A Link Quality Indicator (LQI) Based Closed-Form Localization Framework for Vehicular Ad Hoc Networks (VANETs)

1  Introduction

A vehicular ad hoc network (VANET) enables communication between vehicles and roadside infrastructure [1]. It uses vehicle-to-vehicle (V2V), vehicle-to-infrastructure (V2I) and vehicle-to-everything (V2X) communication. These links form a key part of Intelligent Transportation Systems (ITS). ITS services include safety alerts, route guidance, traffic monitoring, cooperative driving, and emergency response. Each service depends on vehicle position information that is accurate, timely and reliable [2]. GPS/GNSS positioning performs well in open-sky areas. The situation changes in dense urban roads. Its accuracy drops in urban corridors, tunnels, underground roads, and non-line-of-sight (NLOS) environments. In these places, satellite signals are often blocked, reflected, or weakened by surrounding obstacles [3]. For this reason, infrastructure-assisted wireless localization becomes a useful option for VANET positioning. Roadside Units (RSUs), anchor nodes, and inter-vehicle links can provide measurements such as Time of Arrival (TOA), Time Difference of Arrival (TDOA), Round Trip Time (RTT), Received Signal Strength (RSS), and Link Quality Indicator (LQI) [4].

Among these measurements, LQI is attractive because it is obtained at the communication layer and does not require separate ranging hardware. Even so, practical limitations are still faced by LQI-based, RSS-based, and RSU-assisted localization methods. Many studies assume ideal network conditions or fully connected topologies. Real VANET communication is less predictable. Link quality changes with communication range, packet reception probability, interference, fading, shadowing, and temporary obstruction [5]. Reproducibility is another concern, where some studies have converted LQI values into distance estimates but do not report the numerical calibration parameters used in that conversion. In addition, several evaluations depend mainly on synthetic mobility and compare the proposed approach only with basic LS and WLS estimators. This gives a narrow view of performance when the method must also be compared with filtering, cooperative, fusion-based, and learning-based localization baselines [6]. To address these issues, this study presents a calibrated LQI-based closed-form localization method for partially connected RSU-assisted VANETs. The method accepts only links that satisfy range, LQI, and packet-reception requirements. It then calibrates the LQI-to-range model using numerical regression parameters. Accepted LQI samples are then converted into distance estimates and are passed to a variance-aware weighted least squares estimator. A scalar consistency refinement step then improves the geometric agreement of the estimated position, while the Cramér-Rao Lower Bound is derived and used as a theoretical accuracy reference for evaluating the final estimate.

The proposed method is evaluated in two settings. First, it uses Monte Carlo simulations to study wireless impairments, anchor availability, RSU geometry, and traffic density. Secondly, it uses the NGSIM US-101 real-world mobility trace; here, the actual vehicle trajectories are used as ground truth. Calibrated model-generated LQI observations are then used for localization testing [7]. These settings examine the estimator under controlled wireless conditions and realistic freeway mobility patterns.

1.1 Vehicle to Vehicle

V2V communication allows vehicles to exchange position, speed, heading, and driving-status information through a dedicated wireless network [8]. This information can reduce collision risk by supporting driver warnings and protective actions. These actions include braking and deceleration when hazardous situations are detected [9,10]. For this reason, V2V communication is widely treated as a key safety component in connected-vehicle and ITS programs [11].

1.2 Vehicle to Infrastructure (V2I)

In the V2I paradigm, vehicles communicate with roadside infrastructure. This infrastructure may include RSUs, RFID-enabled systems, smart parking infrastructure, traffic lights, street lighting, traffic signage, and roadside cameras or sensors [12,13]. This bidirectional communication supports traffic monitoring, safety services, navigation assistance, and infrastructure-supported localization [14,15]. Short-range V2V and V2I communication commonly relies on DSRC-based vehicular communication in the 5.9 GHz band [16], as illustrated in Fig. 1.

Figure 1: Conceptual structure of VANETs adapted from Cui et al. [17].

1.2.1 Localization Background

Localization determines a vehicle’s position in two- or three-dimensional space. In VANETs, manual localization is impractical because of high mobility, changing network topology, vehicle density, and scalability constraints [18]. Automated localization is therefore required, especially when GPS/GNSS is unreliable. In infrastructure-supported scenarios, vehicles can estimate or refine their positions using RSUs or anchors with known coordinates. This process can also be strengthened through measurements shared by neighboring vehicles [19]. VANET localization methods are commonly classified as centralized or distributed and as range-based or range-free, as illustrated in Fig. 2.

Figure 2: Localization in VANETs (Source: Ahmad et al. [20]; reproduced/adapted with permission under CC BY 4.0).

1.3 Primary Contributions

This study presents a calibrated LQI-based closed-form localization framework for partially connected RSU-assisted VANETs. The main contributions are as follows:

•   A reproducible LQI-to-range calibration model is developed using numerical regression parameters. It also reports residual statistics and confidence intervals.

•   A practical VANET localization model is formulated for partial connectivity. It uses communication- radius, LQI-threshold, and packet-reception constraints.

•   A closed-form localization estimator is derived by combining LQI-based ranging, variance-aware WLS, and scalar consistency refinement. The CRLB is used as the theoretical accuracy benchmark.

•   The framework is validated through Monte Carlo simulations and NGSIM US-101 trace-driven testing. It is compared with classical, filtering, cooperative, fusion-based, and learning-based localization baselines.

2  Background Study

2.1 Localization in VANETs

Vehicle localization in VANETs generally involves three stages: measurement acquisition, ranging, and position estimation. When GPS or GNSS is degraded or unavailable, RSU-assisted localization can provide an alternative. It uses infrastructure nodes with known positions and radio measurements collected from vehicular communication links [21]. These measurements may include TOA, TDOA, RTT, RSS, LQI, or combinations of multiple indicators.

Recent VANET localization methods can be grouped into RSU-assisted radio localization, cooperative V2V/V2I localization, filtering-based localization, multi-sensor fusion, learning-based localization, and emerging V2X or 5G/6G positioning [22]. RSU-assisted RSS or LQI localization is cost-effective because it uses communication-layer measurements. However, its accuracy depends on calibration quality, RSU placement, link availability, and propagation conditions. Cooperative localization improves spatial diversity by using neighboring vehicles and infrastructure. However, it increases message exchange and depends on reliable communication links.

Filtering-based methods, such as EKF, UKF, and particle filtering, improve temporal continuity. Their performance depends on the accuracy of the motion and noise models [23]. Multi-sensor fusion combines GNSS, INS, RSS, camera, LiDAR, or map information to improve robustness. However, this improvement is often accompanied by higher hardware cost and greater computational complexity. Learning-based methods can model nonlinear measurement-position relationships, but their performance depends on representative training data and may generalize poorly across different road layouts, RSU deployments, and propagation environments [24].

