General equations of optimal nonlinear filtering, interpolation and extrapolation of partially observable random processes

1977 ◽  
pp. 297-328
Author(s):  
R. S. Liptser ◽  
A. N. Shiryayev
Keyword(s):  
Nonlinear Filtering ◽  
Random Processes ◽  
Partially Observable ◽  
Optimal Nonlinear Filtering

Optimal Nonlinear Filtering

1976 ◽  
Vol 22 (8) ◽  
pp. 516-522
Author(s):  
B. V. Rao
Keyword(s):  
Nonlinear Filtering ◽  
Optimal Nonlinear Filtering

scholarly journals Optimal nonlinear filtering of M-PSK signals against a background of harmonic interference with a random initial phase

2021 ◽  
Vol 9 (6) ◽  
pp. 46-56
Author(s):  
G. V. Kulikov ◽  
Trung Tien Do ◽  
E. V. Samokhina
Keyword(s):  
Initial Phase ◽  
Nonlinear Filtering ◽  
Noise Immunity ◽  
Signal To Noise Ratio ◽  
Radio Channel ◽  
Complete Suppression ◽  
Two Phase ◽  
Probability Of Error ◽  
Useful Signal ◽  
Optimal Nonlinear Filtering

Objectives. The widespread use of radio data transmission systems using signals with multiposition phase shift keying (MPSK) is due to their high noise immunity and the simplicity of constructing the transmitting and receiving parts of the equipment. The conducted studies have shown that the presence of non-fluctuation interference, in particular, harmonic interference, in the radio channel significantly reduces the noise immunity of receiving discrete information. The energy loss in this case, depending on the interference intensity, can range from fractions of dB to 10 db or more. Therefore, interference suppression is an important task for such radio systems. The aim of the work is to synthesize and analyze an algorithm for optimal nonlinear filtering of MPSK signals against a background of harmonic interference with a random initial phase.Methods. The provisions of the theory of optimal nonlinear signal filtering and methods of statistical radio engineering are used.Results. The synthesis and analysis of the algorithm of optimal nonlinear filtering of MPSK signals against the background of harmonic interference with a random initial phase are carried out. The synthesized receiver contains a discrete symbol evaluation unit, two phase-locked frequency circuits of reference generators that form evaluation copies of the signal and interference, and cross-links between them. Analytical expressions are obtained that allow calculating the dependences of the bit error probability on the signal-to-noise ratio and the interference intensity µ. It is established that uncompensated fluctuations of the initial phase of the useful signal have a greater effect on the receiver noise immunity than similar fluctuations of the phase of harmonic interference, especially with low positional signals.Conclusions. Comparison of the obtained results with the results obtained in the case when there are no harmonic interference compensation circuits shows that the use of the obtained phase filtering algorithms allows for almost complete suppression of harmonic interference. Thus, if µ = 0.5 and the probability of error is 10−2, the energy gain at M = 2 is about 2.5 dB, at M = 4 – about 6 dB, at M = 8 and M = 16 – at least 10 dB.

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