Analysis of Multimodal Systems

The estimation of a multimodal linear system whose mode-to-mode transitions are described by a finite-state Markov chain is described. The problem has application in studying separation standards in an air traffic control environment. An optimal solution is formulated which is computationally infeasible. A suboptimal estimator is then derived which closely approximates the optimal estimator. An example is presented to illustrate the technique.     

Finite-dimensional filters with nonlinear drift. V: solution to Kolmogorov equation arising from linear filtering with non-Gaussian initial condition

Despite its usefulness, the Kalman-Bucy filter is not perfect. One of its weaknesses is that it needs a Gaussian assumption on the initial data. Recently Yau and Yau introduced a new direct method to solve the estimation problem for linear filtering with non-Gaussian initial data. They factored the problem into two parts: (1) the on-line solution of a finite system of ordinary differential equations (ODEs), and (2) the off-line calculation of the Kolmogorov equation. Here we derive an explicit closed-form solution of the Kolmogorov equation. We also give some properties and conduct a numerical study of the solution.     

Interference between FM Carriers and a Digitally Modulated SCPC Circuit

The interference from the digital single channel per carrier (SCPC) circuits into frequency-modulated carrier systems has been calculated by convolving the desired and the interfering spectra extending the previously published works. Resulting interference noise power in FDM/FM systems covering a wide range of modulation indices and basebands has been presnted. Also plots of interference noise power as a function of the number of SCPC circuits have been presented for various values of carrier power to interference power ratios.     

Probing the era of galaxy formation via TeV gamma ray absorption by the near infrared extragalactic background

We present models of the extragalactic background light (EBL) based on several scenarios of galaxy formation and evolution. We have treated galaxy formation with the Press-Schecter approximation for both cold dark matter (CDM) and cold+hot dark matter (CHDM) models, representing a moderate (z _f 3) and a late (z _f 1) era of galaxy formation respectively. Galaxy evolution has been treated by considering a variety of stellar types, different initial mass functions and star formation histories, and with an accounting of dust absorption and emission. We find that the dominant factor influencing the EBL is the epoch of galaxy formation. A recently proposed method for observing the EBL utilizing the absorption of 0.1 to 10 TeV gamma-rays from active galactic nuclei (AGN) is shown to be capable of discriminating between different galaxy formation epochs. The one AGN viewed in TeV light, Mrk 421, does show some evidence for a cutoff above 3 TeV; based on the EBL models presented here, we suggest that this is due to extinction in the source. The large absorption predicted at energies > 200 GeV for sources at z > 0.5 indicates that observations of TeV gamma-ray bursts (GRB) would constrain or eliminate models in which the GRB sources lie at cosmological distances.Now at University of Chicago, Dept. of Astronomy & Astrophysics.     

Aerosols on the Giant Planets and Titan

On the giant planets and Titan, like on the terrestrial planets, aerosols play an important part in the physico-chemistry of the upper atmosphere (P ≤ 0.5 bar). Above all, aerosols significantly affect radiative transfer processes, mainly through light scattering, thus influencing the atmospheric energy budget and dynamics. Because there is usually significant coupling between atmospheric circulation and haze production, aerosols may constitute useful tracers of atmospheric dynamics.More generally, since their production is directly linked to some kind of energy deposition, their study may also provide clues to external sources of energy as well as their variability. Finally, aerosols indirectly influence other processes such as cloud formation and disequilibrium chemistry, by acting either as condensation nuclei or as reaction sites for surface chemistry. Here, I present a review of observational and modeling results based on remote sensing data, and also some insights derived from laboratory simulations. Despite our knowledge of the effects of aerosols in outer planetary atmospheres, however, relatively little is understood about the pathways which produce them, either endogenously (as end-products of gas-phase photochemical or shock reactions) or exogenously (as residues of meteroid ablation).     

PHD filters of higher order in target number

The multitarget recursive Bayes nonlinear filter is the theoretically optimal approach to multisensor-multitarget detection, tracking, and identification. For applications in which this filter is appropriate, it is likely to be tractable for only a small number of targets. In earlier papers we derived closed-form equations for an approximation of this filter based on propagation of a first-order multitarget moment called the probability hypothesis density (PHD). In a recent paper, Erdinc, Willett, and Bar-Shalom argued for the need for a PHD-type filter which remains first-order in the states of individual targets, but which is higher-order in target number. In this paper we show that this is indeed possible. We derive a closed-form cardinalized PHD (CPHD) filter, which propagates not only the PHD but also the entire probability distribution on target number.     

Matched Filter Criteria and Range Weighting for Weather Radar

The effective weighting function for weather radar is defined. This weighting function considers the effects of both the transmitted signal and the receiver filter. It is used to assign effective ranges to samples taken at prescribed times. For uniformly distributed targets it is shown that "signal"-to-noise ratio depends on the receiver filter, transmitted signal envelope, and receiver noise spectral density. Maximization of this signal-to-noise ratio when range resolution constraints are imposed is discussed, and a receiver design approach specifically adapted for Doppler weather radars is developed.     

Susceptibility of DS/FH,M, Binary DPSK to Partial and Full Band Barrage Jamming

Spread spectrum signaling schemes have been proposed to counter unfriendly, electrical jamming threats. In order to establish their effectiveness, such schemes must be analyzed. This work takes a step in this direction by developing the susceptibility equation, or equivalently, the probability of error, of a direct sequence/frequency hopped (DS/FH), binary differential phase-shift keying (DPSK) system when subjected to a barrage jamming signal. Specific system models are established for the receiving system as well as for the jamming signal and the spread spectrum techniques. Both partial and full band jamming strategies are considered. Graphical results are presented with the conclusions summarizing the spread spectrum effectiveness and the deficiencies of the FH processing gain definition.     

Calibration of the MERIC full-polarimetric radar: theory and implementation

This paper describes the architecture and calibration design of the experimental ground based radar station MERIC. This full-polarimetric radar is conceived for the analysis and the recognition of non cooperative aircraft in flight.We carefully study how the full-polarimetric capability is obtained for a simultaneous transmit (simultaneous transmission of two linear FM with opposite slopes) radar system, using analogue deramping with a replica.The phase distortions of the signal propagating in the four polarimetric channels are carefully estimated. We define a phase calibrating method compatible with the outdoor measurements conditions and few constraints on reference targets.We show the phase accuracy obtained with the proposed calibration method on real measurements.     

An Optimum Phase Reference Detector for Fully Modulated Phase-Shift Keyed Signals

Many modern telemetry systems which use phase-shift keying (PSK) have receivers which derive a coherent reference from the fully modulated PSK signal itself and thus conserve the energy which otherwise would be allocated to a discrete reference signal. In this paper, an optimum receiver structure for estimating a phase reference from the PSK signal itself is derived and its realization discussed. It is shown that at low signal-to-noise ratios, the optimum detector can be realized with a Costas loop. Since a Costas loop and squaring loop exhibit identical performance, it follows that either of these simple devices gives optimum performance for low-input signal-to-noise ratios.