scholarly journals Inferring the connectivity of coupled chaotic oscillators using Kalman filtering

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
E. Forero-Ortiz ◽  
G. Tirabassi ◽  
C. Masoller ◽  
A. J. Pons
Keyword(s):  
Parameter Estimation ◽  
Kalman Filtering ◽  
Coupling Strength ◽  
Network Architecture ◽  
Coupled Oscillators ◽  
Complexity Science ◽  
Single Variable ◽  
Chaotic Oscillators ◽  
Simulation Results ◽  
Interaction Topology

AbstractInferring the interactions between coupled oscillators is a significant open problem in complexity science, with multiple interdisciplinary applications. While the Kalman filter (KF) technique is a well-known tool, widely used for data assimilation and parameter estimation, to the best of our knowledge, it has not yet been used for inferring the connectivity of coupled chaotic oscillators. Here we demonstrate that KF allows reconstructing the interaction topology and the coupling strength of a network of mutually coupled Rössler-like chaotic oscillators. We show that the connectivity can be inferred by considering only the observed dynamics of a single variable of the three that define the phase space of each oscillator. We also show that both the coupling strength and the network architecture can be inferred even when the oscillators are close to synchronization. Simulation results are provided to show the effectiveness and applicability of the proposed method.

scholarly journals Evasion guidance for air-breathing hypersonic vehicles against unknown pursuer dynamics

2021 ◽  
Author(s):  
Tian Yan ◽  
Yuanli Cai ◽  
Bin Xu
Keyword(s):  
Parameter Estimation ◽  
Gradient Descent ◽  
Rapid Development ◽  
Energy Optimization ◽  
Hypersonic Vehicles ◽  
Air Breathing ◽  
Related Research ◽  
Practical Guidance ◽  
Simulation Results ◽  
Guidance Algorithm

AbstractThe rapid development of hypersonic vehicles has motivated the related research dramatically while the evasion of the hypersonic vehicles becomes one of the challenging issues. Different from the work based on the premise that the pursuers’ information is fully known, in this paper the evasion guidance for air-breathing hypersonic vehicles (AHVs) against unknown pursuer dynamics is studied. The gradient descent is employed for parameter estimation of the unknown dynamics of the pursuer. The energy-optimized evasion guidance algorithm is further developed by taking the acceleration constraint and energy optimization into consideration. Under the proposed algorithm, the system can deal with the unknown pursuer dynamics effectively and provide more practical guidance for the evasion process. The simulation results show that the proposed method can enable the AHV to achieve successful evasion.

A RELAX Based Method for Spotlight SAR Imaging

2012 ◽  
Vol 500 ◽  
pp. 362-367
Author(s):  
Xiao Zhen Ren ◽  
Yao Qin ◽  
Hong Liang Fu
Keyword(s):  
Parameter Estimation ◽  
Estimation Problem ◽  
Noisy Environment ◽  
Parameter Estimation Problem ◽  
Imaging Algorithm ◽  
Imaging Results ◽  
Sar Imaging ◽  
Simulation Results ◽  
Noisy Condition

The imaging problem of spotlight SAR is converted to a parameter estimation problem of several monochromatic signals in additive white Gaussian noisy condition in this paper. Moreover, a spotlight SAR imaging algorithm based on RELAX is presented in detail. Traditional polar format algorithm and the presented method are applied to spotlight SAR imaging respectively, and the imaging results are compared. Simulation results show that the polar format algorithm doesn’t give satisfactory imaging results, while the proposed method adapts the noisy environment better and obtains better results.

