The Application of Function Approximation Algorithm

in Magnetic Parking Detection

Liye Zhao and Yaojie Sun

School of Electronics and Information Engineering, Hebei University of Technology,

5340 Xiping Road, Beichen District, Tianjin, China

zhao_1829@163.com,sunyaojie@hebut.edu.cn

Keywords: Magnetic sensors, parking detection, CORDIC algorithm, digit-by-digit algorithm.

Abstract: In order to improve the accuracy of magnetic parking location detection, the microcontroller needs to use

transcendental function to exclude the parking interference of adjacent parking process. Because the

microcontroller does not contain hardware multipliers, the function approximation algorithm is introduced.

In this paper, the CORDIC algorithm and digit-by-digit algorithm are used to estimate the square root and

arccosine function in the process of magnetic data processing. Experiments show that after adding the

algorithm, the running time of the microcontroller is much less than the sampling interval of the sensor. The

experimental results prove that the algorithm can exclude the interference of adjacent parking process in real

time.

1 INTRODUCTION

In recent years, the problem of urban congestion and

air pollution is becoming more and more serious

with the rapid increase of vehicle volume. The

phenomenon of a low parking utilization rate has

attracted the attention of scholars. As a part of the

intelligent transportation system, the performance of

the parking detection system directly affects the

traffic congestion near the parking lot.

At present, there are a variety of methods to

realize vehicle parking detection. In the field of

image processing, the grayscale projection and first

derivative method were used to find the height of a

vehicle in one image and the status of multiple

parking spaces in one image can be judged (Choorat

et al 2017). In the ultrasonic detection field, there

were two ultrasonic sensors had been installed on

the same side of the entrance or the exit, when the

vehicle to enter or exit the parking lot then two

sensors were blocked at the same time, and the

number of idle parking spaces in the parking lot can

be obtained (Zadeh et al 2016). A detection system

based on RSSI (Received Signal Strength

Indication) had been proposed, in which the data

receiving node and data sending node were installed

on the top and bottom of each parking space

respectively, and the occupancy of parking space

was judged according to the received signal strength

(Li, 2016). In the field of magnetic detection, the

detection system was made up of magnetic sensors,

routing nodes and sink nodes. The magnetic sensor

realized parking detection, and its result was

transmitted from the routing node to the sink node

(Zhu, 2016).

By analyzing the environment of indoor and

outdoor parking lot, it can be found that using image

processing to detect parking space is convenient and

feasible. But the accuracy of detection is easily

disturbed by light conditions, shielding and other

environmental factors, and the cost of equipment is

high. The use of ultrasonic detection is low cost,

high accuracy and easy installation. However, its

detection results are affected by extreme weather

and will fluctuate with temperature changes. The

RSSI detection system requires the data receiving

node and data sending node to be arranged at the

upper and lower ends of the parking space, which is

not conducive to the application of the outdoor

parking lot. The magnetic sensor had the

characteristics of small volume, high sensitivity,

strong adaptability to bad environment and so on

(Qian et al 2009). It is widely used in parking lot

detection system.

There were fixed threshold algorithm, adaptive

threshold algorithm, state machine algorithm in

magnetic parking detection system (Zhang et al

450

Zhao, L. and Sun, Y.

The Application of Function Approximation Algorithm in Magnetic Parking Detection.

In 3rd International Conference on Electromechanical Control Technology and Transportation (ICECTT 2018), pages 450-454

ISBN: 978-989-758-312-4

2013). The core of each detection algorithm is to

analyze and extract the characteristics of the change

of magnetic curve caused by the vehicle. The actual

magnetic field of parking detection was the

superposition of a variety of magnetic disturbance

vectors (Han et al 2009; Wu et al 2014). In this

paper, the parking interference of adjacent parking

process is analyzed, and the threshold detection

algorithm is supplemented.

2 INFORMATION PROCESSING

2.1 Information Acquisition

The information collection system of vehicle

parking space is composed of the superior computer

and the inferior machine. The inferior machine is

responsible for collecting data and transmitting it in

a wireless way to the superior computer.

