1. Optical Flow Based Step Length Estimation for
Indoor Pedestrian Navigation on a Smartphone
Jiuchao Qian, Ling Pei*, Danping Zou, Kai Qian, Peilin Liu
School of Electronic Information and Electrical Engineering
Shanghai Jiao Tong University (SJTU)
Shanghai, China
andychin9@gmail.com
Abstract—In this paper, an optical flow based step length
estimation algorithm for indoor pedestrian navigation is
proposed. To address the challenge of interferences arising from
hands shaking during walking, the pose of a smartphone is
computed by attitude and heading reference system (AHRS)
algorithm and used to improve the performance of optical flow
algorithm. Moreover, the motion information of pedestrians can
be captured by calculating the alteration and relevance between
sequential pixels and frames of camera snapshots when steps are
detected. Accordingly, online training and calibration of step
length estimation in pedestrian dead-reckoning system (PDR) are
accomplished. To verify the performance of proposed step length
estimation algorithm, several field tests with a smartphone were
conducted in various environments. Experimental results show
that the proposed algorithm achieves accurate performance in
terms of step length estimation.
Keywords—indoor pedestrian navigation; PDR; step length
estimation; optical flow; AHRS algorithm
I. INTRODUCTION
In recent years, there has been a growing concern in
Location Based Services (LBS) that are information services
accessible with mobile devices through a communication
network and aim at providing information relevant to the
current location and context of a mobile user [1]. With the
rapid development and gradual maturating of global satellite
positioning systems, outdoor positioning and LBS have shown
excellent performance. However, for indoor environments,
Global Positioning System (GPS), including other satellite
navigation systems, cannot achieve satisfactory usability due to
signal fading and multipath effect. Therefore, reliable and
accurate indoor navigation has gained increasing interest and
become a research focus of LBS. The emergence and
dissemination of smartphone make it possible to collect users’
information for indoor pedestrian navigation using various
sensors in their smartphones, such as accelerometer, gyroscope,
magnetometer, camera, etc.
In view of MEMS based IMU in a smartphone, which is
only able to provide required indoor positioning accuracy for
brief moments due to the accumulative sensor bias and drift
errors, pedestrian dead reckoning (PDR) is adopted to provide
means of reducing the inertial error accumulation to navigation
solution by taking advantage of the sequential characteristics of
pedestrian motion. The algorithm is a relative navigation
technique, which computes the relative location of a pedestrian
by using step detection, step length estimation, and heading
determination. Typically, the accelerometer measurements are
utilized to carry out step detection and step length estimation,
and heading determination is simultaneously completed by
fusing the information from gyroscopes and magnetometers
[2]. As an important procedure of a PDR system, step length
estimation introduces the main errors which degrade PDR
system performance.
A number of papers have described the methods of step
length estimation for PDR systems, such as empirical model
based on user’s height and weight [3], linear model of step
frequency and acceleration variance [4, 5, 6, 7], and neural
network model depends on statistical properties of acceleration
measurement [8]. However, in most of these methods, the
model parameters are trained offline, which may bring tedious
training process and become an obstacle to practical
applications. Several other researchers have pointed out that the
step length estimation model parameters can be calibrated
online by GPS [9, 10, 11]. However, this method is just
suitable for outdoor situation due to Non-Line-of-Sight
(NLOS) conditions in indoor environments. Furthermore,
considering diverse walking modes of different pedestrians, it
is impossible to design a unique step length estimation model
with high accuracy unless the model can be adjusted online
with real-time sensor data.
Camera, as a common sensor of most current smartphones,
provides opportunities to achieve the above-mentioned goal
using optical flow algorithm. Optical flow is the pattern of
apparent motion of objects, surfaces, and edges in a visual
scene caused by the relative motion between an observer (an
eye or a camera) and the scene [12, 13]. Using sequences of
ordered images recorded by the camera, the pedestrian motion
can be estimated as either instantaneous image velocities or
discrete image displacements. Consequently, through
transformation from image coordinate to global coordinate, the
parameters of step length estimation model are able to be
trained and calibrated online.
This paper is organized as the follows. First of all, we
introduce the PDR algorithm employed in our work including
step detection and step length estimation. Then an attitude
acquisition algorithm based on MARG sensor arrays
* Corresponding author. Email: ling.pei@sjtu.edu.cn
205

2. (accelerometers, gyroscopes and magnetometers) in
smartphones is presented. Afterward, optical flow algorithm
based on images taken by the smartphone camera is
investigated and it is integrated with attitudes of the
smartphone to determine pedestrians’ motion and displacement.
Hereafter, online training of the pedestrians’ step length
estimation model is accomplished and personalized parameters
of different pedestrians are stored and utilized repeatedly until
training phase is reset or user is changed. After that, the
performance of the proposed algorithms is evaluated through
several field tests indoor and outdoor. Finally, the conclusion
and future works are drawn in the last section.
II. PEDESTRIAN DEAD RECKONING ALGORITHM
Pedestrian Dead Reckoning (PDR) algorithm based on self-
contain sensors, such as MEMS sensors, is widely applied to
indoor navigation for its easy employment and ubiquitous
computing. As mentioned above, the algorithm provides
estimates of relative position by fusing the information from
MARG sensors. Step detection and step length estimation are
detailed in following section, and heading determination is out
of the concerns of this paper.
A. Step Detection Algorithm
Step detection is a basic technique and foundation of PDR
systems. In our algorithm, to cope with tedious and time-
consuming training work, step length model is trained and
updated every time when steps are detected. Therefore, reliable
step detection is crucial to influence the performance of our
algorithm. Specifically, each miscount in step detection leads
to approximately 0.5 meter on average. Furthermore,
parameters of step length estimation model such as step
frequency and acceleration variance are also depended on the
accuracy of step detection.
There are many proposed approaches to detecting steps of
pedestrians [14, 15]. The cross gravity approach is adopted in
our algorithm [16]. As previously mentioned, the
accelerometer signal is usually employed to detect steps.
Experiments indicate that the output of accelerometer may
present harmonic oscillation waveform during the natural walk.
The magnitude of total acceleration is used because it is
insensitive to the orientation of accelerometer sensors. The
magnitude maga can be expressed as:
2 2 2
, , , ,mag k x k y k z ka a a a= + + (1)
where ,x ka , ,y ka and ,z ka are the measurements from the triaxial
accelerometer.
According to the value of maga , a candidate step at time kt ,
where k denotes the index of steps, is identified by following
criteria (as shown in Fig. 1):
C1. The total acceleration magnitude maga has to cross the
threshold thδ from negative to positive.
Fig. 1. Identification criteria of candidate steps
C2. The time interval tΔ between two consecutive steps
defined by C1 must be within mintΔ to maxtΔ .
C3. The difference ma between extreme values of maga
during a step phase and the threshold thδ has to be
among mina to maxa , otherwise a perturbation point is
recorded.
In the light of the irregular fluctuations of maga due to
various individual way of walking, the threshold thδ in C1 is
updated dynamically according to the mean value of maga over
a step period, i.e.
11
( )
k
k
t
th magt
k
a t dt
t
δ
+
=
Δ ∫ (2)
B. Step Length Estimation Model
Step length estimation is utilized to compute the traveled
distance and update the position of the pedestrian on condition
that the previous position is known. As described in related
works, the step length of a pedestrian is not constant and varies
with step frequency, signal variance and incline of the road [6,
9]. In order to estimate the travel distance of the PDR system
accurately, adaptive step length estimation must be adopted
according to these variations.
In this paper, the step length is estimated using a linear
combination model of step frequency and acceleration variance.
The step length is estimated through following equations:
step length L a f b v c= ⋅ + ⋅ + (3)
where f is step frequency, v is acceleration variance during
one step; a , b and c are linear regression parameters of the
estimation model. The step frequency and acceleration
variance in (3) are obtained as:
1
1
2
1 ( )
( )k
k
k k k
t
k k
k
t t
f t t
a a
v
n−
−
=
= −⎧
⎪
−⎨
=⎪
⎩
∑
(4)
where kf and kv are step frequency and acceleration variance
at kt ; kt means timestamp of the step k ; ka is acceleration
206

3. signal and ka is average acceleration during one step; n is the
number of sensor sampling points.
III. ATTITUDE ACQUISITION AND OPTICAL FLOW
INTEGRATION FOR STEP LENGTH ESTIAMTION
In general, a smartphone in hand is impossible parallel to
the ground all the time and it always shakes when pedestrians
are normally walking. In this case, the displacement calculated
by optical flow algorithm depends on the angle between the
smartphone and ground. Therefore, it is necessary to acquire
the smartphone’s attitude during walking and combine it with
optical flow estimation to get more accurate translation
information. Accordingly, the translation information is
projected into displacements of pedestrians from image
coordinate to global coordinate.
A. Attitude and Heading Reference System
Attitude and Heading Reference System (AHRS), which
contains accelerometer, gyroscope and magnetometer, can
provide attitude and heading information of sensors. In this
paper, the attitude of sensors is used to determine the angles
between smartphone camera and ground, and then improve the
performance of optical flow algorithm. With the development
and deployment of MEMS sensors, it becomes possible to
acquire the real-time attitude of smartphones.
Attitude is generally described in three ways: Direction
Cosine Matrix (DCM), Euler angle and quaternion. To avoid
redundancy in DCM form and singularity in Euler angle form,
quaternion is adopted to represent the attitude of smartphone
sensors as following:
ˆ [ ] cos sin sin sin
2 2 2 2
AB x y zq a b c d r r r
θ θ θ θ⎡ ⎤
= = − − −⎢ ⎥
⎣ ⎦
(5)
where ˆABq denotes the quaternion describing orientation; xr , yr
and zr define the components of unit vector ˆAr in the x , y
and z axes of frame A respectively; θ denotes the rotation
angle from frame B relative to frame A . Nevertheless, Euler
angle form is an appropriate visual representation of
smartphone sensors frame as shown in Fig. 2.
Roll Axis
Pitch AxisYaw Axis
Fig. 2. The diagram of roll, pitch and yaw axes illustrated in a smartphone
The Kalman filter is usually applied to attitude acquisition
algorithms [17, 18]. However, sampling rates demanded in the
Kalman process are so high that it is difficult to satisfy in
smartphone platform. In addition, large computational load is
another inevitable obstacle for application in practice. Thus, we
calculate the attitude quaternion of the IMU by adopting a
gradient-descent AHRS algorithm instead of the Kalman filter
algorithm, which claims to be both computationally
inexpensive and effective at low sampling rates and is
described in [19] in detail.
B. Optical Flow Algorithm
The classic dense optical flow algorithm in [20] is used for
optical flow estimation in our paper.
Let ( , , )E x y t be the image brightness at the point ( , )x y in
the image plane. In consideration of the brightness of a
particular point is constant, we get:
0
dE
dt
= (6)
By applying the chain rule, optical flow constraint equation
is derived:
0x y tE u E v E+ + = (7)
where xE , yE and tE are the partial derivatives of image
brightness with respect to x , y and t . And ( , )u v is the flow
velocity, which is defined as:
and
dx dy
u v
dt dt
= = (8)
Then the flow velocity is estimated by minimizing an
objective function defined in (9). This function consists of two
terms: a data term and a smoothness term.
2 22 2
( , ) ( ) ( )x y tE u v E u E v E u v dxdyα= + + + ∇ + ∇∫∫ (9)
whereα is a parameter to control the weight of the smoothness
term compared to the optical flow term, u∇ and v∇ are the
gradient of the flow that are defined as:
and
u u v v
u v
x y x y
∂ ∂ ∂ ∂
∇ = + ∇ = +
∂ ∂ ∂ ∂
(10)
The minimization of the above objective function yields the
following equation:
2 2 2
2 2 2
x x y x t
x y y y t
E u E E v u E E
E E u E v v E E
α
α
+ = ∇ −
+ = ∇ −
(11)
The Laplacian is approximated as:
2 2
( ) and ( )u u u v v v∇ ≈ − ∇ ≈ − (12)
where u and v are local averages of flow velocity( , )u v .
Solving above equations for ( , )u v and arranging the terms,
we obtain that
207

4. 2 2 2
2 2 2
( )( ) ( )
( )( ) ( )
x y x x y t
x y y x y t
E E u u E E u E v E
E E v v E E u E v E
α
α
+ + − = − + +
+ + − = − + +
(13)
With certain boundary condition, we can finally obtain flow
velocity estimates 1 1
( , )n n
u v+ +
from the estimated derivatives
and the average of the previous velocity estimates ( , )n n
u v by
1
2 2 2
1
2 2 2
n n
x y tn n
x
x y
n n
x y tn n
y
x y
E u E v E
u u E
E E
E u E v E
v v E
E E
α
α
+
+
+ +
= −
+ +
+ +
= −
+ +
(14)
After the sequential images captured by the smartphone
camera, the flow velocity of the stored images is calculated
according to the above algorithm. Fig. 3 shows the optical flow
velocity of two consecutive images captured during walking.
Red arrows in the figure indicate flow velocity vectors in pixels
and green arrows highlight the noise interferences that issue
from the pedestrian’s leg, foot and their shadows. In addition,
several green arrows in the upper left corner of the image are
also noise interferences result from other factors including
hand shaking, outside dust and so on.
To mitigate the influence of the noise interferences shown
in Fig. 3, an outlier detection procedure is proposed as:
• A velocity vector which has the same heading as the
pedestrian’s forward direction is selected as a basis
vector from the flow velocity matrix.
• The magnitude differences between the basis vector
and other velocity vectors are calculated for statistical
computations.
• A dynamic threshold, which is applied for outlier
detection, is obtained from the statistical results of
above differences. For instance, from the statistical
histogram shown in Fig. 4, we can find that 90%
differences are less than 1.44 pixels. Therefore, we
select 1.44 as the threshold for outlier detection.
Fig. 3. Optical flow velocity and noise interferences of an example image
0 5 10 15
0
50
100
150
Bin Count: 144
Bin Center: 0.719
Bin Edges: [-Inf, 1.44]
Differences (Pixel)
Numberofvectors
20
40
60
80
100
120
140
160
Fig. 4. Differences between criterion vector and other flow velocity vectors
C. Integration of Attitude Acquisition and Computer Vision
Algorithms Based on Smartphone Sensors
In order to transform the optical flow velocity in image
coordinate system into the velocities in world coordinate
system, the smartphone camera has to been calibrated with
camera calibration toolbox, such as corner extraction method
based on images of a planar checkerboard. After calibration, a
camera’s calibration matrix K is obtained:
0
0
0 0 1
x x
y y
f c
K f c
⎛ ⎞
⎜ ⎟
= ⎜ ⎟
⎜ ⎟
⎝ ⎠
(15)
where xf and yf are focal length; xc and yc are principal point;
skew coefficient is approximately 0 in the first row of K .
During pedestrian’s walking, the smartphone is hold in a
landscape manner as shown in Fig.5. The smartphone’s
coordinate system is shown at upper left corner of the figure.
The distance and the angle between the smartphone and ground
is h andφ , respectively.
Fig. 5. Variables and coordinates definition during pedestrian’s walking
208

5. From Fig. 2, it can be inferred that the angleφ is equal to
the roll angle of the smartphone. When the parameters K , h
and φ is known, the transformation can be completed as
following procedure.
Firstly, the flow velocity( , )u v in image coordinate system
is transformed into camera coordinate system:
x
x
y
y
u c
u
f
v c
v
f
−⎧
=⎪
⎪
⎨ −⎪ =
⎪
⎩
(16)
Then, the variable ( , )u v is transformed into world coordinate
system by:
1
w
w w c w
w
x u
P y R v
z
→
⎛ ⎞ ⎛ ⎞
⎜ ⎟ ⎜ ⎟
= = ⋅⎜ ⎟ ⎜ ⎟
⎜ ⎟⎜ ⎟
⎝ ⎠⎝ ⎠
(17)
where c wR → is transfer matrix, and it is defined as:
1 0 0
0 cos sin
0 sin cos
c wR φ φ
φ φ
→
⎛ ⎞
⎜ ⎟
= ⎜ ⎟
⎜ ⎟−⎝ ⎠
(18)
Substituting (18) into (17), we can get
cos sin
sin cos
w
w
w
x u
y v
vz
φ φ
φ φ
⎛ ⎞ ⎛ ⎞
⎜ ⎟ ⎜ ⎟
= −⎜ ⎟ ⎜ ⎟
⎜ ⎟⎜ ⎟ +⎝ ⎠⎝ ⎠
(19)
The coordinate of intersection point wPλ ⋅ between optical line
and ground satisfies:
wz hλ ⋅ = (20)
where λ is proportionality factor. Solving with (19) for λ we
see that
sin cos
h
v
λ
φ φ
=
+
(21)
Finally, substituting (16) and (21) into wPλ ⋅ we can find that
( )
( )sin cos
( )cos sin
( )sin cos
y x
w
x y x y
y y
w
y y
f u c
x h
f v c f f
v c f
y h
v c f
φ φ
φ φ
φ φ
−⎧
= ⋅⎪
− +⎪
⎨
− −⎪ = ⋅
⎪ − +⎩
(22)
Therefore, the relationship between the optical flow
velocity in image plane and velocities of the pedestrian in
global frame is established. Moreover, the displacements
among sequenced images can be computed and thus each step
length can also be obtained by summing up these
displacements.
IV. EXPERIMENT
A. Experimental Setup
In our experiment, five field tests, including three outdoor
tests and two indoor tests, were conducted at different locations
of Shanghai Jiao Tong University such as asphalt road, lawn,
front door and two classrooms. To verify the adaptability of the
proposed algorithm, thus scenarios with different texture
ground were tested not only indoor areas. A Huawei Ascend P6
smartphone was used to collect MARG data and record video.
The MARG data rate was 100 Hz and the video was recorded
at 30 frames per second with a resolution of 720 × 1280 pixels.
To relieve the computation load, the images were compressed
to 144× 176 pixels in post-processing. The timestamp of all
sensors data stored in the log files was consistent, which
provided convenience for data analysis.
The trajectories of the five field tests were all straight lines.
Turning and stairs situations were not considered in our
experiment. Two sets of data were collected in each field test.
One data was used for training, and the other data was used for
testing. While training data was collected, the test participant
was required to keep shooting the ground in front of him as
shown in Fig. 5 and change step frequency during walking.
Corresponding to the training phase, the testing data was
collected without turning on the camera and the total traveling
distance were known values for evaluating errors.
B. Experimental Results
Fig. 6 shows the experimental results obtained in various
scenarios. The first row shows one frame of the images
captured during walking. To demonstrate roll angle changes in
the third row, images with larger roll angle are selected, hence,
there is no foot and leg in these images. The second row shows
the flow velocity of the images in the first row. In order to
display clearly, every 15th
flow velocities from the images
instead of all pixels are picked. The last row is the curve that
illustrates step length changes when a step is detected.
From Fig. 6, we can derive the following conclusions:
• Without noise interferences from feet, legs and their
shadows, almost all optical flow velocities in the image
are consistent, which guarantees the accuracy of step
length estimation.
• At the beginning, roll angles are unstable, thus the test
participant has to remain stationary for a while to
initialize the attitudes of the smartphone sensors. In
addition, accurate attitude acquisition algorithm also
contributes to improve the performance of step length
estimation.
• As described in [9], the step length is not constant but
varies with step frequency, acceleration variance and
other factors.
Proposed optical flow based step length estimation
algorithm is evaluated with testing data in different scenarios,
and the results is summarized in TABLE I. We can see that the
maximum mean error for each step is 1.627 centimeter, and for
the best situation the mean error is only 0.309 centimeter.
209

6. 0 20 40 60
60
70
80
90
100
110
Steps
Steplength(cm)
0 30 60 90 120
70
75
80
85
90
95
100
Steps
Steplength(cm)
0 30 60 90 120
60
70
80
90
100
110
120
Steps
Steplength(cm)
0 20 40 60
60
70
80
90
100
110
120
Steps
Steplength(cm)
0 30 60 90 120
75
80
85
90
95
100
105
Steps
Steplength(cm)
(1) Asphalt road (2) Lawn (3) Front door (4) Classroom_s (5) Classroom_x
0 1000 2000 3000 4000 5000
-20
0
20
40
60
80
Sampling points
Rollangle(degree)
0 2000 4000 6000 8000
-10
0
10
20
30
40
50
Sampling points
Rollangle(degree)
0 2000 4000 6000 8000
0
10
20
30
40
Sampling points
Rollangle(degree)
0 1000 2000 3000 4000 5000
-20
0
20
40
60
Sampling points
Rollangle(degree)
0 2000 4000 6000 8000
0
10
20
30
40
50
Sampling points
Rollangle(degree)
Fig. 6. Optical flow velocity, roll angle and step length estimated in different scenarios
TABLE I. STEP LENGTH ESTIMATION RESULTS
Scenarios
Proposed Optical Flow Based Step Length Estimation
Total distance
(m)
Step
counts
Travel
distance
errors (m)
Mean errors
of step length
estimation
(cm)
Asphalt road 50 57 0.364 0.639
Lawn 100 110 1.599 1.453
Front door 100 118 1.046 0.886
Classroom_s 50 54 0.167 0.309
Classroom_x 100 110 1.790 1.627
V. CONCLUSIONS
This paper presents an optical flow based step length
estimation algorithm using smartphone self-contained
sensors. From the results of varying field tests, it can be
concluded that the proposed algorithm achieves an accurate
performance. In future research, we will integrate the
proposed algorithm into our existing PDR solutions [21]-[25]
and improve the algorithm for real-time positioning
applications.
ACKNOWLEDGMENT
The research work is jointly funded by Beidou Navigatio
n Satellite System Management Office (BDS Office) and the
Science and Technology Commission of Shanghai Municipal
ity. The funding project number is BDZX005.
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