additive (Gaussian) noise. The fuzzy adaptation technique is also applicable to multiple-input multiple-output applications for the cases where the states are higher-order moments of motion. The fuzzy processing is driven by an inaccurate online estimate of signal-to-noise ratio for the signal being tracked. A robust Bayes scheme calculates the filter gain coefficients from the signal-to-noise estimate. In our implementation, the inaccurate signal-to-noise estimate is corrected by the use of fuzzy membership functions. Performance comparisons are given between optimum, fuzzy-tuned adaptive, and fixed-gain Kalman filters for the second-order position-velocity model.<<ETX>>

Recursive Ideal Observer Detection of Known M-ary Signals in Multiplicative and Additive Gaussian Noise

This paper presents the derivation of the recursive algorithms necessary for real-time digital detection of M -ary known signals that are subject to independent multiplicative and additive Gaussian noises. The motivating application is minimum probability of error detection of digital data-link messages aboard civil aircraft in the earth reflection multipath environment. For each known signal, the detector contains one Kalman filter and one probability computer. The filters estimate the multipath disturbance. The estimates and the received signal drive the probability computers. Outputs of all the computers are compared in amplitude to give the signal decision. The practicality and usefulness of the detector are extensively discussed.

Designing Pseudorandom Coded Ranging Systems

This paper develops a set of mathematical tools for system design or analysis of a type of pseudorandom coded ranging system used in several space programs. Certain probabilities of failure of the system to perform the ranging function and the times required for the system to perform prescribed ranging functions are defined and related to system parameters. A set of sample calculations is presented for clarification of the computational techniques.

Hypertrapezoidal Fuzzy Membership Functions for Decision Aiding

This paper reports research pushing forward the theory and application of fuzzy logic and fuzzy control. The push is in a theoretical area needed to apply fuzzy logic to the interpretation and management of systems of increasing complexity. Hypertrapezoidal fuzzy membership functions (HFMFs) are a new mechanism for designing multidimensional fuzzy sets. Unlike their one-dimensional counterparts traditionally used in fuzzy engineering, HFMFs model the correlation that exists between the variables of the state space. Additionally, the manner in which HFMFs are electronically stored makes them ideal for applications requiring training or on-line adaptation. This paper contains the background and practical application of HFMFs in an on-board pilot advisory system for general aviation aircraft. The pilot advisory system serves as an example of the usefulness of HFMFs for decision aiding. HFMFs have proved to be an essential element for flight mode analysis, and will likely find many other useful applications.

Intelligent system design with fixed-base simulation validation for general aviation

This paper reviews research conducted in the Texas A&M University Flight Simulation Laboratory on intelligent systems for general aviation. Over the last eight years several intelligent cockpit systems and pilot decision-aiding tools have been created and developed for general aviation aircraft, using fix-based flight simulation validation and evaluation. This paper reviews these results, and also presents current research on advanced cockpit systems designed to satisfy the technological requirements posed by the general aviation Free Flight and Small Aircraft Transportation System concepts.

Integrating the evolving modern cockpit

This paper applies to Free Flight some lessons learned from ten years of investigation into computing in the modern cockpit. Early efforts concluded that Artificial Intelligence was better suited to Flight Management and Pilot Decision Support than to aircraft control. Later efforts produced an AI-based cockpit software decision system for inferring current flight operation without querying the pilot. That decision system was used to drive adaptive displays and a rulebased Pilot Advisor. This prior work implemented a state of the art fixed-base engineering flight simulator, whose software was favorably evaluated by a team of pilots. Currently, an innovative Flight Management System is being implemented, based on cooperating software agents. The technology focus is not just on hardware but on the software that can integrate new Free Flight functionality, in terms of increasing pilot situational awareness, while not increasing his workload. Software methods integrate data from multiple sources, dealing with weather, traffic, terrain, and route. Such data fusion results in an integrated, pilot-centered, smart guidance and display system.

Fuzzy decision and control, the Bayes context

This paper shows how it is that fuzzy control may be viewed as a particular kind of stochastic (Bayesian) control. With the Bayes approach, fuzzy control may be viewed as an ensembled-average control, where the average is taken over a set of competing uncertain antecedent events, predefined on the system state space.<<ETX>>