• Bulletin of the Korean Mathematical Society
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• v.39 no.1
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• pp.165-174
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• 2002

A polynomial if k-fold integer-valued if itself and its derivatives up to order k are integer-valued. Necessary and sufficient conditions are established far (i) polynomials with rational coefficients to be k-fold integer-valued, and for (ii) a quotient of two k-fold integer-valued polynomials to be k-fold integer-valued.

• Journal of The Institute of Information and Telecommunication Facilities Engineering
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• v.5 no.1
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• pp.1-11
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• 2006

Lifting scheme based integer transforms provides very useful properties on the multimedia coding. An integer transform outputs the integer form when the input has integer value. This doesn't produce quantization errors on coding, so integer transforms are adequate to lossless coding, In this paper, we present an integer DCT algorithm which is able to transform audio signal with longer length. Also the proposed method can be easily implemented recursively even though input is long time. We present the method to overcome the poor approximation which is produced by recursive lifting step. And we have applied the proposed integer DCT to lossless audio coding.

• Journal of Institute of Control, Robotics and Systems
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• v.5 no.1
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• pp.62-68
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• 1999

The attitude of a vehicle can be precisely determined using GPS carrier phase measurements from more than two antennas attached to a vehicle and an efficient integer ambiguity resolution technique. Many methods utilizing the known baseline length as a constraint of independent elements of integer ambiguities are proposed to resolve integer ambiguity at real time. Three-dimensional search space is reduced to two-dimensional search space with this constraint. Thus the true integer ambiguity can be easily determined with less computational burden and fewer number of measurements. But there are still strong requirements for the real time integer ambiguity resolution, which uses single epoch measurement of long baseline. In this paper, a new constraint from the geometry of multiple baselines is derived. With this new constraint, two-dimensional search space is further reduced to one-dimensional search space. It makes possible to determine integer ambiguity with single epoch measurement. The proposed method is applied to real data to show its effectiveness.

• East Asian mathematical journal
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• v.30 no.3
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• pp.303-310
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• 2014

We study the existence of regular polygons and regular solids whose vertices have integer coordinates in the three dimensional space and study side lengths of such squares, cubes and tetrahedra. We show that except for equilateral triangles, squares and regular hexagons there is no regular polygon whose vertices have integer coordinates. By using this, we show that there is no regular icosahedron and no regular dodecahedron whose vertices have integer coordinates. We characterize side lengths of such squares and cubes. In addition to these results, we prove Ionascu's result [4, Theorem2.2] that every equilateral triangle of side length $\sqrt{2}m$ for a positive integer m whose vertices have integer coordinate can be a face of a regular tetrahedron with vertices having integer coordinates in a different way.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.37 no.7
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• pp.678-684
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• 2009

Many researches on the GNSS integer ambiguity resolution methods for precise positioning and attitude determination applications have been done. However, by the time invariant property of the integer ambiguity, the reuse of integer ambiguity without performing time consuming integer search procedure is possible. In this paper, a new efficient integer ambiguity propagation method is proposed. The initial integer ambiguity can be determined using the famous LAMBDA method and it is propagated with the propagation method. The proposed method can reconfigure the integer ambiguity using the previous epoch's integer ambiguity and new carrier phase measurements under environmental variations such as geometry changes, signal blockage and reacquisition. Experiments with real measurements show the proposed method can determine an integer ambiguity effectively.