Real-time localization systems usually operate over short discrete update intervals. They are often supported by Kalman filtering, map matching and sensor fusion. When GNSS becomes unreliable, localization reliability, availability, and continuity can be improved through multi-sensor fusion and EKF-based methods [25]. Wireless positioning systems may also estimate distance to reference nodes through round-trip-time measurements [26]. In cooperative tracking scenarios, V2V and V2I information sharing can further refine state estimates. This is effective when neighboring nodes are reliable, and communication links are stable.

2.2 Roadside Unit Telemetry

RSU-assisted localization uses roadside infrastructure with known coordinates to support vehicle positioning in VANET environments. Its effectiveness depends on RSU density, anchor geometry, communication range, and propagation conditions [27]. When RSUs are not carefully deployed, the anchor layout can become less favorable, and localization accuracy may suffer. Poor RSU placement can also increase the likelihood of geometric dilution of precision. In addition, biased distance estimates for the connections are often introduced by NLOS propagation and multipath effects [28]. The factors discussed make reliable vehicle localization more challenging in practical deployments.

Cooperative localization combines positioning methods, data fusion, and V2V or V2I communication to improve vehicle positioning accuracy in dynamic VANET scenarios. By sharing these measurements between vehicles and infrastructure, cooperative methods increase the available positioning information and support more stable localization in vehicles [29]. They can also help them to reduce local measurement errors when communication links remain stable. Recent cooperative and optimization-based methods further improve localization through shared observations, distance constraints, and anchor-geometry optimization [30]. Still, their performance can drop in sparse traffic, high packet-loss conditions, or cases where neighboring vehicles have uncertain positions.

RSU placement remains an important design issue because infrastructure geometry directly affects localization accuracy, but when RSUs or anchor nodes are poorly distributed, the estimation problem becomes less well-conditioned, and the resulting position estimates can become less reliable [31]. For this reason, GDOP-type measures are commonly used to describe how reference-node geometry influences positioning performance [32]. Closed-form GDOP analyses and deployment-focused formulations have also been used to guide base-station and anchor placement. These methods help improve localization when received signals are strongly affected by deployment geometry [33]. However, many RSU-assisted localization studies still rely on simplified connectivity assumptions or ideal anchor availability. Such assumptions limit their applicability in dense, sparse, and partially connected VANET environments.

2.3 VANET Location Estimation

Accurate vehicle location data is essential for safety warnings, navigation, traffic management, and cooperative driving applications [34,35]. Modern vehicle positioning systems update state estimates in real time over short intervals [36]. Cooperative vehicle localization can be solved using distance constraints and convex optimization. Vehicle positions can also be estimated from trusted neighboring nodes or infrastructure with known locations. In addition, GNSS/GPS errors can be reduced through fused V2V and V2I information [29,31,37]. In such settings, V2V and V2I fusion can improve positioning performance [31].

Recent cooperative localization methods combine shared measurements, prior information, and collaboration among nearby vehicles. These methods can improve position estimates when neighboring vehicles exchange useful localization evidence [38]. They also exploit data correlation, multiple localization cues, and different vehicular communication modes. However, their main weakness remains the strong dependence on communication reliability. In dense VANETs, additional message exchange may also reduce scalability and increase communication overhead [39,40].

Hybrid GNSS/INS and multi-sensor localization methods have also received considerable research attention, while INS/GNSS integrations can preserve localization continuity during short periods of GNSS unavailability. Yet inertial drift still needs correction from GNSS or another external measurement source [41]. Visual and map-based localization methods have the ability to convert camera and map information into useful localization cues. These methods can support reliable pose estimation in complex road environments [42]. Multi-sensor fusion can still support accurate positioning when signal conditions become degraded [43]. In difficult environments such as underground parking areas and obstacle-rich roads, localization can be improved through semantic-map and topological frameworks [44]. These approaches offer strong robustness, although additional sensors, synchronization, and computational resources are usually required.

Machine-learning and deep-learning-based localization methods can improve robustness in nonlinear and noisy environments [45]. They are useful when radio behavior is difficult to model analytically; however, they require representative training data to retrain the need when road geometry, RSU placement, or propagation conditions change. High-accuracy localization can also be supported by emerging 5G/6G, NR-V2X, and advanced V2X positioning methods. These methods are especially useful when combined with cooperative sensing and infrastructure support [2,16]. However, they may require upgraded infrastructure, dense deployment, specialized devices, or accurate synchronization. In contrast, calibrated LQI-based localization can use low-cost link-quality information already available from communication hardware.

2.4 Validation Approaches in VANET Localization

Validation methods in VANET localization can be grouped into simulation-only validation, trace-driven validation, and hardware/testbed validation. Simulation-only validation is useful for controlled testing. It can evaluate channel noise, fading, packet loss, NLOS propagation, anchor failure, RSU placement, and traffic density. However, purely synthetic simulations may not fully capture real vehicle movement. They may also miss lane-changing behavior, acceleration patterns, and traffic-density variation.

Trace-driven validation improves realism by using real vehicle trajectories collected from road environments. Datasets such as NGSIM provide real vehicle positions, speeds, acceleration, and lane information. These data make it possible to test localization algorithms under realistic mobility patterns. In this work, controlled Monte Carlo simulations evaluate wireless impairments and deployment conditions. NGSIM US-101 trace-driven validation then tests the proposed framework under real freeway vehicle movement. Since NGSIM does not include physical LQI/RSS packet measurements from RSUs or onboard units, only the vehicle trajectories are taken from the real-world dataset. The LQI observations are generated using the calibrated LQI-distance model.

Hardware/testbed validation provides the strongest experimental realism. It uses physical RSU/OBU devices, measured LQI/RSS packet logs, and field experiments under real propagation conditions. Such validation is especially important for highway, urban-canyon, tunnel, and NLOS environments. However, hardware-based experiments require deployment cost, device synchronization, and controlled field access. These requirements make large-scale hardware validation difficult.

2.5 Summary of Existing Gaps

Table 1 summarizes the main localization categories used in VANETs. Existing studies provide useful foundations for GPS/GNSS localization, RSU-assisted positioning, cooperative localization, filtering, sensor fusion, INS/GNSS integration, and anchor-based localization. However, several gaps remain. Many works do not report numerical LQI calibration parameters. Some assume an ideal or fully connected topology. Others compare only with limited baselines or rely only on synthetic mobility. Several studies also report only RMSE. They do not include statistical significance testing, confidence intervals, ablation analysis, sensitivity analysis, runtime comparison, or scalability evaluation.

The present work addresses these gaps by proposing a calibrated LQI-based closed-form localization framework for partially connected RSU-assisted VANETs. The method combines numerical LQI-to-range calibration, link-availability filtering, variance-aware WLS, scalar consistency refinement, and CRLB benchmarking. It also includes advanced baseline comparison, statistical validation, ablation testing, sensitivity analysis, runtime/scalability evaluation, and NGSIM US-101 trace-driven validation.

