Twin IMU-HSGPS Integration for Pedestrian Navigation - CiteSeerX

Twin IMU-HSGPS Integration for Pedestrian Navigation Jared B. Bancroft, Gérard Lachapelle, M. Elizabeth Cannon, and Mark G. Petovello Position, Location And Navigation Group Department of Geomatics Engineering Schulich School of Engineering University of Calgary BIOGRAPHY Jared B. Bancroft is a Ph.D. Candidate in the PLAN Group of the Department of Geomatics Engineering at the University of Calgary. He received his B.Sc. in Geomatics Engineering in 2007 and has worked with navigation techniques since 2004. Jared's research interests include pedestrian and vehicular navigation through data fusion of multiple inertial units and satellite navigation data. Dr. Gérard Lachapelle holds a CRC/iCORE Chair in Wireless Location in the Department of Geomatics Engineering, where he also heads the PLAN group. He has been involved with GPS developments and applications since 1980 and has received major awards for his contribution. Dr. M. Elizabeth Cannon is Dean of the Schulich School of Engineering. She has been involved with GPS research since 1984 and has published numerous papers on static and kinematic positioning. She is a Past President of the ION and the recipient of the 2001 Kepler Award. Dr. Mark Petovello is an Assistant Professor in the Position, Location And Navigation (PLAN) group in the Department of Geomatics Engineering at the University of Calgary. Since 1998, he has been involved in various navigation research areas including software receiver development, satellite-based navigation, inertial navigation, reliability analysis and dead-reckoning sensor integration. More biography information http://plan.geomatics.ucalgary.ca.

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ABSTRACT Pedestrian navigation includes locating individuals of interest, including citizens, police officers, fire fighters, search and rescue personnel, and cell phone users. GPS can typically provide users with this ability. In signal

ION GNSS 2008, Session E3, Savannah, GA, 16-20 September 2008

degraded areas such as in the indoors, underground parkades and urban canyons, GPS must be integrated with additional sensors to provide availability to users with a reasonable amount of accuracy. Fusing GPS with one inertial unit is a common integration strategy. Because pedestrian navigation systems are typically low cost, MEMS inertial units are used. To mitigate the large errors of these inertial units, they are placed on the foot facilitating zero velocity updates when the foot is at rest during the stance phase of the gait cycle. This paper discusses a Kalman filter that incorporates two inertial units. The twin filter contains two 27 state filters, with each block filter providing the position, velocity, attitude, and error states of a single IMU. With knowledge of the human gait cycle, relative updates between the positions of the IMUs are incorporated to further improve the accuracy of the system. The relative update can either use the distance between the feet (IMUs), or the three vector components. The filter’s performance is shown through data collected under trees, in bushes and indoor where multipath errors are extreme. The improvement when using a second IMU filter is shown relative to the single IMU case. When using the relative distance updates there is a 58 to 71% improvement when indoor with comparable performance outdoor, where the GPS only solution is sufficient. The correlation between each IMUs error states is also analyzed to show there are no significant correlations generated from the relative updates. INTRODUCTION Users of navigation systems that are becoming more common include pedestrians, law enforcement, fire fighters, first responders and rescue personnel, all of whom benefit from real time location. Location based services are also among a large range of stakeholders now utilizing this technology. The E911 mandate is also driving cellular phone providers to provide location indoors. Real time locations can also aid with rescue of emergency responders should they require assistance. For

