# Robust Self-Contained Pedestrian Navigation by Fusing the IMU and Compass Measurements via UFIR Filtering

Authors: Meng Hou; Yuan Xu; Xiao Liu
Journal: Journal of Electrical and Computer Engineering
 (2018)

---

## Abstract

In order to overcome the poor observability of yaw measurement for foot-mounted inertial measurement unit (IMU), an integrated IMU+Compass scheme for self-contained pedestrian navigation is presented. In this mode, the compass measurement is used to provide the accurate yaw to improve the accuracy of the attitude transformation matrix for the foot-mounted IMU solution. And then, when the person is in a stance phase during walk, a unbiased finite impulse response (UFIR) filter based on the self-contained pedestrian navigation scheme is investigated, which just needs the state vector sizeMU and the filtering horizon size NU, while ignoring the noise statistics compared with the Kalman filter (KF). Finally, a real test has been done to verify the performance of the proposed self-contained pedestrian navigation using the IMU and compass measurements via UFIR filter. The test results show that the proposed filter has robust performance compared with the KF.


---

## Body

## 1. Introduction

Indoor pedestrian navigation (PN), which provides the position and the heading information of the target person in indoor environment, has received a topic [1, 2].In order to provide the accurate position information of the person in indoor environment, many approaches have been proposed. For example, in [3, 4], the radio frequency identification (RFID)-based technologies have been proposed provide object self-localization. Yang and Shao and Ma et al. proposed in [5, 6] an autonomous positioning system operating on WiFi, which is also able to achieve the indoor localization in indoor environment. However, it should be pointed out that although the RFID- and WiFi-based methods mentioned above are able to provide the position information in indoor environment, the accuracy of such approaches is on meter-level. In order to improve the positioning accuracy, ultrasonic-based approaches are proposed in [7]. However, it should be pointed that although the ultrasonic-based approaches are on centimeter-level, it is easy to be outage. Meanwhile, the ultra wideband (UWB) technology [8] is employed in some approaches. For example, a location detection and tracking of moving targets by a 2D IR-UWB radar system is presented in [9]. It should be emphasized that the methods mentioned above have to employ extra infrastructures; moreover, the sampling time of these methods is larger [1, 10].In order to overcome the disadvantages of the methods mentioned above, the inertial navigation systems (INS) have been employed for providing the human position in global positioning system- (GPS-) denied areas. One of the famous examples is the navigation shoe proposed in [11], which employs the foot-mounted inertial measurement unit (IMU) to correct the error drift of the INS solution. Based on this model, there are many improving approaches. For example, in [12–14], the magnetic sensor is used to correct the positioning error of the foot-mounted IMU. On the other hand, there are also many approaches for the signal processing in INS. For example, the analysis for microelectromechanical system (MEMS) gyroscope within wide-temperature range is shown in [15].Based on the INS, the Kalman filter (KF) and its improving methods are widely used to correct the INS solution error [16, 17]. However, despite great progress in the development of the KF approach, the recursive KF-based algorithms demonstrate good performance mostly when the noise statistics are known exactly, and the model perfectly matches the process; otherwise, the KF-based estimators often demonstrate poor performance [18–20]. In order to provide the robust estimation, the unbiased finite impulse response (UFIR) filter has been proposed in [21–23]. Then, there are some improving UFIR filters proposed to improve the performance [24–27]. Compared with the KF-based filters, UFIR filters just need the state vector size and the filtering horizon size, while ignoring the noise statistics [25, 28, 29].In this paper, we propose a self-contained pedestrian navigation by fusing the IMU and compass measurements via UFIR filtering. To the self-contained pedestrian navigation scheme, the compass measurement is used to provide the accurate yaw to improve the accuracy of the attitude transformation matrix for the foot-mounted IMU solution. Moreover, we investigate the UFIR filter based on the self-contained pedestrian navigation scheme, which just needs the state vector sizeMU and the filtering horizon size NU, while ignoring the noise statistics. Finally, a real test has been done to verify the performance of the proposed self-contained pedestrian navigation using the IMU and compass measurements via UFIR filter. The test results show that the proposed filter has robust performance compared with the KF. The remaining part of this paper is organized as follows. Section 2 designs the scheme of the self-contained pedestrian navigation using the IMU and compass measurements. Section 3 presents the UFIR algorithms for the self-contained pedestrian navigation. Testing and results are discussed in Section 4. Finally, Section 5 gives the conclusions.