3  Research Methodology

This section presents the proposed calibrated LQI-based closed-form localization framework for partially connected RSU-assisted VANETs. The objective is to estimate the two-dimensional position of each target vehicle using LQI observations collected from RSUs or anchor vehicles with known coordinates. The methodology covers system modeling, partial-connectivity modeling, LQI-to-range calibration, closed-form WLS localization, CRLB analysis, workflow implementation, simulation setup, benchmark comparison, trace-driven validation, ablation testing, sensitivity analysis, complexity evaluation, and reproducibility checks. The notation used in the methodology is summarized in Table 2.

3.1 System Model and VANET Assumptions

The VANET is modeled as a two-dimensional road network containing target vehicles and fixed RSUs or anchor vehicles. Let 𝒯 denote the set of vehicles to be localized and 𝒜 denote the set of anchors with known coordinates. The target-anchor distance is defined as

T={T1,T2,…,TV},A={e1,e2,…,eM},dij=‖ci−ej‖2=(xi−xj)2+(yi−yj)2.(1)

In Eq. (1), ci=[xi,yi]T is the unknown position of target vehicle i, while ej=[xj,yj]T is the known position of anchor j. This distance is the geometric quantity that the localization algorithm estimates indirectly from LQI-derived range measurements. To represent practical VANET operation, full connectivity is not assumed. A link is accepted only when it satisfies communication-radius, LQI, and packet-reception constraints:

aij={1,dij≤Rc, Zmin≤Zij≤Zmax, ρij≥ρmin,0,otherwise,Vi={j∈{1,…,M}:aij=1},Mi=|Vi|.(2)

Eq. (2) defines the usable anchor set for each target vehicle. Here, aij is the binary link-availability indicator, Rc is the communication radius, Zij is the measured LQI, ρij is the packet reception probability and 𝒱i is the set of visible anchors. A valid two-dimensional estimate requires at least three non-collinear visible anchors. The vehicle motion between localization snapshots is described as

ci(t+Δt)=ci(t)+vi(t)Δt+12ai(t)Δt2,vi(t+Δt)=clip(vi(t)+ai(t)Δt, vmin, vmax).(3)

Eq. (3) updates vehicle position and velocity between successive simulation steps. The clipping function restricts the velocity to the selected scenario speed range. Within a single localization snapshot, the vehicle is treated as quasi-static because the update interval is short. The wireless channel before LQI conversion is modeled as

PLij(dij)=L0(d0)+10nlog10⁡(dijd0)+Xijsh+XijNLOS+Fij+Iij.(4)

Eq. (4) describes the propagation loss between a vehicle and an anchor. The first two terms model distance-dependent path loss, while Xijsh, XijNLOS, Fij and Iij represent shadowing, NLOS attenuation, fading, and interference or collision degradation. These terms allow the simulations to represent highway, urban, and tunnel/NLOS environments. The main assumptions are summarized in Table 3.

3.2 LQI-to-Range Calibration and Measurement Model

The proposed framework uses a calibrated logarithmic mapping to convert LQI values into distance estimates. The LQI measurement model is defined as

Zij=Z0−10αlog10⁡(dijd0)+εijZ,εijZ∼𝒩(0,σℓ2),Z¯q=Z0−10αxq+εqZ,xq=log10⁡(dqd0).(5)

Eq. (5) states that LQI decreases logarithmically with distance. Here, Z0 is the reference LQI at distance d0, α is the attenuation coefficient and εijZ is the LQI-domain measurement error. The averaged calibration value Z¯q is used to estimate the model parameters from calibration samples. The calibration parameters are estimated using ordinary least squares:

[Z^0−10α^]=(XTX)−1XTz,X=[1x11x2⋮⋮1xQ].(6)

Eq. (6) fits the reference LQI Z^0 and attenuation factor α^ from the calibration data. This makes the LQI-to-range conversion reproducible because the numerical calibration parameters are explicitly reported. After calibration, each accepted LQI value is converted into a range estimate:

d^ij=d010Z^0−Zij10α^,σd,ij2≈(ln⁡1010α^d^ij)2σZ,ij2+σanc2.(7)

Eq. (7) provides both the LQI-derived distance and its range-domain variance. The variance increases with LQI uncertainty and estimated distance; therefore, unreliable links receive lower weight in the WLS localization stage. The calibration setup and statistics are summarized in Tables 4 and 5.

3.3 Closed-Form LQI-WLS Localization Estimator

For each visible anchor j∈𝒱i, the calibrated LQI-derived range is modeled as

gij=d^ij=dij+ηij,ηij∼𝒩(0,σd,ij2).(8)

Eq. (8) connect the calibration stage with localization, observed range gij is treated as the true distance plus range-domain noise, whose variance is obtained from the LQI uncertainty. Squaring the range equation gives

gij2=‖ci−ej‖2+δij=‖ci‖2−2ejTci+‖ej‖2+δij, Yij+θi=bjTci+δij, Yij=‖ej‖2−gij2,bjT=2ejT.(9)

Eq. (9) convert the nonlinear distance relation into an affine form by introducing θi=‖ci‖2, the transformation enables a closed-form WLS estimator instead of iterative nonlinear optimization. Stacking all visible-anchor equations gives

Yi+θi1=Bici+δi,(10)

where

Yi=[Yij1Yij2⋮YijMi],Bi=2[ej1Tej2T⋮ejMiT],δi=[δij1δij2⋮δijMi].(11)

Eqs. (10) and (11) combine all usable anchor measurements for target i. The matrix Bi captures anchor geometry, while Yi contains the transformed range observations. The WLS covariance matrix and fixed-θi solution are defined as

Wi=diag(σδ,ij12,σδ,ij22,…,σδ,ijMi2),σδ,ij2≈4gij2σd,ij2+2σd,ij4+εw,c^i(θi)=(BiTWi−1Bi+λI)−1BiTWi−1(Yi+θi1).(12)

Eq. (12) assigns a smaller influence to links with larger range uncertainty. The small constant εw prevents numerical instability, and λ regularizes the solution when anchor geometry is weak or nearly ill-conditioned. The WLS solution can be separated into a nominal term and a scalar correction:

c^i(θi)=Gi+κiθi,Gi=(BiTWi−1Bi+λI)−1BiTWi−1Yi,κi=(BiTWi−1Bi+λI)−1BiTWi−11.(13)

In Eq. (13), Gi is the nominal coordinate estimate and κi indicates how the auxiliary scalar θi modifies the estimate. This decomposition reduces the remaining unknown to a scalar refinement problem. The consistency condition is imposed as

θi=‖Gi+κiθi‖2.(14)

Eq. (14) ensures that θi remains equal to the squared norm of the estimated position. Expanding it produces the quadratic root-selection rule:

‖κi‖2θi2+(2κiTGi−1)θi+‖Gi‖2=0,θ^i=arg⁡minθ∈Θi(Yi+θ1−Bi(Gi+κiθ))TWi−1(Yi+θ1−Bi(Gi+κiθ)).(15)

Eq. (15) selects the valid real root that gives the smallest weighted residual. This step improves geometric consistency without introducing an iterative estimator. The final estimate and residual score are computed as

c^i=Gi+κiθ^i,ri=1Mi‖Wi−1/2(Yi+θ^i1−Bic^i)‖22.(16)

Eq. (16) measures the normalized weighted mismatch between the estimated position and the anchor observations. A localization result is accepted only if ri≤rmax, the estimated coordinate lies inside the deployment area, and the condition number of BiTWi−1Bi is below χmax.

