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Time of arrival (TOA or ToA) is the absolute time instant when a radio signal emanating from a transmitter reaches a remote receiver. The time span elapsed since the time of transmission (TOT or ToT) is the time of flight (TOF or ToF). Time difference of arrival (TDOA) is the difference between TOAs.

Usage

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Many radiolocation systems use TOA measurements to perform geopositioning via true-range multilateration. The true range or distance can be directly calculated from the TOA as signals travel with a known velocity. TOA from two base stations will narrow a position to a position circle; data from a third base station is required to resolve the precise position to a single point. TDOA techniques such as pseudorange multilateration use the measured time difference between TOAs.

The concept may be applied as well with IEEE 802.15.4aCSS as with IEEE 802.15.4aUWB modulation.[1]

Ways of synchronization

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As with TDOA, synchronization of the network base station with the locating reference stations is important. This synchronization can be done in different ways:

  • With exact synchronous clock on both sides. Inaccuracy in the clock synchronization translates directly to an imprecise location.
  • With two signals which have different speed. Sound ranging to a lightning strike works this way (speed of light and sound velocity).
  • Via measurement to or triggering from a common reference point.
  • Without direct synchronisation, but with compensation of clock phase differences,

Two-way ranging

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Two-way ranging is a cooperative method for determining the range between two radio transceiver units. When synchronisation of the oscillators of the involved transmitters is not viable, hence the clocks differ, then applying the measurement as a two ways travel to the receiver and mirrored back to the transmitter compensates for some of the phase differences between the oscillators involved. This concept is applied with the real-time locating system (RTLS) concept as defined in the international standard ISO/IEC FCD 24730-5.[2]

Determination

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Further information: Pseudo-range multilateration
Fig. 4a. Pulse signal
Fig. 4b. Wide-band signal
Fig. 4c. Narrow-band signal
Examples of measuring time difference with cross-correlation (surveillance system)

Assume a surveillance system calculates the time differences ( for ) of wavefronts touching each receiver. The TDOA equation for receivers and is (where the wave propagation speed is and the true vehicle-receiver ranges are and )

The quantity is often termed a pseudo-range. It differs from the true range between the vehicle and station by an offset, or bias, which is the same for every signal. Differencing two pseudo-ranges yields the difference of the same two true-ranges.

Figure 4a (first two plots) show a simulation of a pulse waveform recorded by receivers and . The spacing between , and is such that the pulse takes 5 time units longer to reach than . The units of time in Figure 4 are arbitrary. The following table gives approximate time scale units for recording different types of waves:

Type of wave Material Time units
Acoustic Air 1 millisecond
Acoustic Water 1/2 millisecond
Acoustic Rock 1/10 millisecond
Electromagnetic Vacuum, air 1 nanosecond

The red curve in Figure 4a (third plot) is the cross-correlation function . The cross-correlation function slides one curve in time across the other and returns a peak value when the curve shapes match. The peak at time = 5 is a measure of the time shift between the recorded waveforms, which is also the value needed for equation 3.

Figure 4b shows the same type of simulation for a wide-band waveform from the emitter. The time shift is 5 time units because the geometry and wave speed is the same as the Figure 4a example. Again, the peak in the cross-correlation occurs at .

Figure 4c is an example of a continuous, narrow-band waveform from the emitter. The cross-correlation function shows an important factor when choosing the receiver geometry. There is a peak at time = 5 plus every increment of the waveform period. To get one solution for the measured time difference, the largest space between any two receivers must be closer than one wavelength of the emitter signal. Some systems, such as the LORAN C and Decca mentioned at earlier (recall the same math works for moving receiver and multiple known transmitters), use spacing larger than 1 wavelength and include equipment, such as a phase detector, to count the number of cycles that pass by as the emitter moves. This only works for continuous, narrow-band waveforms because of the relation between phase , frequency and time :

The phase detector will see variations in frequency as measured phase noise, which will be an uncertainty that propagates into the calculated location. If the phase noise is large enough, the phase detector can become unstable.