## 2. The Self-Contained Pedestrian Navigation Using the IMU and Compass Measurements

In this section, the scheme of self-contained pedestrian navigation using the IMU and compass measurements will be designed. Then, the state and measurement equations based on the scheme which we designed will be investigated.


### 2.1. The Scheme of Self-Contained Pedestrian Navigation Using the IMU and Compass Measurements

In this subsection, we will introduce the scheme of self-contained pedestrian navigation using the IMU and compass measurements. The architecture of the self-contained pedestrian navigation employing the recent IMU and compass measurements is shown in Figure1. In this work, we employ inertial measurement unit (IMU) and compass measurements for the indoor self-contained pedestrian navigation. The IMU is fixed on the shoe, and the compass is fixed on the shoulder. In this paper, the IMU is used to provide the acceleration a, angular velocity w, pitch, and the roll, which are used to compute the position and posture of the target person. Compared with the IMU fixed on the shoe, thigh, shank, and waist, the IMU fixed on the shoulder has the best performance for yaw measurement. Thus, we employ shoulder-mounted IMU to provide the yaw measurement for the solution, which can improve the accuracy of the attitude transformation matrix for the foot-mounted IMU solution. In theory, the true velocity of the pedestrian shoes should be zero when the shoe is on the floor (so called stance phase). Thus, the velocity measured from the foot-mounted IMU will be the error measurement of the velocity in the stance phase. And when the person is in a stance phase, the unbiased finite impulse response (UFIR) filter works; it employs the measurement of the velocity error derived from the foot-mounted IMU to estimate the INS position error; then, the INS solution is corrected by the error estimation.Figure 1
The architecture of the self-contained pedestrian navigation using the IMU and compass measurements.Meanwhile, the body frame (so called b-frame) and the navigation frame (so called n-frame (East-North-Up, ENU)) used in this paper are also shown in this figure. Compared with the outdoor navigation, the area of the indoor self-contained pedestrian navigation is very small; thus, the earth’s rotation is not considered in this paper.


### 2.2. The State and Measurement Equations for the UFIR Filter

In this subsection, the state and measurement equations for the UFIR filter will be designed. Based on the self-contained pedestrian navigation scheme proposed in Section2.1, a UFIR filter with a 15-element vector will be introduced in this paper. The state equation of the UFIR filter used in this paper at time step tt is listed as(1)ϕttnδVttn∇ttnεttn︸Xtt=I3×303×303×3I3×3TSfttnTI3×3I3×3T03×303×303×3I3×303×303×303×303×3I3×3︸Attϕtt-1nδVtt-1n∇tt-1nεtt-1n︸Xtt-1+ωtt-1,where ϕttn,δVttnT denotes attitude and velocity error vectors in n-frame at time step tt and ∇ttb,εttbT denotes the biases for accelerometers and gyroscopes in b-frame at time step tt, respectively. All these 5 components mentioned above have 3 elements each:(2)Sfttn=0aDttn-aNttn-aDttn0aEttnaNttn-aEttn0;here, aEttnaNttnaDttn is the acceleration in n-frame (East-North-Up, ENU) at time step tt; T denotes the sampling time; ωtt is a system noise at time step tt with the covariance Qtt.The measurement equation is listed in(3)δV~ttn︸Ztt=03×3I3×303×303×3︸HttϕttnδVttn∇ttnεttn︸Xtt+ηtt,where δV~ttn is the observations for the velocity error in n-frame at time step tt; ηtt is a measurement noise with covariance is Rtt.