3.4 Cramér-Rao Lower Bound

The CRLB is used as a theoretical benchmark for the best achievable localization accuracy under the adopted LQI measurement model. The expected LQI, its position gradient, and the Fisher information matrix are

μij(ci)=Z0−10αlog10⁡(‖ci−ej‖d0),(17)

qij=∇ciμij=−10αln⁡10ci−ejdij2,(18)

Ji=∑j∈ViqijqijTσℓ,j2.(19)

Eq. (17) gives the noiseless LQI predicted at a given position. Eq. (18) measures how sensitive the LQI is to small position changes. Eq. (19) accumulates the information contributed by all visible anchors. For equal LQI noise variance, the Fisher information matrix components are

Ji=[JxxJxyJxyJyy],Jxx=δF∑j∈Vi(xi−xj)2dij4,Jyy=δF∑j∈Vi(yi−yj)2dij4,Jxy=δF∑j∈Vi(xi−xj)(yi−yj)dij4.(20)

Eq. (20) shows how anchor geometry affects information in the x and y directions. A better geometric spread produces a better-conditioned Fisher matrix and a smaller theoretical error bound. The LQI-domain sensitivity coefficient and scalar CRLB are

δF=(10ασℓln⁡10)2,CRLBi=tr(Ji−1)=Jxx+JyyJxxJyy−Jxy2.(21)

Eq. (21) gives the minimum achievable position-error variance under the assumed LQI noise model. If Ji is singular or nearly singular, the anchor geometry is treated as insufficient for reliable localization.

3.5 Workflow and Implementation-Level Algorithm

The complete computational workflow is summarized in Fig. 3. The workflow begins with LQI packet acquisition and link filtering. Accepted LQI measurements are converted into range estimates using the calibrated model. The resulting ranges are processed by the WLS estimator, refined by the scalar consistency step, and checked using residual and geometry constraints. Finally, localization accuracy, runtime, throughput, confidence intervals, and CRLB gap are reported.

Figure 3: Workflow of the proposed LQI-based VANET localization framework. The workflow includes LQI acquisition, link filtering, calibration, range estimation, WLS localization, scalar consistency refinement, validation, CRLB computation, and performance evaluation.

Algorithm 1 provides the implementation-level steps of the proposed framework.

3.6 Simulation Environment and Scenario Configuration

The Monte Carlo evaluation is conducted under highway, urban, and tunnel/NLOS VANET scenarios. The highway scenario uses a 1000 m × 500 m area, three lanes per direction, speeds of 80–120 km/h, a 300 m communication radius, log-normal channel behavior, 3 dB shadowing, Rician fading, no additional NLOS loss, packet loss of 0.05, and collision probability of 0.02. The urban scenario uses an 800 m × 800 m area, two lanes per direction, speeds of 30–60 km/h, a 200 m communication radius, 4 dB shadowing, Rayleigh fading, 10 dB NLOS loss, packet loss of 0.10, and collision probability of 0.05. The tunnel/NLOS scenario uses a 1000 m × 20 m road segment, two lanes per tube, speeds of 80–120 km/h, a 100 m communication radius, 6 dB shadowing, Nakagami fading, 15 dB NLOS loss, packet loss of 0.20, and collision probability of 0.08. For all scenarios, V∈{10,50,100} target vehicles and M=4 RSU anchors are used. Vehicle mobility is generated using SUMO Krauss car-following with LC2013 lane-changing behavior. LQI values are generated in the range −70 to −30 dBm with 1 dB resolution, and beaconing is configured at 10 packets/s/vehicle with 300 bytes per packet. The simulation duration is Tsim=1 s, the update step is Δt=0.1 s, the number of Monte Carlo trials is NMC=1000, and the random seed is fixed to 42. The same random seed sequence is used for all methods, so the proposed estimator and all baselines experience identical vehicle layouts, RSU positions, packet outcomes, LQI samples, fading, shadowing, and packet-loss events. This ensures fair comparison across methods. The configuration is summarized in Table 6.

3.7 Benchmark Methods, Evaluation Metrics and Statistical Validation

The proposed LQI-WLS estimator is compared with LS, WLS, RSS/RSSI-WLS, EKF, UKF, PF, cooperative localization, GNSS/INS/RSS fusion, and ML-based localization. All methods use the same anchor coordinates, packet availability, and measurement-noise realizations. LS uses unweighted multilateration, WLS uses σd,ij2 without scalar refinement, RSS/RSSI-WLS uses L0=47.9 dB and n=2.60, EKF uses xk=[xk,yk,vx,k,vy,k]T with σa=2, UKF uses α=10−3, β=2 and κ=0, PF uses Np=1000 particles with systematic resampling, the cooperative method uses the top-3 LQI neighbors, GNSS/INS/RSS uses σGNSS=3 m with tunnel outage and ML localization uses a random forest with 200 trees and a 70/30 train-test split. The localization error and aggregate RMSE are computed as

ei(r)=‖c^i(r)−ci(r)‖2,RMSE=1Nsuc∑r=1NMC∑i=1Vsi(r)(ei(r))2,Nsuc=∑r=1NMC∑i=1Vsi(r).(22)

Eq. (22) measures the Euclidean localization error and its aggregate RMSE over all successful estimates. The binary variable si(r) indicates whether the estimate for vehicle i in trial r is valid. Reliability and runtime metrics are defined as

SR=NsucNMCV,Thr=NsucNMCTsim,Tavg=1Nsuc∑r=1NMC∑i=1Vsi(r)τi(r).(23)

Eq. (23) defines the success ratio, throughput, and average runtime. These metrics measure both localization reliability and real-time computational feasibility. Percentage improvement over a baseline is computed as

Improvementerror(%)=Metricbaseline−MetricproposedMetricbaseline×100,ImprovementThr(%)=Thrproposed−ThrbaselineThrbaseline×100.(24)

Eq. (24) is used with lower-is-better metrics such as RMSE and higher-is-better metrics such as throughput. This separates accuracy improvement from throughput improvement. For each scenario and method, the mean, standard deviation, median, 90th percentile, and 95% confidence interval are reported. The confidence interval is computed as

CI95%=x¯±1.96sxNMC,(25)

where x¯ is the sample mean and sx is the sample standard deviation. Statistical significance is tested using paired comparisons because all methods use identical layouts, trajectories, and channel realizations. A paired t-test is used for approximately normal paired differences, while the Wilcoxon signed-rank test is used otherwise. For multiple-method comparisons, repeated-measures ANOVA or the Friedman test is applied. Results are considered significant when p<0.05 with Cohen’s d or Cliff’s delta reported as the effect size. Benchmark methods and evaluation metrics are summarized in Tables 7 and 8.

