Wi-Fi-based radio-SLAM (simultaneous localization and mapping) estimates the positions of users and access points (APs) simultaneously in GPS-denied indoor environments. To address the observability degradation in radio-SLAM caused by using only relative distance measurements between APs and the user, this paper proposes a positioning method based on the extended Kalman filter (EKF) and global geometry constraints. This method first uses the relationship between signal strength and ranging in the free space path loss (FSPL) model to determine the visibility of the AP. Then, it establishes a globally constrained positioning framework by integrating AP's observed visibility and estimated visibility (from the estimated results of the geometric collision detection of walls). Simulation results show the improvement of our positioning methods, compared with the traditional EKF, the proposed method improves user positioning accuracy (RMSE) by 34%, and AP location estimation accuracy by 37%, enhancing users' perception capability in unknown environments.
when simultaneously estimating both agent and AP positions using only relative distance measurements between them. Morales’s research [11] shows that in such radio-SLAM system, poor observability can cause the clock biases of the receiver and transmitter to be random and unobservable, and the estimated error variance to diverge. As a result, the lack of global constraints leads to translational and rotational errors in the estimated localization results. Existing research has not fully utilized the important prior information contained in building floor plans to enhance the physical consistency of the solution.
To address the challenges, this paper proposes an innovative radio-SLAM framework by integrating signal transmission characteristics with environmental structural constraints. Our contributions are: • proposes an observed visibility classification method based on joint analysis of RTT and RSSI. By thoroughly examining the residual between these two measurements, we can identify LOS and NLOS propagation states. • introduces geometric constraints from building floor plans. Rather than simply adjusting noise variance based on visibility, we leverage the consistency between the estimated user-AP relative visibility and the prior map’s visibility information.
In a LOS environment, the RSSI and RTT distance measurement should conform to the FSPL model; if there is occlusion, RSSI will be significantly lower than the theoretical value due to additional attenuation. The residual of the measurement RSSI and predicted RSSI based on FSPL is used to determine the visibility. If < , the signal is determined as an LOS signal. Otherwise, the signal is a NLOS signal. is the dynamic threshold determined by diferent environments, = · .
= {︃LOS,
if < ,
NLOS, if ≥ . = {︃NLOS, if ⃗ and L intersect,
LOS,
if ⃗ and L do not intersect,
In terms of the estimated visibility, it is determined by whether the line from the user and AP intersects with the wall derived from the floor plan[3]. Expressed as: where ⃗ is the line segments connecting estimated user = (, ) and AP locations = ( , ), L is the vector set of the wall. Therefore, the consistency of visibility is:
= XNOR(, ), where the XNOR operation returns true only when both inputs are equal.
Distance measurement is a nonlinear equation of AP and user locations. We choose the Extended Kalman Filter (EKF) to solve the nonlinear problem through local linearization. The nonlinear prediction equation and measurement equation are diferentiated and linearized by replacing the tangent line. It is a first-order Taylor expansion at the mean.
The state vector contains the user’s position (, ), user’s velocity (˙, ˙) and the positions of APs ( , ): x = [︀ ˙ ˙ 1 1 · · · ]︀ ∈ R2+4.
The status prediction is:
x^|− 1 = Fx^− 1|− 1,
(
*MEASUREMENT: VO = LOS 30 state transition Jacobian matrix: where x− 1|− 1 is the posterior state at − 1, x|− 1 is the prior state, F ∈ R(2+4)× (2+4) is the · · · . ... ⎥⎥⎦ ⎢⎢⎣ ... 1 2 . .
. 0 0 · · · 0 0 · · · .2 ⎥⎥⎥ . (10) (7) (8) (9) (11) estimated AP estimated user VE = LOS VE = NLOS =
= where the measurement Jacobian matrix H is:
H = ℎ ⃒⃒ x ⃒⃒ x^|− 1 The measurement prediction function is : ⎡1 ⎤ ⎢2 ⎥ ⎢⎢⎣ ... ⎥⎥⎦ = ⎢ ⎢ ⎣ ⎢ ⎡ √︀( − 1)2 + ( − 1)2 ⎤ √︀( − 2)2 + ( − 2)2 ⎥ . .
. √︀( − )2 + ( − )2 ⃒⃒ x ⃒⃒ x^− 1|− 1
where Q is defined as
P|− 1 = FP− 1|− 1F + Q, Q = diag(︁ 2, 2 , 2˙, 2˙, 21, 21, . . . , 2 , ,
2 )︁ y = z −
Hx^|− 1, corresponding to diferent variances of the status. The residuals to the measurement value z is: (12) (13) (14) (15) (16) corresponding to the variances of measurements. Considering the influence of visibility consistency, where is the trust scaling factor, if visibility is inconsistent, the corresponding measurement value has higher noise variance. The state and covariance update is:
K = P|− 1H (HP|− 1H + R)− 1,
R = diag(︁ 21, ..., ,
2 )︁ = {︃ ,
if = 1 · , if = 0, x^| = x^|− 1 + Ky, P| = (I −
KH)P|− 1.
where
In our framework, the visibility consistency of APs serves as a reliability indicator for measurement validation. Specifically, when visibility consistency is satisfied, the corresponding AP’s measurements are deemed more trustworthy, and we proceed with standard state update and prediction following the EKF workflow. Figure 1 shows an example of this process. Assume that, based on RSSI and RTT, is classified as LOS. If the segment connecting AP and user intersects the wall, is NLOS, which is inconsistent compared to . Therefore, this measurement value is unreliable, and the value of the element of the measurement noise covariance matrix of AP increases.
