Worst case system identification in H/sub ∞/: validation of a priori information, essentially optimal algorithms, and error bounds

1995 ◽  
Vol 40 (7) ◽  
pp. 1260-1265 ◽  
Author(s):  
Jie Chen ◽  
C.N. Nett ◽  
M.K.H. Fan
Keyword(s):  
System Identification ◽  
Error Bounds ◽  
A Priori ◽  
Optimal Algorithms ◽  
A Priori Information ◽  
Worst Case ◽  
Case System ◽  
Priori Information

Worst case system identification in l1: Optimal algorithms and error bounds

1992 ◽  
Vol 19 (6) ◽  
pp. 419-424 ◽  
Author(s):  
C.A. Jacobson ◽  
C.N. Nett ◽  
J.R. Partington
Keyword(s):  
System Identification ◽  
Error Bounds ◽  
Optimal Algorithms ◽  
Worst Case ◽  
Case System

Algorithms for automatic detection and recognition of low contrast radar objects using noise-like broadband signals

2021 ◽  
Author(s):  
E.V. Egorova ◽  
A.N. Ribakov ◽  
M.Kh. Aksayitov
Keyword(s):  
Spectral Methods ◽  
Block Diagram ◽  
A Priori ◽  
Original Method ◽  
Optimal Algorithms ◽  
A Priori Information ◽  
Low Contrast ◽  
Priori Information ◽  
Detection And Recognition

An algorithm for automatic detection and recognition of low-contrast ground targets using noise-like broadband signals and the use of combined processing of radar signals against the background of interference is presented; the proposed original method for processing signals from airborne objects during their detection and determination of their coordinates synthesizes optimal algorithms for detecting radar objects in the case of a priori information about useful signals and interference, as well as the ability to determine the range and speed of movement; the block diagram of the mathematical model of signal processing is considered on the basis of the developed algorithms for identifying stationary targets against the background of local objects by the radar portrait, as well as by the envelope of the radar signal; the results of testing mathematical modeling of the algorithm for recognizing signals from stationary targets and a forest with an equal probability of the appearance of these targets in the analyzed space are presented. The results of domestic theoretical and experimental research today characterize the main areas of research in the field of detection and recognition of various radar objects. The main research tool of most works is the search and development of promising mathematical models of objects and the modeling of secondary radiation for their recognition, which in some cases allows obtaining additional information about these objects. Correlation and spectral methods of their processing are currently being considered in relation to the noise sounding signal of a radar station. This article analyzes the application of correlation and spectral methods in processing noise signals with the identification of the disadvantages and advantages of each of the methods; the functioning of the block diagram of the known single-channel noise radar stations with sequential spectral processing of the total signal is considered. The proposed original method for processing signals from airborne objects during their detection and determination of their coordinates synthesizes optimal algorithms for detecting targets in the case of a priori information about useful signals and interference, as well as the ability to determine the distance and speed of movement. It should be noted the promising application of combined processing of radar signals against the background of interference, taking into account simultaneously the spatial, polarization, temporal and frequency features of the signals reflected from objects. With regard to the problem of recognizing the shape of objects, both in Russia and abroad, intensive work is being carried out to improve the resolution of on-board radars with a synthesized broadband antenna array, while raising the range resolution and increasing the angular resolution allow obtaining long-range portraits of these objects, as well as seeing them. elements and obtain images of targets. In the study of methods for detecting radar objects based on Gaussian noise signals with a large base, it is shown that such signals are promising for detecting subtle objects at ranges greater than with conventional monopulse radar. When receiving noise signals with a large base, spectral methods of signal extraction turn out to be more advantageous in comparison with the known correlation method of signal processing. Based on the use of noise signals, recognition of ground and air objects is realized, while the method of long-range portraits can have an advantage over the envelope method. Based on the results of mathematical modeling, the possibility of automatic recognition of stationary ground objects by two different methods was confirmed with a high probability of their recognition.

scholarly journals Distribution-Dependent Weighted Union Bound

Entropy ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 101
Author(s):  
Luca Oneto ◽  
Sandro Ridella
Keyword(s):  
Statistical Learning ◽  
High Probability ◽  
A Priori ◽  
Sufficient Conditions ◽  
A Priori Information ◽  
Proposal Distribution ◽  
Worst Case ◽  
Learning Procedure ◽  
Union Bound ◽  
Priori Information

In this paper, we deal with the classical Statistical Learning Theory’s problem of bounding, with high probability, the true risk R(h) of a hypothesis h chosen from a set H of m hypotheses. The Union Bound (UB) allows one to state that PLR^(h),δqh≤R(h)≤UR^(h),δph≥1−δ where R^(h) is the empirical errors, if it is possible to prove that P{R(h)≥L(R^(h),δ)}≥1−δ and P{R(h)≤U(R^(h),δ)}≥1−δ, when h, qh, and ph are chosen before seeing the data such that qh,ph∈[0,1] and ∑h∈H(qh+ph)=1. If no a priori information is available qh and ph are set to 12m, namely equally distributed. This approach gives poor results since, as a matter of fact, a learning procedure targets just particular hypotheses, namely hypotheses with small empirical error, disregarding the others. In this work we set the qh and ph in a distribution-dependent way increasing the probability of being chosen to function with small true risk. We will call this proposal Distribution-Dependent Weighted UB (DDWUB) and we will retrieve the sufficient conditions on the choice of qh and ph that state that DDWUB outperforms or, in the worst case, degenerates into UB. Furthermore, theoretical and numerical results will show the applicability, the validity, and the potentiality of DDWUB.

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