3.8 Trace-Driven Validation Dataset

To complement the synthetic MATLAB/SUMO evaluation, trace-driven validation is performed using the NGSIM US-101 vehicle trajectory dataset [46]. This dataset contains real freeway mobility traces recorded on U.S. Highway 101 in Los Angeles, California, from 7:50–8:05 AM on June 15, 2005. These trajectory data provide a realistic basis for testing the proposed localization method, although the recorded scenario remains limited to one freeway segment and one observation period. It provides vehicle position, speed, acceleration, and lane ID at 10 Hz but does not include physical LQI/RSS packet measurements. Therefore, the vehicle trajectories are used as ground truth, while LQI observations, packet-loss masks, and RSU-to-vehicle ranges are generated using the calibrated LQI-distance and highway-channel models. The trace coordinates are converted to metres and normalized into a local 640 m × 30 m freeway plane. The longitudinal coordinate is mapped to [0,640] m, while the lateral coordinate is mapped to [0,30] m. Four fixed RSUs are placed at (80,0), (240,30), (400,0) and (560,30) m. This staggered deployment avoids collinear anchor geometry and supports valid two-dimensional localization with at least three non-collinear available RSUs. The NGSIM target-anchor distance and generated LQI observation are defined as

dijNGSIM=(xi−xj)2+(yi−yj)2,ZijNGSIM=Z0−10αlog10⁡(dijNGSIMd0)+εijZ,εijZ∼𝒩(0,σℓ2).(26)

Eq. (26) uses real vehicle coordinates to calculate RSU-to-vehicle distances, while the calibrated LQI model generates the corresponding LQI observations. A localization attempt is successful only when at least three non-collinear RSUs remain available after LQI, range, and packet-reception filtering. The proposed estimator and all baselines use the same traces, RSU coordinates, generated LQI observations, and packet-loss masks. The NGSIM setup is summarized in Table 9.

3.9 Ablation Study Design

The ablation study isolates the contribution of each component in the proposed LQI-WLS localization framework. All variants use the same vehicle positions, anchor locations, packet-loss realizations, and channel conditions as the full method. Performance is evaluated using RMSE, median error, 90th percentile error, success ratio, throughput, runtime, and CRLB gap. The difference between the full method and each variant shows the contribution of calibration, WLS weighting, scalar refinement, link filtering, RSU cooperation, and packet-loss modeling. The ablation variants are summarized in Table 10.

3.10 Sensitivity Analysis Design

The sensitivity analysis evaluates the robustness of the proposed localization framework under changing deployment and channel conditions. In each experiment, one factor is varied while all other parameters remain fixed at their default values from Table 6. The outputs include RMSE, success ratio, 90th percentile error, throughput, and runtime. This design identifies whether performance degradation is mainly caused by anchor geometry, anchor failure, packet loss, LQI noise, shadowing, NLOS propagation, traffic density, communication radius, or vehicle speed. The tested sensitivity factors are summarized in Table 11.

3.11 Computational Complexity and Scalability

The computational complexity is evaluated per target vehicle and per network snapshot. Let Mi be the number of visible anchors, P be the number of received packets per anchor, and d=2 be the coordinate dimension. The proposed method includes LQI filtering, range conversion, weight computation, matrix construction, WLS solving, scalar refinement, and residual validation. Since d=2 is fixed, the matrix inversion cost remains small, and the dominant cost grows approximately linearly with Mi and P. For one vehicle, the full proposed pipeline has complexity

O(MiP+Mid2+d3).

With fixed d=2 and fixed packet count P, this reduces approximately to O(Mi). For one network snapshot with V vehicles, the complexity becomes

O(∑i=1V(MiP+Mid2+d3)).

Thus, the proposed estimator scales mainly with the number of usable target-anchor links. The complexity comparison is summarized in Table 12.

3.12 Assumption Justification and Reproducibility

The proposed methodology follows practical VANET assumptions involving two-dimensional positioning, known RSU anchors, quasi-static localization snapshots, partial connectivity, LQI uncertainty, and trace-driven validation. These assumptions are chosen to match road-level localization while keeping the estimator reproducible and comparable across all baselines. Some are restrictive. However, each assumption can be relaxed or tested through the sensitivity experiments shown in Table 11, which makes the evaluation more transparent. All experiments are reproducible using the parameters reported in Tables 3, 4, 6, 7 and 9–11. For each Monte Carlo trial, the implementation stores the random seed, vehicle positions, anchor coordinates, LQI samples, packet-loss masks, and method outputs. For the NGSIM validation, the selected vehicle IDs, time frames, normalized coordinates, RSU coordinates, generated LQI observations, and packet-loss masks are also stored. This ensures that the proposed method and all baselines are evaluated under identical mobility, channel, and network conditions. The modeling assumptions, justifications, and mitigation checks are summarized in Table 13.

4  Results

This section evaluates the proposed LQI-based closed-form localization framework using controlled Monte Carlo simulations and NGSIM US-101 trace-driven validation. The simulations test different VANET densities, RSU geometries, channel impairments, packet loss, NLOS effects, and benchmark methods with NMC=1000 trials unless stated otherwise and main vehicle densities of V∈{10,50,100} using four RSU anchors. The NGSIM experiment tests the same framework on real freeway trajectories with lane, speed, and density variation. The proposed method is compared fairly with LS, WLS, RSSI-WLS, EKF, UKF, PF, cooperative localization, hybrid GNSS/INS/RSS fusion, and an ML baseline using the same anchors, packets, measurements, and channel realizations. Performance is reported using ranging error, localization RMSE, dB error, success ratio, throughput, runtime, latency, packet overhead, outlier rate, P90 error and RMSE-CRLB gap with confidence intervals from Eq. (25) and paired statistical significance tests.

4.1 Experimental Layouts for 10, 50, and 100 Vehicles

The target-density layouts for the controlled simulations are shown in Fig. 4. Fig. 4a–c show the 10-vehicle, 50-vehicle, and 100-vehicle cases, respectively. All layouts use the same RSU deployment model and differ mainly in vehicle density, link availability, and packet-collision probability. These layouts show how the estimator behaves from sparse to dense network operation. The 10-vehicle case tests baseline accuracy under low interference. The 50-vehicle case represents moderate traffic where more packets are available, but interference begins to appear. The 100-vehicle case is the most demanding case because it has higher density, more simultaneous transmissions, and more degraded links.

Figure 4: Experimental layouts for the evaluated VANET target densities. The scenarios use V={10,50,100} target vehicles, M=4 RSU anchors, calibrated LQI measurements, packet rate 10 packets/s/vehicle, NMC=1000 Monte Carlo trials, and the highway/urban mobility settings listed in Table 6.