The hardware block diagram of the collection

system is shown in Figure 1. The white one-way

arrow shows the direction of electric energy

transmission. The grey bidirectional arrow indicates

the direction of data transmission. STM8L151K4T6

is chosen as a microcontroller, because it has five

low power modes and a short start time as well as a

variety of available wake-up sources. The chip is

internally integrated with 16MHz and 38KHz two

kinds of clocks. Under working mode, the

appropriate working clock can be selected for CPU

and peripherals by programming the preset

frequency register, and the power consumption is

reduced while ensuring the execution efficiency. The

point-to-point communication module SKB360 is

chosen as the wireless module. It is a Bluetooth

transmission module for the Nordic scheme based on

nRF51822 and supports Bluetooth 4.0 BLE and

BR/EDR stack. The magnetic sensor uses Freescale's

MAG3110. It has a two working modes of the low

power consumption and three sampling axes, the

data rate and sampling ratio of the control register

can be configured to determine the data output rate.

TPS62110 is chosen as the power supply chip,

which is to realize stabilizing voltage by using a

PWM wave and its switching frequency of 1MHz,

compared to linear regulator chip which has higher

conversion efficiency. Its input voltage range of

3.1V to 17V, and the output voltage range of 1.2V to

16V. Its maximum output current of 1.5A, and the

typical quiescent current value 20uA.

2.2 Information processing

The magnetic sensor has three vertical sampling

axes, and the data on each axis are the components

of the magnetic disturbance vector. Compared with

the case of the adjacent vehicle and passing vehicles,

in which the parking detector are not covered by

vehicles, the angle of the covered parking detector

between the magnetic disturbance vector and the

vertical sampling axis of the sensor is larger(Chen et

al 2015). This feature can be used as the basis to

exclude the parking interference of adjacent parking

spaces. At present, the vehicle position detection

algorithm is based on the threshold detection.

Figure 1: The hardware block diagram of acquisition system.

The Application of Function Approximation Algorithm in Magnetic Parking Detection

451

In order to improve the accuracy of parking

detection, the angle calculation between the

magnetic disturbance vector and the vertical

sampling axis is added in threshold detection.

However, the microcontroller does not have the

hardware multiplier to calculate the floating-point

number and the transcendental function, then the

function approximation algorithm is introduced in

this paper.

Because of the high frequency interference in the

original data of the magnetic sensor, a sliding filter

is needed to eliminate the high frequency

interference first. The principle of sliding filtering is

shown as formula (1). The





is the original

magnetic data, the





is the filtered data, and the

N is the length of the sliding filtering interval. The

intensity of the magnetic disturbance vector and the

angle between the magnetic disturbance vector and

the vertical sampling axis are shown by the formula

(2) and formula (3). In formula (2),



ri xyz

the component of the magnetic vector on each axis,

and

r

is the strength of the magnetic vector. In

the formula (3), the calculation of the division and

the inverse cosine function is included in the process

of solving the angle.

The whole data processing is summarized as four

steps: sliding filtering, square root, division and

arccosine. In the next section, the function

approximation algorithm of microcontrollers to

process data can be introduced.



    

 

ss sk

sk N sk N sk











 











(1)

222

xyz

r rrr  

(2)

arccos













(3)

3 APPROXIMACTION

3.1 CORDIC Algorithm

The CORDIC (COordinate Rotation DIgital

Computer) algorithm, also known as Volder’s

algorithm, is an effective algorithm for calculating

hyperbolic functions and trigonometric functions. As

the only operations it requires are addition,

subtraction, bit-shift and table lookup, the algorithm

has a strong portability and high execution

efficiency. The estimation method of trigonometric

functions is described in this paper. The process to

estimate an inverse cosine function of a known value

is equivalent to estimate an angle between the vector

and the abscissa axis’s positive direction in the unit

circle, and the known value is abscissa of the vector.

The iterative schematic diagram of the CORDIC

algorithm is shown in Figure 2. The

is the initial

vector, and the coordinate rotation formula is shown

in formula (4). The

can be get after rotating

i-1

into



.In order to simplify the computational

complexity,



need to satisfy the formula (5). In

this way, the multiplication of the coordinate

rotation formula can be replaced by bit-shift. The

coefficients

in the coordinate rotation formula

are shown in formula (6),



and

can be recorded

in the table.



1tan

tan 1

1tan















(4)



tan 2









(5)



1tan 12









(6)

Figure 2: CORDIC algorithm iteration diagram.