TWOFOLD IMPACT OF DELAYED FEEDBACK ON COUPLED OSCILLATORS

2007 ◽  
Vol 17 (07) ◽  
pp. 2517-2530 ◽  
Author(s):  
OLEKSANDR V. POPOVYCH ◽  
VALERII KRACHKOVSKYI ◽  
PETER A. TASS
Keyword(s):  
Time Delay ◽  
Coupling Strength ◽  
Coupled Oscillators ◽  
Phase Synchronization ◽  
Threshold Value ◽  
Phase Oscillators ◽  
Intermediate Coupling ◽  
Rich Variety ◽  
Dynamical Regimes ◽  
The Impact

We present a detailed bifurcation analysis of desynchronization transitions in a system of two coupled phase oscillators with delay. The coupling between the oscillators combines a delayed self-feedback of each oscillator with an instantaneous mutual interaction. The delayed self-feedback leads to a rich variety of dynamical regimes, ranging from phase-locked and periodically modulated synchronized states to chaotic phase synchronization and desynchronization. We show that an increase of the coupling strength between oscillators may lead to a loss of synchronization. Intriguingly, the delay has a twofold influence on the oscillations: synchronizing for small and intermediate coupling strength and desynchronizing if the coupling strength exceeds a certain threshold value. We show that the desynchronization transition has the form of a crisis bifurcation of a chaotic attractor of chaotic phase synchronization. This study contributes to a better understanding of the impact of time delay on interacting oscillators.

FREQUENCY SYNCHRONIZATION IN NETWORKS OF COUPLED OSCILLATORS, A MONOTONE DYNAMICAL SYSTEMS APPROACH

2009 ◽  
Vol 19 (12) ◽  
pp. 4107-4116 ◽  
Author(s):  
WEN-XIN QIN
Keyword(s):  
Dynamical Systems ◽  
Coupling Strength ◽  
Coupled Oscillators ◽  
Systems Approach ◽  
System Size ◽  
Coupling Scheme ◽  
Frequency Synchronization ◽  
Nonlinear Coupling ◽  
New Approach ◽  
Monotone Dynamical Systems

We propose a new approach to investigate the frequency synchronization in networks of coupled oscillators. By making use of the theory of monotone dynamical systems, we show that frequency synchronization occurs in networks of coupled oscillators, provided the coupling scheme is symmetric, connected, and strongly cooperative. Our criterion is independent of the system size, the coupling strength and the details of the connections, and applies also to nonlinear coupling schemes.

scholarly journals Integration and Simulations of INS/GNSS System using the Approach of Carrier Phase Measurements

2015 ◽  
Vol 4 (4) ◽  
pp. 243
Author(s):  
Khan Badshah ◽  
Qin Yongyuan
Keyword(s):  
Kalman Filtering ◽  
Carrier Phase ◽  
Closed Loop ◽  
Position Estimation ◽  
Integrated System ◽  
Integer Ambiguity ◽  
Font Size ◽  
Phase Measurements ◽  
Simulation Results ◽  
Lever Arm Effect

