Novel frequency of arrival‐based emitter localisation methods based on multiple moving observers

Abstract

Abstract It is well known that the Doppler frequency shift contains the emitter location information. The problem of emitter location based on frequency of arrival (FOA) measurements of multiple moving observers is focussed. In contrast to most relevant works, the newly proposed positioning methods consider the influence of signal frequency deviation due to source instability and present two mathematical models of the frequency deviation. The first model assumes that the frequency offset is a small random parameter. A two‐stage closed‐form location method (called method a) is proposed. In stage 1, a set of pseudo‐linear equations are established according to the geometric relationship between the observers and emitter, so as to obtain an intermediate estimate of source position. Stage 2 returns to the original FOA measurement model and uses the estimation result in stage 1 to construct the second set of pseudo‐linear equations, yielding the final positioning result. The second model assumes that the signal frequency deviation is a large deterministic parameter. We propose an alternative two‐stage localisation method (called method b). In stage 1, a decoupling optimisation algorithm is developed based on the pseudo‐linear equations derived in stage 1 of method a, and intermediate estimates of the source position and frequency deviation are obtained successively. Stage 2 returns to the original FOA measurement model again and forms the second set of pseudo‐linear equations, yielding the final closed‐form solutions of emitter position and frequency offset. Both methods are proved analytically to achieve the Cramér–Rao bound (CRB) under the moderate noise level. Simulation results demonstrate the superior performance of the new methods.

Keywords

• closed‐form solution
• Cramér–Rao bound (CRB)
• Doppler shift
• emitter localisation
• frequency‐of‐arrival (FOA)
• performance analysis