## 2.1. The Scheme of Self-Contained Pedestrian Navigation Using the IMU and Compass Measurements

In this subsection, we will introduce the scheme of self-contained pedestrian navigation using the IMU and compass measurements. The architecture of the self-contained pedestrian navigation employing the recent IMU and compass measurements is shown in Figure1. In this work, we employ inertial measurement unit (IMU) and compass measurements for the indoor self-contained pedestrian navigation. The IMU is fixed on the shoe, and the compass is fixed on the shoulder. In this paper, the IMU is used to provide the acceleration a, angular velocity w, pitch, and the roll, which are used to compute the position and posture of the target person. Compared with the IMU fixed on the shoe, thigh, shank, and waist, the IMU fixed on the shoulder has the best performance for yaw measurement. Thus, we employ shoulder-mounted IMU to provide the yaw measurement for the solution, which can improve the accuracy of the attitude transformation matrix for the foot-mounted IMU solution. In theory, the true velocity of the pedestrian shoes should be zero when the shoe is on the floor (so called stance phase). Thus, the velocity measured from the foot-mounted IMU will be the error measurement of the velocity in the stance phase. And when the person is in a stance phase, the unbiased finite impulse response (UFIR) filter works; it employs the measurement of the velocity error derived from the foot-mounted IMU to estimate the INS position error; then, the INS solution is corrected by the error estimation.Figure 1
The architecture of the self-contained pedestrian navigation using the IMU and compass measurements.Meanwhile, the body frame (so called b-frame) and the navigation frame (so called n-frame (East-North-Up, ENU)) used in this paper are also shown in this figure. Compared with the outdoor navigation, the area of the indoor self-contained pedestrian navigation is very small; thus, the earth’s rotation is not considered in this paper.


## 2.2. The State and Measurement Equations for the UFIR Filter

In this subsection, the state and measurement equations for the UFIR filter will be designed. Based on the self-contained pedestrian navigation scheme proposed in Section2.1, a UFIR filter with a 15-element vector will be introduced in this paper. The state equation of the UFIR filter used in this paper at time step tt is listed as(1)ϕttnδVttn∇ttnεttn︸Xtt=I3×303×303×3I3×3TSfttnTI3×3I3×3T03×303×303×3I3×303×303×303×303×3I3×3︸Attϕtt-1nδVtt-1n∇tt-1nεtt-1n︸Xtt-1+ωtt-1,where ϕttn,δVttnT denotes attitude and velocity error vectors in n-frame at time step tt and ∇ttb,εttbT denotes the biases for accelerometers and gyroscopes in b-frame at time step tt, respectively. All these 5 components mentioned above have 3 elements each:(2)Sfttn=0aDttn-aNttn-aDttn0aEttnaNttn-aEttn0;here, aEttnaNttnaDttn is the acceleration in n-frame (East-North-Up, ENU) at time step tt; T denotes the sampling time; ωtt is a system noise at time step tt with the covariance Qtt.The measurement equation is listed in(3)δV~ttn︸Ztt=03×3I3×303×303×3︸HttϕttnδVttn∇ttnεttn︸Xtt+ηtt,where δV~ttn is the observations for the velocity error in n-frame at time step tt; ηtt is a measurement noise with covariance is Rtt.


## 3. UFIR Algorithms for the Self-Contained Pedestrian Navigation

In this section, the KF and the UFIR filter for the indoor self-contained pedestrian navigation based on the scheme proposed in Section2.1 will be discussed.


### 3.1. KF Algorithm

As one of the most used data fusion algorithm, the Kalman filter (KF) and its improving methods have been widely used in many fields [30–34]. And its pseudo code is listed as Algorithm 1. It should be pointed out that the Kalman filter and its improving methods need the accurate model description and noise description, especially the accurate Q and Rtt, to maintain the performance. However, it is not easy to get the information mentioned above in someplace.Algorithm 1:Kalman filter algorithm for the self-contained scheme.
Data: Ztt, X0, P0, Q, Rtt Result: X^tt (1) begin (2)fortt=1:∞do (3)X^tt∣tt-1=AttX^tt-1 (4)Ptt∣tt-1=Att-1Ptt-1Att-1T+Q (5)Ktt=Ptt∣tt-1HttTHkPtt∣tt-1HttT+Rtt-1 (6)X^tt=X^tt∣tt-1+Ktt(Ztt-Hkx^tt∣tt-1) (7)Ptt=I-KttHttPtt∣tt-1 (8)end for (9) end