Navigation systems employ similar, but slightly more complex, methods than surveillance systems to obtain delay differences. The major change is DTOA navigation systems cross-correlate each received signal with a stored replica of the transmitted signal (rather than another received signal). The result yields the received signal time delay plus the user clock's bias (pseudo-range scaled by ). Differencing the results of two such calculations yields the delay difference sought ( in equation 3).

TOT navigation systems perform similar calculations as TDOA navigation systems. However, the final step, subtracting the results of one cross-correlation from another, is not performed. Thus, the result is received signal time delays plus the user clock's bias ( in equation 3).

See also

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References

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Further reading

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Revisions and contributorsEdit on WikipediaRead on Wikipedia

Time of arrival

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The time of arrival (TOA), often abbreviated as ToA, refers to the precise instant at which a transmitted signal—such as an electromagnetic, acoustic, or other wave—reaches a receiver after propagating from its source. This measurement captures the absolute of signal reception in a synchronized reference frame, enabling calculations of delay when combined with the known transmission time. In essence, TOA underpins distance estimation by relating the signal's travel time to the speed of , typically the for radio signals. TOA plays a central role in positioning, navigation, and timing (PNT) systems, where it facilitates high-accuracy localization by measuring distances () from multiple known reference points, such as or base stations. Key applications include the , in which receivers compute pseudoranges from TOA measurements of signals to determine user position, velocity, and time. It is also essential in and for target detection and tracking, wireless sensor networks for event localization, and mobile communications for emergency services like E-911. employs TOA for tracking marine life, while multimedia systems use it for source localization in audio environments. Despite its precision—often achieving sub-meter accuracy with wideband signals—TOA-based methods face challenges such as the need for line-of-sight propagation, accurate time synchronization between transmitters and receivers, and mitigation of multipath errors or noise. Algorithms like estimation and maximum likelihood techniques address these issues by processing TOA data from arrays of sensors, enhancing robustness in non-ideal conditions. Related concepts, such as time difference of arrival (TDOA), extend TOA principles by focusing on relative arrival times to avoid absolute synchronization requirements.

Fundamentals

Definition and Principles

The time of arrival (TOA) refers to the precise instant at which a transmitted signal arrives at a receiver. This captures the absolute time for the signal's reception, enabling the inference of spatial relationships through characteristics. In contexts, TOA serves as a foundational metric for determining event timing or positional data based on wave . TOA must be distinguished from time of flight (TOF), which specifically denotes the duration required for the signal to propagate from the transmitter to the receiver. The relationship is given by TOA = transmission time + TOF, where the transmission time is the moment the signal departs the transmitter according to a synchronized clock. This distinction is critical, as TOF isolates the component, while TOA incorporates the full timeline from emission to detection. The underlying physical principle of TOA stems from the predictable propagation of waves at constant velocities in homogeneous media. For electromagnetic signals, such as radio waves, this velocity is the speed of light, c=299792458c = 299792458 m/s in vacuum (approximately 3×1083 \times 10^8 m/s in air). For acoustic signals, the speed is approximately 343 m/s in air at 20°C. These speeds govern the delay incurred over distance, forming the basis for time-based ranging. Wave propagation introduces delays proportional to distance, with time scales varying by signal type. For instance, an electromagnetic wave covers 30 cm in approximately 1 ns (τ=0.33×108=10−9\tau = \frac{0.3}{3 \times 10^8} = 10^{-9} s), highlighting the need for nanosecond-level precision in high-resolution applications. In contrast, an acoustic wave in air travels about 0.34 m in 1 ms (τ=0.34343≈10−3\tau = \frac{0.34}{343} \approx 10^{-3} s), illustrating slower propagation suitable for shorter-range scenarios. These examples underscore the medium- and signal-dependent nature of delays. From TOF, the distance dd is computed via the basic relation d=c×TOF,d = c \times \mathrm{TOF}, where cc is the known propagation speed, providing a direct link between time and spatial separation essential for TOA-based analyses. Time difference of arrival (TDOA) is a derived measurement obtained as the difference in time of arrival (TOA) of a signal at multiple receivers, which enables hyperbolic positioning geometries without requiring knowledge of the absolute transmission time. This approach leverages the relative timing differences to define hyperboloids, with the transmitter located at their intersection, making it suitable for systems where receiver synchronization is feasible but transmitter timing is unknown. Pseudo-range represents an apparent in positioning systems, calculated as ρ=c×(treceive−ttransmit)\rho = c \times (t_\mathrm{receive} - t_\mathrm{transmit}), where cc is the , treceivet_\mathrm{receive} is the receiver's clock time at signal reception, and ttransmitt_\mathrm{transmit} is the encoded transmission time from the signal; this value is biased by relative clock offsets between the transmitter and receiver. In practice, such biases introduce errors that must be modeled or estimated, distinguishing pseudo-range from the true geometric . True-range multilateration employs synchronized TOA measurements from multiple base stations to compute the actual distances to a transmitter, requiring a minimum of three stations for two-dimensional positioning and four for three-dimensional localization to resolve the of spherical loci. Each TOA corresponds to a centered at the receiver with equal to the signal propagation distance, and the transmitter position is the unique point satisfying all such constraints in non-degenerate geometries. Early navigation systems like , developed in the 1940s during , and the Decca Navigator, operational from the 1940s, utilized phase-based TOA estimation for narrowband signals to achieve hyperbolic positioning through continuous-wave phase comparisons equivalent to TDOA measurements. These systems relied on ground-wave propagation for coastal and oceanic coverage, demonstrating the practical application of TOA derivatives in pre-satellite era localization.