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example, firefighters who collapse while in a burning building can be located and rescued in a more efficient manner when using accurate and reliable position information. Pedestrian navigation techniques in recent years have integrated additional sensors with GNSS, in particular the GPS. Because GNSS users are susceptible to signal blockage and low signal availability, Inertial Measurement Units (IMUs) are used to provide continuous navigation through Inertial Navigation Systems (INS). The fusion of satellite and inertial measurements can provide a continuous navigation solution during GPS signal outages (Jekeli 2001). High Sensitivity GPS (HSGPS) receivers currently are able to track low power signals, albeit are more susceptible to larger multipath and increased noise errors in the process (Ray 2007). Pedestrian INS in the past has employed triads of low cost micro electro-mechanical systems (MEMS) accelerometers and gyroscopes. Cost and size remain among the most significant barriers for IMUs used in pedestrian navigation applications. Inherent to MEMS IMUs are substantially large biases that can be accounted for in a Kalman Filter (KF). In this paper, the IMUs are placed on the foot, such that during the stance phase of the gait cycle when the IMU is at rest, Zero Velocity Updates (ZUPTs) are applied. This technique has been successfully employed by numerous authors including Mezentsev (2005), Godha et al (2006), and Lachapelle (2003). GPS pseudorange updates provide absolute positioning to the system. GPS Doppler measurements are commonly used in INS, however because the inertial unit and GPS antenna do not experience the same velocities (the antenna is on the head, while the IMU is on a foot), Doppler observations are not used in a foot mounted INS, unless the lever arm and relative velocity of the IMU are accurately accounted for. A current limitation of single IMU is the position drift of the user during a GPS signal blockage or outage (Godha et al 2006). While there are some post processing techniques which can reduce this error (such as RauchTung-Streibel (RTS) smoothing (Gelb 1974)), the real time solution is still limited by the time correlated position drift during GPS outages and low observability. McMillan et al (1993) introduced using two inertial sensors through a Kalman filter based approach in marine navigation, which they termed Dual Inertial Integrated Navigation System (DIINS). The purpose was to provide reliability to ship navigation, while incorporating redundancy in case of IMU failure. The system incorporated fault detection of the inertial units. It has been used as a reference solution in numerous other technical papers for evaluating low cost marine

ION GNSS 2008, Session E3, Savannah, GA, 16-20 September 2008

navigation systems, such as Scherzinger et al (1996, 1997). Brand and Phillips (2003) incorporated two IMUs for personal navigation in addition to using range measurements between feet (done through additional radio frequencies). The filter consisted of two sets of navigation and IMU error states and the errors associated with the ranging between feet. This method utilizes the additional distance observed between the feet in the filter, but requires additional hardware in order to measure the range between feet. The filter also incorporated a barometer for height control. Petovello et al (2005) used a dual-GPS/INS approach to measure ship flexure aboard an aircraft carrier. This method was used to determine the relative vector between the inertial systems which could be observed through the two GPS antennas. The topic of this paper is to improve the long term accuracy, availability, reliability and continuity of pedestrian based navigation solutions during GPS signal blockages and degradation of pedestrian navigation systems using two IMUs. It aims to reduce the position error by incorporating two IMUs, which are placed on each foot and incorporating updates to constrain the relative location of the IMUs. Specifically, the two inertial units are “linked” together using the approximately known geometry of the walking gait cycle. Using two IMUs provides further reliability, more redundancy, and continued navigation in the event of an IMU failing to provide raw data. Because each IMU requires individual error corrections for their respective sensors (e.g. biases and scale factors), a KF incorporating two IMUs must estimate the errors of each IMU. In addition, because each IMU experiences different motion (on different feet), it is not realistic to combine the raw measurements. Thus the filter must also estimate the position, velocity and attitude of each IMU. The proposed filter thus contains twice the number of inertial states of a single IMU configuration INS (in addition to any GPS receiver clock error states if required). Because two inertial units are fused with GPS observations, the specifics of the modified Kalman filter used is described herein. The use of relative updates is also discussed. The filter performance is analyzed through data collected under operational conditions. SINGLE IMU INERTIAL NAVIGATION SYSTEMS The proposed twin IMU filter contains two single-IMU filters (more details later). Thus it is necessary to discuss

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the structure of a single IMU filter as it pertains to this paper. Consider the measurement model given below: z (t ) = H (t )x(t ) + η (t ) (1) where

z (t ) H (t ) x(t ) η (t )

is the observations, is the design matrix, is the unknown parameters (states), and is the measurement noise.

Now consider the system dynamics as follows: (2) x& (t ) = F (t )x(t ) + G (t )w(t )

where

F (t ) G (t ) w(t )

is the dynamics matrix, is the shaping matrix, is the process driving noise.

In the context of an INS KF, the system operates in discrete time mode. Thus the conversion of the system dynamics and the measurement model to discrete time is required. For brevity, Gelb (1974) discusses this in detail, and readers are also referred to Godha (2006) or Petovello (2003) for overviews.

to the nature of an immeasurable time varying lever arm in pedestrian navigation, the use of Doppler observations in not valid. Thus, for the purpose of this work, the observations to the filter include the pseudoranges and zero velocities. The filter adopts a tight coupling integration strategy (e.g. Knight 1999) whereby the GPS measured pseudoranges and INS predicted pseudoranges are used as filter input (as with zero velocities). Tight coupling in the context of pedestrian navigation is preferred to loose coupling because the filter can be updated with less than four satellites, which is the minimum number required for a GPS-only solution used in a loose coupling strategy. This is of critical importance considering that it is not uncommon to observe fewer than four satellites in urban canyons or indoor. Figure 1 represents the data flow of the single INS integration scheme. The inertial measurements are corrected from the estimated error states and are then integrated using the Earth Centered Earth Fixed (ECEF) frame (navigation frame) mechanization equations (ElSheimy 2007). Following the mechanization equations, the filter covariance is predicted to the current time. As GPS observations become available, the system performs an update stage whereby the measured pseudoranges are input into the EKF.

