ANALYSING THE ACQUISITION AND TRACKING IN GPS

ANALYSING THE ACQUISITION AND TRACKING IN GPS

TRANSEIVER USING SDR AND KALMAN FILTER

N.R. Raajan*1, G.MadhuPriya1, K.S.Lavanya1, S.Raghavi1, S.Greeta1, V.S. Ramya

Lakshmi1,K.Hariharan2

1School of Electrical & Electronics Engineering, SASTRA Deemed University, Thanjavur, India.

2School of Computing, SASTRA Deemed University, Thanjavur, India.

[email protected],[email protected],

[email protected],[email protected], [email protected],

[email protected]

Abstract

In order to overcome the challenges due to operating environment a flexible configurable soft

GPS is designed using MATLAB. The algorithm consists of acquisition and tracking. In the early

stage the RF signal received from the satellite are down converted to intermediate frequency

signals which are further digitized by ADC which is fed as input to the SDR. In acquisition the

visibility of the satellites are analyzed and the navigational message bits are XOR’ed with the

PRN code. PRN code is unique for each satellite in the geostationary orbit. Due to the atomic

density variation in ionosphere there is a change in the doppler shift which affects the actual

positioning of the satellite. The tracking corrects the doppler shift by means of Kalman filter

algorithm.

Keywords: ADC, SDR, PRN code, Acquisition, Tracking, Kalman filter.

International Journal of Pure and Applied MathematicsVolume 119 No. 12 2018, 16391-16402ISSN: 1314-3395 (on-line version)url: http://www.ijpam.euSpecial Issue ijpam.eu

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1 Introduction

The antenna receives the signal transmitted from the GPS satellites. Radio frequency

(RF) is the input signal which is amplified to get amplitude and the frequency in properly and a

desired output frequency is obtained by converting. The output signal is digitized by using an

analog-to-digital converter (ADC) which is given as input to Software Defined Radio. The

receiver uses the hardware of antenna, RF and ADC. After digitizing the signal it get processed

with SDR. Acquisition means to find the visibility of a certain satellite. The tracking is used to

find the navigation data’s phase transition. The subframes and navigation data are obtained from

the navigation data’s phase transition. Navigation data gives Ephemeris data and pseudo ranges.

Satellite positions can be obtained from the ephemeris data. Hardware collects the digitized data

and the software finds the user position is discussed. Scintillation in ionosphere results in 20dB

and a corresponding phase jitter is introduced. The PLL loop reduces the carrier lock threshold

by greater than 1dB in relation with arctangent and Costas detector. The variable loop of

bandwidth in Kalman filter reduces the carrier threshold greater than 7dB compared to the loop

of constant bandwidth Kalman filter mitigates receiver noise and adapts the loop bandwidth to

CNR. Hence PLL slip is avoided resulting in a considerable increase in CNR and doppler shift

correction takes place.

2 Methodology

satellite navigation systems are processed on the basis of channelized structure. In this

signal acquisition is carried out by acquisition and tracking is shown for both PLL and Kalman

filter based PLL.

A. Acquisition

The geostationary orbit consists of 24 satellites. The acquisition detects the visibility of

the satellites in order to know which satellite transmits the data. Each satellite has an unique code

sequence given, to know from which satellite signal is coming from. First is to generate replica

of code for that code phase should be known to remove it in tracking part from incoming signal.

Then carrier phase should be determined, here Doppler shift affects the frequency. So this

frequency should be detected and corrected. Acquisition can be carried out with two algorithm

both of parallel search acquisition with frequency space search algorithm and code phase search

algorithm. Comparing proposed code phase search algorithm and frequency space search

algorithm, proposed algorithm is convenient. In parallel frequency space search algorithm,

incoming signal is correlated with the Pseudo Random Noise sequence and using fast Fourier

transform Function step search is performed. But 1023 search steps are required. In Parallel

code phase search Algorithm only 41 steps are performed. Cross correlation between incoming

signal and PRN sequence is replaced for the code length steps multiplication with incoming

signal which is shown in Fig .

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The PRN code is generated by DFT in frequency domain which generates sinusoidal signals for

base conversion. The raw data is mixed to the baseband data and transformed to frequency

domain. Conversion to time domain via IDFT takes place and the results are recorded. If all the

frequency bins are tested then PRN code phase, carrier frequency and magnitude of maximum

peak are found. At the receiver end the PRN code is extracted and refinement in frequency

estimation is done via DFT. The acquisition metrics are computed and the results are recorded.

In parallel code phase search algorithm, the incoming signal is compounded by a code which is

locally generated. The compounded signal results in the generation of the H(amplitude) signal

and a 90◦ phase-shifted version of the signal generates the P(phase) signal. The H and P signals

in combination forms a complex input signal y(n) = H(n)+ jP(n) to the DFT function. Frequency

is transformed in the generated Pseudo Random Noise code and the resultant data is complex

combinatorial.

B. Tracking

Function of tracking is to correct the doppler effect/shift occurring in the operating

environment. It tracks the GPS signals which is being allocated to each channel. The following

parameter are to be considered: the front end recorded signal, channel structure, sinusoidal C/A

code tables. The block in front end processes the samples and results in two structures: Results of

tracking and an updation in channel structure.


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Fig 1: Flow diagram of Acquisition

no

yes

no

yes

no yes

Acquisition.m

Find Pseudo Random

Noise code, carrier

frequency bin, and

magnitude of maximum peak

Preallocate arrays

Is there is any

signal present?

