Richard J. Hartnett

On the use of cyclotomic polynomial prefilters for efficient FIR filter design

The authors present an efficient FIR (finite impulse response) filter design algorithm that generalizes existing cascaded FIR prefilter-equalizer methods. They propose using cyclotomic polynomial building blocks to form a multiplierless prefilter with impressive stopband performance, and they provide a straightforward strategy for choosing the polynomials to match filter specification. Two options for design of the equalizer are provided. A uniformly spaced equalizer can be optimally (L/sub infinity /) designed via a modified Parks-McClellan algorithm. A new algorithm, based on complex basis function subset selection methods, is also proposed for optimal design of a more efficient, nonuniformly spaced equalizer. The techniques, which can be applied to a broad class of filter design problems, typically provide a 35%-85% reduction in the number of additions and multiplications required, with a cost of 10%-45% additional delays. The methods also provide reduced coefficient quantization sensitivity and reduced roundoff noise. >

Improved filter sharpening

We propose a natural extension to Kaiser-Hamming (1977) filter sharpening methods to allow for a piecewise linear desired amplitude change function (ACF). The primary advantages of the proposed ACF over piecewise constant ACFs is that we obtain better control of selective improvement (or degradation) in either the passband or stopband or both, and we are not restricted to applying our methods to filters with piecewise constant pass and stopbands, since linear segments of slope 1 can be used to retain existing filter performance in either passband or stopband. The proposed ACF approximating polynomial (AP) is easy to compute, may be constrained to have simple (or integer) coefficients, and may be expressed as the AP of Kaiser and Hamming plus a correction polynomial. We also provide applications for motivation.

Discrete time robust stability design of PID controllers autonomous sailing vessel application

This paper presents a successful graphical technique for finding all discrete-time proportional integral derivative (PID) controllers that satisfy a robust stability constraint for heading control of a 2 meter autonomous sailing vessel. This problem is solved by finding all achievable discrete time PID controllers that simultaneously stabilize the closed-loop characteristic polynomial and satisfy constraints defined by a set of related complex polynomials. The bilinear transformation is used to describe the discrete time PID controllers. The discrete-time model of the vessel is identified from a sampled data system with uncertain communication delay. Experimental data taken from this vessel at the U. S. Coast Guard Academy is used to demonstrate the application of this methodology.

An Evaluation of eLoran as a Backup to GPS

In 2001, the Volpe National Transportation Systems Center completed an evaluation of the Global Positioning System (GPS) vulnerabilities and the potential impacts to transportation systems in the United States. One of the recommendations of this study was for the operation of backup system(s) to GPS; Loran C, which has been operated by the U.S. Coast Guard for the past 40 years, was identified as one possible backup system. The Federal Aviation Administration (FAA) has been leading a team consisting of members from industry, government, and academia to evaluate the future of Loran-C in the United States. In a recently completed Navigation Transition Study, the FAA concluded that Loran-C, as an independent radionavigation system, is theoretically the best backup for the GPS; however, in order for Loran-C to be considered a viable back-up system to GPS, it must be able to meet the requirements of non-precision approach (NPA) for the aviation community and the harbor entrance and approach (HEA) requirements for the maritime community. The accuracy requirements for Loran to be used as a backup system are 307 m for NPA and 20 m for HEA. In addition, there are integrity, availability, and continuity requirements. The current Loran system of 24 stations provides a stated absolute accuracy in navigation position of only 0.25 NM; however, enhanced Loran or eLoran has the capability of meeting the stringent requirements for NPA and HEA. In order to meet the accuracy requirements user receivers must use additional secondary factors (ASFs) in calculating the user position. ASFs are propagation time adjustments that are subtracted from the receivers times of arrival (TOAs) to account for propagation over non-seawater paths. These ASFs vary both spatially and temporally and both types of variations need to be accounted for to meet the accuracy targets. The current approaches to meeting the needs of the aviation and maritime communities are slightly different. For maritime navigation, the spatial variations will be accounted for through the use of a grid of ASF values that is known by the receiver a priori. As one component of the eLoran system, a reference station located nearby the harbor will be used to estimate the temporal changes in the ASFs relative to the published spatial grid; these differences will be broadcast using the Loran data channel (9th pulse) to the user receiver. This general method to HEA navigation was discussed by the authors in 2003 (ION AM 2003). More recently (ION GNSS 2006) we developed a technique to process survey data into a harbor grid. For the aviation community the approach is to measure and publish a set of ASF values for each airport. These airport ASFs will be adjusted to be in the middle of the seasonal variation in order to minimize the maximum error. This approach has been discussed by the authors most recently in papers presented in 2005 (ILA 34) and 2006 (ION NTM 2006). In this paper we show results from both flight tests at various airports around the U.S. and maritime tests in the Thames River in CT. These results demonstrate the ability of eLoran to meet the accuracy requirements for both NPA and HEA using the ASF methods we have proposed.

