Complex Ambiguity Function Research Articles

Approximate Maximum Likelihood Radio Emitter Geolocation With Time-Varying Doppler

Direct geolocation of radio emitters has traditionally been formulated using short measurement intervals over which delay and Doppler frequency shift are approximated as constant. In this paper, we consider maximum likelihood position estimation using long measurement intervals for which the Doppler is time varying. A series of assumptions and approximations are used to develop an efficient solution involving coherent combining of traditional, complex ambiguity function processing outputs. Simulation results are used to demonstrate potential gains.

CAF 이용 다중 발기하에서의 CRLB 성능 분석

In this paper, we described the Cramer-Rao Lower Bound (CLRB) performances of Time Difference of Arrival (TDOA) and Frequency Difference of Arrival (FDOA) methods when there are multiple emitters. The TDOA and FDOA values between two receivers can be simultaneously estimated by using the so-called Complex Ambiguity Function (CAF). In the case of multiple emitters, there exist Inter Symbol Interferences (ISIs) in the measurement data. Therefore, it is required to reduce the effect of ISI and provide a performance evaluation method of TDOA and FDOA estimations. In order to eliminate the ISIs, using of a filter bank before calculating CAF is proposed when the carrier frequencies of the emitters are different to one another. Angle of Arrival (AOA) or Received Signal Strength (RSS) methods before calculating CAF were proposed to reduce the ISIs when the carrier frequencies are the same. In order to evaluate the CRLB of TDOA and FDOA estimations, we employed the conditional probability distribution method and described the numerical comparison results.

A Detailed Analysis of GPS Live-Sky Signals Without a Dish

This paper explores a premise that, with appropriate application of digital signal processing techniques, much of the detailed signal analysis typically associated with a dish can instead be done with a standard low-gain GNSS antenna. To do so, the signals of the recently launched GPS IIF satellites are examined, with particular attention on the L5 signal. Notably, using a high-quality non-directional GNSS antenna, we demonstrate observations of: (1) signal bandpass and dispersive characteristics, (2) chip shape, (3) eye and constellation diagrams, and (4) millisecond-level transient events. Such observations are enabled by use of the computationally efficient GNSS Complex Ambiguity Function (GCAF) technique. The methods used to process the GCAF data to produce these results are discussed in detail, with careful attention to the limitations of the techniques. Qualitative comparisons are made to similar dish-based measurements found in open literature. Copyright © 2014 Institute of Navigation.

Complex ambiguity functions using nonstationary higher order cumulant estimates

The complex ambiguity function based on second-order statistics (CAF-SOS) has been used to simultaneously estimate the frequency-delay of arrival (FDOA) and time-delay of arrival (TDOA) between two signal measurements; its performance, however, is sensitive to the correlation between two additive noise sources. When the noise sources are assumed to be Gaussian, we develop a new complex ambiguity function based on higher order statistics (CAF-HOS) that reduces the unknown noise-correlation effect. The new CAF-HOS algorithm utilizes nonstationary higher order cross cumulant estimates and their Fourier transform. In fact, we suggest a nonstationary estimate of fourth-order cross-cumulants and obtain the analytical expressions for its mean value and variance. We compare the analytical expressions with results obtained by Monte Carlo runs. Also, we compare the performance of the new complex ambiguity function based on fourth-order statistics (CAF-FOS) against the CAF-SOS algorithm using different Gaussian noise sources, different signals of interest, different signal-to-noise ratios, and different lengths of data.

Differential delay/Doppler ML estimation with unknown signals

Previously published analyses on the maximum-likelihood estimation of joint frequency and time offsets between two noisy versions of a common signal have assumed a Gaussian random signal with a known power spectrum. In many applications, the common signal is not Gaussian and there may be no prior knowledge of its detailed structure. Instead, estimation of a hypothesized common signal can be construed as another element in the estimation process. The analysis is straightforward and shows that the complex ambiguity function (CAF) still represents the ML approach when the noise is Gaussian and spectrally flat. Additional interpretation shows that use of interference-rejection filtering followed by a CAF is an attractive suboptimum approach in an environment of narrowband interferers.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Algorithms for ambiguity function processing

Calculation of the complex ambiguity function is viewed as the basis for joint estimation of the differential delay and differential frequency offset between two waveforms that contain a common component plus additive noise. In many applications, the required accuracy leads to a need for integration over long data sets that can become a challenge for near real-time digital processing. The nature of the ambiguity processing is interpreted, and an algorithm approach is shown that minimizes the processing burden over a broad category of applications without affecting performance.

Reconstructions of images of partially coherent objects from samples of mutual intensity

It is known that if the mutual intensity is sampled on an array of spacings, such samples can be Fourier transformed to yield images of incoherently radiating objects. In this paper, this result is extended to the imaging of partially coherent and coherent objects. An analysis of partially coherent imaging is first developed using a rather new approach, and the role of the complex ambiguity function in such imaging is emphasized. Next, using sampling theory, it is shown that in order to reconstruct images of partially coherent objects it is necessary to sample the mutual intensity on a discrete array of translations as well as on a discrete array of spacings. The required spacing and translation increments are shown to be inversely proportional to the object size and coherence extent, respectively. These requirements are stated in the form of a sampling theorem. Based on these results, an image synthesis procedure is outlined, and the capability of such a procedure for removing misfocus and other imaging aberrations is discussed. Lastly, experimental results are presented that demonstrate the aberration removal capability of this technique, using a coherent imaging system with defocus error.