Inverse trigonometric functions

About: Inverse trigonometric functions is a research topic. Over the lifetime, 854 publications have been published within this topic receiving 11141 citations. The topic is also known as: arcus function & antitrigonometric function.

Phase detector and position detector

Abstract: PROBLEM TO BE SOLVED: To provide a phase detector capable of detecting the phase with a simple configuration. SOLUTION: The phase detector 5 has a segment specification section 27 for specifying which segment, of eight segments formed by dividing the range from 0 to 2π by π/4 from 0, includes the phase θ, based on the positive/negative of a sine wave signal Ssa, the positive/negative of a cosine wave signal Sca, and size relation between the absolute value of the sine wave signal Ssa and the absolute value of the cosine wave signal Sca. The phase detector 5 also has an arc tangent calculation section 37 for adjusting the positive/negative of the sine wave signal Ssa and cosine wave signal Sca so that the combination of the positive/negative of the sine wave signal, the positive/negative of the cosine wave signal, and size relation between the absolute value of the sine wave and the absolute value of the cosine wave become constant, setting one of the sine wave signal Ssa and cosine wave signal Sca as sine wave, setting the other as cosine wave, and calculating the inverse of the tangent based on the sine wave and the cosine wave by a procedure common in eight segments. COPYRIGHT: (C)2009,JPO&INPIT

Inverse tangent reaching law for discrete sliding mode control with application to inventory management

Abstract: In this paper we propose a modified, non-switching type reaching law for quasi-sliding mode control of linear discrete time dynamic systems. The reaching law determines the sliding variable rate of change proportional to the negative value of the inverse tangent of this variable. The approach proposed in this work helps satisfy input and state constraints in the controlled system, and at the same time it does not excessively damp the system convergence rate when the sliding variable is small. In the second part of this paper the proposed reaching law is successfully applied to solve the periodic review inventory management problem, with suppliers' constraints explicitly taken into account.

Real-time detection and elimination of nonorthogonality error in interference fringe processing

Abstract: In the measurement system of interference fringe, the nonorthogonality error is a main error source that influences the precision and accuracy of the measurement system. The detection and elimination of the error has been an important target. A novel method that only uses the cross-zero detection and the counting is proposed to detect and eliminate the nonorthogonality error in real time. This method can be simply realized by means of the digital logic device, because it does not invoke trigonometric functions and inverse trigonometric functions. And it can be widely used in the bidirectional subdivision systems of a Moire fringe and other optical instruments.

Method and apparatus for a control signal generating circuit

Abstract: A control signal generating circuit ( 460 ) for an automatic frequency control (AFC) circuit ( 465 ), in accordance with the present invention receives a digital timing control signal directly from the output of a digital loop filter ( 138 ) of a tracking circuit ( 430 ), and produces a frequency control signal that is provided to a VCXO ( 110 ). The control signal generating circuit ( 460 ) comprises a multiplier ( 462 ) and an integrator ( 466 ) which are relatively simple to implement, and does not require complex processing, such as determining an inverse tangent as taught by the prior. Consequently, approximation errors associated with inverse tangent processing are avoided.

Calibration method and calibration system for camera external parameters of vehicle-mounted camera system

Abstract: The invention provides a calibration method for camera external parameters of a vehicle-mounted camera system, which is applied to electronic equipment and comprises the following steps: acquiring a frame of image information, and worldwide identifying lane line information in the image information through a lane line detection method; randomly selecting at least two feature points on each lane line, calculating coordinates of the feature points on a world coordinate system, and solving an angle correction amount by utilizing an inverse trigonometric function in combination with the height ofthe camera; and performing iterative compensation on the camera external parameter angle by using the correction angle through an iterative method to obtain an accurate camera external parameter angle. According to the invention, a front road image is obtained through the forward-looking camera; the lane line and target vehicle position information in the road image is extracted, the lane line information is combined with the static calibration result and the inverse trigonometric function to dynamically solve the external parameter angle of the camera, the more accurate external parameter angle of the camera is solved, and the distance of the target relative to the vehicle body is solved according to the position of the target vehicle in the image.