Pulse-diverse radar waveform design for delay-doppler estimation.

by Wing-Kit Chung.Thesis (M.Phil.)--Chinese University of Hong Kong, 2000.Includes bibliographical references (leaves 123-127).Abstracts in English and Chinese.Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Application of Time Delay and Doppler Shift Estimation in Active Radar --- p.1Chapter 1.2 --- Joint Time delay and Doppler Shift Estimation Algorithm based on Correlation --- p.4Chapter 1.3 --- A Brief Review of Radar Signal Design --- p.6Chapter 1.3.1 --- Suppression of Range Sidelobes Level --- p.6Chapter 1.3.2 --- Reduction of Ambiguity of Delay-Doppler Plane --- p.8Chapter 1.4 --- Goal and Outline of the Thesis --- p.9Chapter 2 --- CAF and Pulse Diversity for Radar Signals --- p.11Chapter 2.1 --- Radar Ambiguity Function --- p.12Chapter 2.1.1 --- Properties of Radar Ambiguity Function --- p.12Chapter 2.1.2 --- Ideal Ambiguity Function --- p.13Chapter 2.2 --- Composite Ambiguity Function (CAF) --- p.14Chapter 2.2.1 --- Properties of Composite Ambiguity Function --- p.15Chapter 2.3 --- CAF of Joint Phase and Frequency Shift Keying (PSK-FSK) Mod- ulated Signal --- p.17Chapter 2.4 --- Summary --- p.21Chapter 3 --- CAF Algorithm and Its Performance Analysis --- p.22Chapter 3.1 --- CAF Algorithm for Time Delay and Doppler Shift Estimation --- p.23Chapter 3.2 --- The Cramer-Rao Lower Bound of the CAF Algorithm --- p.24Chapter 3.3 --- Performance Analysis of the CAF Algorithm --- p.28Chapter 3.4 --- Global Accuracy --- p.31Chapter 3.5 --- Numerical Results for Derivation of CAF Algorithm --- p.35Chapter 3.5.1 --- Simulation Results of CRLB for Various Multi-pulse Signals --- p.35Chapter 3.5.2 --- Simulation Results of Global Accuracy for Various Multi- pulse Signals --- p.36Chapter 3.5.3 --- Simulation on Global Accuracy with Different Parameters --- p.37Chapter 3.6 --- Summary --- p.39Chapter 4 --- Optimum Pulse-Diverse Waveforms Design --- p.46Chapter 4.1 --- Criteria for Optimum Waveforms --- p.46Chapter 4.2 --- Optimum Signals Based on Joint Phase and Frequency Shift Key- ing (PSK-FSK) Modulated Signal --- p.48Chapter 4.3 --- Genetic Algorithm (GA) --- p.50Chapter 4.4 --- Numerical Results --- p.54Chapter 4.4.1 --- "Comparison of Optimized PSK, FSK and PSK-FSK Signals" --- p.55Chapter 4.4.2 --- Simulation on Large Number of Pulses for Pulse-diverse Waveform Set --- p.59Chapter 4.4.3 --- Simulation Results of CAF algorithm for Time Delay and Doppler Shift Estimation --- p.63Chapter 4.4.4 --- Various Distribution of Ambiguity Volume on the Delay- Doppler Plane --- p.70Chapter 4.5 --- Summary --- p.74Chapter 5 --- Wideband CAF (WCAF) and Its Analysis --- p.75Chapter 5.1 --- WCAF Algorithm for Time Delay and Doppler Stretch Estimation --- p.76Chapter 5.2 --- Theory of Wavelet Packets --- p.77Chapter 5.3 --- Design of Wideband Optimum Waveforms for WCAF Algorithm --- p.80Chapter 5.4 --- Performance Evaluation --- p.82Chapter 5.4.1 --- The Cramer-Rao Lower Bound of WCAF Algorithm --- p.83Chapter 5.4.2 --- The Global Accuracy of WCAF Algorithm --- p.84Chapter 5.4.3 --- Numerical Results --- p.86Chapter 5.5 --- Summary --- p.89Chapter 6 --- Conclusion and Suggestion for Future Research --- p.90Chapter 6.1 --- Conclusion --- p.90Chapter 6.2 --- Suggestion for Future Research --- p.93Chapter A --- Derivation of Ambiguity Function and CAF --- p.94Chapter A.1 --- Properties of Radar Ambiguity Function --- p.94Chapter A.2 --- Properties of Composite Ambiguity Function --- p.96Chapter B --- Derivation of Fisher Information Matrix of CAF Algorithm --- p.98Chapter C --- Derivation of Performance Analysis of CAF Algorithm --- p.103Chapter C.1 --- Derivation of TD and DS Estimate by Proposed Estimator --- p.103Chapter C.2 --- Derivation the Asymptotic Variance of The Estimates --- p.106Chapter D --- Derivation of Probability of Decision Error --- p.113Chapter E --- PSK-FSK Modulating Code of Various Multi-pulse Signals --- p.116Chapter F --- Derivation of Wavelet-Based Wideband CAF --- p.120Chapter F.1 --- Volume of Wideband Ambiguity Function --- p.120Chapter F.2 --- Volume of Wideband Composite Ambiguity Function --- p.121Bibliography --- p.12

