An efficient method for the discrete linear 𝐿₁ approximation problem

Abdelmalek, Nabih N.

doi:10.1090/s0025-5718-1975-0378354-8

Cited by 9 publications

(3 citation statements)

References 8 publications

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“…Several different algorithms for discrete linear L1 regression have been developed recently [1,[3][4][5]. A thorough evaluation of the performance of such algorithms requires a procedure for generating data representative of a wide variety of L1 regression problems.…”

Section: Introductionmentioning

confidence: 99%

A Test Problem Generator for Discrete Linear L ₁ Approximation Problems

Hoffman

Shier

1980

ACM Trans. Math. Softw.

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Described here are the theoretmal development and computer implementation of a procedure that generates test problems for L~ esth-nation of the linear model y= Xfl + u. The generation procedure allows the user flembdlty m specifying the problem dimensions, the LI solution vector fl*, the distribution of the observed residuals ~, as well as the column rank, row repetitions, and degree of degeneracy of the matrix X The user can also specify the distributional form, mean, and variance for each independent variable An lraportant feature of the generator is that any problem it creates is guaranteed to have a umque solutmn ~ whenever X has full rank

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Section: Introductionmentioning

confidence: 99%

A Test Problem Generator for Discrete Linear L ₁ Approximation Problems

Hoffman

Shier

1980

ACM Trans. Math. Softw.

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“…To amend the efficiency of the algorithm in [43] the transition to the dual form of the problem is carried out ( 15) and ( 16)…”

Section: Least Modulus Methodsmentioning

confidence: 99%

“…To solve the problem ( 17) and ( 18) the simplex method is applied. Detailed description of the algorithm of L 1 -optimization can be found in [43]. This method provides an accurate solution despite the fact that it does not require significant computing resources.…”

Section: Least Modulus Methodsmentioning

confidence: 99%

Robust Data Fusion of UAV Navigation Measurements with Application to the Landing System

Kolosov

Miller

2020

Remote Sensing

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To perform precise approach and landing concerning an aircraft in automatic mode, local airfield-based landing systems are used. For joint processing of measurements of the onboard inertial navigation systems (INS), altimeters and local landing systems, the Kalman filter is usually used. The application of the quadratic criterion in the Kalman filter entails the well-known problem of high sensitivity of the estimate to anomalous measurement errors. During the automatic approach phase, abnormal navigation errors can lead to disaster, so the data fusion algorithm must automatically identify and isolate abnormal measurements. This paper presents a recurrent filtering algorithm that is resistant to anomalous errors in measurements and considers its application in the data fusion problem for landing system measurements with onboard sensor measurements—INS and altimeters. The robustness of the estimate is achieved through the combined use of the least modulus method and the Kalman filter. To detect and isolate failures the chi-square criterion is used. It makes possible the customization of the algorithm in accordance with the requirements for false alarm probability and the alarm missing probability. Testing results of the robust filtering algorithm are given both for synthesized data and for real measurements.

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