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The fusion of ultra-wideband (UWB) and inertial measurement unit (IMU) is an effective solution to overcome the challenges of UWB in nonline-of-sight (NLOS) conditions and error accumulation of inertial positioning in indoor environments. However, existing systems are based on foot-mounted or body-worn IMUs, which limit the application of the system to specific practical scenarios. In this paper, we propose the fusion of UWB and pedestrian dead reckoning (PDR) using smartphone IMU, which has the potential to provide a universal solution to indoor positioning. The PDR algorithm is based on low-pass filtering of acceleration data and time thresholding to estimate the step length. According to different movement patterns of pedestrians, such as walking and running, several step models are comparatively analyzed to determine the appropriate model and related parameters of the step length. For the PDR direction calculation, the Madgwick algorithm is adopted to improve the calculation accuracy of the heading algorithm. The proposed UWB/PDR fusion algorithm is based on the extended Kalman filter (EKF), in which the Mahalanobis distance from the observation to the prior distribution is used to suppress the influence of abnormal UWB data on the positioning results. Experimental results show that the algorithm is robust to the intermittent noise, continuous noise, signal interruption, and other abnormalities of the UWB data.

Indoor positioning technology has a wide range of applications from supermarket shopping assistance to drone positioning and patient tracking in hospitals [

There are a few works in the literature on combining UWB and inertial sensors. Fan et al. [

There are many methods for outliers detection. The most direct method is to reject the observations with large residual directly. However, this method may lead to a lack of continuity in the estimates of the covariance [

To address the above challenges, in this paper, we propose a tightly coupled UWB/PDR fusion method based on smartphone IMU for positioning in indoor environments. To the best of our knowledge, the proposed method is the first to address the UWB/PDR fusion using smartphone IMU. We also adopt the Madgwick algorithm for heading estimation in smartphone-based PDR and show that a significant improvement in heading estimation accuracy can be achieved. Finally, we propose the use of Mahalanobis distance from the observation to the prior distribution to suppress the influence of abnormal UWB data on the positioning results.

The remainder of the paper is organized as follows: In Section

An overview of the proposed method for UWB/PDR fusion is shown in Figure

Framework of the research.

The UWB/PDR fusion is done based on the EKF algorithm. To make the fusion robust against abnormal and outlying sensor readings, the use of the Mahalanobis distance from the observation to the prior distribution is proposed. As shown by experimental evaluation, the proposed method is robust to intermittent noise, continuous noise, signal interruption, and other abnormalities of the UWB data.

The PDR algorithm consists of step detection, step length estimation, and heading estimation. Based on the movement characteristics of the pedestrian, the accelerometer data are used to measure the number of steps and estimate the step length. Then, in combination with the heading information obtained from the IMU, the current position of the pedestrian is calculated by using equation (

Walking is characterized by a periodic acceleration pattern. With the foot from lifting to landing, that is, with the gravity center from rising to falling, the acceleration data in the vertical direction follow a curve from peak to trough. Therefore, the detection of a step can be done based on acceleration measurements. Smooth region detection [

In this work, the method proposed in [

Identification of maxima and minima in the step detection.

The commonly used step length calculation models can be roughly divided into three types: constant model, linear model, and nonlinear model. Among them, the constant model is the simplest one; however, it has the drawback that it cannot adapt to the real-time changes of the pedestrian velocity. A statistical table of step length at different levels is presented in [

For the linear model, Levi and Judd [

When the pedestrian walks with the smartphone held horizontally, the azimuth of the smartphone can be regarded as the heading angle of the pedestrian. The azimuth can be calculated by the built-in algorithm based on the gyroscope or the magnetometer in the smartphone. However, this heading calculation is largely influenced by the smartphone pose and the user’s body movement. Figure

Comparison of the heading angles.

In order to improve the accuracy of the heading calculation, the state-of-art Attitude and Heading Reference Systems (AHRS), i.e., the Madgwick algorithm, is introduced into the PDR algorithm in this paper. In this algorithm, in order to estimate the direction, the measurements of accelerometer, gyroscope, and magnetometer are combined with two absolute fields, the geomagnetic field and the gravity field, whose directions and intensities are known. The advantage of the AHRS algorithm is that the attitude error can be compensated continuously, improving the accuracy of the direction. As can be seen from Figure

Initially, it is assumed that the sensor is either in a stationary state or moves at a constant velocity, so that only the gravity vector is measured by the accelerometer. In addition, it is assumed that the magnetic field is nondisturbed, and therefore, only the geomagnetic field is measured by the magnetometer. The pitch (

The value of yaw (

In the geographic frame, the

Navigation frame and geographic frame.

