Figures (10)  Tables (9)

    • Figure 1. 

      Structure of the proposed robust indoor UWB localization framework.

    • Figure 2. 

      Workflow of the proposed UWB outlier removal algorithm.

    • Figure 3. 

      Workflow of the proposed improved iterative ensemble Kalman filter backend.

    • Figure 4. 

      Experimental setup of the indoor UWB localization test, including four fixed anchors, the UAV-mounted mobile tag, reference points, and the data acquisition computer.

    • Figure 5. 

      UWB range measurements before and after multi-channel outlier removal in one representative experimental run.

    • Figure 6. 

      Two-dimensional trajectory comparison of different localization methods in two representative experimental runs. (a) Representative run 1. (b) Representative run 2.

    • Figure 7. 

      Trajectory-to-reference-path deviation and reference-point positioning error comparison of different filtering methods in one representative experimental run. (a) Trajectory-to-reference-path deviation. (b) Reference-point positioning error.

    • Figure 8. 

      CDF curves of reference-point positioning errors for different filtering methods in one representative experimental run.

    • Figure 9. 

      Backend filter comparison under the same cleaned UWB measurements in one representative experimental run. (a) Two-dimensional trajectory comparison. (b) Reference-point positioning errors.

    • Figure 10. 

      Ablation comparison of different front-end and back-end configurations in one representative experimental run. (a) Two-dimensional trajectory comparison. (b) Reference-point positioning error distribution.

    • Input: Previous posterior ensemble $ \{{\boldsymbol{x}}_{k-1|k-1}^{(i)}\}_{i=1}^{M} $, cleaned UWB measurement $ {\boldsymbol{z}}_{k}^{{\rm{clean}}} $, state transition function $ {\boldsymbol{f}}(\cdot) $, measurement function $ {\boldsymbol{h}}(\cdot) $
      Output: Posterior state estimate $ \hat{{\boldsymbol{x}}}_{k|k} $
      1: Adapt $ {\boldsymbol{Q}}_k $ using the previous innovation statistics and the bounded scaling rule
      2: for $ i = 1 $ to $ M $ do
      3: Draw process noise $ {\boldsymbol{\eta}}_{k}^{(i)} \sim {\cal{N}}({\boldsymbol{0}}, {\boldsymbol{Q}}_k) $
      4: Predict ensemble member:
      ${\boldsymbol{x}}_{k|k-1}^{(i)} = {\boldsymbol{f}} \left({\boldsymbol{x}}_{k-1|k-1}^{(i)}\right) + {\boldsymbol{\eta}}_{k}^{(i)} $
      5: end for
      6: Compute forecast ensemble mean $ \bar{{\boldsymbol{x}}}_{k|k-1} $
      7: Compute predicted measurements $ {\boldsymbol{y}}_{k|k-1}^{(i)} = {\boldsymbol{h}}({\boldsymbol{x}}_{k|k-1}^{(i)}) $
      8: Compute innovation and residual statistics using $ {\boldsymbol{z}}_{k}^{{\rm{clean}}}-\bar{{\boldsymbol{y}}}_{k|k-1} $ and the ensemble-predicted observation dispersion
      9: Construct channel-aware $ {\boldsymbol{R}}_k $ using residual statistics and gating rules
      10: Initialize the iterative analysis with $ {\boldsymbol{x}}_{k}^{(i,0)} = {\boldsymbol{x}}_{k|k-1}^{(i)} $
      11: for $ \ell = 1 $ to $ L $ do
      12: Propagate the current ensemble through the nonlinear measurement function
      13: Compute the sample cross-covariance and innovation covariance
      14: Compute the Kalman gain $ {\boldsymbol{K}}_{k}^{(\ell)} $
      15: Perform the damped ensemble update with damping factor $ \mu_{\ell} $
      16: end for
      17: Compute the posterior state estimate:
      $\hat{{\boldsymbol{x}}}_{k|k} = \dfrac{1}{M}\sum\limits_{i=1}^{M}{\boldsymbol{x}}_{k}^{(i,L)} $

      Table 1. 

      Improved IEnKF for indoor UWB localization

    • Item Value
      UWB device Nooploop LinkTrack UWB modules
      Number of UWB anchors 4
      Anchor coordinates $ {\rm{A0:}}\;(0,0)\; {\rm{m}} \quad {\rm{~A}} 1:(0,8.55)\; {\rm{m}}$
      ${\rm{A2:}}\;(6.35,8.38)\; {\rm{m}} \quad {\rm{~A}} 3:(6.34,0) \;{\rm{m}} $
      Sampling rate 10 Hz (0.1 s sampling interval)

      Table 1. 