Possible Optimizations for the US Loran System

The United States has a significant capital investment in the current Loran system in its 24 stations and towers nationwide. As the existing system was developed in the 1970’s, the question arises: Is it possible to re-use the existing infrastructure to better serve the position, navigation, and timing communities given today’s technologies? As a terrestrial radionavigation system at 100 kHz, Loran provides a good complement to the GPS system in that it is not subject to the same vulnerabilities and failure modes. In this paper we re-examine the potentials of Loran, reopening some of the degrees of freedom in the design process. While we keep certain hard constraints – tower locations, station power levels, and spectrum – and, for now, impose the limits of a pulsed system using the existing antennas, we investigate several options: • What is the improvement gained by assuming that all stations are time-synchronized (TOT control) and that receivers make use of both rates of dual-rated stations to improve TOA estimates? • What is the improvement to be gained by single-rating all stations? If we keep the fastest rate at each station, how does this improve performance? For this option we look at the improved SNR due to decreased transmitter jitter when single-rated, no cross-rate blanking at the transmitter, and reduced cross-rate interference as compared to the reduced number of pulses available under option 1. • We re-examine chain assignments; the trade-offs are maintaining sufficient pulse rate while minimizing cross-rate interference. After single-rating, what improvement do we get from changing the number of chains?

Estimate of discrete-time PID controller parameters for H-infinity complementary sensitivity design: Autonomous sailboat application

This paper presents some of the successful design methodologies used to predict the robustness of a heading controller for a 2 meter autonomous sailing vessel. A graphical technique is introduced to estimate the discrete-time proportional integral derivative (PID) controller coefficients to satisfy H-infinity complementary sensitivity constraints for vessel control. We show that this problem can be solved by finding all achievable PID controllers that simultaneously stabilize the closed-loop characteristic polynomial and satisfy constraints defined by a set of related complex polynomials. Experimental data taken from this vessel at the U. S. Coast Guard Academy is used to demonstrate the application of this methodology.

Innovative approaches to teaching analog and digital filter design concepts

We present a new approach to teaching filter design. In the classroom, students see graphical design methods emphasizing relationships between poles/zeros and frequency response (e.g., Chebyshev pole locations, low-pass to band-pass mapping, and bilinear transformation). In lab, each student develops a MATLAB® program, capable of designing analog or digital, low-pass/high-pass/band-pass/notch, and Butterworth or Chebyshev filters. Using a “bottom-up” approach, students write individual functions as topics are covered in class, thereby creating “student toolboxes” that make no use of inherent MATLAB filter design functions. Students then craft a “main program” to implement filter design logic by calling their (tested) lower level functions. Finally, students use their programs to filter individually corrupted music files. Students design a digital filter to remove that band-limited noise, while preserving music fidelity, in an iterative process, exploring tradeoffs between maximum passband attenuation, minimum stopband attenuation, filter type, passband and stopband cutoffs, filter order and fidelity. Using graphical techniques, along with bottom-up program development, provides significant insight into fundamental tradeoffs in the filter design process not attainable through design by table lookup or inherent MATLAB function calls. Furthermore, feedback suggests the final design project is very gratifying and unites theory and real world design.

Lower Bounds on DOP

Code phase Global Navigation Satellite System (GNSS) positioning performance is often described by the Geometric or Position Dilution of Precision (GDOP or PDOP), functions of the number of satellites employed in the solution and their geometry. This paper develops lower bounds to both metrics solely as functions of the number of satellites, effectively removing the added complexity caused by their locations in the sky, to allow users to assess how well their receivers are performing with respect to the best possible performance. Such bounds will be useful as receivers sub-select from the plethora of satellites available with multiple GNSS constellations. The bounds are initially developed for one constellation assuming that the satellites are at or above the horizon. Satellite constellations that essentially achieve the bounds are discussed, again with value toward the problem of satellite selection. The bounds are then extended to a non-zero mask angle and to multiple constellations.

A novel approach to teaching phased array antenna systems

We describe a simple, yet elegant method to provide a full sensory experience that describes the operation of a phased array antenna system. Our method is based on using an audio source that feeds an array of speakers appropriately spaced apart such that when a listener walks around the array, they experience the null points as well as the primary lobe and minor lobes. It is extremely profound for the student to experience a relatively loud tone, and then when moving just a few inches perceives the complete absence of the tone. The apparatus is economical and relatively easy to implement and test as compared to an RF antenna phased array. The ideas presented are applicable to other courses in electrical and mechanical engineering that cover signal processing and acoustics. Student assessment has shown that the proposed method greatly enhances understanding of phased array systems.

A novel approach to teaching amplitude and phase distortion concepts using time domain methods

We present an alternative method to teach amplitude and phase distortion concepts using time domain methods. Typically, these concepts are taught using relatively expensive network analyzers. Here we show how a transcendental waveform, generated using relatively inexpensive waveform generators, and observed using standard lab oscilloscopes, can be used to illustrate amplitude and phase distortion, enabling the student to better understand systems whose magnitude responses are not flat, or whose phase responses may not be linear. Our methods allow students the opportunity to gain more insight into the characteristics of high fidelity (audio) systems.