Location:Training / Embedded Development / DSP / Random Signal Processing National University of Defense Technology / The definition and properties of orthogonal projection

Stochastic signal processing is a core course for graduate students in electronics and communications engineering. This course mainly studies the basic theories of stochastic process foundation, parameter estimation, optimal filtering and signal detection. Stochastic process foundation mainly introduces the basic concepts of stochastic process and the linear process of stochastic process. System analysis, including definition and classification, statistical description, stationary random process and power spectrum, linear system analysis, commonly used time series models, matched filter theory, etc.; through the study of parameter estimation theory, master the general methods of parameter estimation and the basic principles of estimation and performance evaluation methods; through the study of optimal filtering theory, master the basic concepts of optimal filtering, master the basic theory of Kalman filtering, and be proficient in the derivation method of the Kalman filtering algorithm, the application of the algorithm, and the performance (simulation) evaluation method. Master the basic concepts and methods of nonlinear filtering (extended Kalman filtering method), be able to establish signal and observation models based on actual problems, establish corresponding algorithms, and use computers to analyze (simulate) algorithm performance. Signal detection includes two parts: the basic theory of hypothesis testing and signal detection in noise. Master the concepts and judgment criteria of hypothesis testing (including compound hypothesis testing), and be able to construct statistical models for hypothesis testing and select appropriate judgment criteria for practical problems. Analyze the performance of decisions. Be able to apply the mathematical theory of hypothesis testing to the problem of signal detection in noise, deduce the structure of the optimal receiver in Gaussian noise environment, and master the basic form of the optimal receiver in Gaussian noise, the performance analysis method of the receiver and the optimal Optimal signal design issues. Master the methods of signal detection in non-Gaussian noise.