4.2 Ranging Error under Different Vehicle Densities

The ranging-error curves for the three vehicle densities are shown in Fig. 5. The plots compare CRLB, LS, WLS, and the proposed LQI-based estimator. The error bars or shaded bands show the 95% confidence intervals from NMC=1000 Monte Carlo trials. The numerical results are given in Table 14. The proposed estimator stays closer to the CRLB than LS and WLS for all densities. This is because the calibrated LQI-to-range mapping reduces range bias, and the variance-based weighting reduces the effect of unreliable links. The improvement is clearer in dense cases because noisy and weak links are down-weighted instead of being treated equally.

Figure 5: Ranging-error comparison for V={10,50,100} target vehicles using M=4 RSU anchors, calibrated LQI measurements, NMC=1000 Monte Carlo trials, packet rate 10 packets/s/vehicle and the channel parameters in Table 6. Error bars or shaded regions indicate 95% confidence intervals.

In Table 14, the proposed method obtain −9.066 dB for 10 vehicles, −8.90 dB for 50 vehicles and −8.20 dB for 100 vehicles. Although the performance gradually decreases as the vehicle count increases, the degradation is smaller than that of LS and WLS. This indicates that the proposed calibration and weighting stages help preserve ranging reliability when the number of simultaneous vehicular links increases.

4.3 Localization Accuracy Compared with Advanced Baselines

The localization-error comparison with classical and advanced baselines is summarized in Table 15. The table includes LS, WLS, RSSI-WLS, EKF, UKF, PF, cooperative localization, hybrid GNSS/INS/RSS fusion, and an ML-based localization method. All methods use the same anchor geometry, packet reception conditions, and Monte Carlo samples. LS is sensitive to range errors because all anchors are treated equally. WLS reduces this effect by assigning a lower weight to high-variance links, but it cannot fully remove LQI-to-distance bias. EKF and UKF benefit from temporal prediction but may degrade when the measurement model is biased or when lane changes are rapid. PF handles nonlinear effects but needs higher computation and depends on the particle count. The proposed method improves the ranging stage through calibration, reduces unreliable-link effects through WLS, and applies scalar refinement to reduce nonlinear reconstruction error.

4.4 Localization Error for 10, 50, and 100 Vehicles

The localization-error plots for 10, 50, and 100 vehicles are shown in Fig. 6. The figure includes 95% CI bars or shaded bands for all methods. The numerical results are reported in Table 16. The proposed method gives lower localization error than LS and WLS and stays closer to the CRLB. The gap from the CRLB increases with vehicle density because packet collisions, partial connectivity, and interference reduce reliable geometric information.

Figure 6: Localization-error results for V={10,50,100} vehicles using M=4 RSUs, calibrated LQI measurements, packet rate 10 packets/s/vehicle, NMC=1000 trials and the channel/mobility parameters in Table 6. The plotted confidence bands or error bars show 95% confidence intervals.

For the 10-vehicle case in Table 16, the proposed method obtains −9.18 dB while LS and WLS obtain −6.22 and −4.61 dB respectively. At 50 vehicles, the proposed method maintains −8.90 dB, which indicates that the estimator remains stable when moderate network density increases the number of radio links. At 100 vehicles, the proposed method obtains −8.00 dB, and the reduction compared with the lower density cases is mainly caused by increased packet contention, degraded link quality, and less favorable link availability under dense traffic.

4.5 Statistical Significance of Localization Improvements

The statistical significance of the localization gains is summarized in Table 17. The table compares the proposed method with each baseline using the same Monte Carlo realizations. The p-values and effect sizes are computed using paired tests. A small p-value shows that the gain is unlikely to come from random geometry or channel noise. The effect size is also reported because a large sample size can make a small gain statistically significant. Therefore, Table 17 is interpreted using both p-value and effect size.

4.6 Throughput Analysis

The comparison includes only executable localization algorithms. CRLB is excluded because it is a theoretical lower bound rather than a localization algorithm. The curves for the three target densities are shown in Fig. 7. The figure uses the same packet rate, RSU setup, and link-filtering criteria as the localization experiments.

Figure 7: Throughput comparison for V={10,50,100} vehicles using M=4 RSUs, packet rate 10 packets/s/vehicle, NMC=1000 trials and the same link-filtering criteria for all methods. Throughput is measured in successful localizations/s, and error bars indicate 95% confidence intervals.

The numerical throughput values are reported in Table 18. The proposed method improves throughput because it rejects unreliable estimates through residual validation and resolves accepted locations using a closed-form computation rather than an iterative update. The gain does not mean that the physical packet rate increases; it means that the algorithm produces more valid localization outputs per unit time.

The throughput gain for the 100-vehicle case is computed from the raw values in Table 19. The proposed method increases throughput from 0.614 to 1.169 successful localizations/s compared with LS:

1.169−0.6140.614×100=90.39%.

It also increases throughput from 0.591 to 1.169 successful localizations/s compared with WLS:

1.169−0.5910.591×100=97.80%.

Thus, the reported gain uses the raw throughput values rather than normalized levels. Table 19 confirms that the proposed method achieves higher throughput than LS and WLS in the 100-vehicle case. Reporting the raw values, confidence interval, and statistical test removes ambiguity from the percentage-gain statement.

4.7 Confidence Intervals and Visual Uncertainty Reporting

The uncertainty visualization for RMSE, localization error, and throughput is shown in Fig. 8. The figure presents 95% confidence intervals using error bars and is exported in high-resolution format.

Figure 8: Confidence-interval summary for localization error, throughput and RMSE under V={10,50,100} vehicles, M=4 RSUs, calibrated LQI measurements and NMC=1000 Monte Carlo trials. Error bars indicate 95% confidence intervals computed using Eq. (25).

The numerical confidence-interval summary for Fig. 8 is reported in Table 20, which gives the mean, standard deviation, and 95% confidence bounds instead of only descriptive CI discussion. These intervals should be read with the paired significance tests in Table 17. Narrow intervals show stable Monte Carlo behavior. Overlapping intervals do not always mean non-significance because the paired test uses trial-by-trial differences.

4.8 Error Distribution and Tail Behavior

The localization-error distribution statistics are reported in Table 21; these values show whether a method improves only average RMSE or also reduces tail errors needed for safety-related VANET use. Table 21 shows that the proposed method reduces both central and tail error. The median error decreases because calibration improves the LQI-to-distance mapping. The 90th percentile and outlier rate decrease because WLS down-weights high-variance links and residual validation rejects geometrically inconsistent estimates.

4.9 Trace-Driven Validation Results

Fig. 9 provides a graphical comparison of the trace-driven localization results reported in Table 22. Fig. 9a shows that the proposed LQI-based method achieves the lowest RMSE for all vehicle densities. Fig. 9b shows the same trend for median localization error. Fig. 9c shows that the proposed method reduces the 90th percentile error, which indicates improved robustness under difficult trace-driven conditions. Fig. 9d shows that the proposed method obtains the highest success ratio for all vehicle densities.

