Analysis of the Multiplexing Method of New System Navigation Signals of GPS III First Star L1 Frequency in China’s Regional

Compared with the previous GPS satellites, the first GPS III satellite adds a new civil signal L1C to the signal components of the L1 frequency in addition to the improvement of positioning accuracy, anti-interference ability, and service life. The selection and combination of signal modulation and multiplexing methods will affect the power ratio and phase relationship in the process of signal transmission. In the distribution of constellation of different modulation modes, the signal amplitudes of different signal constellation points will be affected by the nonlinear amplifiers of satellites. The analysis can assess its impact on navigation performance. The iGMAS monitoring and evaluation center of the 54th Research Institute of China Electronics Technology Group Corporation uses the low-distortion data acquisition and processing platform and refined signal software receiving processing algorithm of the iGMAS monitoring and evaluation center to complete the signal acquisition of the first satellite of GPS III over China, and processes accordingly for its signal modulation mode. Compared with the previous generation GPS of old system signals, it is found that the GPS signal of the new system not only adds the L1C frequency, but also the constant envelope multiplexing mode of the L1 frequency signal, and the power ratio of the internal signal components are also adjusted.

Discretization analysis of bifurcation based nonlinear amplifiers

Recently, for modeling biological amplification processes, nonlinear amplifiers based on the supercritical Andronov–Hopf bifurcation have been widely analyzed analytically. For technical realizations, digital systems have become the most relevant systems in signal processing applications. The underlying continuous-time systems are transferred to the discrete-time domain using numerical integration methods. Within this contribution, effects on the qualitative behavior of the Andronov–Hopf bifurcation based systems concerning numerical integration methods are analyzed. It is shown exemplarily that explicit Runge–Kutta methods transform the truncated normalform equation of the Andronov–Hopf bifurcation into the normalform equation of the Neimark–Sacker bifurcation. Dependent on the order of the integration method, higher order terms are added during this transformation.A rescaled normalform equation of the Neimark–Sacker bifurcation is introduced that allows a parametric design of a discrete-time system which corresponds to the rescaled Andronov–Hopf system. This system approximates the characteristics of the rescaled Hopf-type amplifier for a large range of parameters. The natural frequency and the peak amplitude are preserved for every set of parameters. The Neimark–Sacker bifurcation based systems avoid large computational effort that would be caused by applying higher order integration methods to the continuous-time normalform equations.

Implementation of a digital evaluation platform to analyze bifurcation based nonlinear amplifiers

Recently, nonlinear amplifiers based on the supercritical Andronov–Hopf bifurcation have become a focus of attention, especially in the modeling of the mammalian hearing organ. In general, to gain deeper insights in the input-output behavior, the analysis of bifurcation based amplifiers requires a flexible framework to exchange equations and adjust certain parameters. A DSP implementation is presented which is capable to analyze various amplifier systems. Amplifiers based on the Andronov–Hopf and Neimark–Sacker bifurcations are implemented and compared exemplarily. It is shown that the Neimark–Sacker system remarkably outperforms the Andronov–Hopf amplifier regarding the CPU usage. Nevertheless, both show a similar input-output behavior over a wide parameter range. Combined with an USB-based control interface connected to a PC, the digital framework provides a powerful instrument to analyze bifurcation based amplifiers.

Ambiguities in input-output behavior of driven nonlinear systems close to bifurcation

Since the so-called Hopf-type amplifier has become an established element in the modeling of the mammalian hearing organ, it also gets attention in the design of nonlinear amplifiers for technical applications. Due to its pure sinusoidal response to a sinusoidal input signal, the amplifier based on the normal form of the Andronov-Hopf bifurcation is a peculiar exception of nonlinear amplifiers. This feature allows an exact mathematical formulation of the input-output characteristic and thus deeper insights of the nonlinear behavior. Aside from the Hopf-type amplifier we investigate an extension of the Hopf system with focus on ambiguities, especially the separation of solution sets, and double hysteresis behavior in the input-output characteristic. Our results are validated by a DSP implementation.