Kinematics of gait: new method for angle estimation based on accelerometers.
ABSTRACT A new method for estimation of angles of leg segments and joints, which uses accelerometer arrays attached to body segments, is described. An array consists of two accelerometers mounted on a rigid rod. The absolute angle of each body segment was determined by band pass filtering of the differences between signals from parallel axes from two accelerometers mounted on the same rod. Joint angles were evaluated by subtracting absolute angles of the neighboring segments. This method eliminates the need for double integration as well as the drift typical for double integration. The efficiency of the algorithm is illustrated by experimental results involving healthy subjects who walked on a treadmill at various speeds, ranging between 0.15 m/s and 2.0 m/s. The validation was performed by comparing the estimated joint angles with the joint angles measured with flexible goniometers. The discrepancies were assessed by the differences between the two sets of data (obtained to be below 6 degrees) and by the Pearson correlation coefficient (greater than 0.97 for the knee angle and greater than 0.85 for the ankle angle).
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ABSTRACT: A new data processing method is described for estimation of angles of leg segments, joint angles, and trajectories in the sagittal plane from data recorded by sensors units mounted at the lateral side of leg segments. Each sensor unit comprises a pair of three-dimensional accelerometers which send data wirelessly to a PC. The accelerometer signals comprise time-varying and temperature-dependent offset, which leads to drift and diverged signals after integration. The key features of the proposed method are to model the offset by a slowly varying function of time (a cubic spline polynomial) and evaluate the polynomial coefficients by nonlinear numerical simplex optimization with the goal to reduce the drift in processed signals (angles and movement displacements). The angles and trajectories estimated by our method were compared with angles measured by an optical motion capture system. The comparison shows that the errors for angles (rms) were below 4° and the errors in stride length were below 2%. The algorithm developed is applicable for real-time and off-line analysis of gait. The method does not need any adaptation with respect to gait velocity or individuality of gait.Journal of biomechanics 09/2012; · 2.66 Impact Factor
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ABSTRACT: Measuring the kinematic parameters in unconstrained human motion is becoming crucial for providing feedback information in wearable robotics and sports monitoring. This paper presents a novel sensory fusion algorithm for assessing the orientations of human body segments in long-term human walking based on signals from wearable sensors. The basic idea of the proposed algorithm is to constantly fuse the measured segment's angular velocity and linear acceleration via known kinematic relations between segments. The wearable sensory system incorporates seven inertial measurement units attached to the human body segments and two instrumented shoe insoles. The proposed system was experimentally validated in a long-term walking on a treadmill and on a polygon with stairs simulating different activities in everyday life. The outputs were compared to the reference parameters measured by a stationary optical system. Results show accurate joint angle measurements (error median below 5°) in all evaluated walking conditions with no expressed drift over time.Computer methods and programs in biomedicine 12/2013; · 1.14 Impact Factor
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ABSTRACT: The paper presents a multifunctional joint sensor with measurement adaptability for biological engineering applications, such as gait analysis, gesture recognition, etc. The adaptability is embodied in both static and dynamic environment measurements, both of body pose and in motion capture. Its multifunctional capabilities lay in its ability of simultaneous measurement of multiple degrees of freedom (MDOF) with a single sensor to reduce system complexity. The basic working mode enables 2DOF spatial angle measurement over big ranges and stands out for its applications on different joints of different individuals without recalibration. The optional advanced working mode enables an additional DOF measurement for various applications. By employing corrugated tube as the main body, the sensor is also characterized as flexible and wearable with less restraints. MDOF variations are converted to linear displacements of the sensing elements. The simple reconstruction algorithm and small outputs volume are capable of providing real-time angles and long-term monitoring. The performance assessment of the built prototype is promising enough to indicate the feasibility of the sensor.Sensors 01/2013; 13(11):15274-89. · 1.95 Impact Factor
Sensors 2011, 11, 10571-10585; doi:10.3390/s111110571
Kinematics of Gait: New Method for Angle Estimation Based on
Milica D. Djurić-Jovičić 1,2*, Nenad S. Jovičić 1 and Dejan B. Popović 1,3
1 School of Electrical Engineering, University of Belgrade, Bulevar kralja Aleksandra 73, Belgrade,
Serbia; E-Mails: firstname.lastname@example.org (N.S.J.); email@example.com (D.B.P.)