Figure 9: Trace-driven localization performance on the NGSIM US-101 dataset for different vehicle densities: (a) RMSE, (b) median error, (c) 90th percentile error and (d) success ratio. The vehicle trajectories are real NGSIM freeway traces, while LQI observations are generated from the calibrated LQI-distance model.

Table 22 reports the NGSIM US-101 trace-driven results. The proposed method is evaluated using RMSE, median error, 90th percentile error, and success ratio. Vehicle positions are taken from real freeway trajectories, while LQI observations are generated using the calibrated LQI-distance model in Section 3.8. The proposed method gives RMSE values of 2.39, 2.55, and 3.14 m for 10, 50, and 100 vehicles with success ratios of 0.96, 0.94, and 0.92. In the 100-vehicle case, LS gives 7.63 m RMSE and 0.79 success ratio, while the proposed method gives 3.14 m RMSE and 0.92 success ratio. This gain occurs because calibration reduces LQI-to-range bias, WLS suppresses unreliable links, and scalar refinement improves geometric consistency. Since NGSIM does not provide physical LQI/RSS packet measurements, this experiment validates mobility realism rather than hardware radio measurements. Therefore, the NGSIM results should be interpreted as real-world mobility trace-driven validation with calibrated model-generated radio observations.

4.10 Ablation Study

The ablation results are shown in Fig. 10. This figure compares the full proposed method with variants that remove calibration, WLS weighting, scalar refinement, link filtering, and RSU cooperation.

Figure 10: Ablation-study results for the proposed method using V=100 vehicles, M=4 RSUs, calibrated LQI channel settings, packet rate 10 packets/s/vehicle and NMC=1000 trials. Error bars indicate estimated 95% confidence intervals.

The numerical ablation results are shown in Table 23. The full method gives the best RMSE of 2.35 m, median error of 1.96 m, and P90 error of 3.56 m. Removing calibration gives the largest RMSE increase to 4.85 m, which shows the effect of LQI-to-range bias. Removing scalar refinement increases RMSE to 3.95 m, while removing link filtering increases it to 3.45 m due to unreliable packets. No RSU cooperation gives a lower throughput of 0.98 loc/s because fewer anchors reduce geometric diversity.

4.11 Sensitivity Analysis

The sensitivity curves are shown in Fig. 11 the figure includes RMSE and success-ratio trends under different RSU placements, number of RSUs, anchor failure rates, packet loss rates, LQI noise levels, fading severities, traffic densities, communication radii and NLOS percentages.

Figure 11: Sensitivity analysis of the proposed LQI localization method under changing RSU placement, number of anchors, anchor failure rate, packet loss rate, LQI noise, fading severity, traffic density, communication radius, and NLOS percentage. Each curve uses NMC=1000 trials and reports estimated 95% confidence intervals.

The numerical sensitivity results are reported in Table 24, one parameter is varied at a time while the others remain fixed at the default settings in Table 6. The results show that more RSUs improve geometry and reduce rank-deficient cases. Higher packet loss or anchor failure lowers the success ratio because fewer valid links remain after filtering. Higher LQI noise increases uncertainty and widens the confidence intervals. Higher NLOS percentage reduces accuracy because obstruction and multipath bias the received link quality.

4.12 Realistic Scenario Evaluation

The realistic-scenario comparison is shown in Fig. 12. The figure separately reports highway, urban canyon, tunnel, NLOS/multipath, sparse traffic, dense traffic, and trace-driven mobility conditions.

Figure 12: Realistic-scenario localization performance under highway, urban canyon, tunnel, NLOS/multipath, sparse traffic, dense traffic, and NGSIM trace-driven mobility settings. Simulation-based scenarios use calibrated LQI measurements, M=4 RSUs, NMC=1000 trials and the channel parameters listed in Table 6.

The realistic-scenario results are summarized in Table 25. Highway, urban, tunnel, NLOS/multipath, sparse-traffic, and dense-traffic cases are controlled simulations. The trace-driven case uses NGSIM US-101 trajectories with calibrated model-generated LQI observations. No physical hardware measurement is reported. Highway LOS gives the lowest error because the LQI-distance relation is close to the calibrated log-distance model. Urban canyon and tunnel cases increase RMSE and outliers due to multipath and NLOS bias. Dense traffic improves measurement availability but also increases packet collisions. The trace-driven result shows stable performance under real freeway mobility, although the LQI values are still model-generated.

4.13 Noise Sensitivity

The LQI-noise sensitivity trend is shown in Fig. 13. The figure reports RMSE as a function of σℓ for LS, WLS, and the proposed method.

Figure 13: Noise-sensitivity comparison under σℓ∈{1,2,3} dB using M=4 RSUs, NMC=1000 trials and the default vehicle-density configuration. Error bars indicate estimated 95% confidence intervals.

The noise-sensitivity values are reported in Table 26. Increasing σℓ degrades all methods, but the proposed estimator shows the smallest RMSE growth. This is because high-variance LQI observations are assigned a lower weight in the WLS system. The propagated range variance prevents uncertain links from dominating the coordinate estimate.

4.14 Impact of Anchor Geometry

The anchor-geometry impact is illustrated in Fig. 14, which shows RMSE and CRLB gap under good, moderate, and poor RSU geometries.

Figure 14: Effect of anchor geometry on localization accuracy under good, moderate, and near-collinear RSU placement. The experiment uses NMC=1000 trials, σℓ=2 dB, and the same LQI calibration parameters for all layouts. Error bars indicate estimated 95% confidence intervals, and the line shows the CRLB gap ratio.

The GDOP-style anchor-geometry results are summarized in Table 27. Anchor placement remains important even with LQI calibration and WLS. Near-collinear RSUs increase error because the geometry matrix becomes ill-conditioned. In this case, small LQI-based range errors are amplified along the weak geometric axis. Better angular separation reduces this effect and moves the RMSE closer to the CRLB.

4.15 Runtime, Latency, Packet Overhead, and Scalability

The runtime, latency, packet overhead, and energy-cost values are summarized in Table 28. These metrics matter because VANET localization must satisfy real-time limits and cannot be judged through RMSE alone. The proposed method records the lowest runtime at 0.60 ms, latency of 100.60 ms, 4 packets per epoch, energy cost of 1.00×, and SR of 0.96. By contrast, PF reaches 18.50 ms runtime and 4.00× energy cost. Cooperative localization achieves SR 0.94 but needs 7 packets per epoch. Overall, calibrated RSU/anchor links give the proposed method a practical balance between accuracy and feasibility.

The theoretical complexity and measured runtime are summarized in Table 29, following the definitions in Section 3.11 and showing that the proposed LQI-WLS-Refined method has complexity O(MiP+Mid2+d3) with the lowest runtime of 35 ms. Since the localization dimension remains fixed at d=2, the method scales mainly with visible anchors and packet samples, while LS needs 65 ms, WLS needs 3110 ms, and Particle Filter rises sharply to 372 ms because repeated particle propagation adds heavier computation.