### 3.2. UFIR Filtering Algorithm

Compared with KF, the UFIR filter does not need the accurateQ and Rk to keep its accuracy [26, 35]. Based on the self-contained scheme proposed in Section 2.1, the UFIR filtering algorithm is listed in Algorithm 2. Thus, we can say that the UFIR filter is more robust than the KF filter.Algorithm 2:UFIR filter algorithm for the self-contained scheme.
Data: Ztt, MU, NU Result: X^tt (1)begin (2)fortt=NU:∞do (3)m=tt-NU+1,s=m+MU-1 (4) Hs,m=Hm+3Am+3Am+2Am+1Hm+2Am+2Am+1Hm+1Am+1Hm (5)As,0t=AsAs-1⋯Am+1 (6)Gs=As,0tHs,mTHs,m-1As,0tT (7)iftt=Nthen (8)Zs,m=Zm+3TZm+2TZm+1TZmTT (9)X~s=As,0Hs,mTHs,m-1Hs,mTZs,mT (10)end if (11)iftt>Nthen (12)X~s=X^tt (13)end if (14)forkk=s+1:ttdo (15)X~kk∣kk-1=AkkX~kk-1+ωkk (16)Gkk=HkkTHkk+AkkGkk-1AkkT-1-1 (17)Kkk=GkkHkkT (18)X~kk=X~kk∣kk-1+Kkk(Zkk-HkkX~kk|kk-1) (19)end for (20)X^tt=X~tt (21)end for (22) end (23) †  MU is the state vector size (24) †  NU is the filtering horizon size


## 3.1. KF Algorithm

As one of the most used data fusion algorithm, the Kalman filter (KF) and its improving methods have been widely used in many fields [30–34]. And its pseudo code is listed as Algorithm 1. It should be pointed out that the Kalman filter and its improving methods need the accurate model description and noise description, especially the accurate Q and Rtt, to maintain the performance. However, it is not easy to get the information mentioned above in someplace.Algorithm 1:Kalman filter algorithm for the self-contained scheme.
Data: Ztt, X0, P0, Q, Rtt Result: X^tt (1) begin (2)fortt=1:∞do (3)X^tt∣tt-1=AttX^tt-1 (4)Ptt∣tt-1=Att-1Ptt-1Att-1T+Q (5)Ktt=Ptt∣tt-1HttTHkPtt∣tt-1HttT+Rtt-1 (6)X^tt=X^tt∣tt-1+Ktt(Ztt-Hkx^tt∣tt-1) (7)Ptt=I-KttHttPtt∣tt-1 (8)end for (9) end


## 3.2. UFIR Filtering Algorithm

Compared with KF, the UFIR filter does not need the accurateQ and Rk to keep its accuracy [26, 35]. Based on the self-contained scheme proposed in Section 2.1, the UFIR filtering algorithm is listed in Algorithm 2. Thus, we can say that the UFIR filter is more robust than the KF filter.Algorithm 2:UFIR filter algorithm for the self-contained scheme.
Data: Ztt, MU, NU Result: X^tt (1)begin (2)fortt=NU:∞do (3)m=tt-NU+1,s=m+MU-1 (4) Hs,m=Hm+3Am+3Am+2Am+1Hm+2Am+2Am+1Hm+1Am+1Hm (5)As,0t=AsAs-1⋯Am+1 (6)Gs=As,0tHs,mTHs,m-1As,0tT (7)iftt=Nthen (8)Zs,m=Zm+3TZm+2TZm+1TZmTT (9)X~s=As,0Hs,mTHs,m-1Hs,mTZs,mT (10)end if (11)iftt>Nthen (12)X~s=X^tt (13)end if (14)forkk=s+1:ttdo (15)X~kk∣kk-1=AkkX~kk-1+ωkk (16)Gkk=HkkTHkk+AkkGkk-1AkkT-1-1 (17)Kkk=GkkHkkT (18)X~kk=X~kk∣kk-1+Kkk(Zkk-HkkX~kk|kk-1) (19)end for (20)X^tt=X~tt (21)end for (22) end (23) †  MU is the state vector size (24) †  NU is the filtering horizon size


