• Infrared and Laser Engineering
  • Vol. 50, Issue 9, 20200484 (2021)
Yan Liang1、2, Qingdong Zhang1, Ning Zhao1, and Chuanmiao Li1
Author Affiliations
  • 1School of Mechanical Engineering, University of Science and Technology, Beijing 100083, China
  • 2Beijing Xinfeng Aerospace Equipment Co. Ltd, Beijing 100089, China
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    DOI: 10.3788/IRLA20200484 Cite this Article
    Yan Liang, Qingdong Zhang, Ning Zhao, Chuanmiao Li. Indoor location method based on UWB and inertial navigation fusion[J]. Infrared and Laser Engineering, 2021, 50(9): 20200484 Copy Citation Text show less

    Abstract

    In response to the increasingly complex indoor environments where a single positioning system is no longer able to satisfy positioning precision demands, an indoor positioning method applying Ultra-Wide Band (UWB) ranging and inertial navigation fusion was proposed. First, the problem that UWB ranging results were proved to be affected by the environment was given, UWB ranging calibration was carried out in the experimental environment. Thereafter, the outliers in the ranging process were eliminated by applying the modified Mahalanobis distance outliers detection method. Then, a tightly coupled Kalman filter was adopted, where UWB ranging values were taken as the extended Kalman filter observation quantity, the position and attitude of the inertial navigation were taken as the extended Kalman filter prediction value, and UWB ranging values were used to constantly correct the position and attitude data of the inertial navigation solution. Finally, to verify the feasibility and effectiveness of the proposed method, trolley-mounted rectangular motion experiments were conducted with UWB positioning alone, as well as positioning by UWB and inertial navigation fusion. According to the comparison of experimental data, in interfered rectangular trajectory positioning experiments, when UWB was combined with inertial navigation positioning, the average precision was increased by 36.6% than that with UWB positioning alone; The comparison of the error results show that the error fluctuation of the fusion positioning using UWB and inertial navigation is smaller, but with higher robustness; The results indicate that, compared with algorithms utilizing the UWB technology alone for positioning, such fusion positioning algorithm can effectively suppress interferences in the positioning process. Furthermore, the robustness and positioning precision of the positioning system in indoor environments can be significantly improved.
    $\left\{ \begin{array}{l} {T_{round}} = {T_{a2}} - {T_{a1}} \\ {T_{reply}} = {T_{b2}} - {T_{b1}} \\ {{\overset{\frown} t}_f} = \left( {{T_{round}} - {T_{reply}}} \right)/2 \\ \end{array} \right.$(1)

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    $y = 0.029\;87{x^4} - 0.010\;73{x^3} - 0.504\;6{x^2} + 0.910\;8x + 1.544$(2)

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    $\left\{ \begin{array}{l} d = \sqrt {{B^{\rm T}}{S^{ - 1}}B} \\ B = \left[ {{x_i} - T} \right] \\ \end{array} \right.$(3)

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    ${\overset{\frown} \omega } = {{\textit{z}}_{gyro}}$(4)

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    ${{\textit{z}}_{gyro}} = \omega + {\eta _{gyro}}$(5)

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    $a = \ddot X - g + {\eta _{acc}}$(6)

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    $\xi \left( k \right) = \left( \begin{array}{l} X \\ \rho \\ \delta \\ \end{array} \right) = \left( {\begin{array}{*{20}{c}} x\;\;y \;\;{\textit{z}}\;\;{{\rho _x}} \;\;{{\rho _y}}\;\;{{\rho _z}} \;\;{{D_0}}\;\;{{D_1}}\;\;{{D_2}} \end{array}} \right)$(7)

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    $\delta = \left( {\begin{array}{*{20}{c}} {{D_0}}&{{D_1}}&{{D_2}} \end{array}} \right)$(8)

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    $ [\kern-0.15em[ \delta ]\kern-0.15em] = \left[ {\begin{array}{*{20}{c}} 0&{{D_2}}&{ - {D_1}} \\ { - {D_2}}&0&{{D_0}} \\ {{D_1}}&{ - {D_0}}&0 \end{array}} \right]$(9)

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    $\exp \left( { [\kern-0.15em[ \delta ]\kern-0.15em] } \right) = \left( {I + [\kern-0.15em[ \delta ]\kern-0.15em] } \right)$(10)

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    ${\overset{\frown} R} = {{\overset{\frown} R} _{ref}}\left( {I + [\kern-0.15em[ {\overset{\frown} \delta } ]\kern-0.15em] } \right)$(11)

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    ${{\overset{\frown} R} _{ref,post}} = \exp \left( { [\kern-0.15em[ \delta ]\kern-0.15em] } \right){{\overset{\frown} R} _{ref,pre}}$(12)

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    $\left\{ \begin{array}{l} \Delta {x^b} = {\rho _{x,k}}\Delta t + \dfrac{1}{2}{a_{x,k}}\Delta {t^2} \\ \Delta {y^b} = {\rho _{y,k}}\Delta t + \dfrac{1}{2}{a_{y,k}}\Delta {t^2} \\ \Delta {{\textit{z}}^b} = {\rho _{{\textit{z}},k}}\Delta t + \dfrac{1}{2}{a_{{\textit{z}},k}}\Delta {t^2} \\ \end{array} \right.$(13)

