The applicability of biased estimation in model and model order selection

Biased estimation has the advantage of reducing the mean squared error (MSE) of an estimator. The question of interest is how biased estimation affects model selection. In this paper, we introduce biased estimation to a range of model selection criteria. Specifically, we analyze the performance of the minimum description length (MDL) criterion based on biased and unbiased estimation and compare it against modern model selection criteria such as Kay's conditional model order estimator (CME), the bootstrap and the more recently proposed hook-and-loop resampling based model selection. The advantages and limitations of the considered techniques are discussed. The results indicate that, in some cases, biased estimators can slightly improve the selection of the correct model. We also give an example for which the CME with an unbiased estimator fails, but could regain its power when a biased estimator is used.

A miniaturised wideband frequency synthesiser

Wideband frequency synthesisers have application in many areas, including test instrumentation and defence electronics. Miniaturisation of these devices provides many advantages to system designers, particularly in applications where extra space and weight are expensive. The purpose of this project was to miniaturise a wideband frequency synthesiser and package it for operation in several different environmental conditions while satisfying demanding technical specifications. The four primary and secondary goals to be achieved were: 1. an operating frequency range from low MHz to greater than 40 GHz, with resolution better than 1 MHz, 2. typical RF output power of +10 dBm, with maximum DC supply of 15 W, 3. synthesiser package of only 150  100  30 mm, and 4. operating temperatures from 20C to +71C, and vibration levels over 7 grms. This task was approached from multiple angles. Electrically, the system is designed to have as few functional blocks as possible. Off the shelf components are used for active functions instead of customised circuits. Mechanically, the synthesiser package is designed for efficient use of the available space. Two identical prototype synthesisers were manufactured to evaluate the design methodology and to show the repeatability of the design. Although further engineering development will improve the synthesiser’s performance, this project has successfully demonstrated a level of miniaturisation which sets a new benchmark for wideband synthesiser design. These synthesisers will meet the demands for smaller, lighter wideband sources. Potential applications include portable test equipment, radar and electronic surveillance systems on unmanned aerial vehicles. They are also useful for reducing the overall weight and power consumption of other systems, even if small dimensions are not essential.