A New Compact Delay, Doppler Stretch and Phase Estimation CRB with a Band-Limited Signal for Generic Remote Sensing Applications

Since time-delay, Doppler effect and phase estimation are fundamental tasks in a plethora of engineering fields, tractable lower performance bounds for this problem are key tools of broad interest for a large variety of remote sensing applications. In the large sample regime and/or the high signal-to-noise ratio regime of the Gaussian conditional signal model, the Cramér–Rao bound (CRB) provides an accurate lower bound in the mean square error sense. In this contribution, we introduce firstly a new compact CRB expression for the joint time-delay and Doppler stretch estimation, considering a generic delayed and dilated band-limited signal. This generalizes known results for both wideband signals and the standard narrowband signal model where the Doppler effect on the band-limited baseband signal is not considered and amounts to a frequency shift. General compact closed-form CRB expressions for the amplitude and phase are also provided. These compact CRBs are expressed in terms of the baseband signal samples, making them especially easy to use whatever the baseband signal considered, therefore being valid for a variety of remote sensors. The new CRB expressions are validated in a positioning case study, both using synthetic and real data. These results show that the maximum likelihood estimator converges to the CRB at high signal-to-noise ratios, which confirms the exactness of the CRB. The CRB is further validated by comparing the ambiguity function and its 2nd order Taylor expansion where the perfect match also proves its exactness

Velocity Dealiased Spectral Estimators of Range Migrating Targets using a Single Low-PRF Wideband Waveform

Wideband radars are promising systems that may provide numerous advantages, like simultaneous detection of slow and fast moving targets, high range-velocity resolution classification, and electronic countermeasures. Unfortunately, classical processing algorithms are challenged by the range-migration phenomenon that occurs then for fast moving targets. We propose a new approach where the range migration is used rather as an asset to retrieve information about target velocitiesand, subsequently, to obtain a velocity dealiased mode. More specifically three new complex spectral estimators are devised in case of a single low-PRF (pulse repetition frequency) wideband waveform. The new estimation schemes enable one to decrease the level of sidelobes that arise at ambiguous velocities and, thus, to enhance the discrimination capability of the radar. Synthetic data and experimental data are used to assess the performance of the proposed estimators

Simultaneous Range-Velocity Processing and SNR Analysis of AFIT\u27s Random Noise Radar

This paper presents two research objectives aimed at advancing the AFIT RNR signal processing algorithm and modeling capability toward the overarching goal of performing collision avoidance on an autonomous vehicle. In both research efforts, analytical, simulated, and measured results are provided and used to draw research conclusions. The first research effort is aimed at reducing the memory required for 2D processing in the time domain in order to distribute the processing algorithm across hundreds of processors on a GPU. Distributed processing reduces the overall 2D processing time and the feasibility of a near real-time implementation is studied. The second effort consists of improving a Simulink® model of the AFIT RNR. Each component of the AFIT RNR, as well as the target environment, is modeled and compared to measured results. A robust model will provide a useful tool to study the signal-to-noise ratio (SNR) of the RNR at all points within the radar system