ICECTT 2018 - 3rd International Conference on Electromechanical Control Technology and Transportation

452

3.2 Digit-by-digit Calculation

Digit-by-digit calculation is an efficient algorithm

for calculating square root. Compared with other

algorithms, the algorithm is applicable to any system.

Taking the decimal system as an example, the

detailed calculation steps of the algorithm are

summarized as follows:

(1) The square number be converted to decimal

form, and separate the digits into pairs, starting from

the decimal point and going both left and right.

Beginning with the left-most pair of digits

d , and

calculate the current value

based on the remainder

of the previous pair



, in which

100

ii i

cr d



 ,and the initial remainder



(2) Finding the largest integer

that satisfies the

inequality





iiii

px c

, and to figure out





ii ii

yx px

, the initial

0p  .The

as a

digit of the root has been placed above the two digits

of the square

d . Then update the value of

ii i

pp x



.

(3) Updating the remainder

r ,

iii

rcy.

(4) To determine whether

r and



are 0, if

both of them are 0, the iteration be stopped,

otherwise it returns to the first step.

4 EXPERIMENT

In this paper, the vector components of the magnetic

disturbance produced during the vehicle parking

process are collected by a large number of

experiments. The calculation of the sliding filter,

vector strength and vector angle of the magnetic data

is completed in the superior computer. By

comparing the magnitude of the angle between the

magnetic disturbance vector and the vertical

sampling axis generated during the neighboring

parking process and the parking process of covering

the sensor, we can determine the valid bits of the

threshold to exclude the interference brought by the

neighboring parking, and improve the accuracy of

threshold detection algorithm.

In the experimental process, the sampling rate of

the magnetic sensor MAG3110 is set to 80Hz. The

microcontroller approximate the computation result

of the superior computer by digit-by-digit algorithm

and CORDIC algorithm. The iteration ends when the

valid digits of the microcontroller’s output is equal

to the valid digits of the threshold. The operation

time of the algorithm in the microcontroller is

recorded to ensure that the microcontroller can

handle the data in real time. In the experiment, the

magnetic data acquisition interface of the superior

computer is shown in Figure 3. Figure 3 shows the

magnetic component curve processed by sliding

filter of the vehicle in and out of a parking space.

The collection personnel can set the range of the

filter interval through the interface, and observe the

magnetic component on each axis of the sensor in

real time, and intuitively analyze the magnetic curve

and save the effective magnetic experimental data.

Figure3: The acquisition interface of superior computer.

The Application of Function Approximation Algorithm in Magnetic Parking Detection

453

The experimental process of data acquisition is

shown in Figure 4. The experiment is to collect the

parking process of the covering sensor and the

adjacent vehicles respectively. After a lot of

experiments, it is concluded that the angle between

the magnetic vector and the vertical axis of the

sensor should be retained at least four valid digits to

identify whether it is the interference from adjacent

parking process. Microcontroller after receiving the

magnetic data through sliding average, square root,

division and arccosine several steps to obtain the

final angle, the whole process needs to consider the

accuracy and running time of the calculation. There

are three methods of calculation in the experiment,

and the retained valid digits in different stages is

different, as shown in Table 1. Microcontroller

system clock select 16 MHz, and the Method1’s

running time is the fastest and far less than the

sampling interval of 12500us (80Hz). The

experimental results show that the magnetic data can

be processed in real time after adding the angle

calculation based on the existing threshold detection

algorithm.

5 CONCLUTIONS

Since the microcontroller does not have hardware

multipliers, in this paper, the digit-by-digit algorithm

and the CORDIC algorithm are used to complete the

estimation of the square root and the arccosine

function. The retained valid digits of the angle

threshold is determined by experiment. Experiments

show that after adding digit-by-digit algorithm and

CORDIC algorithm, the running time of micro-

controller is much shorter than the sampling interval

of sensors, it ensure that magnetic data are processed

in real time, and the accuracy of parking detection

can be improved.

The Inferior

Machine

The Neighboring

Parking

USB-UART

Bluetooth

Module

The Superior

Computer

Figure4: The experimental process.

Table 1: The valid digits and time of different methods.

Stages Method1 Method2 Method3

Slidin

filterin

43 2

uare root 1 2 3

Division 3 3 3

Arccosine 3 3 3

Runnin

time 41.125us 44.812us 46.437us

ACKNOWLEDGEMENTS

This work is supported partly by Tianjin science and

technology special project under Grant No.

16JCTPJC50600.

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