Additionally, because the system is non-linear, linearization is required through a Taylor series expansion. The readers are referred to Grewal and Andrew (2001) and Brown and Hwang (1997) for detailed derivations of the linearization process. In discrete nonlinear mode, equation (1) and (2) of the KF appears as: (3) ∂x = Φ ∂x + w k +1

k ,k +1

k

k

∂z k +1 = H∂x k +1 + η k +1

(4)

where

Φ k ,k +1

is the transition matrix.

The Kalman Filter in non-linear mode that uses the previous epoch’s state as a point of expansion is referred to as an Extended Kalman Filter (EKF). In the context of a single INS the states include position (3), velocity (3), and attitude (3), accelerometer and gyroscope biases (6), scale factors (6) and turn on biases (6). Thus there are 27 states for the INS filter. Note however that if the INS operates in single point mode, two additional states are required for the GPS receiver clock bias and clock drift. Observables to the filter include pseudoranges, Doppler observations, and double differenced phase observations when operating in differential GPS mode. However, due

ION GNSS 2008, Session E3, Savannah, GA, 16-20 September 2008

Figure 1 - Single INS Integration As the IMU is placed on the fore foot (see Figure 2), the IMU experiences the repetitive nature of the human gait cycle (Kwakkel 2008). The stance phase is of particular interest to this application as it indicates when the foot is at rest, thereby allowing ZUPTs to be used to update the filter. Godha et al (2006) describes the stance phase detection process in detail. It uses a three sample variance of the raw accelerometer signal and accordingly determines the magnitude of motion against predetermined thresholds.

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The twin filter, omitting the clock errors states for simplicity but without a loss of generality, can be expressed in terms of equation (3) and (4) are:

⎡∂x1k +1 ⎤ ⎡Φ1k ,k +1 0 ⎤ ⎡∂x1k ⎤ ⎡ w1k ⎤ = ⎥⎢ 2 ⎥ + ⎢ 2 ⎥ ⎢ 2 ⎥ ⎢ 2 Φ 0 ∂ x , 1 k k + ⎣ k +1 ⎦ ⎣ ⎦ ⎣∂xk ⎦ ⎣ wk ⎦ ⎡∂z 1k +1 ⎤ ⎡ H k1+1 0 ⎤ ⎡∂x1k +1 ⎤ ⎡η k1+1 ⎤ = ⎢ 2 ⎥ ⎢ ⎥⎢ ⎥+⎢ ⎥ H k2+1 ⎦ ⎣∂xk2+1 ⎦ ⎣η k2+1 ⎦ ⎣∂z k +1 ⎦ ⎣ 0 Figure 2 - MEMS IMUs located on feet A user stance phase is typically 25% of the walking gait cycle, which occurs for roughly 1 – 1.2 s. Thus it is not uncommon to perform several ZUPTs (one per IMU measurement epoch) during each gait cycle. The system operates at 20 Hz, thus facilitating the ability to detect steps and the stance phase accurately. The detection and application of ZUPTs is of critical importance to maintain accuracy of a pedestrian INS. TWIN IMU INERTIAL NAVIGATION SYSTEM Since each inertial unit requires it own set of error states, its own position, velocity and attitude, the proposed twin EKF effectively consists of the combination of two single EKFs. Thus the model contains 56 states; 27 for each IMU plus two states for the GPS receiver clock bias and drift rate. Each single IMU filter will herein be referred to as a “block filter” and the entire filter is referred to as the twin filter. It is noted that although only two IMUs are considered, the structure of the filter is sufficiently generic that any number of IMUs could be used. Figure 3 represents the data flow of the twin IMU integration scheme. Similar to the single IMU case, the system operates in a tight coupling mode utilizing the GPS pseudoranges. Each IMU has its own mechanization, its own misclosures and its own error estimates.

where,

(5)

(6)

Φ1k , k +1

is the 1st block filter transition matrix,

Φ k2 ,k +1

is the 2nd block filter transition matrix,

∂x1k +1

is the 1st block filter states (27 state model),

∂xk2+1

is the 2nd block filter states (27 state model), is the misclosure vector from the 1st block filter of the observations, is the misclosure vector from the 2nd block filter of the observations, is the process driving noise of each block filter, is the measurement noise of each block filter.

