Brad R. Jackson

Direction of Arrival Estimation Using Directive Antennas in Uniform Circular Arrays

The effect of directional antenna elements in uniform circular arrays (UCAs) for direction of arrival (DOA) estimation is studied in this paper. While the vast majority of previous work assumes isotropic antenna elements or omnidirectional dipoles, this work demonstrates that improved DOA estimation accuracy and increased bandwidth is achievable with appropriately-designed directional antennas. The Cramer-Rao Lower Bound (CRLB) is derived for UCAs with directional antennas and is compared to isotropic antennas for 4- and 8-element arrays using a theoretical radiation pattern. The directivity that minimizes the CRLB is identified and microstrip patch antennas approximating the optimal theoretical gain pattern are designed to compare the resulting DOA estimation accuracy with a UCA using dipole antenna elements. Simulation results show improved DOA estimation accuracy and robustness using microstrip patch antennas as opposed to conventional dipoles. Additionally, it is shown that the bandwidth of a UCA for DOA estimation is limited only by the broadband characteristics of the directional antenna elements and not by the electrical size of the array as is the case with omnidirectional antennas.

Hybrid RSS/AOA emitter location estimation based on least squares and maximum likelihood criteria

Linear least squares (LS) and maximum likelihood (ML) estimators are derived for emitter geolocation using both received signal strength (RSS) and angle of arrival (AOA) information obtained from an heterogeneous sensor array. The results of simulation experiments provide useful insights into the behavior of these hybrid approaches and demonstrate that the use of simple RSS sensors to augment traditional AOA sensors can significantly improve the attainable geolocation accuracy.

Relationship between the maximum likelihood emitter location estimators based on received signal strength (RSS) and received signal strength difference (RSSD)

Under the assumption of a log-normal path loss model, maximum likelihood (ML) emitter location estimators are derived for both received signal strength (RSS) and received signal strength difference (RSSD) information. It is then shown that these ML estimators are identical, contrary to the seemingly common perception that the RSS-based ML location estimator should outperform the RSSD-based ML location estimator. The Cramer-Rao lower bounds (CRLB) for the average miss distance are also shown to be identical. Using the least squares estimation criterion, a non-linear least squares (NLS) emitter location estimator is also formulated in this paper for comparison. These theoretical developments are illustrated by computer simulation experiments.

Impact of Emitter-Sensor Geometry on Accuracy of Received Signal Strength Based Geolocation

The Cramer-Rao lower bound (CRLB) is derived for the miss distance of an emitter geolocation system using received signal strength (RSS) measurements from spatially dispersed sensors. This result can be written as the product of several factors, one of which completely characterizes the effect of the emitter-sensor geometry on geolocation accuracy. This particular factor, which depends only on the relative positions of the emitter and sensors, is referred to as the geometric dilution of precision (G) in this paper. The properties of G can be analyzed using a combination of computer simulations and statistical analysis. These results provide useful insights into the problem of optimal sensor placement with respect to the area of interest for RSS based geolocation.

A novel density-based geolocation algorithm for a noncooperative radio emitter using power difference of arrival

This paper presents a novel density-based geolocation algorithm for locating a non-cooperative radio emitter using measurements of the power difference of arrival (PDOA), also known as received signal strength difference (RSSD). Consider a 2D space in a Cartesian coordinate system with N sensors and one stationary radio emitter and assume that the distance from a sensor to the radio emitter is the hypotenuse of a right triangle. For any combination of three sensors, there exists a system of three Pythagorean equations that can be transformed into a system of three circle equations whose centers and radii are related to the corresponding PDOA measurements. The intersections of the circles represent possible locations for the radio emitter. For N sensors, we can have a maximum of N(N-1) intersections of the circles. Dividing the 2D space into a grid, each grid cell contains a certain number of intersections. This method finds the grid cell with the highest intersection density and uses the center of this cell as the position fix estimate. MATLAB-based numerical simulations were used to evaluate the performance of this algorithm for various scenarios and parameters.

Performance Characterization of AOA Geolocation Systems Using the Von Mises Distribution

Circular (angular) random variables, such as the angle of arrival(AOA) in direction finding systems and the phase error in digital phase-locked loops and digital phase interferometers, are best modeled by the von Mises distribution, not the ubiquitous Gaussian distribution. However, the Gaussian distribution has been commonly preferred in the performance analysis of AOA geolocation systems, mostly due to its mathematical tractability. This paper demonstrates the use of the von Mises distribution to model AOA measurement errors in direction finding systems and derives simple expressions for the Fisher information matrix (FIM) and the Cramer-Rao lower bound for the average miss distance. These results show that the use of the von Mises model in the performance analysis of AOA geolocation systems is entirely practicable.

Covert and broadband direction finding using low-profile slot spiral antennas

A broadband direction finding (DF) array is presented in this work using low-profile slot spiral antennas. Often, DF systems use omnidirectional dipole or monopole antenna elements which can result in a limited bandwidth and an obvious visual signature. In contrast, the slot spirals employed in this work are low-profile and can be flush-mounted on metallic objects which can enable a covert DF implementation. Simulation results are shown using four slot spiral antenna elements placed on a vehicle model from 400 MHz to 1.2 GHz (100% fractional bandwidth). The near-constant characteristics of the slot spiral over a wide frequency range provides broadband DOA estimation accuracy performance. Results are shown for both vertically and horizontally polarized terrestrial incoming signals with various signal-to-noise ratios.

Probable regions for emitter localization

A probable region (PR) for the location of an emitter is useful for quantifying the reliability of a location estimate and for defining a search region. Previous investigations have yielded equations that define PRs having the form of error or uncertainty ellipses (or ellipsoids) given the assumption of Gaussian probability density functions (pdfs). The new derivation proposed in this paper differs in the use of polar or spherical coordinates instead of Cartesian coordinates. In addition to being simpler in some respects, it has the further advantage of being extensible to other PRs that contain arbitrary regions-of-interest. Numerical examples give results that are in close agreement with the theoretical values.

Uniform circular array with integrated microstrip tapered baluns

This paper presents the design, simulation, and measurement results of a 4-element uniform circular array (UCA) using dipole antenna elements with integrated microstrip tapered baluns to convert between balanced and unbalanced signals. These baluns are compact, integrated into the array support structure, and can provide a balanced signal over a relatively wide bandwidth. Simulation results are shown for the amplitude and phase balance of the balun from 1.6 GHz to 2.2 GHz. The array was fabricated and its manifold was measured in an anechoic chamber at a frequency of 1.7 GHz. The gain and phase responses of the array are presented and are compared to a simulated ideal dipole UCA in free-space.

Received Signal Strength-Based Emitter Geolocation Using an Iterative Maximum Likelihood Approach

Batch-mode maximum likelihood (ML) received signal strength (RSS) emitter geolocation algorithms produce location estimates from a block of data collected over an observation period using either a single sensor or collected at one time instant by multiple spatially dispersed sensors. Due to practical constraints such as processor speed, memory for data storage, time for data transfer and communications bandwidth, batch-mode algorithms can only be implemented in real-time for small data sets. This paper presents an iterative formulation of the likelihood function for the ML RSS geolocation algorithm for real-time implementation with large data sets. Simulation and experimental results are included to validate the proposed formulation.