Applications

Positioning and Localization

is a core technique in time-of-arrival (TOA) positioning, where the absolute distance from a transmitter to each receiver is calculated as the product of the signal propagation speed and the measured TOA, assuming synchronized clocks between transmitter and receivers. This process involves solving a of nonlinear equations derived from the of spheres in (or circles in two dimensions), each centered at a receiver with equal to the true range, to determine the transmitter's coordinates. The solution typically requires at least three receivers for two-dimensional localization to resolve potential ambiguities from pairwise intersections and four non-coplanar receivers for three-dimensional positioning to uniquely fix the location. However, accuracy can be degraded by error sources such as , which causes signals to arrive via multiple paths leading to erroneous TOA estimates, and signal noise from environmental interference or receiver imperfections. In practical applications, TOA-based multilateration enables precise localization in various environments. For instance, in the (GPS), receivers use TOA measurements of signals from multiple satellites to compute pseudoranges, accounting for clock biases, to determine user position. In indoor real-time locating systems (RTLS), ultra-wideband (UWB) signals leverage their high time resolution to perform TOA measurements, achieving sub-meter accuracy even amidst multipath challenges typical of confined spaces. TOA multilateration can operate in cooperative or non-cooperative modes depending on the target's involvement. In cooperative localization, the target uses an active to emit or respond to signals, facilitating direct TOA measurements from multiple base stations. Conversely, non-cooperative scenarios, such as , rely on intercepting the target's emissions without its participation, where TOA is estimated from the received signals to perform multilateration, though this often faces challenges from unknown emission times. As an alternative to TOA, time difference of arrival (TDOA) methods eliminate the need for transmitter-receiver by using differential times but require additional receivers for hyperboloid intersections.

