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The precise measurement of the spin speed of a high-speed autonomous unmanned aerial vehicle (HSA-UAV) is a key element in mastering flight stability, and the measurement of roll angle is the key to determining the accuracy of navigation control systems. We put forward a novel method for measuring roll angle. This method starts from the time–frequency domain analysis of the output signal of the geomagnetic sensor, extracts the time–frequency ridge of the time–frequency matrix (TFM) to obtain the spin speed of the HSA-UAV, and reconstructs the output signal of the geomagnetic sensor. It can calculate the roll angle when the calibration parameters of the geomagnetic sensor are unknown and have good engineering practical value. In addition, we also propose an improved nonlinear short-time Fourier transform with high-frequency resolution and a forward penalty dynamic path ridge-extraction method with frequency jump suppression to extract instantaneous frequency in the TFM. [ABSTRACT FROM AUTHOR]

Let { (N j , B j , L j) : 1 ⩽ j ⩽ m } be finitely many Hadamard triples in R . Given a sequence of positive integers { n k } k = 1 ∞ and ω = (ω k ) k = 1 ∞ ∈ { 1 , 2 , ... , m } N , let μ ω , { n k } be the infinite convolution given by μ ω , n k = δ N ω 1 − n 1 B ω 1 ∗ δ N ω 1 − n 1 N ω 2 − n 2 B ω 2 ∗ ⋯ ∗ δ N ω 1 − n 1 N ω 2 − n 2 ⋯ N ω k − n k B ω k ∗ ⋯. In order to study the spectrality of μ ω , { n k } , we first show the spectrality of general infinite convolutions generated by Hadamard triples under the equi-positivity condition. Then by using the integral periodic zero set of Fourier transform we show that if g c d (B j − B j) = 1 for 1 ⩽ j ⩽ m , then all infinite convolutions μ ω , { n k } are spectral measures. This implies that we may find a subset Λ ω , { n k } ⊆ R such that { e λ (x) = e 2 π i λ x : λ ∈ Λ ω , { n k } } forms an orthonormal basis for L 2 (μ ω , { n k }). [ABSTRACT FROM AUTHOR]