∂z1k +1 ∂z k2+1

w1k , wk2

η k1 +1 ,η k2+1

As can be seen, each block filter is independent of the other filter. In particular, the transition matrix for the twin IMU filter is block diagonal which means that the state propagation is effectively independent for each IMU (more details on this in the next section). The design matrix is also block diagonal which allows the observations to each IMU to be processed independently and/or asynchronously, as necessary (see, e.g., Petovello 2003). That said, GPS measurements are used to update both IMUs at the same time (i.e., the observations are effectively used twice). Although this is theoretically invalid, it simplified initial algorithm development and testing. Future work will address this point in more detail. As IMUs are placed on both feet, they experience gait cycles that are out of phase. During walking, typically one foot will be swinging, while the other will be in the stance phase. Thus in order to apply a ZUPT to the IMU on the foot in stance phase, it becomes necessary to access an individual block filter inside the twin filter. For example, assume that a ZUPT is to be applied to the second block, while the first block experiences swinging motion. In this case, the update will have the form:

Figure 3 - Twin INS Integration

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⎡vˆ − 2 − v) ⎤ ⎡δv e ⎤ ⎡0 L 0 1 0 0 ... 0⎤ 0 x ⎢ INS ⎥ ⎢ n⎥ ) ⎢ ⎥ − ⎢vˆ INS y2 − v 0 ⎥ = ⎢0 L 0 0 1 0 ... 0⎥ ∂x 54 x1 + ⎢δv ⎥ ⎢ − ) ⎥ ⎢δv u ⎥ ⎢0 L 0 0 0 1 ... 0⎦⎥ 3 x 54 − v0 ⎥ vˆ ⎣ ⎦ 1x 3 ⎣⎢ INS z2 ⎦ 3 x1 ⎣ ∂z = H ∂x + η

where − is the estimated x axis velocity (ECEF frame) of vˆINS 2 x

) v0

the second block filter,

is the independently observed zero velocity (or known velocity) in the x axis.

Thus it is possible to update a block of the twin filter independently with this construction. This is of critical importance because each IMU experiences its own independent velocities during the gait cycle. One aspect which is of critical importance to the twin IMU filter is the timing of the system. Not only does the GPS measurement not coincide with the IMU measurements (and are typically at different data rates), but the IMU measurements between themselves do not coincide. Furthermore, the propagation of the states should be performed at the same time for both block filters.

block of the filter.

The RVUPT is similar to the RDUPT, but uses the relative vector between the IMU positions rather than the absolute distance. The vector is determined in the body frame, with the rear foot determining the frame. The stride length provides the approximate distance, the width is assumed to be a nominal shoulder width and the vertical difference is assumed to be zero. The assumption would fail if the user were climbing stairs or an incline, however the effect on the horizontal position error is minimal. For the update to be preformed in the ECEF frame a rotation must be applied to the observed relative vector. The RVUPT update will have the form:

(

)

(

)

⎡ rˆ e 1 − rˆ e 2 − ∆r) e ⎤ ⎡1 L −1 L 0⎤ ⎡η x ⎤ x INS x x ⎢ INS )e ⎥ ⎢ e e L L 0⎥⎥ ∂x + ⎢⎢η y ⎥⎥ −1 ⎢ rˆINS 1y − rˆINS y2 − ∆ry ⎥ = ⎢ 1 ⎢ e ) ⎥ e ⎢⎣η z ⎥⎦ 1 L − 1 L 0⎥⎦ rˆ − rˆINS − ∆rze ⎥ ⎢⎣ 2 z ⎣⎢ INS 1z ⎦ ∂z = ∂x + η H

(

)

where e is the X coordinate of the 1st block filter in the rˆINS 1 x ECEF frame, ) ∆rxe

is the X axis relative distance between the feet.