Passive acoustic method for aircraft localization

The present thesis investigates a passive acoustic method to locate maneuvering aircraft. The method is based on the acoustical Doppler effect, as a particular effect of the signals received by a mesh of spatially distributed microphones. A one-dimensional version of the ambiguity function allows for the calculation of the frequency stretch factor that occurs between the sound signals received by a pair of microphones. The mathematical expression for this frequency stretch is a function of the aircraft position and velocity, both of them being estimated by a genetic algorithm. The method requires only a minimum of seven microphones and the prior knowledge of the aircraft position and velocity at a given time. The advantages of the method are that it is suitable for all kind of aircraft, not only propeller-driven, and is not restricted to low heights above the ground. Its applicability could be, for instance, to supplement aircraft noise monitoring systems or to supervise small airports activities. This doctoral research includes the theoretical background of the method as well as the detailed description of its implementation. To assess the performance of the method, results from computer simulations are discussed. First of all, noise propagation is considered in a lossless medium, thus only geometrical spreading influences the sound emitted by the source traveling to the receivers. The accuracy of each step of the method has been evaluated and the results obtained reveal acceptable performance. Due to the large distances between microphones and the aircraft in flight, the atmospheric attenuation plays a major roll. Therefore, computer simulations have also been carried out under the assumption of an homogeneous but non lossless medium to evaluate the influence of the atmospheric absorption on the aircraft location. Under these conditions, the performance of the method with respect to the microphone distribution is discussed. Moreover, the location method has also been tested for a possible inaccuracy on the microphones synchronization. Finally, an outdoor experimental validation of the acoustic method has been carried out with a radio control airplane. The description of the experimental test is detailed in the present work as well as the results obtained.La tesi desenvolupa, implementa i valida un mètode acústic per a la localització d’aeronaus. El mètode es basa en l’efecte Doppler que es percep en els registres de diferents micròfons distribuïts al voltant d’un aeroport. La versió u-dimensional de la funció d’ambigüitat permet el còmput del factor de compressió o expansió que sorgeix entre els registres freqüencials d’ un parell de micròfons. Aquest factor Freqüencial es pot expressar matemàticament en funció de la posició i velocitat de l’aeronau, que s’estimen en aquesta tesi a partir d’algoritmes genètics. El mètode només requereix de set micròfons i el coneixement previ de la posició de l’avió en un moment donat. Els principals avantatges del mètode són que és un mètode vàlid per qualsevol tipus d’aeronau, no només per avions d’hèlix o helicòpters, i que no restringeix a vols de baixa alçada. La seva aplicació podria ser, per exemple, complementar un sistema de monitorització de soroll aeri o bé supervisar l’activitat dels aeroports petits que no disposen de sistemes de radar. Aquesta investigació inclou el desenvolupament teòric del mètode així com la descripció detallada de la seva implementació. Per tal d’avaluar l’efectivitat del mètode, es presenten i analitzen resultats obtinguts a partir de diverses simulacions. Com a primer cas, es considera que el so es propaga en un medi conservatiu, és a dir, el so que es propaga des de la font fins als receptors només es veu afectat per l’atenuació geomètrica. Sota aquest model senzill de propagació, s’ha analitzat l’accuracy de cada un dels passos del mètode i els resultats obtinguts posen de manifest una bona ... del mètode. Tenint en compte que les distàncies entre els micròfons i l’avió en vol són llargues, l’atenuació atmosfèrica influeix també en la propagació del so emès per l’avió. Per tant, el segon cas de simulacions que s’han dut a terme considera un medi de propagació homogeni i no conservatiu amb l’objectiu d’avaluar la influència de l’atenuació atmosfèrica en la localització acústica de l’aeronau. Sota aquestes condicions, també s’ha analitzat l’eficàcia del mètode en funció de la distribució de micròfons. A més, el mètode de localització s’ha posat a prova sota possibles errors en la sincronització dels set micròfons. Finalment, s’ha dut a terme una validació experimental del mètode amb una avioneta de radio control al Club Aeronàutic Egara. La descripció d’aquest test experimental es detalla en la tesis així com els resultats obtinguts que demostren la validesa satisfactòria del mètode

State-Space Approaches to Ultra-Wideband Doppler Processing

National security needs dictate the development of new radar systems capable of identifying and tracking exoatmospheric threats to aid our defense. These new radar systems feature reduced noise floors, electronic beam steering, and ultra-wide bandwidths, all of which facilitate threat discrimination. However, in order to identify missile attributes such as RF reflectivity, distance, and velocity, many existing processing algorithms rely upon narrow bandwidth assumptions that break down with increased signal bandwidth. We present a fresh investigation into these algorithms for removing bandwidth limitations and propose novel state-space and direct-data factoring formulations such as * the multidimensional extension to the Eigensystem Realization Algorithm, * employing state-space models in place of interpolation to obtain a form which admits a separation and isolation of solution components, * and side-stepping the joint diagonalization of state transition matrices, which commonly plagues methods like multidimensional ESPRIT. We then benchmark our approaches and relate the outcomes to the Cramer-Rao bound for the case of one and two adjacent reflectors to validate their conceptual design and identify those techniques that compare favorably to or improve upon existing practices

Сравнение статистических характеристик оценок доплеровской деформации и задержки сигнала с результатами узкополосной модели

Narrowband approximation of Doppler effect by a frequency shift is inappropriate for some problems of radiolocation, hydro acoustics or passive location. In this case it is necessary to use Doppler stretch (time-scaling) as a signal parameter. Statistical performance of joint Doppler stretch and delay for arbitrary spectral width signal without narrowband approximations is derived in this paper.Narrowband and wideband parameters relations are investigated for triangle impulse with linear spectral modulation. Besides, Fisher Information Matrices (FIM) differences are analyzed. In the narrowband limit consideration of results in well-known FIM of Doppler shift and delay estimation are proposed. Another feature of wideband FIM is reference time dependence on time delay variance. Transition from Doppler stretch to Doppler frequency shift considering narrowband limitations results in translation invariant FIM.The article shows that reference time variance of delay estimation is related to estimated parameter modification and velocity influence on delay. Also, estimation variances in narrowband signal model differ from wideband parameter variances by magnitude of spectrum width to central frequency ratio. Изучаются статистические характеристики совместных оценок доплеровской деформации и задержки сигнала с произвольной шириной спектра, т. е. без допущений узкополосной модели. Исследован переход между параметрами узкополосной и широкополосной моделей на примере треугольного импульса с линейной частотной модуляцией, проведен анализ отличий в элементах информационных матриц. Проанализирована неинвариантность дисперсии оценки масштаба/задержки к выбору начала отсчета и приведено объяснение причин указанного эффекта.Показано, что неинвариантность дисперсии оценки задержки сигнала к выбору начала отсчета связана с изменением оцениваемого параметра и влиянием скорости цели на задержку. Полученные дисперсии оценок узкополосной модели совпадают с результатами широкополосной модели с точностью до поправки порядка отношения ширины спектра к центральной частоте.