## 4. Test and Discussion

In this paper, we employ a real indoor test to verify the performance of the proposed self-contained pedestrian navigation using the IMU and compass measurements via UFIR filter. The real test was done in the Machine Building of the University of Jinan, Jinan, China. In this section, the real test will be designed and we will investigate the corresponding results. Firstly, the real test will be designed. Then, the performances of the KF and UFIR filter will be compared.


### 4.1. Setting

The test platform used in the real test consists of one 9 degree of freedom (DOF) IMU, one compass, one computer, and one encoder. The 9-DOF IMU is fixed on the shoe; it employs ADXL203, ADXRS620, and HMC5983 as accelerometer, gyroscope, and magnetometer, respectively, which is able to provide the human position. Then, one HMC5983-based compass which is fixed on the shoulder is used to provide more accurate yaw measurement, which helps improve the accuracy of the yaw for the foot-mounted IMU. The computer is used to collect the sensor data. The encoder used in the real test is able to provide the reference velocity of the person. The sampling timeT used in (1) is 0.03 s. From Algorithm 2, we can see that the performance of the UFIR filter is just need MU and NU. From (1), we can get that MU=12 and we employ NU=13 in this paper. The prototype of the test platform is shown in Figure 2.Figure 2
The prototype of the test platform.


### 4.2. The Performance of the UFIR Filter

The position error of the UFIR filter for self-contained pedestrian navigation using the IMU and compass measurements will be discussed in this section. In this subsection, we employ two groups of parameters which listed in Table1.Table 1
The parameters for the tests.
X 0 P 0 Q R N U Group 1 0 12 × 1 I 12 × 12 I 12 × 12 I 3 × 3 13 Group 2 0 12 × 1 I 12 × 12 1 0 - 2 I 12 × 12 I 3 × 3 13(1) INS Position Errors–Group 1. Trajectories measured by INS + ZUPT + KF and INS + ZUPT + UFIR for the first group of possible parameters (Group 1) are shown in Figures 3 and 4. From the figures, firstly, we can see that the proposed self-contained pedestrian navigation scheme is able to provide the person position without any auxiliary equipment. Secondly, we can see that the trajectories estimated by the KF and the UFIR filter are similar.Figure 3
Trajectory measured by INS + ZUPT + KF for the first group of possible parameters (Group 1).Figure 4
Trajectory measured by INS + ZUPT + UFIR for the first group of possible parameters (Group 1).The absolute average position errors by the KF and UFIR filter in Test 1 (Group 1) are listed in Table2. From the table, we can see that the position errors of the KF and UFIR filter are similar. Thus, we can see that the performances of KF and UFIR filter are similar in Test 1 (Group 1).Table 2
Absolute average position errors by different filters in Test 1 (Group 1).
Model Absolute average position errors [m] East direction North direction KF 0.25 0.29 UFIR 0.22 0.31(2) INS Position Errors–Group 2. We now repeat the experiment for the second group of possible parameters (Group 2). The trajectories measured from UWB only model using least square algorithm and the INS/UWB loosely coupled integrated model using the KF and UFIR filter for the second group of possible parameters (Group 2) are shown in Figures 5 and 6. And the absolute average position errors by the KF and UFIR filter in Test 2 (Group 2) are listed in Table 3. From the figures, we can see easily that the KF has been diverged, while the performance of the UFIR filter is still good.Table 3
Absolute average position errors by different filters in Test 2 (Group 2).
Model Absolute average position errors [m] East direction North direction KF 0.88 2.79 UFIR 0.22 0.31Figure 5
Trajectory measured by INS + ZUPT + KF for the second group of possible parameters (Group 2).Figure 6
Trajectory measured by INS + ZUPT + UFIR for the second group of possible parameters (Group 2).


