Multi-frequency System Research Articles

Exponential Stability of Invariant Manifold for a Nonlinear Impulsive Multifrequency System

We study the exponential stability of a trivial invariant manifold of nonlinear extension of the dynamical system on a torus with impulsive jumps at nonfixed moments of time. The deduced sufficient conditions for the exponential stability of the trivial torus take into account the information on the qualitative properties of the dynamics of the system on the invariant manifold and weaken sufficient conditions available in the literature for a wide class of dynamical systems. New theorems impose constraints on a nonwandering set of the dynamical system guaranteeing the exponential stability of trivial manifold and are especially beneficial for the stability analysis of the extensions of dynamical systems with simple structures of the limit sets and recurrent trajectories.

Multifrequency Phase-Shifted Control for Multiphase Multiload MCR WPT System to Achieve Targeted Power Distribution and High Misalignment Tolerance

With urgent market demand for multiload electronic applications, multiload magnetically coupled resonant (MCR) wireless power transfer (WPT) system has caused widespread concern. In the practical applications, multiload MCR WPT system should have the capability to realize targeted power distribution among loads and stable output power against misalignment of load. To achieve this goal, a multiphase multifrequency system with multiple loads is proposed in this article, where multi-phase structure of transmitting coils can enhance the misalignment tolerance, and multiple operating frequencies are beneficial to achieve multiload identification and targeted power distribution. For simplicity, this article mainly studies a two-phase dual-frequency system with two loads and proposes two phase-shifted control strategies. The equivalent circuit model of the system is established, and the output power in the open-loop system under two phase-shifted control methodologies are analyzed. According to that, the targeted power distribution strategy by adjusting the resonant frequency of the transmitter is implemented. Moreover, the closed-loop control schemes based on phase-shifted control methodologies are adopted to realize stable output power precisely against the misalignment of loads. Finally, a prototype of two-phase dual-frequency MCR WPT system with two loads is built in the laboratory. The experimental results prove the correctness of the theoretical analysis.

Establishment of polynomial regional ionospheric delay model by using GNSS dual-frequency combined observations

The Global Navigation Satellite System (GNSS) is currently one of the more effective observation methods for measuring the Total Electron Content (TEC) of the ionosphere. At the same time, the ionospheric delay is also one of the most serious error sources affecting the accuracy of GNSS technology. The establishment of the ionospheric model can eliminate and weaken the delay error and improve the accuracy of navigation and positioning. There are many existing ionospheric delay models. For small regions, the ionospheric delay error is usually polynomial model, but the parameters and precision of the polynomial model are not studied deeply. In this paper, by means of Continuously Operating Reference Station (CORS) and precise ephemeris, the data is preprocessed and the combined observation of the P code pseudo-ranges is smoothed by combined observations, so that polynomial ionospheric delay model with different parameters and joint hardware delay of receiver and satellite are generated. And then the accuracy of the model is analyzed and evaluated, it can be concluded that the parameter value of the polynomial regional ionospheric delay model (i=2,k=3) is appropriate, the Klobuchar model can correct the ionospheric delay error from 2.5m to 3.5m, the polynomial model can reach 0.263m or even higher, especially in today’s multi-frequency and multi-satellite system development.

Multi-frequency ultrasonic underground cavity scanning detection technology in borehole

Abstract In order to solve the current situation that underground cavity contour detection is difficult, this paper proposes a multi-frequency ultrasonic cavity scanning detection technology in borehole. It is a scanning technology that uses a combination of multiple frequency ultrasonic probes to obtain more effective detection information and achieve the cavity contour accurate measurement, which provides an important reference for the underground cavity detection. Firstly, in view of the spatial arrangement of multiple ultrasonic transducers, the corresponding structural design scheme is proposed to realize the structural design of multi-frequency ultrasonic scanning system. Then, in order to better adapt to the detection requirements, through the simulation of ultrasonic sound field, the ultrasonic beam characteristics are analyzed. The frequency response factor concept of multi-frequency ultrasonic is proposed, and the weight distinction of different frequency acoustic signals and the evaluation of multi- frequency ultrasonic response weight are realized. Finally, combined with the actual detection environment, the influence of scanning time interval and scanning speed on the detection results is analyzed. The parameter matching relationship between mechanical scanning and space detection target is constructed, and the parameters of scanning detection system are determined. In addition, in order to verify the feasibility and accuracy of the technology proposed in this paper, based on the principle of multi-frequency ultrasonic detection and the design of scanning detection system, the corresponding multi-frequency ultrasonic scanning detection system is independently developed. The detection capability and reliability of the system are tested and analyzed by using the developed detection system. The error of the detection result is small, which verifies the feasibility and accuracy of the multi-frequency ultrasonic underground cavity scanning detection technology proposed in this paper.

Assessment of multi-frequency global navigation satellite system precise point positioning models using GPS, BeiDou, GLONASS, Galileo and QZSS

The development of a global navigation satellite system (GNSS) brings the benefit of positioning, navigation and timing (PNT) services with three or even more available frequency signals. This paper developed five-system multi-frequency precise point positioning (PPP) models based on mathematical and stochastic models. Static positioning performances were evaluated and analyzed with multi-GNSS experiment (MGEX) network datasets and a vehicle-borne kinematic experiment was conducted to verify the kinematic PPP performances. In addition, the receiver clock, zenith tropospheric delay (ZTD), inter-frequency bias (IFB) and differential code bias (DCB) estimates were discussed. Results show that the triple-frequency PPP performances perform slightly better than the dual-frequency solutions, apart from the GPS-related PPP models based on a single ionosphere-free (IF) combined measurement. By introducing the external ionospheric products, the mean convergence time is reduced. For instance, the mean convergence time of ionosphere-constrained (IC) multi-frequency PPP is reduced by 7.4% from 35.7 to 33.1 min and by 19.0% from 7.8 to 6.3 min, for Galileo-only and five-constellation solutions, respectively, compared with dual-frequency IF PPP models. Similarly, the kinematic PPP can also achieve improved performances with more frequency signals and multi-GNSS observations.

BAND-PASS FILTER CIRCUIT DESIGN FOR MULTI-FREQUENCY ELECTRICAL IMPEDANCE TOMOGRAPHY SYSTEM

BAND-PASS FILTER CIRCUIT DESIGN FOR MULTI-FREQUENCY ELECTRICAL IMPEDACE TOMOGRAPHY SYSTEM . Electrical Impedance Tomography (EIT) is one of the emerging imaging technologies recently. The principle of EIT system is inject electric current into impedance object and measure the voltage based on the electrodes array. The current source that precise, stable, and wide-bandwidth is required to obtain voltage measurements accurately. The current source used for this EIT system is Voltage-Controlled Current Source (VCCS). The VCCS block circuit consists of several circuits, one of them is a filter circuit. The suitable filter for multi-frequency EIT system is band-pass filter. This research has been designed and fabricated a band-pass filter with cut-off frequency 1 and 250 kHz, which is using Butterworth coefficient, unity gain, and Sallen-Key topology.

Software and hardware system of multi-frequency oblique sounding the ionosphere

Background. The ionosphere was and will be the main channel for the propagation of radio waves of various bands (from extremely low to super-high frequencies). A feature of this channel is the dependence of its parameters on the state of space weather. Space weather is formed primarily by processes on the Sun and by processes on Earth (to a lesser extent). High-energy processes of man-made origin can also make a certain contribution to the state of space weather. Means of oblique sounding (OS) have significant opportunities for research in the field of geospace radiophysics, study of the channel of propagation of radio waves and dynamic processes in the geospace. In this case, both own radio transmitting devices and a network of broadcasting stations can be used. With the help of OS, it is possible to cover significant regions of the globe (up to global ones), and thereby study the dynamic processes in the geospace over these regions. The purpose of this work is to briefly describe the multi-frequency multiple-path radio system of the OS ionosphere and to illustrate its performance using the example of studying dynamic processes in the geospace. Techniques and Methodology. A coherent multi-frequency multiple-path oblique sounding radio system of the ionosphere is described. It is intended for radiophysical monitoring of dynamic processes in the geospace caused by variations in space weather, the impact on the ionosphere of high-energy sources of space and terrestrial origin. The complex is capable of receiving radio signals in the low-frequency (LF) and high-frequency (HF) ranges. Original software has been developed, depending on the range of tasks to be solved. The number of radio paths and their orientation depend on the specifics of the tasks being solved. The operation of the complex is based on measurements of the Doppler shift of frequency and amplitude or phase and amplitude of the signal. The autoregressive algorithm provides a Doppler frequency resolution of up to 0.02 Hz and a time resolution of 1 min. After obtaining the time dependences of the Doppler spectra, phases and amplitudes for various radio propagation paths, further processing of the time series is performed. Results. At V. N. Karazin Kharkiv National University, a multi-frequency multi-path radio engineering complex for oblique sounding of the ionosphere has been developed and is operating, designed for radiophysical monitoring of dynamic processes in the geospace caused by variations in space weather, the impact on the ionosphere of high-energy sources of space and terrestrial origin. Conclusions. The successful functioning of the complex is demonstrated by the example of studying the dynamic processes in the geospace caused by the action of various sources of energy release.

Efficient implementation of the ARKN and ERKN integrators for multi-frequency oscillatory systems with multiple time scales

It is known that, a notable feature of both the multi-frequency and multidimensional ARKN (Runge-Kutta-Nyström methods adapted to oscillatory system) and ERKN (extended Runge-Kutta-Nyström) integrators when they are applied to multi-frequency and multidimensional oscillatory system q″+Mq=f(t,q) with multiple time scales is that they exactly integrate the multi-frequency oscillatory homogeneous system q″+Mq=0. With regard to the efficient implementation issues of the integrators, it is significant to calculate efficiently the matrix-valued functions ϕ0(V) and ϕ1(V) which are involved in the two kinds of integrators, where V=h2M and h is a stepsize. In this paper, we pay attention to efficient implementation issues of the multi-frequency and multidimensional ARKN and ERKN integrators which are closely related to the calculations of ϕ0(V) and ϕ1(V). Using the properties of ϕ0(V) and ϕ1(V) and their relations, we present an efficient algorithm to calculate the two matrix-valued functions at lower cost. Two illuminating numerical examples are accompanied and the numerical results show the remarkable efficiency of the algorithm. We also give an essential stability analysis for ARKN and ERKN integrators on the basis of the different approximations to ϕ0(V) and ϕ1(V) which gains an insight into the importance of the calculations of ϕ0(V) and ϕ1(V).

Loss Minimization With Optimal Power Dispatch in Multi-Frequency HVac Power Systems

Low-frequency high-voltage ac transmission scheme has recently been proposed as an alternative approach for bulk power transmission. This paper proposes a multi-period optimal power flow (OPF) for a multi-frequency HVac transmission system that interconnects both conventional 50/60-Hz and low-frequency grids using back-to-back converters with a centralized control scheme. The OPF objective is to minimize system losses by determining the optimal dispatch for generators, shunt capacitors, and converters. The OPF constraints include the operational constraints of all HVac grid and converter stations. The resulting mixed-integer nonlinear programing problem is solved using a proposed framework based on the predictor-corrector primal-dual interior-point method. The proposed OPF formulation and solution approach are verified using a multi-frequency HVac transmission system that is modified from the IEEE 57-bus system. The results with the optimal dispatch from the proposed method during a simulated day show a significant loss reduction and an improved voltage regulation compared to those when an arbitrary dispatch is chosen.

Recent Doppler backscattering applications in Globus-M tokamak

Recently, a four-frequency Doppler backscattering (DBS) system was installed on the Globus-M tokamak. In addition to the classical DBS application for determining the mean plasma rotational velocities, DBS was used for the investigation of different plasma oscillatory processes in the spherical Globus-M tokamak. Application of various DBS data processing allowed us to reveal and investigate plasma oscillations, such as geodesic acoustic mode, limit cycle oscillations and Alfvén modes. It has been shown that DBS also allows registering filament like structures, which manifest as quasi-coherent oscillations in signals of various DBS channels. The multi-frequency DBS system makes it possible to localize plasma oscillations, their poloidal and radial sizes and mode structure. The main results of the DBS application for the study of these oscillations are presented. A comparison of the DBS data with the data of other diagnostics is also given.

Fully digital multi‐frequency compact high‐frequency radar system for sea surface remote sensing

Compared with single-frequency high frequency surface wave radar (HFSWR), a multi-frequency (MF) system provides more feasibility in sea surface dynamic parameters measurement and target detection. In this study, a novel multi-frequency compact HFSWR based on a fully digital architecture is developed. This system employs a flexible signal processing procedure with low hardware complexity. Without changing the circuit, it can realise two typical multi-frequency schemes, including time-division MF (TDMF) and frequency-division MF (FDMF). Furthermore, a waveform selection criterion is proposed by analysing the difference between the TDMF and FDMF schemes in frequency-modulated interrupted continuous wave (FMICW). The system performance is preliminarily validated in two frequencies by both close-loop test and field experiment. It is shown that the range processing of two frequencies are coherent with an amplitude variation 0.93 and a root-mean-square error between 11.0 and 13.0 cm/s.

An Enhanced Fusion Strategy for Reliable Attitude Measurement Utilizing Vision and Inertial Sensors

In this paper, we present a radial basis function (RBF) and cubature Kalman filter (CKF) based enhanced fusion strategy for vision and inertial integrated attitude measurement for sampling frequency discrepancy and divergence. First, the multi-frequency problem of the integrated system and the reason for attitude divergence are analyzed. Second, the filter equation and attitude differential equation are constructed to calculate attitudes separately in time series when visual and inertial data are available or when there are only inertial data. Third, attitude errors between inertial and vision are sent to the input layer of RBF for training. After this, through the activation function of the hidden layer, the errors are transferred to the output layer for weighting the sums, and the training model is established. To overcome the problem of divergence inherent in a multi-frequency system, the well-trained RBF, which can output the attitude errors, is utilized to compensate the attitudes calculated by pure inertial data. Finally, semi-physical simulation experiments under different scenarios are performed to validate the effectiveness and superiority of the proposed scheme in accurate attitude measurements and enhanced anti-divergence capability.

Noise Immunity Research of Multi-Frequency Information Transmission System with Code Division of Channels

In this paper, there is noise immunity research of one version of construction multi-frequency information transmission system with code division of user's channels. An engineering method for noise immunity estimate is developed. Error probability dependences on average signal-to-noise ratio are calculated for the cases of uniform multipath intensity profile. Researchable system comparison of noise immunity with single-frequency system of CDMA standard is made.

A New GPS SNR-based Combination Approach for Land Surface Snow Depth Monitoring

Snow is not only a critical storage component in the hydrologic cycle but also an important data for climate research; however, snowfall observations are only sparsely available. Signal-to-noise ratio (SNR) has recently been applied for sensing snow depths. Most studies only consider either global positioning system (GPS) L1 or L2 SNR data. In the current study, a new snow depth estimation approach is proposed using multipath reflectometry and SNR combination of GPS triple frequency (i.e. L1, L2 and L5) signals. The SNR combination method describes the relationship between antenna height variation and spectral peak frequency. Snow depths are retrieved from the SNR combination data at YEL2 and KIRU sites and validated by comparing it with in situ observations. The elevation angle ranges from 5° to 25°. The correlations for the two sites are 0.99 and 0.97. The performance of the new approach is assessed by comparing it with existing models. The proposed approach presents a high correlation of 0.95 and an accuracy (in terms of Root Mean Square Error) improvement of over 30%. Findings indicate that the new approach could potentially be applied to monitor snow depths and may serve as a reference for building multi-system and multi-frequency global navigation satellite system reflectometry models.

Ionospheric processes observed with the passive oblique-incidence HF Doppler radar

Urgency. The urgency is caused by the need to continuously monitor with radio instrumentation dynamic processes acting in the ionosphere, which arise due to variations in space weather, the impact of high-energy sources of natural and anthropogenic origin. To meet this challenge, V. N. Karazin National University and Harbin Engineering University specialists has developed a coherent multi-frequency multi-path radio system for obliquely probing the ionosphere. Purpose of Work. The paper illustrates the instrument capability for the study of dynamic processes arising in the ionosphere during a solar terminator, a moderate earthquake, a strong ionospheric storm, and in the cource of a partial solar eclipse. Techniques and Methodology. The system design is base on the software-defined radio (SDR) technology. The system is capable of receiving radio waves in the 10 kHz – 30 MHz band. The versatile computer software permits us to adjust the system for solving various problems. The number of the radio propagation paths and their orientation depends on the problem being solved. The premise upon which this radio system operation is based is measurements of the Doppler shift of the frequency. The autoregressive algorithm provides a 0.02 Hz root-mean-square Doppler line error and 7.5-s time resolution. Having the Doppler spectrum time dependencies for various radio paths archived, time series corresponding to various radio-wave modes undergo further processing. Results. As an example of successful instrument performance, dynamic processes operating in the course of a dusk terminator, the moderate (magnitude 5.9) earthquake on July 7, 2018, the strong ionospheric storm on August 26, 2018, and the partial (0.74 magnitude) solar eclipse over China on August 11, 2018 have been investigated. The ionospheric response to the impact of energy sources of various nature has been detected and investigated; it was accompanied by an increase in the number of rays, Doppler spectrum broadening, aperiodic and quasi-periodic variations in the Doppler shift of the frequency, generation of alternating sign variations in the electron density and wave disturbances having atmospheric gravity wave and infrasound parameters. Conclusions. The radio system located at the Harbin Engineering University campus successfully performs continuous radio monitoring of dynamic processes caused by various energy source in the ionosphere.

HF radio-wave characteristic variations over China during moderate earthquake in Japan on September 5, 2018

Urgency. The Earth's interior layers – atmosphere – ionosphere – magnetosphere (EAIM) form a one system, which is open, dynamic, and nonlinear. There are direct and reverse, positive and negative linkages among the subsystems within the EAIM system, which are currently insufficiently studied. The release of energy from a high-power source in one of the subsystems triggers the interaction among the subsystems. In this paper, a moderate earthquake of Richter magnitude M » 6.6 is considered as such a source. The aim of the paper is to describe time variations in the characteristics of the HF radio waves observed along the radio propagation paths over the People's Republic of China during the earthquake of September 5, 2018 in Japan. Techniques and Methodology. To observe the temporal variations in the characteristics of radio waves, we used the multi-frequency multiple-path coherent radio system at the Harbin Engineering University. Broadcasting stations located in the People's Republic of China, the South Korea, Japan, Russia, and Mongolia are used as transmitters. The time variations in the Doppler spectra, the Doppler shift of frequency of the main mode, and signal amplitudes were subjected to analysis. The measurements were performed in the frequency range of 5 – 10 MHz over 14 radio propagation paths extending from ~ 900 km to 1800 km and having various orientations. The Doppler spectra are calculated in 7.5-s step with the root-mean-square Doppler line error of 0.02 Hz. Results. The response of the ionosphere to a moderate earthquake was observed and studied. The delay time of the assumed response and the apparent speed of propagation of the disturbances were estimated. It was demonstrated that the seismic shock was followed by Doppler spectra spreading and the Doppler frequency shift of the main mode varying with time quasi-periodically with an ~3-min period of infrasound and an ~20 – 30-min period of atmospheric gravity wave. Conclusions: Moderate earthquakes are capable of launching disturbances in the ionosphere detectable at distances of ~1000 km from the epicenter of earthquake.

Electromagnetic survey to constraints ore mining exploration in the eastern Anti-Atlas belt (case of Imiter inlier, Morocco):Application of frequency electromagnetic helicopter-borne method

The present work is based on data of a geophysical survey of the Imiter inlier that was carried out by DIGHEMV multi-coil, multi-frequency helicopter-borne electromagnetic system. Its main goals are (i) to interpret the results of this survey in light of regional geological settings; (ii) to define how geological factors controlled mineralization in the world-class Imiter silver mine, which is located in the central western part of the survey area; (iii) to correlate the modalities of this control with the electromagnetic response observed in the Imiter mine district; and (iv) to extend the model thus obtained to the whole study area in view of locating other potentially mineralized ore bodies.The obtained results showed that the Imiter mine district is covered by two important electromagnetic anomalies and three conductor axes, which are interpreted as directly reflecting the presence of metallic deposits in the subsurface. The most intense of these anomalies (B2) is located in the northern bloc of the main Imiter Fault, in an area which is highly fractured by secondary faults, is covered by Ediacaran volcanic and has never been mined. All mineralized bodies exploited so far are localized in the southern block of this important fault and are all essentially hosted by the Cryogenian black shales. Since we have established that there is a direct relation between faulting and mineralization, and that the intensity of the electromagnetic anomaly is directly related to ore concentration in hosted rocks; we conclude that the area covered by the electromagnetic anomaly B2 would be even more interesting to explore that the southern bloc presently in exploitation. Extending these results to the rest of the survey area, it was found that two other areas to the south-east of the Imiter mine district are also two potentially mineralized zones meriting future exploration.

Design of a Multiband Global Navigation Satellite System Radio Frequency Interference Monitoring Front-End with Synchronized Secondary Sensors.

This paper investigates the challenges of developing a multi-frequency radio frequency interference (RFI) monitoring and characterization system that is optimized for ease of deployment and operation as well as low per unit cost. To achieve this, we explore the design and development of a multiband global navigation satellite system (GNSS) front-end which is intrinsically capable of synchronizing side channel information from non-RF sensors, such as inertial measurement units and integrated power meters, to allow the simultaneous production of substantial amounts of sampled spectrum while also allowing low-cost, real-time monitoring and logging of detected RFI events. While the inertial measurement unit and barometer are not used in the RFI investigation discussed, the design features that provide for their precise synchronization with the RF sample stream are presented as design elements worth consideration. The designed system, referred to as Four Independent Tuners with Data-packing (FITWD), was utilized in a data collection campaign over multiple European and Scandinavian countries in support of the determination of the relative occurrence rates of L1/E1 and L5/E5a interference events and intensities where it proved itself a successful alternative to larger and more expensive commercial solutions. The dual conclusions reached were that it was possible to develop a compact low-cost, multi-channel radio frequency (RF) front-end that implicitly supported external data source synchronization, and that such monitoring systems or similar capabilities integrated within receivers are likely to be needed in the future due to the increasing occurrence rates of GNSS RFI events.

A Low-Cost Portable Wireless Multi-frequency Electrical Impedance Tomography System

Electrical impedance tomography (EIT) is an approach to reconstruct electrical resistivity images of the body noninvasively. Here we present a novel wireless high-speed frequency division multiplexing and flexible switching-based EIT system with increased temporal resolution using raspberry pi. Proposed multi-frequency electrical impedance system has good performance, portable, energy and cost-efficient. Current is injected to all the electrodes simultaneously having different frequencies which increase the speed for capturing the fast change in impedances. Proposed system can reconstruct real-time 2D images for continuously monitoring applications where impedance changes rapidly. It can capture 70 frames/sec, and its power consumption is 10 mW. The system is designed for a bandwidth of 1 kHz–1 MHz, which covers most of the medical impedance investigations. Performance of the system was measured at 25 KHz by calculating parameter of blur radius (PBR) and percentage of position error (PPE). Average PBR and PPE obtained were 0.985 and 7.24%, respectively. SNR, linearity and stability were calculated after proper calibration by applying a small current of $$500\,\upmu \hbox {A}$$ . SNR of the system is more than 70 dB. Amplitude and phase measurement repeatability were 0.7% and $$1^{\circ }$$ , respectively. CMRR of both wired and wireless systems were measured to find the effect of noise on the wireless system. Result shows that the proposed WMFEIT system has comparable performance with the reference systems and has good scope to be used for clinical imaging applications.

Performance analysis of dual-frequency receiver using combinations of GPS L1, L5, and L2 civil signals

Processing of GNSS signals from more than one frequency band enhances the accuracy and integrity of a position solution in both standalone and differential positioning. The modern GPS program and newly launched GNSS systems such as GALILEO, BeiDou allow civilians to access signals from multiple frequencies in the L-band spectrum. While there are some advantages in triple-frequency processing in carrier phase applications, in general most of the standalone kinematic receivers get benefit from dual-frequency signals for ionosphere error correction. In implementing a dual-frequency receiver, it is necessary to select a combination of frequencies leading to an optimum performance of the existing civilian signals. In the current research work, we have analyzed the performance of dual-frequency receiver in terms of combined signal observation noise, sensitivity and robustness using analytical models by taking the combination of GPS L1, L2C and L5 signals as an example. Further, we have investigated the benefits of common Doppler estimate-based two-frequency signal tracking to reduce the noise in linear combination of observations. Through analytical and experimental results, it is confirmed that the L1/L5 signal combination in GPS system has low observation noise, which is suitable to use in high accuracy and precise positioning applications using standalone dual-frequency receiver. Further, it is shown that common Doppler estimate-based dual-frequency signal tracking has improved receiver tracking loop performance in terms of observation noise and multipath in linear combination of observations and enhanced receiver sensitivity and robustness. In GPS system, L1/L5 signals processed using common Doppler estimate-aided two-frequency signal tracking architecture, it is possible to effectively mitigate ionosphere delay and other receiver observation errors, to achieve less than 1 m position accuracy using unambiguous code phase observations. Proposed analysis is applicable of finding an optimal two-frequency signal combination in multi-frequency GNSS system and suitable signal processing architecture to obtain high accuracy and precise ionosphere-free position solution using code phase observations in standalone dual-frequency receiver.