An Optimization Method of Ambiguity Function Based on Multi-Antenna Constrained and Application in Vehicle Attitude Determination

The global navigation satellite system (GNSS)-based multi-antenna attitude determination method has the advantages of a simple algorithm and no error accumulation with time in long endurance operation. However, it is sometimes difficult to simultaneous obtain the fixed solutions of all antennas in vehicle attitude determination. If float or incorrect fixed solutions are used, precision and reliability of attitude cannot be guaranteed. Given this fact, a baseline-constrained ambiguity function method (BCAFM) based on a self-built four GNSS antennas hardware platform is proposed. The coordinates obtained by BCAFM can replace the unreliable real-time kinematic (RTK) float or incorrect fixed solutions, so as to assist the direct method for attitude determination. In the proposed BCAFM, the baseline constraint is applied to improve search efficiency (searching time), and the ambiguity function value (AFV) formula is optimized to enhance the discrimination of true peak. The correctness of the proposed method is verified by vehicle attitude determination results and baseline length difference. Experimental results demonstrate that the function values of error peaks are reduced, and the only true peak can be identified accurately. The valid epoch proportion increases by 14.95% after true peak coordinates are used to replace the GNSS-RTK float or incorrect fixed solutions. The precision of the three attitude angles is 0.54°, 1.46°, and 1.15°, respectively. Meanwhile, the RMS of baseline length difference is 3.8mm.

Chaos Based Frequency Modulation for Joint Monostatic and Bistatic Radar-Communication Systems

In this article, we propose the utilization of chaos-based frequency modulated (CBFM) waveforms for joint monostatic and bistatic radar-communication systems. Short-duration pulses generated via chaotic oscillators are used for wideband radar imaging, while information is embedded in the pulses using chaos shift keying (CSK). A self-synchronization technique for chaotic systems decodes the information at the communication receiver and reconstructs the transmitted waveform at the bistatic radar receiver. Using a nonlinear detection scheme, we show that the CBFM waveforms closely follow the theoretical bit-error rate (BER) associated with bipolar phase-shift keying (BPSK). We utilize the same nonlinear detection scheme to optimize the target detection at the bistatic radar receiver. The ambiguity function for both the monostatic and bistatic cases resembles a thumbtack ambiguity function with a pseudo-random sidelobe distribution. Furthermore, we characterize the high-resolution imaging capability of the CBFM waveforms in the presence of noise and considering a complex target.

The relative exponential growth rate of subgroups of acylindrically hyperbolic groups

We introduce a new invariant of finitely generated groups, the ambiguity function, and we prove that every finitely generated acylindrically hyperbolic group has a linearly bounded ambiguity function. We use this result to prove that the relative exponential growth rate lim n → ∞ ⁡ | B H X ⁢ ( n ) | n \lim_{n\to\infty}\sqrt[n]{\lvert\vphantom{1_{1}}{B^{X}_{H}(n)}\rvert} of a subgroup 𝐻 of a finitely generated acylindrically hyperbolic group 𝐺 exists with respect to every finite generating set 𝑋 of 𝐺 if 𝐻 contains a loxodromic element of 𝐺. Further, we prove that the relative exponential growth rate of every finitely generated subgroup 𝐻 of a right-angled Artin group A Γ A_{\Gamma} exists with respect to every finite generating set of A Γ A_{\Gamma} .

Sequence Set Design for a New LFM-PC Hybrid Modulated Radar Signal

In this paper we study the code design problem of a new form of linear frequency modulation phase-coded (LFM-PC) hybrid signal with wide Doppler tolerance based on a range-Doppler discrete ambiguity function (DAF) to get better detection performance and anti-jamming capability. The DAF of the LFM-PC inter pulse signal is derived within the Doppler tolerance. Two optimization models are established. One is single pulse sequence design (SSD) for Doppler tolerance extension based on minimum integral normalized sidelobe level (INSL); the other is multi pulse sequence set design (MSSD) for signal orthogonality based on the minimizing sum of the normalized DAF sidelobe (NDAFSL) and discrete cross ambiguity function (DCAF). Two low-complexity signal optimization methods based on alternating direction method of multiplier (ADMM) are proposed, respectively. The simulation results show that the optimized signals have either wide Doppler tolerance or good orthogonal performance, and the optimization methods (i.e., SSD-ADMM and MSSD-ADMM) have the characteristics of fast convergence speed and low operation amount.