• Journal of Positioning, Navigation, and Timing
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• v.7 no.4
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• pp.235-243
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• 2018

Conventional Real Time Kinematics (RTK) collect measurements in stationary state for several minutes to resolve the integer ambiguity in the carrier phase measurement or resolve the integer ambiguity on the move assuming low maneuvering movement. In this paper, an On The Move-RTK (OTM-RTK) technique that resolves the integer ambiguity on the move for fast and precise positioning of ground vehicles such as high maneuvering vehicles was proposed. The OTM-RTK estimates the precise amount of movement between epochs using the carrier phase measurements acquired on the move, and by using this, resolves the integer ambiguity within a short period of time by evaluating the integer ambiguity candidates for each epoch. This study analyzed the integer ambiguity resolution performance using field driving experiment data in order to verify the performance of the proposed method. The results of the experiment showed that the precise trajectory including the initial position bias can be obtained prior to resolving the integer ambiguity, and after resolving the integer ambiguity on the move, it was possible to obtain the bias-corrected precise position solution. It was confirmed that the integer ambiguity can be resolved by collecting measurements of about 10 epochs from the moving vehicle using a dual frequency receiver.

• Proceedings of the KIEE Conference
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• 2008.04a
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• pp.91-92
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• 2008

본 논문에서는 기존의 H.264/AVC의 spatial 영역에서 Intra prediction 기법과 달리 H.264/AVC에서 사용하는 Integer DCT 영역에서 Intra prediction 기법을 제안한다. 이를 위하여 Integer DCT 영역에서 Intra prediction을 수행하는 모든 과정을 matrix multiplication으로 표현하여 Intra prediction을 수행하는 matrix를 유도한다. Intra prediction을 수행하는 matrix를 각 모드에 알맞게 설계하고, 이 matrix를 Integer DCT 영역에서 사용할 수 있도록 orthogonal한 Integer matrix를 설계한다. 실험을 통하여 제안한 Integer DCT 영역에서 Intra prediction 기법이 기존의 H.264/AVC의 spatial 영역에서 intra prediction 기법과 성능이 동일하면서 어떻게 matrix multiplication에 연산들을 포함시켜서 단순화 할 수 있는지를 보여주겠다. 또한 H.264/AVC에서 제공하는 intra prediction 각 모드에 대해 계산상 복잡도를 분석하였다.

• Journal of Institute of Control, Robotics and Systems
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• v.6 no.8
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• pp.719-726
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• 2000

A real-time precise positioning is possible with GPS carrier phase measurements with efficient integer ambiguity resolution techniques. It is known that more reliable and fast integer ambiguity resolution is possi-ble as the number of measurements increases. Most precise positioning systems use dual frequency measurements and the wide-lnae technique to resolve integer ambiguity. The wide-lane technique magnifies the measurement noise while it reduces the number of candidates to be examined. In this paper a new integer ambiguity resolution method using dual frequency is proposed The proposed method utilizes the relationship between the wide-lane single frequency and the narrow-lane ambiguities to resolve narrow-lane integer ambiguity after fixing the wide-lane integer ambiguity. Experiments with real data show that the proposed method gives fast and reliable results.

• Proceedings of the Korea Society of Information Technology Applications Conference
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• 2005.11a
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• pp.255-258
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• 2005

A blind-mode integer frequency offset estimation algorithm is proposed for an OFDM system. Imperfect integer frequency offset estimation causes ambiguity in the data sub-carrier position. Morelli's blind integer frequency offiet estimation algorithm exploits the likelihood function by comparing the power in sub-carriers. It, however, shows performance degradation when there is the fractional frequency offset. The proposed algorithm solves this by using interpolation in the frequency domain. In this algorithm, it is exploited that the effect of the frequency offset is shown as a shift of power spectrum. By calculating the covariance of over-sampled samples, most approximate samples to integer point are obtained. It enables integer frequency offset estimation less affected by fractional frequency offset.

• Proceedings of the IEEK Conference
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• 2003.07e
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• pp.2072-2075
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• 2003

This paper is studied the high speed processing moving picture encodec to compress and encode a moving picture by real time. This is used the new motion vector search algorithm with smallest search point in H.263 encodec, and is applied the integer DCT for the encodec by converting a moving picture. The integer DCT behaves DCT by the addition operation of the integer using WHT and a integer lifting than conventional DCT that needs the multiplication operation of a floating point number. Therefore, the integer DCT can reduce the operation amount than basis DCT with having an equal PSNR because the multiplication operation of a floating point number does not need.