RELATIVE POSITIONING UPDATES A unique characteristic of the twin filter is that it contains two navigation solutions (position, velocity, and attitude). Additionally, since the feet are separated by a repeating gait cycle, the relative distance and vector components between them is information that can be used to constrain the filter. Thus two methods of relative updates are described herein. The first is a Relative Distance Update (RDUPT). The second is a Relative Vector Update (RVUPT). The RDUPT uses the person’s stride as an update to the system. The stride length of the user is determined by integrating the velocity between steps, a method described in Godha et al (2006) with an error typically less than 2.5% (Note: a nominal stride length ranges between 1.2 m – 1.7 m). The RDUPT observation equation is:

[dˆ

e 2 →1

]

) ⎡X − X − ∆d d = ⎢ 1 e 2 ˆ ⎣⎢ d 2→1 ∂z

=

Y1 − Y2 dˆ e 2 →1

Z1 − Z 2 dˆ e

L

2 →1

X 2 − X1 dˆ e 2 →1

Y2 − Y1 dˆ e 2 →1

⎤ Z 2 − Z1 L⎥ ∂x + η dˆ2e→1 ⎦⎥

H

∂x + η

where

dˆ2e→1 ) ∆d d

is the distance between the estimated position of the first and second block filters, is the distance between feet as estimated from the stride length, X A , YA , Z A are the coordinates in the ECEF frame of each estimated position in the “A”

ION GNSS 2008, Session E3, Savannah, GA, 16-20 September 2008

Using the relative updates effectively correlates the positions between the block filters and allows for more consistent results when GPS is unavailable to provide position updates. The observation variance of the relative updates was determined through filter tuning. The standard deviation of the RDUPT was 3 m, while the RVUPT was 4 m (each axis). These values are high when considering the step length is known to within 2.5% of a stride length. This high standard deviation is attributed to the error associated to the unknown lever arm(s) in the system. Because GPS updates provide the same position to each block filter and a relative update provides a separated distance (i.e. different block positions), the filter is essentially provided with contradicting information. The effect of this contradiction requires relaxed variances of the relative updates. It should also be noted that the noise of the pseudoranges and the error of an individual block filter is expected to far exceed the error resulting from an unknown lever arm. DATA COLLECTION EVALUTION

AND

PREFORMANCE

The system performance was evaluated using real data collected under challenging GPS conditions. Data was collected using the University of Calgary’s NavBox which logs data using a 12-channel SiRFStarIII GPS

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receiver (1 Hz) and up to nine Cloud Cap Technology Crista IMUs (100 Hz). The Crista IMU incorporates triads of ADXL accelerometers and ADXRS gyroscopes from Analog Devices. Covariance matrices of the pseudorange observations are formed using the carrier-tonoise density ratio (C/No) (Wieser et al 2005). When indoor, the variances of the pseudoranges are artificially increased (by a factor of 100) to better accommodate the extreme multipath error (future work will investigate how to detect these conditions automatically). ZUPT observation variances were scaled by the variance of the three previous accelerometer samples as per Godha et al (2006). The filter is processed at 20 Hz to facilitate step detection and accurate zero velocity detection.

based geometry errors, under small bushes (leaved) and under large poplar and evergreen trees. The test includes three repeated indoor circuits with an approximate duration of three minutes (per circuit) and includes areas beside open windows and basements. After the three minutes indoor, the user then spends approximately three minutes outdoor, both beside and away from the building.

Time varying components of the gyro biases, accelerometer biases and scale factors are modeled as Gauss Markov processes. The turn on biases of both the gyros and the accelerometers are modeled as random constants. Each single IMU filter was tuned prior to tuning the twin filter. A reference trajectory was computed using a NovAtel SPAN system, consisting of an OEM4 and a Honeywell HG1700 (1 °/hr) IMU. The solution was post processed with RTS smoothing (Gelb 1974) to provide continuity indoor. The HG1700 IMU and OEM4 receiver were placed in a heavy rigid backpack, as shown Figure 4, to provide stability. The estimated horizontal accuracy (DRMS) of the reference trajectory is 1.2 m outdoor and less than 6.1 m indoor. Figure 5 - Data Collection Pictures and Trajectory Figure 6 and Figure 7 show the number of satellites tracked and the average C/No during the test. Results are only shown for the 1st circuit, but are indicative of all circuits. As shown, the HSGPS receiver tracked more than nine satellites while outside with C/No values ranging from 34 to 45 dB-Hz. While inside complete outages occurred for 53 s, 62 s, and 47 s for each loop respectively and the C/No ranged from10 to 29 dB-Hz. The number of satellites tracked indoor ranged between zero and nine. It should be noted that Figure 6 and Figure 7 represent the ability of the receiver to track, not the number of satellites used in computing the updates.