The relationship of the geomagnetic data between b-frame and geographic frame is

The heading angle can be calculated by Formula (

For a specific vector, its magnitude and direction are the same when it is represented by different coordinate systems. This is the principle of the attitude calculation. However, error exists in the transformation matrix between the two coordinate systems. When a vector is transformed by a rotation matrix with error, a deviation between the transformed result and the original vector will appear. This deviation can be used to correct the rotation matrix, and the attitude is thus corrected. In the Madgwick algorithm, this rotation matrix is represented by a quaternion, and the attitude is calculated by modifying the quaternion. The accelerometer and the magnetometer are the main measured objects in the attitude calculation process. In the Madgwick algorithm, the current attitude is updated by the gyroscope:

The error equation is defined as

The above formula is solved by the Gauss–Newton method:

The UWB provides absolute positioning, but its performance is affected by the NLOS conditions. In contrast, the PDR method based on smartphone IMU data provides relative positioning characterized by error accumulation, but it is independent of the environmental conditions. Therefore, a UWB/PDR fusion algorithm is expected to outperform the individual techniques. In this section, a UWB/PDR fusion algorithm based on the robust EKF is presented.

The acceleration data of the IMU are firstly used to determine whether the state is stationary or moving. At the beginning of the positioning, the pedestrian stands still for a few seconds. Gross error of the UWB positioning result in the stationary state is eliminated, and the average value is calculated as the starting position of the PDR algorithm. The initial orientation angle is obtained by using the Madgwick algorithm, and then, the PDR calculation is performed according to Formula (

The state equation of the EKF algorithm is

It is assumed that the position coordinate and the dynamic noise of the heading obey a Gaussian distribution with the mean of 0 and the covariance of

The UWB ranging measurement

The measurement noise matrix is

Suppose the UWB observation obeys Gaussian distribution, that is,

Filtering: for

State prediction

Recalculate

State update

For observation with larger Mahalanobis distance, its covariance is required to be increased to reduce its influence on the posterior estimation. The covariance matrix for the new observation can be updated according to the following formula:

For computational complexity, REKF is just added lines 2–7 for robust processing with respect to EKF. The problem here is to calculate the number of while loops. From the fourth line of the algorithm, we can see that each cycle

The test site is the underground garage of the University of Melbourne. As shown in Figure

Experimental setup and equipment. (a) The underground garage and (b) UWB tag and smartphone.

Two routes are set in the experiment: one is a rectangular route with fewer turnings and the other is an 8-shaped route with more turnings, as shown in Figure

Experimental routes. (a) Route 1 and (b) Route 2.

The PDR experiment was conducted by two boys and two girls. The height and weight of the two boys are 1.8 meters and 70 kilograms and 1.78 meters and 72 kilograms, respectively. The height and weight of the two girls are 1.65 meters and 55 kilograms and 1.64 meters and 50 kilograms, respectively. The step detection result is shown in Figure

Step detection result.

In the table, “Walk” represents the normal walking pattern and “Run” represents the running pattern, including split-step running, stride running, and normal running. It can be seen from the accuracy rate that when the user is walking forward at normal velocity, the accuracy rate of step detection is up to 98% or more, with an average of 99.2%, and the number of wrongly detected step is within 2; when the user is running forward at different velocities, the average accuracy rate is 97.2%, with the minimum accuracy rate of 94.2%, and the maximum wrongly detected step number is 5. The results show that this method can be well applied to the normal walking pattern, while for the abnormal movement patterns, the parameters of step detection are required to be further studied and optimized.

Formulas (

Seven sets of data for the normal walking pattern, including walking along the straight line, walking along the fold lines, etc., are firstly selected. All the step lengths are accumulated to calculate the pedestrians’ movement distance, and the calculated value is compared to the actual distance. The least square method is used to solve the regression coefficients of the linear model and the coefficient of the nonlinear model. The regression coefficients of the linear model are

Table

Normal gait step length calculation (unit: m).