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    $R = \left[ {\begin{array}{*{20}{c}} {{R_{00}}}&{{R_{01}}}&{{R_{02}}} \\ {{R_{10}}}&{{R_{11}}}&{{R_{12}}} \\ {{R_{20}}}&{{R_{20}}}&{{R_{22}}} \end{array}} \right]$(14)

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    $\left\{ \begin{array}{l} {x_{k + 1}} = {x_k} + {R_{00}}\Delta {x^b} + {R_{01}}\Delta {y^b} + {R_{02}}\Delta {{\textit{z}}^b} \\ {y_{k + 1}} = {y_k} + {R_{10}}\Delta {x^b} + {R_{11}}\Delta {y^b} + {R_{12}}\Delta {{\textit{z}}^b} \\ {{\textit{z}}_{k + 1}} = {{\textit{z}}_k} + {R_{20}}\Delta {x^b} + {R_{21}}\Delta {y^b} + {R_{22}}\Delta {{\textit{z}}^b} \\ \end{array} \right.$(15)

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    $\left\{ \begin{array}{l} {\rho _{x,k + 1}} = {\rho _{x,k}} + {a_{x,k}}\Delta t \\ {\rho _{y,k + 1}} = {\rho _{y,k}} + {a_{y,k}}\Delta t \\ {\rho _{{\textit{z}},k + 1}} = {\rho _{{\textit{z}},k}} + {a_{{\textit{z}},k}}\Delta t \\ \end{array} \right.$(16)

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    ${\delta _{k + 1}} = \exp \left( { [\kern-0.15em[ d ]\kern-0.15em] } \right){\delta _k}\exp {\left( { [\kern-0.15em[ d ]\kern-0.15em] } \right)^{\rm T}}$(17)

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    $d = \left( {{d_0},{d_1},{d_2}} \right) = \left( {\frac{{{\omega _x}dt}}{2},\frac{{{\omega _y}dt}}{2},\frac{{{\omega _z}dt}}{2}} \right)$(18)

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    ${{\overset{\frown} \xi } _{k + 1}} = f\left( {{{{\overset{\frown} \xi } }_k}} \right)$(19)

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    ${d_{i,k}} = \left\| {X - {p_i}} \right\| + {\nu _d}$(20)

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    $ \left\| {X - {p_i}} \right\| = \sqrt {{{\left( {{x_k} - {p_{i,x}}} \right)}^2} + {{\left( {{y_k} - {p_{i,y}}} \right)}^2} + {{\left( {{z_k} - {p_{i,z}}} \right)}^2}} $(21)

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    ${H_i} = \dfrac{{\partial {d_{i,k}}}}{{\partial \xi }} = \left( {\begin{array}{*{20}{c}} {\dfrac{{\partial {d_{i,k}}}}{{\partial X}}}&{\dfrac{{\partial {d_{i,k}}}}{{\partial \rho }}}&{\dfrac{{\partial {d_{i,k}}}}{{\partial \delta }}} \end{array}} \right)$(22)

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    $\left\{ \begin{array}{l} \dfrac{{\partial {d_{i,k}}}}{{\partial X}} = \dfrac{{X - {p_i}}}{{\left\| {X - {p_i}} \right\|}} \\ \dfrac{{\partial {d_{i,k}}}}{{\partial \rho }} = \dfrac{{\partial {d_{i,k}}}}{{\partial \delta }} = 0 \\ \end{array} \right.$(23)

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    ${Z_k} = \sqrt {{{\left( {{{\tilde x}_k} - {p_{i,x}}} \right)}^2} + {{\left( {{{\tilde y}_k} - {p_{i,y}}} \right)}^2} + {{\left( {{{\tilde {\textit{z}}}_k} - {p_{i,{\textit{z}}}}} \right)}^2}} $(24)

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    $\left\{ \begin{array}{l} {{{\overset{\frown} \xi } }_{k + 1|k}} = f\left( {{{{\overset{\frown} \xi } }_{k|k}}} \right) \\ {P_{k + 1|k}} = { \varPhi} {P_{k|k}}{{{\varPhi}} ^{\rm T}} + Q \\ \end{array} \right.$(25)

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    $\left\{ \begin{array}{l} {K_{k + 1}} = {P_{k + 1|k}}{H^{\rm{T}}}{\left( {H{P_{k + 1|k}}{H^{\rm{T}}} + R} \right)^{ - 1}} \\ {{{\overset{\frown} \xi } }_{k + 1}} = {{{\overset{\frown} \xi } }_{k + 1|k}} + {K_{k + 1}}\left( {{Z_{k + 1}} - H{{{\overset{\frown} \xi } }_{k + 1|k}}} \right) \\ {P_{k + 1}} = \left( {I - {K_{k + 1}}H} \right){P_{k + 1|k}} \\ \end{array} \right.$(26)

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    Yan Liang, Qingdong Zhang, Ning Zhao, Chuanmiao Li. Indoor location method based on UWB and inertial navigation fusion[J]. Infrared and Laser Engineering, 2021, 50(9): 20200484
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