      Main experimental setup of the indoor UWB localization test.

    • Channel Raw
      STD (m)      		 Cleaned
      STD (m)      		 Detected
      outlier ratio (%)      		 Detected
      outlier count
      Anchor 1 0.1708 0.0594 0.68 10
      Anchor 2 0.3682 0.0942 1.84 27
      Anchor 3 0.4718 0.2308 2.23 33
      Anchor 4 0.1353 0.0669 1.20 18

      Table 2. 

      UWB ranging residual statistics before and after front-end preprocessing over four experimental runs.

    • Method Path RMSE (m) Path MAE (m) Ref. RMSE (m) Ref. MAE (m)
      EKF 0.3549 0.2642 0.2312 0.2028
      UKF 0.3323 0.2182 0.1901 0.1511
      EnKF 0.3463 0.2295 0.1860 0.1492
      MCC-UKF 0.2404 0.1847 0.1588 0.1336
      RA-CKF 0.2215 0.1822 0.1762 0.1439
      Proposed IEnKF 0.1888 0.1586 0.1451 0.1243

      Table 3. 

      Overall reference-point/path-deviation performance comparison of different methods over four experimental runs.

    • Method RMSE (m) MAE (m)
      Cleaned + EKF 0.2359 0.2036
      Cleaned + UKF 0.1765 0.1439
      Cleaned + EnKF 0.1713 0.1391
      Proposed IEnKF 0.1451 0.1243

      Table 4. 

      Reference-point localization errors of different backend filters under the same cleaned UWB measurements over four experimental runs.

    • Method RMSE (m) MAE (m)
      Raw + EnKF 0.1860 0.1492
      Cleaned + EnKF 0.1713 0.1391
      Raw + IEnKF 0.1708 0.1442
      Cleaned + IEnKF 0.1451 0.1243

      Table 5. 

      Ablation results of different front-end and backend configurations over four experimental runs.

    • Method Adap. Q Ch.-aware R Damped RMSE MAE MAX
      EnKF × × × 0.1713 0.1391 0.3770
      IEnKF × × √ 0.1625 0.1316 0.3570
      Proposed w/o adaptive Q × √ √ 0.1502 0.1260 0.2862
      Proposed w/o Ch.-aware R √ × √ 0.1682 0.1355 0.3792
      Proposed w/o damping √ √ × 0.1503 0.1269 0.2905
      Full proposed √ √ √ 0.1451 0.1243 0.2820

      Table 6. 

      Component-level ablation results of the proposed backend mechanisms over four experimental runs.

    • (a) Proposed IEnKF under different anchor configurations
      Anchor configuration RMSE (m) MAE (m) MAX (m)
      A0-A1-A2-A3 0.1451 0.1243 0.2820
      A1-A2-A3 0.1679 0.1379 0.4002
      A0-A2-A3 0.2309 0.1714 0.6389
      A0-A1-A3 0.2082 0.1705 0.4525
      A0-A1-A2 0.1594 0.1320 0.3355
      (b) RMSE under synthetic NLOS and dynamic occlusion stress tests
      Stress case EKF UKF EnKF MCC-UKF RA-CKF Proposed IEnKF
      Original 0.2312 0.1901 0.1860 0.1588 0.1762 0.1451
      5% NLOS bias 0.2367 0.2041 0.2074 0.1694 0.1937 0.1589
      10% NLOS bias 0.2294 0.2071 0.2089 0.1747 0.1985 0.1575
      15% NLOS bias 0.2325 0.2095 0.2132 0.1842 0.2074 0.1687
      Dynamic occlusion 0.2301 0.2116 0.2157 0.1737 0.2009 0.1620

      Table 7. 

      Controlled post-processing robustness analysis under anchor-channel removal and synthetic ranging disturbances.

    • ParameterTested valuesRecommended valueAvg. best RMSE (m)Avg. RMSE range (m)Sensitivity
      Tukey cutoff2.5/3.0/3.5/4.02.50.14570.0022Low
      Window size5/7/9/1170.14460.0030Low
      Ensemble size30/50/80/100/1201000.14150.0098Low
      Iteration number1/2/3/4/530.14070.0201Medium
      Q scaling bound2/3/4/520.14600.0000Low
      R clipping bound1.5/2.5/3.5/4.51.50.14240.0118Low

      Table 8. 

      Parameter sensitivity results of the proposed localization framework.