## 4.1. Setting

The test platform used in the real test consists of one 9 degree of freedom (DOF) IMU, one compass, one computer, and one encoder. The 9-DOF IMU is fixed on the shoe; it employs ADXL203, ADXRS620, and HMC5983 as accelerometer, gyroscope, and magnetometer, respectively, which is able to provide the human position. Then, one HMC5983-based compass which is fixed on the shoulder is used to provide more accurate yaw measurement, which helps improve the accuracy of the yaw for the foot-mounted IMU. The computer is used to collect the sensor data. The encoder used in the real test is able to provide the reference velocity of the person. The sampling timeT used in (1) is 0.03 s. From Algorithm 2, we can see that the performance of the UFIR filter is just need MU and NU. From (1), we can get that MU=12 and we employ NU=13 in this paper. The prototype of the test platform is shown in Figure 2.Figure 2
The prototype of the test platform.


## 4.2. The Performance of the UFIR Filter

The position error of the UFIR filter for self-contained pedestrian navigation using the IMU and compass measurements will be discussed in this section. In this subsection, we employ two groups of parameters which listed in Table1.Table 1
The parameters for the tests.
X 0 P 0 Q R N U Group 1 0 12 × 1 I 12 × 12 I 12 × 12 I 3 × 3 13 Group 2 0 12 × 1 I 12 × 12 1 0 - 2 I 12 × 12 I 3 × 3 13(1) INS Position Errors–Group 1. Trajectories measured by INS + ZUPT + KF and INS + ZUPT + UFIR for the first group of possible parameters (Group 1) are shown in Figures 3 and 4. From the figures, firstly, we can see that the proposed self-contained pedestrian navigation scheme is able to provide the person position without any auxiliary equipment. Secondly, we can see that the trajectories estimated by the KF and the UFIR filter are similar.Figure 3
Trajectory measured by INS + ZUPT + KF for the first group of possible parameters (Group 1).Figure 4
Trajectory measured by INS + ZUPT + UFIR for the first group of possible parameters (Group 1).The absolute average position errors by the KF and UFIR filter in Test 1 (Group 1) are listed in Table2. From the table, we can see that the position errors of the KF and UFIR filter are similar. Thus, we can see that the performances of KF and UFIR filter are similar in Test 1 (Group 1).Table 2
Absolute average position errors by different filters in Test 1 (Group 1).
Model Absolute average position errors [m] East direction North direction KF 0.25 0.29 UFIR 0.22 0.31(2) INS Position Errors–Group 2. We now repeat the experiment for the second group of possible parameters (Group 2). The trajectories measured from UWB only model using least square algorithm and the INS/UWB loosely coupled integrated model using the KF and UFIR filter for the second group of possible parameters (Group 2) are shown in Figures 5 and 6. And the absolute average position errors by the KF and UFIR filter in Test 2 (Group 2) are listed in Table 3. From the figures, we can see easily that the KF has been diverged, while the performance of the UFIR filter is still good.Table 3
Absolute average position errors by different filters in Test 2 (Group 2).
Model Absolute average position errors [m] East direction North direction KF 0.88 2.79 UFIR 0.22 0.31Figure 5
Trajectory measured by INS + ZUPT + KF for the second group of possible parameters (Group 2).Figure 6
Trajectory measured by INS + ZUPT + UFIR for the second group of possible parameters (Group 2).


## 5. Conclusion

In this paper, a self-contained pedestrian navigation by fusing the IMU and compass measurements via UFIR filtering and both the implement and test are proposed. To the self-contained pedestrian navigation scheme, the compass measurement is used to provide the accurate yaw to improve the accuracy of the attitude transformation matrix for the foot-mounted IMU solution. Moreover, we investigate the UFIR filter based on the self-contained pedestrian navigation scheme, which just needs the state vector sizeMU and the filtering horizon size NU, while ignoring the noise statistics. Finally, a real test has been done to verify the performance of the proposed self-contained pedestrian navigation using the IMU and compass measurements via UFIR filter. The test results show that the proposed filter has robust performance compared with the KF.



---

*Source: 8401967-2018-05-08.xml*