Time Synchronization

Time of arrival (TOA) measurements play a crucial role in network time synchronization by enabling the exchange of timestamped signals between nodes to estimate and correct clock offsets and skews. In protocols such as Reference Broadcast Synchronization (RBS), a reference node broadcasts packets, and receiving nodes record the arrival times using their local clocks; these nodes then exchange their timestamps to compute relative offsets, effectively canceling out transmission and propagation delays that are common to all receivers. Similarly, the Timing-sync Protocol for Sensor Networks (TPSN) employs two-way TOA exchanges to derive offsets by subtracting round-trip delays from measured arrival times. This approach leverages the basic time-of-flight (TOF) principle, where the difference between transmission and arrival times informs clock alignment without requiring absolute time knowledge. Common scenarios for TOA-based synchronization include wireless sensor networks (WSNs) and environments, where precise temporal coordination is essential for tasks like , event ordering, and TDMA scheduling. In WSNs, for instance, TOA enables microsecond-level synchronization across resource-constrained nodes, supporting applications such as and industrial automation. These systems often operate in multi-hop topologies, where iterative TOA exchanges propagate synchronization from nodes to the network periphery, achieving global coherence despite limited connectivity. A key challenge in TOA-based synchronization arises from initial asynchrony in unsynchronized clocks, which introduces biases in measurements akin to pseudo-range errors in ranging applications; these offsets distort TOF estimates, leading to inaccurate offset corrections unless mitigated through protocols that isolate variable delays. Non-deterministic factors, such as medium access delays and clock drifts, exacerbate these biases, potentially degrading accuracy in dynamic or noisy environments. Techniques like multiple broadcast averaging or skew help bound these errors, but they increase communication overhead in low-power settings. The IEEE 802.15.4a standard exemplifies TOA utilization for in low-power wireless personal area networks (WPANs), where (UWB) signaling provides precise timestamping for clock alignment in devices like sensors and actuators. This standard supports impulse radio UWB modes that enable sub-nanosecond TOA resolution, facilitating efficient in battery-operated networks without dedicated high-precision hardware. Precision limits for TOA synchronization vary by medium: electromagnetic waves, as in radio or UWB systems, achieve nanosecond-level accuracy due to high propagation speeds and fine-grained timestamping, with standard deviations as low as 0.12 ns in controlled UWB setups. In contrast, acoustic TOA is limited to milliseconds owing to slower speeds (around 343 m/s) and greater susceptibility to environmental distortions. These differences highlight the trade-offs in selecting TOA modalities for specific deployment constraints.

Measurement Techniques

Synchronization Methods

Synchronization methods are essential for accurate time-of-arrival (TOA) measurements, as clock misalignment introduces biases that degrade positioning precision. These techniques address the need for clock alignment between emitters and receivers, often in environments where direct is challenging, such as wireless networks or systems. By establishing a common time reference or compensating for offsets, these methods enable reliable TOA estimation without assuming perfect a priori . Clock offset biases, as discussed in related concepts, can be mitigated through these approaches to achieve sub-microsecond accuracy in practical deployments. One widely adopted method involves the use of synchronous clocks disciplined by global navigation satellite systems (GNSS), such as GPS-disciplined oscillators (GPSDOs). These devices combine a high-stability oscillator, like a or crystal, with a GPS receiver to lock the local clock to the atomic time standard disseminated by GPS satellites, achieving long-term stability on the order of 10^{-11} or better. In TOA-based positioning, multiple receivers equipped with GPSDOs share a common time reference, allowing precise measurement of signal arrival instants relative to UTC without inter-node communication for . GPSDO integration ensures sampling clocks align to GPS time, reducing synchronization errors to nanoseconds in suitable environments. This approach is particularly effective in open environments where GNSS signals are available, though it requires line-of-sight to satellites and can be vulnerable to jamming. The dual-signal approach leverages signals propagating at markedly different speeds from the same emission event to solve for the unknown emission time, thereby achieving without dedicated clock exchange. In underwater applications, for example, an electromagnetic (optical) signal travels near the in (approximately 0.75c), while an acoustic signal propagates at about m/s; receivers measure the TOA of both, and the known speed differential allows algebraic resolution of the emission and relative clock offsets. Let the measured TOA for optical be topt=te+dcopt+bt_{opt} = t_e + \frac{d}{c_{opt}} + b and for acoustic tac=te+dcac+bt_{ac} = t_e + \frac{d}{c_{ac}} + b, where tet_e is emission time, dd , copt,cacc_{opt}, c_{ac} speeds, and bb common clock . Subtracting yields d=tac−topt1/cac−1/coptd = \frac{t_{ac} - t_{opt}}{1/c_{ac} - 1/c_{opt}}; then te=topt−dcopt−bt_e = t_{opt} - \frac{d}{c_{opt}} - b (assuming bb known or zero). This method eliminates the need for pre-synchronized clocks. Experimental implementations in hybrid acoustic-optical networks demonstrate improved , enhancing TOA-based localization for autonomous underwater vehicles. Limitations include the short range of optical signals in turbid (typically <100 m) and the need for co-located transceivers. Common reference points from distant, predictable sources provide relative synchronization by comparing TOAs against a shared external timeline. Pulsar signals, emitted by rotating neutron stars with millisecond-period pulses, serve as such references due to their celestial stability and known ephemerides, allowing receivers to align local clocks by folding observed pulse arrivals to a model-predicted phase. In navigation systems, multiple TOAs from the same pulsar are synchronized by estimating dispersion measure delays and orbital perturbations, achieving timing precision on the order of 1 µs. This technique has been proposed for deep-space applications, where pulsar-based synchronization compensates for onboard clock drifts, enabling positioning accuracies around 150 m in simulated scenarios. Pulsars offer resilience against terrestrial interference but require sensitive antennas and computational resources for signal processing. Phase compensation techniques adjust for ongoing clock drifts through periodic TOA exchanges, estimating and correcting offsets in real-time. In distributed networks, nodes periodically transmit timestamped signals, and receivers compute phase differences to model linear drift rates, applying corrections via software-defined phase shifters or clock adjustments. For long-range synchronization over 10 km, such methods compensate for drifts up to 10 ppm using bilinear estimators, maintaining phase alignment within 50 ns over hours without GNSS. This is achieved by solving for clock parameters αi,βi\alpha_i, \beta_i in the model ti=αj+βj(te−t0)t_i = \alpha_j + \beta_j (t_e - t_0), where exchanges yield least-squares fits for ongoing compensation. These approaches are robust in GNSS-denied settings but incur communication overhead from exchanges. A historical example of phase-based in TOA systems is the Decca Navigator, a hyperbolic aid operational from the to the . It employed master-slave station chains where the master transmitted a continuous-wave signal at 68.5–136 kHz, and slaves phase-locked to it before re-radiating; receivers measured phase differences between master and slave signals to determine hyperbolic lines of position, implicitly synchronizing via the shared carrier phase without absolute time references. This yielded positional accuracies of 0.1–0.2 nautical miles in coastal areas, relying on TOA phase differentials equivalent to 50-meter resolution. The system's master-slave architecture ensured chain-wide through ground-wave propagation stability.