2 Tecnalia Serbia, Vladetina 13/6, Belgrade, Serbia
3 Center for Sensory Motor Interaction, Aalborg University, Fredrik Bajers Vej 7, Aalborg, Denmark
* Author to whom correspondence should be addressed; E-Mail: firstname.lastname@example.org;
Received: 1 October 2011; in revised form: 24 October 2011 / Accepted: 25 October 2011 /
Published: 7 November 2011
Abstract: A new method for estimation of angles of leg segments and joints, which uses
accelerometer arrays attached to body segments, is described. An array consists of two
accelerometers mounted on a rigid rod. The absolute angle of each body segment was
determined by band pass filtering of the differences between signals from parallel axes
from two accelerometers mounted on the same rod. Joint angles were evaluated by
subtracting absolute angles of the neighboring segments. This method eliminates the need
for double integration as well as the drift typical for double integration. The efficiency of
the algorithm is illustrated by experimental results involving healthy subjects who walked
on a treadmill at various speeds, ranging between 0.15 m/s and 2.0 m/s. The validation was
performed by comparing the estimated joint angles with the joint angles measured with
flexible goniometers. The discrepancies were assessed by the differences between the two
sets of data (obtained to be below 6 degrees) and by the Pearson correlation coefficient
(greater than 0.97 for the knee angle and greater than 0.85 for the ankle angle).
Keywords: accelerometers; ambulatory system; angles; gait assessment
Sensors 2011, 11
Gait analysis is important for objective assessment of the effects of rehabilitation interventions. The
most accurate systems for gait analysis are camera-based systems with reflective markers . These
systems acquire spatial movement (3D) of many markers positioned on the body, while a software
outputs the joint angles and/or other gait parameters. However, camera-based systems require a
dedicated laboratory and limit the length of the analyzed walking distances. Gait laboratories also use
force platforms to measure the ground reaction forces which typically record from only one or two
steps in the middle of the gait sequence. The platforms are 60 × 60 cm, so that aiming for the platforms
hinders the subjects’ natural gait patterns. The alternative to camera-based systems are ultrasound
systems  and magnetic tracking systems , which allow complete 3D kinematic analysis of human
Over the last decade, many gait analysis systems using non-traditional methods have been developed.
These systems, for example, use laser technology or measure near-body air flow [4,5] in order to
estimate kinematics and spatial gait parameters. Also, electronic carpets or wearable force sensors are
used for estimation of ground reaction forces, centre of pressure, and temporal gait parameters [6,7].
Since there is often a need for gait recording in various environments, portable body-mounted systems
are preferred [8,9].
Portable body-mounted systems allow data acquisition from many steps. The portable systems for
kinematics data acquisition directly measure joint angles, or they can record accelerations or angular
velocities of the body segments that carry the sensors. Measurement of joint angles can be done with
various electrogoniometers [9-11]. Particularly convenient are flexible goniometers, which measure
the relative angle between two small blocks that are fixed to the body segments (e.g., Biometrics
flexible Penny & Giles sensors). The advantages of flexible goniometers are: their output is directly
proportional to the angle and their mounting is simpler compared to some other measurement systems.
However, they are not sufficiently robust for daily clinical usage.
An alternative to goniometers, offered by the progress made in micro-electromechanical systems
(MEMS), is the use of accelerometers and gyroscopes. The advantages of these sensors include their
small size and robustness when compared with goniometers. However, the disadvantages of the
accelerometers (and gyroscopes) are computational problems for determining the angles [12-15].
Accelerometers are used for long-term monitoring of human movements, for assessment of energy
expenditure, physical activity, postural sway, fall detection, postural orientation, activity classification
and estimation of temporal gait parameters [16-21]. However, only a few papers report using only
accelerometers for angle estimation, or position and orientation estimation. In most papers some
additional types of sensors are included (gyroscopes, magnetometers, etc.) [22-25].
One method to calculate the angle is to double integrate the measured angular acceleration.
However, the double integration leads to a pronounced drift [13,14]. Several techniques have been
presented in literature for minimization of this drift. For example, Morris  identified the beginning
and the end of each walking cycle and made the signals at the beginning and the end of the cycle equal.
Tong et al.  applied a low cut high pass filter on the shank and thigh inclination angle signals.
However, these methods also removed the static and low-frequency information about the angles and
they cannot be applied to real-time processing.
Sensors 2011, 11
The other method for estimation of joint angles from the measured accelerations is the estimation of
the inclination angles between the segments (sensor) and the vertical, followed by the subtraction of
the angles for neighboring body segments. The results are acceptable only if the segment accelerations
are small compared to the gravity .