The performance of the proposed EKF algorithm is verified by simulation in a dynamic noise environment and compared with other filtering methods.
We set the positions of the walls L, the location of the AP (([− 3, 5], [30, 5], [15, 20]) with the unit as meters), and the trajectory of the user. The user’s movement consists of straight walking and turning, distributed in diferent rooms within 120 seconds.
All parameter settings used in the system and the initial settings of EKF are shown in Table 1.
To analyze the time-error results of our method versus traditional EKF in estimating the positions of the user and three APs, we plotted all curves in the same coordinate system to observe overall trends (Figure 2(b)). The obvious diference between our method and EKF is that the measurement variance matrix is adjusted based on the visibility—— rather than simply adjusting noise variance based on visibility, we leverage the consistency between the estimated user-AP relative visibility and the prior map’s visibility information. While our method does not exhibit significantly faster convergence than EKF for user positioning, the visibility constraints mitigate the initial positioning error amplification caused by biased initial values. After convergence, our method achieves lower steady-state errors. Additionally, the AP error curves demonstrate that our method exhibits smaller oscillations and positioning errors. Quantitative comparisons of key metrics (see Table 2) further confirm our advantages.
The comparative analysis demonstrates that our proposed method significantly outperforms the conventional EKF across most metrics. For positioning accuracy, the mean error improved by 32.7% (from 2.26 to 1.52) for user localization and up to 41.7% (from 2.16 to 1.26) for AP3. The RMSE showed consistent enhancements, particularly for AP1 with 36.9% reduction (from 4.25 to 2.68). Regarding error stability, the standard deviation decreased by 37.6% (from 1.41 to 0.88) for user positioning, though AP2 exhibited a marginal 4.2% increase (from 0.71 to 0.74). Notably, the unchanged maximum error for AP3 (8.60) is attributed to initial value deviation at = 1, suggesting the algorithm’s sensitivity to initialization. The results confirm our method’s superior performance in both accuracy and consistency, while highlighting the need for improved initialization techniques to address outlier cases.
The superior positioning accuracy achieved by our method stems fundamentally from its dynamic adaptation of the measurement noise covariance matrix R in the EKF framework. Specifically, our approach innovatively integrates RSSI/RTT ranging data with posterior visibility verification to establish a dual reliability validation mechanism: when an AP’s observed visibility (based on signal characteristics) aligns with its geometric visibility (determined by intersection tests between estimated positions and walls), the data is deemed reliable and corresponding in R remains unchanged; when discrepancies occur (e.g., signal-indicated LoS conflicts with geometric occlusion), corresponding in R is increased to reduce that AP’s influence. This design fundamentally overcomes the limitations of the traditional EKF in complex environments due to the fixed noise assumption. It integrates environmental information as constraints through a plan view, automatically suppresses interference from unreliable measurements in scenes with inconsistent visibility, and further improves positioning accuracy.
To address the issue of insuficient global constraints in AP position estimation for radio-SLAM, this paper proposes an EKF-based localization method leveraging visibility consistency. By integrating the observed and estimated visibility of APs, the method establishes geometric constraints to enhance global accuracy. Simulation results demonstrate that the proposed residual-based visibility discrimination approach efectively distinguishes between LOS and NLOS signals. In terms of positioning accuracy, multiple evaluation metrics, including RMSE, mean error, and standard deviation, show significant improvements. This work introduces a novel approach by incorporating global geometric constraints when only relative distance measurements of the target parameters are available, ofering a new solution for sensor network node calibration in an environment with mobile devices.
However, the positioning results are sensitive to initial values, and the measurement data is more unstable in indoor environments with severe multipath efects. Future research will focus on developing more robust initial value calibration algorithms and conducting experiments to evaluate the accuracy and stability of our method.
During the preparation of this work, the author(s) used Chat-GPT-4 in order to: Grammar and spelling check. After using these tool(s)/service(s), the author(s) reviewed and edited the content as needed and take(s) full responsibility for the publication’s content. [6] E. Zola, I. Martin-Escalona, Ieee 802.11 mc ranging performance in a real nlos environment, in: 2021 17th International Conference on Wireless and Mobile Computing, Networking and Communications (WiMob), IEEE, 2021, pp. 377–384. [7] B. Amjad, Q. Z. Ahmed, P. I. Lazaridis, M. Hafeez, F. A. Khan, Z. D. Zaharis, Radio slam: A review on radio-based simultaneous localization and mapping, IEEE Access 11 (2023) 9260–9278. [8] C. B. Barneto, E. Rastorgueva-Foi, M. F. Keskin, T. Riihonen, M. Turunen, J. Talvitie, H. Wymeersch, M. Valkama, Millimeter-wave mobile sensing and environment mapping: Models, algorithms and validation, IEEE Transactions on Vehicular Technology 71 (2022) 3900–3916. [9] E. Leitinger, F. Meyer, F. Hlawatsch, K. Witrisal, F. Tufvesson, M. Z. Win, A belief propagation algorithm for multipath-based slam, IEEE transactions on wireless communications 18 (2019) 5613–5629. [10] S. Bai, W. Wen, D. Su, L.-T. Hsu, Graph-based indoor 3d pedestrian location tracking with inertial-only perception, IEEE Transactions on Mobile Computing (2025). [11] J. J. Morales, Z. M. Kassas, Stochastic observability and uncertainty characterization in simultaneous receiver and transmitter localization, IEEE Transactions on Aerospace and Electronic Systems 55 (2018) 1021–1031.