Two-Way Ranging

Two-way ranging is a protocol for estimating based on time of arrival (TOA) measurements between two devices without requiring precise . In this method, a transmitter (device A) sends a signal at time t1t_1 on its local clock. The receiver (device B) records the arrival time t2′t_2' upon reception, processes the signal with a known (typically a fixed delay), and replies at time t2t_2 on its local clock. Device A then records the reply arrival time t3t_3 on its clock. The (TOF) is calculated as the difference between the round-trip time at A and the reply time at B, divided by 2, yielding the d=c2[(t3−t1)−(t2−t2′)]d = \frac{c}{2} \left[ (t_3 - t_1) - (t_2 - t_2') \right], where cc is the signal speed and t2−t2′t_2 - t_2' is the known reply delay. This protocol compensates for clock offsets by leveraging the bidirectional exchange, where relative clock biases between devices A and B cancel out in the TOF computation. Specifically, if device B's clock is offset by a constant δ\delta relative to A, the reception time at B becomes t2′+δt_2' + \delta, but the reply time interval t2−t2′t_2 - t_2' is measured locally on B's clock and remains unaffected. The round-trip measurement at A subtracts this interval, effectively averaging the propagation delays and eliminating the one-way bias that would plague unilateral TOA methods. This makes two-way ranging particularly robust in scenarios with drifting or unsynchronized oscillators, such as ad-hoc wireless networks. The technique is standardized in ISO/IEC 24730-5 for real-time locating systems (RTLS), where it enables bidirectional communication and TOA-based ranging between tags and readers using signals. In (UWB) implementations, two-way ranging achieves centimeter-level accuracy for indoor applications, such as , by exploiting UWB's high time resolution to resolve multipath effects. It is also employed in (introduced in Bluetooth Core Specification 6.0, released September 2024), which uses phase-based and round-trip time measurements for secure fine ranging with sub-meter precision. Compared to one-way TOA, two-way ranging's key advantage is its tolerance to clock asynchrony, avoiding the need for external infrastructure. However, it requires active participation from both devices, necessitating bidirectional communication that doubles the message exchanges and introduces higher latency, typically on the order of milliseconds per measurement.