Figure 4 - Reference Trajectory Data Collection The trajectory (portions seen in Figure 5) included areas alongside a building to provide multipath and satellite

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Figure 6 - Satellite Observability of HSGPS Receiver

Figure 8 - HSGPS Receiver (GPS Only) Solution The horizontal position and vertical errors are shown in Figure 9. Position error statistics are shown in Table 1 and Table 2 for the outdoor (including under trees, etc.) and indoor segments respectively.

Figure 7 - Average C/No of HSGPS Receiver Multipath error is extreme while inside. During the indoor portion of the test, there is no direct line of sight to the satellites, and therefore all pseudorange observables are inherently corrupted with large multipath errors. These errors affect the position solutions computed by the HSPGS receiver as seen in Figure 8. It can be seen that while outdoor the GPS only solution follows the reference trajectory very closely (errors are seen in Figure 9), however as the antenna moves indoor, the multipath errors translate into substantial position errors of the order of 100 - 500 metres. Since pseudoranges are used as the only absolute position updates, and the INS heading is derived from time varying positions derived from these pseudoranges, multipath errors indoor increase the heading errors. For this reason, as discussed above, while indoor the GPS pseudoranges variances are increased, thereby allowing the system to derive its heading from the inertial units and the relative updates, rather than the pseudoranges.

ION GNSS 2008, Session E3, Savannah, GA, 16-20 September 2008

Figure 9 - HSGPS Receiver (GPS Only) Position Errors Using the two relative updates method described above (relative vector and relative distance), these solutions are compared with a single IMU configuration. The parameters used in both the twin and single IMU filters are consistent to avoid any filtering differences. Figure 10 shows the beginning of the trajectory and the first indoor circuit. As the user starts the data collection (~-30 m east and 120 m north), he travels south, passes by the outside of the building and then turn due west. There is a slight deviation from the truth trajectory showing the effect of multipath as the user passes by the building. While the multipath translates into a 5 m horizontal error, it is seen that the effect of multipath and satellite observability on the inertial systems (either twin or single IMU) is not negligible. As the user travels through the bushes and trees (not shown in Figure 10) the system performs with the horizontal error level shown in Table 1.

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Table 1 - Outdoor Horizontal Errors (Under Trees and Bushes) Processing 1 GPS RDUPT RVUPT Strategy IMU Only RMS Error (m) 1.5 1.5 2.2 1.9 Max Error (m) 4.9 4.3 7.0 3.9 As the user moves indoor the system accuracy degrades as a function of time due to incorrectly estimated IMU errors in the filter. Figure 10 shows the estimated positions of the twin IMU filter with the corresponding truth trajectory. It can be seen that the solution using RDUPT outperforms the RVUPT and the single IMU solution. The RDUPT strategy provides a more accurate heading (not shown), although the position is biased to the north. Once the pseudorange variance is lowered after the user returns outside, the position quickly converges to the correct location in a matter of seconds. As the results for all circuits are similar to the first, the plots for the second and third are shown in the Appendix.

The RVUPT method appears to be inferior to the RDUPT. This is somewhat unexpected, as the RDUPT provides less information (one observation). This result is attributed to the error associated with the rotation from the body frame to the ECEF frame. Considering multipath errors and the fact that the pitch and roll are typically estimated to 1° (1σ) and the heading to 8° (1σ), the rotation becomes the weakness of the update. Table 2 - Indoor Horizontal Errors (Improvement Percentages in brackets from 1 IMU) RDUPT RVUPT Processing 1 GPS (2 (2 Strategy IMU Only IMU) IMU) 7.2 16.5 RMS (m) 17.1 98.2 (58 %) (4 %) Circuit 1 13.5 45.5 36.2 195.0 Max (m) (63 %) (-26 %) 14.3 27.4 RMS (m) 43.4 140.7 (67 %) (37 %) Circuit 2 19.1 38.7 Max (m) 66.9 500.2 (71 %) (42 %) 13.1 13.5 RMS (m) 37.7 94.7 (65 %) (64 %) Circuit 3 28.7 29.7 98.0 163.3 Max (m) (71 %) (70 %) It can also be seen that after the second circuit the relative vector update converges more slowly than the relative distance update. At this point, the system is overly optimistic and the GPS updates have less immediate impact on the position errors, as compared to the single IMU and RDUPT cases.