Adding Kalman filtering to the integration procedure decreases the drift and provides for
real-time applications, but it requires calibration and data from other sensors (accelerometers,
gyroscopes, and magnetic sensors in most cases) for error minimization, as well as noise statistics and
good probabilistic models [29-31]. These algorithms can be applied in real-time and seem to give
excellent accuracy for motions which exhibit lower accelerations than the leg segments, and which are
not exposed to impacts like those of heel contacts. For the lower extremities, the performance of the
Kalman filter is considerably reduced when measuring the orientation angles of segments that move
fast . Inertial sensors that consist of accelerometers, gyroscopes, and magnetometers, along with
Kalman filtering, allow a good accuracy for estimation of lower limb angles . However, good
accuracy of angle estimation can also be achieved using fewer sensors and much simpler algorithms
that are not sensitive to the presence of metals and ferromagnetic materials such as those that comprise
Willemsen et al.  developed a technique to estimate joint angles without integration. This
method is based on comparison of weighted accelerations of the joint (e.g., knee or ankle) obtained
from two accelerometer pairs mounted on two adjacent segments of the leg. The method requires
adequate low-pass filtering, which introduces a delay and to a certain extent hinders the real-time
applicability. Further, the accelerometer pairs need to be precisely oriented, so that their axes intersect
at the joint, which is very difficult to achieve considering that the human joints are polycentric. Also,
the distances between sensors and the joints are required for computation.
We have developed an accurate, yet simple method and instrumentation for estimation of absolute
segment and joint angles during the gait (assuming kinematics in the sagittal plane) which minimizes
the effects of drift. The proposed system is based only on accelerometer sensors, which is advantageous
because their calibration is static and less complex than the dynamic calibration required for
gyroscopes. Additional motivation for this paper was the “bad reputation” of accelerometers due to the
pronounced drift. We wanted to investigate if it is possible to use only accelerometers for angle
estimations and evaluate the precision of the results.
2. Experimental Section
2.1. Sensor System
The acquisition system that we developed for gait analysis is designed as a distributed wireless
sensor network. A set of battery powered sensor nodes is placed on the subject, one sensor node for
each leg segment of both legs. Sensor nodes establish communication with the coordinator node
through a low power 2.4 GHz wireless communication link. The coordinator node is connected using a
USB interface to the computer. Wireless communication is bidirectional, with a coordinator node
acting as a master, and the sensor nodes as slaves. The coordinator node manages network traffic and
Sensors 2011, 11
the USB connection with the computer. Data streams from the sensor nodes are synchronized and the
system operates with a 100 Hz sampling rate.
Sensor nodes are realized as a sandwich structure of processor and sensor board with a
Li-ion battery placed between the boards. The compact size design of sensor nodes, with dimensions
70 × 25 × 15 mm and 27 grams weight, enables comfortable wearing and does not hinder the subject’s
movements. Hardware design is based on the Texas Instrument’s CC2430 microcontroller, which
integrates a RF front end and a 8051 core in the same case. Standard microcontroller peripherals
enable interfacing to analog and digital sensors, and different sensor boards can be combined with the
same processor board.
In the configuration used in this research, the sensor board comprises two high performance 12-bit
digital accelerometers LIS3LV02 (SGS-Thomson Microelectronics, USA). The range of the sensors is
either ±2 g or ±6 g, which can be selected in the acquisition software. Accelerometers are aligned to
y axes with distance of 55 mm between centers. This configuration requires the clinician only to fix the
sensor array along the body segment, approximately at the mid section of lateral side of leg (Figure 1).
Figure 1. Setup of the sensor system. (a) photo of the sensors mounted on the body during
the gait analysis, (b) schematic of the system configuration with the coordinate systems.
Goniometers were attached to the leg segments by using double sided adhesive tape and secured
with elastic bands with Velcro endings, mounted over the sensors and around the leg segment. Sensor
nodes were placed in custom made tight sensor node-size elastic pockets placed on elastic bands with
Velcro at their ends.
Sensors 2011, 11
The custom-designed software, created in CVI (LabWindows, National Instruments, USA), is used
for online monitoring and storing of the acquired data.
The mechanics of importance for the analysis considers two sensors (denoted by S1 and S2), which
are mounted on a rigid rod (Figure 2). The distance between the sensors is l. The rod is freely moving
with respect to the fixed global coordinate system (O'x'y'z'), shown in Figures 1(b) and 2. The axis x' of
the global coordinate system is walking direction, and the axis y' is vertical. The center of the rod (O)
is determined by the position vector
To analyze the movement in the sagittal plane, we consider the case when the rod moves in the
O'x'y' plane (2D model). We define the vector l, which connects the centroids of the two sensors. The
positions of the accelerometers are
Figure 2. Rod with two accelerometers and the coordinate system for analysis of
movement in the sagittal plane.
Each accelerometer measures the two Cartesian components of the acceleration vector, with respect
to the local coordinate system Oxy attached to the rod. The equivalent accelerations measured by the
two sensors are:
where g is the gravity acceleration.
The difference of the signals from these two sensors is proportional to the amplitude of the vector
. In this way, we cancel out the influence of the movement of the rod centroid and of the
gravity, and retain information only about the changes of the vector l. The second derivative of the
vector l is: