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Spatial ﬁltering velocimeter using frequency shifting

by the method of rotating kernel

Xin He, Xingwu Long

⇑

, Xiaoming Nie, Jian Zhou

College of Optoelectronic Science and Engineering, National University of Defense Technology, Changsha 410073, China

article info

Article history:

Received 7 January 2015

Received in revised form 15 April 2015

Accepted 6 May 2015

Available online 14 May 2015

Keywords:

Spatial ﬁltering velocimeter

Rotating kernel

Maximum measurable velocity

Standard uncertainty

Power spectrum

abstract

A new approach of frequency shifting by rotating kernel is proposed to improve the

performance of a spatial ﬁltering velocimeter, used to provide accurate velocity informa-

tion for a vehicle self-contained navigation system. A linear CMOS image sensor was

employed both as a spatiotemporal differential spatial ﬁlter and as a photodetector. The

ﬁltering operation was fully performed in FPGA and is realized by applying a rotating ker-

nel to the pixel values of the image. Theoretical analysis showed this method could double

the maximum measurable velocity. The power spectrum of the output signal was obtained

by fast Fourier transform (FFT), and was corrected by a frequency spectrum correction

algorithm, named energy centrobaric correction. This velocimeter was used to measure

the moving velocities of a conveyor belt. Experimental results veriﬁed the method’s ability

of reducing the output signal frequency and standard uncertainty of velocity measurement.

What is more, the undesired output introduced by frequency shifting to the power spec-

trum of the output signal was deeply investigated and a new method was proposed to

eliminate the undesired component in output signals. This velocimeter aims at providing

accurate velocity information for vehicle autonomous navigation system.

1. Introduction

The demand for reliability of autonomous navigation

systems is increasingly high. The navigation system needs

to be fully autonomous and should be able to continuously

position with high accuracy. However, in vehicle autono-

mous navigation systems, the velocity information is pre-

sently provided by accelerometers, which have divergent

trends over time. Therefore, the idea of using a velocimeter

to measure the velocity for the vehicle autonomous navi-

gation system was put forward [1]. There are some meth-

ods of optical velocity measurement, such as laser Doppler

velocimetry, laser speckle velocimetry and spatial ﬁltering

velocimetry. These methods have all been used to measure

the velocity of vehicles relative to ground surfaces [1–4].

Therefore, all of them have the potential for application

to vehicle autonomous navigation systems. However, the

ﬁrst two methods using laser as the illumination cannot

satisfy the requirements of reliability at high ambient tem-

perature, long life of its light source and reasonable cost,

whereas the spatial ﬁltering velocimeter can meet with

all the requirements above.

In spatial ﬁltering velocimetry the spatial ﬁltering

device is the most important element. There are roughly

four types of spatial ﬁlters being applied to the spatial ﬁl-

tering velocimeter [5]: transmission grating type [6],

detector type [7,8], optical ﬁber type [9] and other special

grating type [10–12]. A detector type of spatial ﬁltering

device, a linear image sensor, is used in our system. The

image sensor operates both as a spatial ﬁlter and as a pho-

todetector. However, the frame rate limits the maximum

detectable velocity, making the measurement range unable

to cover all the velocities of the vehicle. Although an

http://dx.doi.org/10.1016/j.measurement.2015.05.013

⇑

Corresponding author.

E-mail address: xwlong110@sina.com (X. Long).

Measurement 73 (2015) 15–23

Contents lists available at ScienceDirect

Measurement

journal homepage: www.elsevier.com/locate/measurement

operation, known as pixel binning, can be used to increase

frame rate [13,14], the sophisticated clocking makes the

system design much more complicated. Most importantly,

not every type of image sensor is equipped with the func-

tion of pixel binning. In this paper, a new approach of fre-

quency shifting by rotating kernel is proposed to increase

the maximum detectable velocity. This new method is sim-

ilar in concept to the system of a liquid crystal transmis-

sion ﬁlter with amplitude-modulated reticle used by

Itakura et al. [15]. Through this method, the upper limit

of measurable velocity can be doubled, which is of great

signiﬁcance when the vehicle is moving at very high

speeds. What is more, this method can greatly reduce the

relative standard uncertainty. The built velocimeter was

used to measure the velocities of a conveyor belt driven

by a high precision and stability rotary table, which has

rate stability better than 0.001% of commanded rate mea-

sured over one revolution. The experimental results show

that this system using the method of rotating kernel has

good potential of application to the vehicle self-contained

navigation system.

2. Principles of spatial ﬁltering velocimeter

2.1. Basic principle of spatial ﬁltering velocimeter

The basic principle and optical system of the spatial ﬁl-

tering velocimeter for a vehicle are shown schematically in

Fig. 1. The velocimeter is deployed in the vehicle to measure

the relative velocity

between the vehicle and the ground

surface. An LED, an active light source, is employed to illu-

minate the ground surface. Part of the illuminating light

rays are scattered by particles on the moving surface and

are collected by the object lens so that the surface can be

imaged onto a spatial ﬁlter that has spatially periodic trans-

mittance in the moving direction of the surface. The total

light intensity collected by the focus lens is temporally peri-

odic due to the motion of the ground surface. Then the

time-periodical light intensity is fed into the photodetector.

As a result, the output of the photodetector contains a tem-

poral frequency f relative to the velocity

of the vehicle.

Then the relationship between the vehicle’s velocity

and

the temporal frequency f could be determined as follows:

f ; ð1Þ

where p is the spatial period of the spatial ﬁlter, and M is

the magniﬁcation of the imaging system consisting of the

object lens.

2.2. Detector type spatial ﬁltering velocimeter

The mathematical model for a detector type spatial ﬁl-

tering velocimeter is shown in Fig. 2. The detector type

spatial ﬁlter is placed at the image plane. The moving

objects are imaged by the imaging lens onto it. Let

p(x,y,t) be the light intensity distribution of the moving

image, which is time-dependant, in the x–y plane before

the spatial ﬁlter and q(x, y) the weighting function of the

spatial ﬁlter. Then the ﬁltered light intensity g(x, y, t)is

given by the convolution integral as:

gðx; y; tÞ¼

pðx; y; tÞqðx; yÞdxdy; ð2Þ

which is performed digitally after the acquisition of the

moving image by

SðtÞ¼gðtÞ¼

P ðr; tÞQðrÞ; ð3Þ

where r is the number of the pixel in the image, P(r, t) is the

grey values of pixels and Q(r) is the weighting function. Eq.

(3) can be represented by the following matrix

multiplication

S ¼ P

1r

 Q

r1

; ð4Þ

where P

1r

is a matrix consisting of all the image pixel val-

ues arrayed spatially sequentially and Q

r1

is the weighting

matrix.

The multiplication of Eq. (4) with a differential weight-

ing matrix is schematically shown in Fig. 3.InFig. 3 white

and grey strips represent pixels of a linear image sensor,

which has r pixels. n neighboring pixels form one group

which corresponds to a transparent or opaque bar of a

transmission grating type spatial ﬁlter. Here the values of

+1 (shown in white) and 1 (shown in grey) form two ﬁl-

ters which can be summed up respectively to generate sig-

nals S

and S

. Due to the spatially

-phase difference of

LED

Ground surface

Vehicle

Object

lens

Focus

lens

Spatial

filter

Photodetector

Fig. 1. Basic principle and optical system of the spatial ﬁltering velocime-

ter for a vehicle.

Fig. 2. Mathematical model for a detector type spatial ﬁltering

velocimeter.

16 X. He et al. / Measurement 73 (2015) 15–23

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