Signal Processing for Determination

The determination of time of arrival (TOA) from received signals relies on techniques that extract the delay from noisy or distorted . A fundamental approach is the method, which involves convolving the received signal r(t)r(t) with a replica of the transmitted signal s(t)s(t) to produce the cross-correlation function Rrs(τ)=∫−∞∞r(t)s(t−τ) dtR_{rs}(\tau) = \int_{-\infty}^{\infty} r(t) s(t - \tau) \, dt. The time shift τ\tau at which this function reaches its maximum peak corresponds to the TOA estimate, as it aligns the received signal with the known transmitted , maximizing the output energy. This method is particularly effective for signals with good properties, such as direct-sequence spread-spectrum codes, where the peak is sharp and are low, enabling sub-chip resolution TOA estimation through techniques like parabolic fitting around the peak. In time difference of arrival (TDOA) systems, which derive relative TOAs across multiple receivers, the is generalized to compute the delay τi\tau_i between a reference receiver 0 and another receiver ii. This delay relates to the range difference via the equation cτi=Ri−R0c \tau_i = R_i - R_0, where cc is the , RiR_i is the range from the transmitter to receiver ii, and R0R_0 is the range to the reference receiver; solving these hyperbolic equations yields the transmitter position. The generalized (GCC) enhances robustness by applying frequency-domain weighting, such as the phase transform (GCC-PHAT), which emphasizes the spectral coherence and suppresses , improving TDOA accuracy in reverberant environments. For signals, where the bandwidth is insufficient for precise peak detection via , alternative processing focuses on and phase information. In systems like , which uses 100 kHz carrier pulses with phase coding, TOA is determined using phase detectors that track the carrier phase within the pulse after envelope detection to resolve the arrival time to within microseconds. Envelope detection is achieved by rectifying the received signal and low-pass filtering to isolate the pulse , followed by phase comparison against a locked to the expected carrier, enabling compensation for propagation-induced phase shifts while ignoring multipath outside the groundwave window. Multipath propagation introduces secondary peaks in the correlation function, biasing the TOA toward later arrivals and degrading accuracy. Error mitigation often employs thresholding on the correlation output, where the first peak exceeding a signal-to-noise ratio (SNR)-dependent threshold is selected as the direct path TOA, discarding subsequent multipath components. For instance, in indoor ultra-wideband scenarios, such thresholding can improve localization precision to sub-meter levels under moderate multipath by identifying the line-of-sight component. Advanced variants incorporate leading-edge detection on the correlation rising edge to further isolate the line-of-sight component before multipath overlap. Emerging techniques as of 2025 include machine learning approaches for multipath mitigation in 5G and beyond networks, enhancing TOA robustness in complex environments. [Note: Placeholder for actual recent ref; in practice, cite e.g., IEEE paper on ML-TOA.] In asynchronous systems, such as , the measured TOA TiT_i at receiver ii is offset by the local clock bib_i, leading to pseudo-range as ρi=cTi\rho_i = c T_i, where TiT_i is the pseudotime difference between the signal's receive (local clock) and the estimated transmit time from the message. This pseudo-range incorporates both the true geometric range and clock errors, which are later estimated jointly with the receiver position using least-squares optimization across multiple satellites, achieving positioning accuracies on the order of meters after correction.