5  Discussion and Comparison

5.1 Interpretation of Proposed Localization Results

The results show that the proposed calibrated LQI-based localization framework provides a low-cost RSU-assisted VANET localization solution whose gains mainly come from LQI-to-range calibration and variance-aware WLS weighting and scalar consistency refinement. Range bias is reduced, unreliable links are suppressed, and agreement with nonlinear localization geometry is improved, which explains the lower ranging error in Table 14 and lower localization error in Table 16 and stronger baseline performance in Table 15. The method also improves central and tail-error behavior because Table 21 shows reduced median error, P90 error, and outlier rate, while Table 20 confirms stable Monte Carlo results and Table 17 shows statistically meaningful gains. Successful localizations per second are improved without reliance on heavy iterative tracking, and the evaluation is strengthened by the NGSIM US-101 results in Table 22 through real freeway vehicle trajectories, while the 10, 50, and 100 vehicle results should be interpreted as real-world mobility trace-driven validation with calibrated model-generated radio observations because physical LQI or RSS packet logs are not provided by NGSIM.

5.2 Comparison with Recent GNSS-Challenged Localization Methods

Table 30 compares the proposed method with recent GNSS-challenged vehicular localization approaches. Kang et al. [56] use LiDAR, V2X, and filtering-based fusion, which improves robustness in GNSS-denied cases but requires additional onboard sensing. Halili et al. [57] use ToA and Doppler radio measurements for tunnel localization, which can achieve high accuracy but depends on synchronization and Doppler processing. Min et al. [58] improve cooperative GNSS/V2V localization through scheduling, although this adds communication and optimization complexity. Chang [59] uses TDoA projection with cellular anchors, which supports GNSS-free localization but requires dense timing infrastructure. Compared with these methods, the proposed framework uses communication-layer LQI information from RSU or anchor links. It does not require LiDAR, camera sensing, dense 5G/6G timing anchors, or full GNSS/INS fusion. The results in Tables 15, 28 and 29 show that this design gives a useful balance between accuracy, runtime, latency, and packet overhead.

5.3 Deployment Implications and Limitations

The deployment results show that localization quality depends strongly on RSU geometry, link quality, and channel conditions. Table 27 shows that near-collinear RSUs increase error because the geometry matrix becomes ill-conditioned. Table 24 shows that packet loss, anchor failure, LQI noise, and NLOS percentage reduce accuracy and success ratio. Table 25 further shows that highway LOS gives the best performance, while urban canyon and tunnel cases increase error due to multipath and NLOS bias. The system-level results in Tables 28 and 29 suggest that the proposed method is suitable for real-time RSU-centric ITS deployments. Its closed-form WLS structure avoids iterative filtering and particle propagation, which reduces runtime and latency. The packet overhead also remains low because the method uses existing RSU/anchor communication links instead of high-bandwidth perception data. The main limitation is the dependence on stable LQI-to-range calibration. Severe NLOS, hardware heterogeneity, antenna variation, weather changes, and RSU relocation can shift the LQI-distance relation.

6  Conclusion and Future Work

This paper presented a calibrated LQI-based closed-form localization framework for partially connected RSU-assisted VANETs. The proposed framework combines LQI-to-range calibration, link-availability filtering, variance-aware WLS estimation, and scalar consistency refinement to improve localization accuracy under practical VANET conditions. Unlike approaches that assume ideal connectivity, the proposed method considers communication-radius limits, LQI thresholds, packet reception constraints, and anchor availability. The CRLB was also used as a theoretical benchmark to compare the empirical localization performance with the achievable lower bound. The proposed framework was evaluated using synthetic Monte Carlo scenarios and real-world NGSIM US-101 mobility traces, while physical LQI hardware measurement remains future work. In the controlled simulation results, the proposed method reduced ranging and localization error compared with LS and WLS and remained closer to the CRLB under favorable anchor geometry. The evaluation was further extended to advanced baselines, including RSSI-WLS, EKF, UKF, particle filtering, cooperative localization, hybrid GNSS/INS/RSS fusion, and ML-based localization. The results indicate that the main performance gains come from calibrated LQI-to-range conversion, partial-connectivity filtering, variance-based WLS weighting, and scalar consistency refinement.

The NGSIM US-101 trace-driven validation further showed that the proposed method remains effective when vehicle mobility is taken from real freeway trajectories rather than synthetic random placement. Under the same trace-driven setup, the proposed method outperformed LS, WLS, RSSI-WLS, EKF, UKF, and PF. It achieved RMSE values of 2.39, 2.55, and 3.14 m for 10, 50, and 100 vehicle cases, respectively, with corresponding success ratios of 0.96, 0.94, and 0.92. These results indicate that the proposed framework provides a low-cost, communication-layer-based localization solution for RSU-supported VANET environments. In the 100-vehicle case, throughput improved from 0.614 to 1.169 successful localizations/s compared with LS, corresponding to a 90.39% gain. Compared with WLS, throughput improved from 0.591 to 1.169 successful localizations/s, corresponding to a 97.80% gain. These values are reported using the raw baseline and proposed throughputs to avoid ambiguity in the percentage-gain claim.

Although NGSIM validates mobility realism, future field experiments will validate the radio measurement model using real LQI and RSS packet logs. Future work will collect physical LQI/RSS traces using RSUs and onboard units under highway, urban canyon, tunnel, and NLOS conditions. Further work will also investigate online adaptive calibration, calibration transfer across different roads and RSU hardware, 5G/6G NR-V2X integration, hybrid GNSS/INS/LQI fusion, map matching, deep-learning-based NLOS detection, and multi-city trace-driven validation.

Acknowledgement: The authors gratefully acknowledge the support provided by the Deanship of Scientific Research, Vice Presidency for Graduate Studies and Scientific Research, King Faisal University, Saudi Arabia, under Grant No. KFU262743 and by the Princess Nourah bint Abdulrahman University Researchers Supporting Project, Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia, under Project No. PNURSP2026R719.

Funding Statement: This work was supported by the Deanship of Scientific Research, Vice Presidency for Graduate Studies and Scientific Research, King Faisal University, Saudi Arabia, under Grant No. KFU262743 and by the Princess Nourah bint Abdulrahman University Researchers Supporting Project, Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia, under Project No. PNURSP2026R719.

Author Contributions: Waqas Ahmad contributed to methodology; Shahzad Anwar contributed to validation; Abid Iqbal contributed to supervision; Abuzar Khan contributed to software; Saad Arif contributed to formal analysis; Ali S. Alzahrani contributed to resources; Mohammed Al-Naeem contributed to investigation; Fatimah Alhayan contributed to review and editing; Syed Hashim Raza Bukhari contributed to technical validation; and Ghassan Husnain contributed to writing, review and editing. All authors reviewed and approved the final version of the manuscript.

Availability of Data and Materials: The authors confirm that the data supporting the findings of this study are available within the article.

Ethics Approval: Not applicable.

Conflicts of Interest: The authors declare no conflicts of interest.

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