Figure 10 - Start of Collection and Circuit 1 Trajectories Figure 11 shows the horizontal errors of the entire data collection (both the indoor and outdoor segments). It is clearly seen that the relative distance method improves the accuracy of the system, while applying the relative vector update still improves upon a single IMU configuration. The position errors resemble a quadratic function, which is typical of the error growth in inertial navigation systems (Jekeli 2007). Table 2 shows the RMS and maximum errors of each processing method. In terms of RMS, for each circuit the RDUPT method outperforms the RVUPT, while the RVUPT outperforms the single IMU, and the single IMU outperforms the GPS only solution.

ION GNSS 2008, Session E3, Savannah, GA, 16-20 September 2008

The results of processing each IMU independently and averaging the final solutions were also compared. Using this approach the system would occasionally perform similar to the relative updates, but yielded inconsistent results. Depending on the error associated in the heading of each IMU solution, the position errors could offset each other if they drifted at the same rate in the opposite direction. However, the position drift would often occur in the same direction and not provide a better solution. Similar results were found by processing the IMUs together, but not using the relative updates. An initial concern was the effect of the relative updates on the correlation between the block filters. Having a larger correlation between the errors of different sensors between IMUs mitigates the benefit of the including more than a single IMU. At the same time, the purpose of the relative position updates is to constrain (and thus correlate) the two IMU positions.

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shows the weakness of the heading solution with the position errors seen in the data. Figure 13 shows the correlation matrix of the twin IMU filter for the RDUPT strategy. Figure 13 is created at the same time as Figure 12 (which was processed as a single IMU). The RVUPT strategy is similar that of the RDUPT and is shown in the Appendix. It is noted that the correlation within the first block is very similar to Figure 12, as should be expected. The second block in Figure 13 shows less correlation in position, velocity and attitude as the system is in motion and no zero velocity updates are being applied.

Figure 11 - Horizontal Errors Resulting from Different Processing Strategies Figure 12 shows a graphical representation of the correlation matrix for a single IMU case. Correlations are derived from the variance covariance matrix of the estimated states. At the time of the output, the system has just preformed a GPS update and at the previous epoch a ZUPT.

Figure 12 – Correlation Coefficient of Covariance Matrix at Time 101.0 s Using this graphical method, it can be seen that there exists a high correlation in the position, attitude, and velocity. This occurs because of the high dynamics that precede a ZUPT (i.e., the foot striking the ground). These correlations eventually reduce to near zero until the next ZUPT. Correlation also exists between the estimated biases which are modeled in two states as a random constant and a Gauss Markov process (i.e. gyro and accelerometer biases). One can also see the correlation between the clocks offset and drift. The correlation between error states of the IMU remains below 20%. It is also possible to note the correlation that exists on the vertical (Z) axis of the Gyro, modeled as a Gauss Markov processes, with position, velocity and attitude. This

ION GNSS 2008, Session E3, Savannah, GA, 16-20 September 2008

Similar inner-correlation can be seen between the block filters and there is minimal correlation between inter block filters. The only significant correlation exists in the positions which are approximately 40 – 70% and varies as a function of time depending on GPS updates. Thus the relative updates create correlation in the position domain, but little correlation in terms of IMU error states, velocity and attitude (which are inherently independent). CONCLUSIONS An integrated navigation system is proposed using two MEMS inertial units for the purpose of pedestrian navigation. The errors of the IMUs are bounded when the IMU is placed on the fore foot and ZUPTs are applied. The two inertial units are integrated into a single Kalman filter. The filter contains two single IMU block filters that can be accessed individually. Accessing the blocks is a requirement considering that the velocities of the feet are not coincident and ZUPTs can then be applied to each block filter at different times. Relative updates incorporating the distance between the feet and the vector between the feet were described. The distance and vector between the feet are estimated by integrating the velocity of the inertial units during the stride. Data was collected under GPS signal degraded environments to show that when relative updates are applied, the solution improved by 58 to 71%. The correlation of inter-sensor errors as a result of the relative updates was shown to be negligible. ACKNOWLEDGMENTS The authors would like thank the Natural Science and Engineering Council of Canada (NSERC) and the Informatics Circle Of Excellence (iCORE) for their financial support. They also acknowledge Aiden Morrison, PhD candidate in the PLAN Group, for the design and construction of the NavBox. REFERENCES Brand, T. and T. Phillips (2003) “Foot-to-Foot Range Measurement as an Aid to Personal Navigation,” in