<p class="MsoNormal" style="margin-top: 12.0pt; margin-right: 0in; margin-bottom: 6.0pt; margin-left: 0in; text-align: justify;"><em><span style="font-size: 9.0pt; font-family: &quot;Arial&quot;,sans-serif; mso-ascii-theme-font: minor-bidi; mso-hansi-theme-font: minor-bidi; mso-bidi-theme-font: minor-bidi;" lang="EN-GB">This paper discusses the techniques of attitude, velocity ad position estimation from GNSS carrier phase measurements, and investigates the performance of the lower precision MEMS-based INS/GNSS system based on carrier phase measurements. Double differenced carrier phase measurements provide more accurate velocity and position estimation compared to code and Doppler measurements. However, integer ambiguity is required to be removed for precise positioning. Multiples<span style="color: red;"> </span>antennae approach is used to derive the attitude information from carrier phase measurements in order to control the large initial misalignment angles for initialization of the integration process or to utilize during benign dynamics. Lever arm effect is considered to compensate for the separation of GNSS antenna and IMU location. The derived three GNSS observables are used to correct the INS through optimal Kalman filtering in a closed loop. Simulation results indicates the effectiveness of the integrated system for airborne as well as for land navigation vehicles</span></em><span lang="EN-GB">. </span></p><div id="_mcePaste" class="mcePaste" style="position: absolute; left: -10000px; top: 0px; width: 1px; height: 1px; overflow: hidden;"><p class="MsoNormal" style="margin-top: 12.0pt; margin-right: 0in; margin-bottom: 6.0pt; margin-left: 0in; text-align: justify;"><em><span style="font-size: 9.0pt; font-family: &quot;Arial&quot;,sans-serif; mso-ascii-theme-font: minor-bidi; mso-hansi-theme-font: minor-bidi; mso-bidi-theme-font: minor-bidi;" lang="EN-GB">This paper discusses the techniques of attitude, velocity ad position estimation from GNSS carrier phase measurements, and investigates the performance of the lower precision MEMS based INS/GNSS system based on carrier phase measurements. Double differenced carrier phase measurements provide more accurate velocity and position estimation compared to code and Doppler measurements. However, integer ambiguity is required to be removed for precise positioning. Multiples<span style="color: red;"> </span>antennae approach is used to derive the attitude information from carrier phase measurements in order to control the large initial misalignment angles for initialization of the integration process or to utilize during benign dynamics. Lever arm effect is considered to compensate for the separation of GNSS antenna and IMU location. The derived three GNSS observables are used to correct the INS through optimal Kalman filtering in a closed loop. Simulation results indicates the effectiveness of the integrated system for airborne as well as for land navigation vehicles</span></em><span lang="EN-GB">. </span></p></div>

PHASE SYNCHRONIZATION OF LINEARLY AND NONLINEARLY COUPLED OSCILLATORS WITH INTERNAL RESONANCE

2009 ◽  
Vol 23 (30) ◽  
pp. 5715-5726
Author(s):  
YONG LIU
Keyword(s):  
Coupling Strength ◽  
Coupled Oscillators ◽  
Internal Resonance ◽  
Natural Frequencies ◽  
Phase Synchronization ◽  
Coupled Systems ◽  
Nonlinear Coupling ◽  
Linear Coupling ◽  
Phase Dynamics ◽  
Diffuse Clouds

Phase synchronization between linearly and nonlinearly coupled systems with internal resonance is investigated in this paper. By introducing the conception of phase for a chaotic motion, it demonstrates that the detuning parameter σ between the two natural frequencies ω1and ω2affects phase dynamics, and with the increase in the linear coupling strength, the effect of phase synchronization between two sub-systems was enhanced, while increased firstly, and then decayed as nonlinear coupling strength increases. Further investigation reveals that the transition of phase states between the two oscillators are related to the critical changes of the Lyapunov exponents, which can also be explained by the diffuse clouds.

Parameter Estimation of Co-Channel AIS Signal Using Ambiguity Function

2014 ◽  
Vol 644-650 ◽  
pp. 4035-4039
Author(s):  
Hao Su Zhou ◽  
Jian Xin Wang
Keyword(s):  
Parameter Estimation ◽  
Gaussian Noise ◽  
Additive White Gaussian Noise ◽  
Reference Signal ◽  
Two Dimensions ◽  
Ambiguity Function ◽  
Weak Signal ◽  
Strong Signal ◽  
Estimated Parameters ◽  
Simulation Results

A new data-aided algorithm for parameter estimation of the co-channel AIS signal transmitted over the additive white Gaussian noise channel is proposed in this paper. The co-channel signal consists of a strong signal with high power and a weak signal with low power. The parameters of the strong signal are estimated by searching the ambiguity function of the co-channel signal in two dimensions. A reference signal is therefore reconstructed with the estimated parameters and the aided data. By removing the ambiguity function of the reconstructed reference signal from that of the original co-channel signal, a new co-channel signal ambiguity function is obtained, from which the parameters of the weak signal are estimated. The simulation results illustrate that the proposed algorithm can estimate the parameters of the co-channel AIS signal effectively.

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