Actual distance | 40.5 | 71.4 | 43.2 | 39.5 | 81.6 | 211.68 | 179 |
---|---|---|---|---|---|---|---|

Constant model | 38.608 | 73.766 | 43.348 | 40.421 | 81.526 | 213.771 | 182.391 |

Linear model | 41.411 | 71.372 | 44.799 | 38.894 | 82.381 | 209.381 | 178.707 |

Nonlinear model | 38.427 | 73.065 | 46.227 | 39.895 | 81.520 | 215.612 | 175.950 |

Abnormal gait step length calculation (unit: m).

Actual distance | 55.2 | 52.5 | 40.5 | 40.8 | 31.8 | 39.5 | 81.6 |
---|---|---|---|---|---|---|---|

Constant model | 46.183 | 52.621 | 36.437 | 40.631 | 35.907 | 51.297 | 73.788 |

Linear model | 46.865 | 54. 992 | 36.072 | 42.554 | 38.021 | 46.854 | 76.173 |

Nonlinear model | 46.377 | 54.656 | 37.393 | 40.131 | 37.717 | 46.490 | 76.270 |

The average absolute distance differences obtained by the three models are 5.298 m, 4.973 m, and 4.713 m, respectively, and the one calculated by Formula (

In summary, when a pedestrian moves in a normal gait, the linear model corresponding to Formula (

As can be seen from Figure

Range measurement of (a) Route 1 and (b) Route 2.

Figure

Positioning results of (a) Route 1 and (b) Route 2.

In subgraph (a), for the UWB, most of the positioning points are consistent with the reference trajectory, but due to the blocking of the column and the pedestrian during walking, some abnormal points appear in the positioning result. For the PDR, the trajectory is relatively smooth, but due to the cumulative error of step length and direction, the overall positioning trajectory deviates from the reference one. For the EKF, advantages of UWB and PDR algorithms are used and most of the positioning result is consistent with the reference trajectory, but several large jumps appear since the abnormal UWB cannot be processed by this algorithm. For the REKF, the positioning result almost coincides with the reference trajectory, presenting strong ability to process abnormal data.

Route 2 is more complex than Route 1. Therefore, in subgraph (b), for the UWB, more data are blocked by the pedestrian and the column, resulting in more abnormal points on the positioning result. For the PDR, the accumulation error of the direction grows with the increase of the number of turnings, resulting in a large shift in the overall trajectory. For the EKF, there are many jumps on the entire trajectory since the algorithm is unavoidably disturbed by the abnormal data. For the REKF, it still shows strong antinoise ability, with its positioning result basically consistent with the reference trajectory.

Table

Positioning error analysis of Route 1 and Route 2.

UWB | PDR | EKF | REKF | |
---|---|---|---|---|

Route 1 (RMSE/m) | 0.92 | 2.34 | 0.78 | 0.35 |

Route 2 (RMSE/m) | 1.44 | 3.26 | 1.04 | 0.45 |

To further analyze the performance of the REKF algorithm, three kinds of noise are injected into the UWB data of Route 2. The first one is uniformly increasing random noise of different ratios; the second one is continuous noise randomly injected; the third one is noise caused by the randomly blocked UWB beacons over a continuous time period.

Gaussian white noise with an intensity of 30 dBW is used. The ratios of the injected noise account for 20%, 10%, and 7% of the total number of measurements, respectively. Figure

4 beacons with 20% Gaussian white noise randomly and uniformly injected.

Figure

Positioning results of Route 2 with UWB noise of different ratios injected.

Figure

3 beacons with continuous noise injected.

Figure

Positioning results of Route 2 with continuous noise injected into Beacons 1–3.

Figure

4 beacons intermittently blocked.

Positioning results of Route 2 with 2–4 beacons’ data intermittently blocked.

A UWB/PDR fusion positioning method based on the robust EKF is proposed in this paper. In this algorithm, the Mahalanobis distance between the observation and the system state is calculated to update the observation covariance, inhibiting the effect of abnormal observations on the positioning results. In addition, the Madgwick algorithm is introduced into the heading calculation of the PDR algorithm, effectively suppressing the cumulative error of the heading calculation. The experimental results show that in the case of intermittent or continuous UWB ranging noise and signal interruption, the proposed method exhibits strong robustness, with positioning accuracy higher than that of the EKF algorithm. However, how to improve the performance of the algorithm in the presence of stronger UWB ranging noise and much more signal interruption is required to be further tested.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that they have no conflicts of interest.

This work was supported by the National Natural Science Foundation of China under grant number 41674030 and the China Postdoctoral Science Foundation under grant number 2016M601909 and a grant from the China Scholarship Council.

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