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Figure 13 – Correlation Coefficient of Twin RDUPT Covariance Matrix at Time 101.0 s Running,” in Proceedings of GNSS08, 16-19 September, Proceedings of the ION 59th Annual Meeting and CIGTF Savannah, GA, Session E3, The Institute of Navigation. 22nd Guidance Test Symposium, 23-25 June, Albuquerque, NM, pp. 113-121, Institute of Navigation. Lachapelle, G., O. Mezentsev, J. Collin, and G. Macgougan (2003) “Pedestrian and Vehicular Navigation El-Sheimy, N. (2007) Integrated Navigation Systems, Under Signal Masking using Integrated HSGPS and Self ENGO 623 Course Notes, Department of Geomatics Contained Sensor Technologies,” 11th World Congress, Engineering, University of Calgary, Canada. International Association of Institutes of Navigation. 2124 October, Berlin. Gelb, A. (1974) Applied Optimal Estimation, The Massachusetts Institute of Technology Press, USA. McMillan J. C., J. Bird, D. Arden (1993) “Techniques for Soft-Failure Detection in a Multisensor Integrated Godha, S., G. Lachapelle and M.E. Cannon (2006) System,” NAVIGATION: Journal of the Institute of “Integrated GPS/INS System for Pedestrian Navigation in Navigation. Vol.4, No.3, pp 2127-248. a Signal Degraded Environment,” in Proceedings of ION GNSS06, 26-29 Sept., Forth Worth, Session A5, pp. 2151 Mezentsev, O. (2005) Sensor Aiding of HSGPS – 2164, The Institute of Navigation. Pedestrian Navigation, PhD Thesis, Department of Geomatics Engineering, The University of Calgary, Godha, S. (2006) Performance Evaluation of Low Cost Canada, Published as Report No. 20212. MEMS-Based IMU Integrated with GPS for Land Vehicle Navigation Application, MSc Thesis, Department of Petovello, M. G. (2003) Real-Time Integration of a Geomatics Engineering, The University of Calgary, Tactical-Grade IMU and GPS for High-Accuracy Canada Published as Report No. 20239. Positioning and Navigation, PhD Thesis, Department of Geomatics Engineering, The University of Calgary, Jekeli, C. (2001) Inertial Navigation Systems with Canada, Published as Report No. 20173. Geodetic Applications, Walter de Gruyter, New York, NY. Petovello, M., G. Lachapelle and M.E. Cannon (2005) “Using GPS and GPS/INS Systems to Assess Relative Kwakkel, S., G. Lachapelle, and M. E. Cannon (2008) Antenna Motion Onboard an Aircraft Carrier for “GNSS Aided In Situ Human Kinematics Studies During Shipboard Relative GPS,” in Proceedings of NTM 2005,

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24-26 January, San Diego, CA, The Institute of Navigation, pp 219 -229. Ray, J. (2007) Advanced GNSS Receiver Technology, ENGO 638 Course Notes, Department of Geomatics Engineering, University of Calgary, Canada. Scherzinger B., J. Hutton, C. McMillan (1996) “Low Cost Inertial/GPS Integrated Position and Orientation System for Marine Applications,” Position Location and Navigation Symposium, IEEE 1996. pp 452 – 456. Scherzinger B., J. Hutton, C. McMillan (1997) “Low Cost Inertial/GPS Integrated Position and Orientation System for Marine Applications,” IEEE AES Systems Magazine. May 1997, pp 15-19. Sterling R., J. Collin, K. Fyfe, and G. Lachapelle (2003) “An Innovative Shoe-mounted Pedestrian Navigation System,” in Proceedings of ION GNSS, 22-25 April, Graz, Austria,

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Wieser, A., M. Gaggl, H.Hartinger (2005) “Improved Positioning Accuracy with High-Sensitivity GNSS Receivers and SNR Aided Integrity Monitoring of Pseudo-Range Observations,” ION GNSS 18th International Technical Meeting of the Satellite Division, 13-16 September 2005, Long Beach, CA. APPENDIX

Correlation Coefficient of Twin RVUPT Covariance Matrix at Time 101.0 s

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ION GNSS 2008, Session E3, Savannah, GA, 16-20 September 2008

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