Abstract
The accuracy of radio-based positioning systems will be limited by multipath interference in realistic application scenarios. This paper derives closed-form expressions for the Cramér–Rao lower bound (CRLB) on the achievable time-of-arrival (ToA) and angle-of-arrival (AoA) estimation-error variances, considering the presence of multipath radio channels, and extends these results to position estimation. The derivations are based on channel models comprising deterministic, specular multipath components as well as stochastic, diffuse/dense multipath. The derived CRLBs thus allow an evaluation of the influence of channel parameters, the geometric configuration of the environment, and system parameters such as signal bandwidth and array geometry. Our results quantify how the ToA and AoA accuracies decrease when the signal bandwidth is reduced, because more multipath will then interfere with the useful LoS component. Antenna arrays can (partly) compensate this performance loss, exploiting diversity among the multipath interference. For example, the AoA accuracy with a 16-element linear array at bandwidth is similar to a two-element array at , in the magnitude order of one degree. The ToA accuracy, on the other hand, still scales by a factor of 100 from the cm-regime to the m-regime because of the dominating influence of the signal bandwidth. The position error bound shows the relationship between the range and angle information under realistic indoor channel conditions and their different scaling behaviors as a function of the anchor–agent placement. Specular multipath components have a maximum detrimental influence near the walls. It is shown for an L-shaped room that a fairly even distribution of the position error bound can be achieved throughout the environment, using two anchors equipped with -array antennas. The accuracy limit due to multipath increases from the 1–10-cm-range at bandwidth to the 0.5–1-m-range at .
Highlights
High-accuracy positioning will be a key enabler for a wide range of novel applications in different sectors of industry, including manufacturing, logistics, retail, and transportation
We extend our previous work on performance limits for high-accuracy localization in multipath channels [19,20] towards antenna arrays and joint ToA and AoA estimation by deriving the waveform-based Cramér–Rao lower bound (CRLB)
We further examine the resulting achievable positioning accuracy to be expected in dense multipath channels, exploiting these ToA and AoA estimates
Summary
High-accuracy positioning will be a key enabler for a wide range of novel applications in different sectors of industry, including manufacturing, logistics, retail, and transportation. In [26], a polarimetric signal model is used to derive general expressions for the waveform-based CRLB for channel parameter estimation including dense multipath components, but the results were not analyzed with respect to the position estimation problem. We extend our previous work on performance limits for high-accuracy localization in multipath channels [19,20] towards antenna arrays and joint ToA and AoA estimation by deriving the waveform-based CRLB. We analyze and evaluate the position error bound for a multi-anchor scenario based on joint ToA and AoA estimation, showing the trade-off between these two measurement parameters and their scaling behaviors with respect to bandwidth and anchor–agent geometry.
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