Multipath propagation represents a dominant error source limiting the accuracy of radio-based ranging and positioning in urban environments. Conventional ranging estimators typically estimate only the range of the first arriving path while neglecting the multipath components. This introduces a bias and causes the estimator's variance to diverge from the Cramér-Rao Bound (CRB). While extensive research has established performance bounds for estimators that jointly estimate all paths, the specific impact on the variance of ignoring these components remains largely unexplored. This paper derives bounds on the bias, variance, and mean square error (MSE) for ranging in multipath channels for the purpose of positioning. We consider Orthogonal Frequency Division Multiplexing (OFDM) signals in multipath channels with deterministic path delays and gains. The paper focuses on time-delay estimation (TDE) in the mid-to-high signal-to-noise ratio (SNR) regime under two scenarios: (i) when the receiver jointly estimates all propagation paths, and (ii) when the receiver underestimates the number of paths. Specifically, for the latter case, we derive a semi closed-form expression for the variance of the time-delay estimator that considers a single-path when in reality there are L paths. This derivation is based on the misspecified Cramér-Rao bound (MCRB). Although unmodelled multipath has been traditionally viewed as detrimental to time-delay estimation, we reveal that in some cases the estimation variance improves. For a two-path channel we show that the variance depends on the relative gain, carrier phase, and separation of the paths. Additionally, the estimation bias is upper-bounded by constructive and destructive path interference. Finally, we empirically process a six-path simulated channel frequency response with fixed path delays and gains, to demonstrate that the derived MSE bound is tight for mid-to-high SNRs. This work characterizes the impact of multipath propagation on the variance of time-delay estimation, which is essential for designing accurate ranging signals and estimators in urban scenarios.

Navigation with radio-signals using GNSS or a terrestrial positioning system in urban environments is susceptible to multipath propagation, which can severely degrade positioning accuracy. In a Line-of-Sight (LOS) multipath channel, the received signal is composed of a direct path component and a sum of time-shifted and attenuated replicas of the transmitted signal. When these multipath components are not accounted for in the time-delay estimation (TDE) model, they may introduce substantial estimation bias. For positioning, only the first arriving path is of interest. Therefore, it is crucial to focus on estimating the reflections that most significantly affect the TDE of this primary path, while ignoring others with negligible impact. To reduce the impact of close-in multipath in TDE, we propose Maximum Likelihood estimators that account for the strongest reflections, with models considering either one or two multi-path components. The Maximum Likelihood Estimation (MLE) problem is optimized using the Space Alternating Generalized Expectation-Maximization (SAGE) method. To reduce computational load, the delay search space for each path is constrained based on the maximum bias observed in the multipath error envelope (MPEE). To assess the ranging accuracy for the various MLE estimators that account for multiple paths, we utilize a synthetically generated channel based on the Saleh-Valenzuela model. Additionally, we benchmark the positioning performance of these estimators using channel impulse responses recorded with a terrestrial positioning prototype system tested at The Green Village on the TU Delft campus.