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The imaging of maneuvering targets may be defocused by the range cell and Doppler frequency migrations (DFMs) initiated by the targets’ complex motions in a long coherent processing interval (CPI). To settle these problems, a generalized matched filtering method driven by the Bayesian motion trajectory inference (BMTI) is presented in this article. Analyses show that any motion trajectory evolutions caused by targets’ movements can be described by the state equations derived from a polynomial prediction model. It is then demonstrated the uncertainties of the targets entering/leaving the radar beam coverage area will make the state equations into a state labeled multi-Bernoulli random finite set (LMBRFS). With the scale-transformation-based processing pipeline, a measurement random finite set (RFS) taking both the statistical properties of the maneuvering target with random appearance and disappearance and the noise/clutter into consideration is coined for the state LMBRFS. In this way, a state-space model for describing the target instantaneous motions in a CPI is established. Once the target motion trajectories are inferred by a modified Bayesian filter, it is shown that the matched filter bank designed by the inferred trajectories can refocus the echo energies. Numerical simulation results verify the correctness of our analytical ones, while it is illustrated that our model and method are universal for indicating high-speed and maneuvering targets with any complex and/or even unknown motion forms in a CPI.

In this article, a Bayesian filtering approach to adaptively extracting the crossed time-frequency (TF) ridges of ultrasonic guided waves (GWs) and retrieving their overlapped modes is proposed. Based on the generalized non-parametric GW signal model, the phase evolution of each overlapped mode can be described by the state transition equation developed by a polynomial prediction model (PPM). When an analyzed GW in the frequency domain is viewed as the measurement equation of the states, a state space model in the frequency domain for describing the GW and its modes is established. As a result, a Bayesian filtering approach can be used to extract the crossed TF ridges and separate the overlapped modes in an analyzed GW when the mode number in the signal is known as a priori. When such a priori is unavailable, an adaptive detection method of the mode number in a GW is acquired by a non-parametric iterative adaptive estimation scheme. In this way, the proposed method can be applied to cases where an analyzed GW with unknown modes can also be extracted and separated accurately. Simulation results show that the proposed method can correctly extract the crossed TF ridges and separate the overlapped modes when the signal-to-noise ratio (SNR) is higher than −5 dB. In the steel plate experiment, the correlation coefficients of ${S}_{{0}}$ , ${A}_{{0}}$ , and ${A}_{{1}}$ modes between the original and retrieved signals are 0.900, 0.772, and 0.915, respectively, which are over the reported results in the literature.