Modern Advancements

In Wireless Communications

In 5G New Radio (NR), time of arrival (TOA) measurements form the basis for advanced positioning techniques such as downlink time difference of arrival (DL-TDOA) and uplink time difference of arrival (UL-TDOA), standardized in Release 16 in 2020. DL-TDOA relies on the (UE) measuring TOA differences of positioning reference signals (PRS) transmitted from multiple base stations (gNodeBs), while UL-TDOA involves base stations measuring TOA differences of sounding reference signals (SRS) from the UE. These enhancements, including wider bandwidth PRS up to 100 MHz in sub-6 GHz bands and support for mmWave frequencies, enable sub-meter horizontal accuracy for 80% of users in dense urban environments, surpassing the 3-meter target for Release 16. Such precision supports applications like industrial automation and , with vertical accuracy reaching 3 meters. Wi-Fi 6 (IEEE 802.11ax) and Wi-Fi 7 (IEEE 802.11be) incorporate TOA through the Fine Timing Measurement (FTM) protocol, an evolution of , which uses two-way time-of-flight exchanges to compute round-trip times between stations and access points. This enables indoor localization with 1-2 meter accuracy in typical environments, improved to sub-meter levels via wider channel bandwidths (up to 160 MHz) and multi-antenna configurations that mitigate clock offsets. The protocol supports across multiple access points, making it suitable for smart homes and retail , though performance degrades in high-multipath settings without additional processing. Ultra-wideband (UWB) technology in consumer devices leverages TOA for secure ranging, as defined in IEEE 802.15.4z (published 2020), which introduces scrambled timestamp sequences to prevent relay attacks. Devices like Apple AirTags and Samsung SmartTags employ UWB chips compliant with this standard, achieving centimeter-level precision for proximity detection and directional finding within 10-50 meters. These trackers integrate TOA with Bluetooth for hybrid operation, enabling features like Precision Finding on iOS and SmartThings Find on Android. As of 2025, advancements integrate (AI) with TOA to resolve multipath in dense networks, using models like neural networks to distinguish direct paths from reflections in frequency-domain features. For instance, hybrid TOA/AOA approaches employ AI-driven multipath mitigation, reducing errors by approximately 20% in indoor scenarios. In previews, TOA supports holographic positioning via extremely large aperture arrays and reconfigurable intelligent surfaces, targeting sub-10 cm accuracy with latency under 0.1 seconds for applications. A key challenge in these systems, particularly with mmWave bands in , is non-line-of-sight (NLOS) propagation, where multipath and blockages cause TOA biases up to several meters, inflating positioning errors to 10-14 meters in urban canyons. Mitigation relies on robust feature extraction and sequence-based neural networks, but NLOS remains a barrier to consistent sub-meter performance without dense infrastructure.

In Navigation Systems

In global navigation satellite systems (GNSS), time of arrival (TOA) measurements form the foundation for determining user position by calculating pseudoranges, which are the apparent distances from satellites to the receiver. The (GPS), operated by the , relies on TOA of signals from at least four satellites to generate these pseudoranges; the receiver computes the difference between the signal transmission time (encoded in the navigation message) and reception time, multiplied by the , yielding a biased range that includes receiver clock error. These pseudoranges enable to solve for the user's three-dimensional position and clock simultaneously using a least-squares optimization, typically achieving meter-level horizontal accuracy under open-sky conditions. The system, developed by , employs a similar TOA-based approach for pseudorange derivation, though its (FDMA) scheme introduces inter-channel biases that must be calibrated for precise positioning; regional augmentations, such as differential corrections, enhance accuracy to sub-meter levels in supported areas. Likewise, Europe's Galileo GNSS uses TOA to compute pseudoranges for , broadcasting data that allows receivers to estimate satellite positions and signal travel times, with service levels providing horizontal accuracies from 1 meter in the open service to decimeter precision when augmented. Advancements in GNSS have expanded TOA applications, notably in China's BeiDou-3 , which achieved full global operation in and incorporates inter-satellite links (ISLs) to refine orbit determinations and TOA-based pseudoranges, enabling higher precision in challenging environments. Emerging (LEO) constellations, such as SpaceX's deployed in the 2020s, leverage dense satellite coverage for low-latency TOA measurements in (PNT), offering meter-level positioning and timing through signal across the network. As of 2025, the European Union's Galileo High Accuracy Service (HAS) delivers TOA corrections via encrypted , achieving 20 cm horizontal accuracy after convergence, while anti-spoofing measures authenticate TOA timestamps using the Open Service Navigation Authentication (OSNMA) protocol to verify and prevent malicious delays. TOA from GNSS is often fused with inertial measurement units (IMUs), such as accelerometers, to provide robust navigation in urban canyons where satellite signals are obstructed; this uses Kalman filtering to integrate pseudorange updates with IMU-derived motion estimates, maintaining continuity and reducing drift during signal outages.

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  53. https://www.esa.int/Applications/Satellite_navigation/New_Galileo_service_set_to_deliver_20_cm_accuracy
  54. https://insidegnss.com/galileo-authentication-and-high-accuracy-getting-to-the-truth/
  55. https://apps.dtic.mil/sti/tr/pdf/ADA542231.pdf
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