We present a direct (non-iterative) method for solving for the location of a radio frequency (RF) emitter, or an RF navigation receiver, using four or more time of arrival (TOA) measurements and an assumed altitude above an ellipsoidal earth. Both the emitter tracking problem and the navigation application are governed by the same equations, but with slightly different interpreta- tions of several variables. We treat the assumed altitude as a soft constraint, with a specified noise level, just as the TOA measurements are handled, with their respective noise levels. With 4 or more TOA measurements and the assumed altitude, the problem is overdetermined and is solved in the weighted least squares sense for the 4 unknowns, the 3-dimensional position and time. We call the new technique the TAQMV (TOA Altitude Quartic Minimum Variance) algorithm, and it achieves the minimum possible error variance for given levels of TOA and altitude estimate noise. The method algebraically produces four solutions, the least-squares solution, and potentially three other low residual solutions, if they exist. In the lightly overdermined cases where multiple local minima in the residual error surface are more likely to occur, this algebraic approach can produce all of the minima even when an iterative approach fails to converge. Algorithm performance in terms of solution error variance and divergence rate for bas eline (iterative) and proposed approach are given in tables.
This paper describes how confidence intervals can be calculated for radiofrequency emitter position estimates based on time-of-arrival and frequency-of-arrival measurements taken at several satellites. These confidence intervals take the form of 50th and 95th percentile circles and ellipses to convey horizontal error and linear intervals to give vertical error. We consider both cases where an assumed altitude is and is not used. Analysis of velocity errors is also considered. We derive confidence intervals for horizontal velocity magnitude and direction including the case where the emitter velocity is assumed to be purely horizontal, i.e., parallel to the ellipsoid. Additionally, we derive an algorithm that we use to combine multiple position fixes to reduce location error. The algorithm uses all available data, after more than one location estimate for an emitter has been made, in a mathematically optimal way.
In this work, we present two methods for solving overdetermined systems of the Time of Arrival (TOA) geolocation equations that achieve the minimum possible variance in all cases, not just when the satellites are at large equal radii. One of these techniques gives two solutions, and the other gives four solutions.
This report describes a new algorithm for the joint estimation of carrier phase, symbol timing and data in a Turbo coded phase shift keyed (PSK) digital communications system. Jointly estimating phase, timing and data can give processing gains of several dB over conventional processing, which consists of joint estimation of carrier phase and symbol timing followed by estimation of the Turbo-coded data. The new joint estimator allows delay and phase locked loops (DLL/PLL) to work at lower bit energies where Turbo codes are most useful. Performance results of software simulations and of a field test are given, as are details of a field programmable gate array (FPGA) implementation that is currently in design.