Convert Psuedo Random

Noise code to the

frequency domain (DFT)

Generate sine/cosine local

oscillator signals for

baseband conversion Remove Pseudo Random

Noise code modulation and

estimate frequency through DFT

Mix raw data to the

baseband and transform to

frequency domain Calculate acquisition metric

and record

Multiple baseband data and

PRN code in the frequency domain

All PRN’s

tested?

Convert to time domain via

inverse DFT and record

result

All frequency

bins tested Return


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The channel block is used to transfer initial information of each channel and for storing the

current channel information. The second process of the channel enables the continues tracking of

information.

The parameters of information has the carrier frequency, PRN code, phase code, locally

generated signals and temporal values in the costas loop. The results of tracking for all channel

for every millisecond in the processed block has the output emerging from six correlators and the

costas loop. This output is fed as input to the post navigation block. In order to plot the tracking

results and to analyze receiver performance extra information may be needed. Finally the

individual channel plots are tracked by execution of command plot.

Fig 2: Flow diagram of Tracking

No

Yes

No

Return Tracking.m

All channels processed?

Predefine arrays to seek in file

to acquisition result and set

PRN to processed

All data processed?

Read in one millisecond of

data to process

Yes

Compute loop discriminators,

apply filters, and update code/carrier frequencies

Generate sine and cosine

local oscillator signals and mix to baseband

Correlator PRN code replicas

with down converted data to obtain

Generate early, prompt, and late code period replicas


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Post Navigation is used to find transitions in bit and track preamble location. Hence bit values

are obtained and ephemeris data are decoded by extracting information from sub frames. The

position is computed and pseudo range code calculation is done by changing appropriate receiver

setting.

C. PLL based on Kalman filter

In Ionosphere, due to the atomic density variation the incoming satellite signal through

the atmosphere has a medium undergoes diffraction which causes and interference in the

electromagnetic wave. The random variations in amplitude and phase of the GPS signal takes

place. This process is called as scintillation which is most commonly found in equatorial region.

The effects of scintillation leads to signal fading, decrease in CNR, increase in the doppler effect

leads to lock or slip loss. The multipath propagation causes considerable attenuation of the

signal coming from the satellite. The reason we need to alleviate scintillation is that the

ionospheric error is predominantly high compared to the errors such as orbital error, troposphere

error, receiver noise and satellite clock. In order to overcome the above problem we replace loop

filter with Kalman filter. The circuit of Kalman filter is shown in fig 3

Fig 3: Circuit of the Kalman filter

n

The scintillation causes 20dB fading and a phase jitter which pauses rapid power fading and

carrier phase variation. In the ionosphere there are several uncertainties and few can be removed

using a dual frequency technique. The other abnormalities are the ionospheric plasma anomalies.

The free electrons and ions present in the ionosphere recombines causing heavy attenuation.

Replacing GPS L1 phase track by means of Kalman overcomes these abnormalities. Kalman

filter is the linear recursive filter that has both the prediction and updation mechanism for the

errors occurring due to introduction of doppler shift.

Prediction in time step i and

the co-variance corresponding to step i of the state

Previous state at time step i-1

Time step I observations

correction in time step i and

the co-variance corresponding to step i of the state


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Fig 4: Scintillation based Adaptive KF PLL

Input signal

Local DLL code

In the first step the dynamic model is proposed. Next step involves correction of errors by

means of observation model so that the error covariance is minimized. Hence it acts as an

optimal estimate .

1.State Vector

The variables of interest are considered which represents the dynamic state and the

degrees of freedom the elements in state vector are position, velocity , time and orientation . The

position includes latitude , longitude and altitude values.

yk=[k, k, k]T

The state vectors has two values namely priori value for prediction and posteriori value for

updation of correction.

yk’=[k’, k’, k’]T

2. Dynamic Model

The transformation of the state vector are considered in time domain.

3.Observation Model

The relation between the estimated and the state measurements are derived in this model.

Kalman filtering follows the distribution of gaussian. The product of two gaussian

random variable results in another gaussian distribution

=+PLLk

Correlator bank

C/N0

Evaluation

NCO

Discriminator

Spectrum

scintillation parameters

Kalman filter


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The final equation is given by

=+L

Fig 5: IF data plot

Fig 6: Acquisition Plot

Fig 7: Tracking


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Fig 8: Output of SDR PRN 26, Channel 3

Fig 9: Output of SDR(KF) PRN 26, Channel 3


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3.Conclusion

The results of the SDR with the carrier track loop and the PLL(Costas loop) defined with

Kalman filter are analyzed and the signal plots are as shown. The phase errors and Doppler

frequency shift which are the effects of scintillations are alleviated. The parallel phase

acquisition algorithm enables the I and Q ie. the amplitude and the phase measurement in the

correlator provides the prominent differences in the carrier tracking phase and the re-constructed

signal which is present in the PLL controlled oscillator. Hence the GPS transceiver is designed

using MATLAB which is flexible in the operating environment and the problem of scintillation

is overcome by means of Kalman filter. The atomic density variation causes diffraction of the

signal received which causes the Doppler shift to occur by constant slip in PLL.As a result the

PLL does not measure the actual delay but a pseudo delay. The prediction and the update

mechanism is provided by the Kalman filter which prevents the slip of PLL and it measures the

actual delay of the signal from the satellite to the receiver. Hence the parameters position along

with the orientation and time can be measured using Soft GPS code.

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ANALYSING THE ACQUISITION AND TRACKING IN GPS