A new kernel-based approach to system identification with quantized output data

In this paper we introduce a novel method for linear system identification with quantized output data. We model the impulse response as a zero-mean Gaussian process whose covariance (kernel) is given by the recently proposed stable spline kernel, which encodes information on regularity and exponential stability. This serves as a starting point to cast our system identification problem into a Bayesian framework. We employ Markov Chain Monte Carlo methods to provide an estimate of the system. In particular, we design two methods based on the so-called Gibbs sampler that allow also to estimate the kernel hyperparameters by marginal likelihood maximization via the expectation-maximization method. Numerical simulations show the effectiveness of the proposed scheme, as compared to the state-of-the-art kernel-based methods when these are employed in system identification with quantized data.Comment: 10 pages, 4 figure

Bayesian kernel-based system identification with quantized output data

In this paper we introduce a novel method for linear system identification with quantized output data. We model the impulse response as a zero-mean Gaussian process whose covariance (kernel) is given by the recently proposed stable spline kernel, which encodes information on regularity and exponential stability. This serves as a starting point to cast our system identification problem into a Bayesian framework. We employ Markov Chain Monte Carlo (MCMC) methods to provide an estimate of the system. In particular, we show how to design a Gibbs sampler which quickly converges to the target distribution. Numerical simulations show a substantial improvement in the accuracy of the estimates over state-of-the-art kernel-based methods when employed in identification of systems with quantized data.Comment: Submitted to IFAC SysId 201

Discrete multitone modulation with principal component filter banks

Discrete multitone (DMT) modulation is an attractive method for communication over a nonflat channel with possibly colored noise. The uniform discrete Fourier transform (DFT) filter bank and cosine modulated filter bank have in the past been used in this system because of low complexity. We show in this paper that principal component filter banks (PCFB) which are known to be optimal for data compression and denoising applications, are also optimal for a number of criteria in DMT modulation communication. For example, the PCFB of the effective channel noise power spectrum (noise psd weighted by the inverse of the channel gain) is optimal for DMT modulation in the sense of maximizing bit rate for fixed power and error probabilities. We also establish an optimality property of the PCFB when scalar prefilters and postfilters are used around the channel. The difference between the PCFB and a traditional filter bank such as the brickwall filter bank or DFT filter bank is significant for effective power spectra which depart considerably from monotonicity. The twisted pair channel with its bridged taps, next and fext noises, and AM interference, therefore appears to be a good candidate for the application of a PCFB. This is demonstrated with the help of numerical results for the case of the ADSL channel

Evaluation of Skylab (EREP) data for forest and rangeland surveys

The author has identified the following significant results. Four widely separated sites (near Augusta, Georgia; Lead, South Dakota; Manitou, Colorado; and Redding, California) were selected as typical sites for forest inventory, forest stress, rangeland inventory, and atmospheric and solar measurements, respectively. Results indicated that Skylab S190B color photography is good for classification of Level 1 forest and nonforest land (90 to 95 percent correct) and could be used as a data base for sampling by small and medium scale photography using regression techniques. The accuracy of Level 2 forest and nonforest classes, however, varied from fair to poor. Results of plant community classification tests indicate that both visual and microdensitometric techniques can separate deciduous, conifirous, and grassland classes to the region level in the Ecoclass hierarchical classification system. There was no consistency in classifying tree categories at the series level by visual photointerpretation. The relationship between ground measurements and large scale photo measurements of foliar cover had a correlation coefficient of greater than 0.75. Some of the relationships, however, were site dependent

Identification of Parametric Underspread Linear Systems and Super-Resolution Radar

Identification of time-varying linear systems, which introduce both time-shifts (delays) and frequency-shifts (Doppler-shifts), is a central task in many engineering applications. This paper studies the problem of identification of underspread linear systems (ULSs), whose responses lie within a unit-area region in the delay Doppler space, by probing them with a known input signal. It is shown that sufficiently-underspread parametric linear systems, described by a finite set of delays and Doppler-shifts, are identifiable from a single observation as long as the time bandwidth product of the input signal is proportional to the square of the total number of delay Doppler pairs in the system. In addition, an algorithm is developed that enables identification of parametric ULSs from an input train of pulses in polynomial time by exploiting recent results on sub-Nyquist sampling for time delay estimation and classical results on recovery of frequencies from a sum of complex exponentials. Finally, application of these results to super-resolution target detection using radar is discussed. Specifically, it is shown that the proposed procedure allows to distinguish between multiple targets with very close proximity in the delay Doppler space, resulting in a resolution that substantially exceeds that of standard matched-filtering based techniques without introducing leakage effects inherent in recently proposed compressed sensing-based radar methods.Comment: Revised version of a journal paper submitted to IEEE Trans. Signal Processing: 30 pages, 17 figure

The S2 VLBI Correlator: A Correlator for Space VLBI and Geodetic Signal Processing

We describe the design of a correlator system for ground and space-based VLBI. The correlator contains unique signal processing functions: flexible LO frequency switching for bandwidth synthesis; 1 ms dump intervals, multi-rate digital signal-processing techniques to allow correlation of signals at different sample rates; and a digital filter for very high resolution cross-power spectra. It also includes autocorrelation, tone extraction, pulsar gating, signal-statistics accumulation.Comment: 44 pages, 13 figure

The Fundamentals of Radar with Applications to Autonomous Vehicles

Radar systems can be extremely useful for applications in autonomous vehicles. This paper seeks to show how radar systems function and how they can apply to improve autonomous vehicles. First, the basics of radar systems are presented to introduce the basic terminology involved with radar. Then, the topic of phased arrays is presented because of their application to autonomous vehicles. The topic of digital signal processing is also discussed because of its importance for all modern radar systems. Finally, examples of radar systems based on the presented knowledge are discussed to illustrate the effectiveness of radar systems in autonomous vehicles