Vector Solutions for Azimuth

Earle, Michael A.

doi:10.1017/s037346330800475x

Cited by 6 publications

(13 citation statements)

References 1 publication

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“…From Figure 3 (left), we know that there are azimuth and elevation biases between the corresponding coordinate axes of the measurement frame and the platform frame. The measurements from the i th radar include the range r i , azimuth θ i (as shown in Figure 3 [right]), the true North direction corresponds to θ = 0, and the clockwise direction denotes the increment of θ which can be seen in Earle (2008), and elevation ε i . These measurements contain the true target position information (such as the true range r it , azimuth θ it and elevation ε it ); radar offset biases (such as the range bias Δ r i , the gain of range k ri which arises for atmospheric refraction, azimuth Δ θ i and elevation bias Δ ε i ); attitude biases (such as yaw bias Δ φ i , pitch Δ η i and roll Δ ψ i ); and random measurement noises (such as the range noise δ ri , azimuth δ θi and elevation δ εi ).…”

Section: Mathematical Modelmentioning

confidence: 99%

Optimized Bias Estimation Model for Mobile Radar Error Registration

et al. 2012

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For mobile 3-D radar installed on a gyro-stabilized platform, its measurements are usually contaminated by the systematic biases which contain radar offset biases (i.e., range, azimuth and elevation biases) and attitude biases (i.e., yaw, pitch and roll biases) of the platform because of the errors in the Inertial Measurement Units (IMU). Systematic biases can NOT be removed by a single radar itself; however, fortunately, they can be estimated by using two different radar measurements of the same target. The process of estimating systematic biases and then compensating radar measurements is called error registration. In this paper, the registration models are established first, then, the equivalent radar measurement error expressions caused by the attitude biases are derived and the dependencies among attitude biases and offset biases are analysed by using the observable matrix criterion. Based on the analyses above, an Optimized Bias Estimation Model (OBEM) is proposed for registration. OBEM uses the subtraction of azimuth and yaw bias as one variable and omits roll and pitch biases in the state vector, which decreases the dimension of the state vector from fourteen of the All Augmented Model (AAM), (which uses all the systematic biases of both radars as state vector) to eight and has about 80% reduction in calculation costs. Also, OBEM can decrease the coupling influences of roll and pitch biases and improve the estimation performance of radar elevation bias. Monte Carlo experiments were made. Numerical results showed that the bias estimation accuracies and the rectified radar raw measurement accuracies can be improved. K E Y WO R D S1. Error Registration.2. Attitude Bias. 3. All Augmented Model (AAM). 4. Optimized Bias Estimation Model (OBEM).

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Section: Mathematical Modelmentioning

confidence: 99%

Optimized Bias Estimation Model for Mobile Radar Error Registration

et al. 2012

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“…William's method for the computation of the distance along the great elliptic arc. This work of Earle (2000) has been recently updated for the calculation of azimuth (Earle 2008). These formulas have the general form of the integral of Formula (2).…”

Section: E X I S T I N G M E T H O D S F O R T H E S O L U T I O N O mentioning

confidence: 99%

“…In the span of the last 25 years many interesting methods and formulas for great elliptic sailing computations have been proposed from the direct and inverse solutions of Bowring (1984) up to the vector solutions for azimuths of Earle (2008). Most of these methods have offered valuable contributions for the complete, straightforward and 1 In traditional navigation the calculations of shortest navigational distances are carried out on the '' navigational sphere'' which has the property that one minute of a great circle arc is equal to one nautical mile (international nautical mile).…”

Section: Introductionmentioning

confidence: 99%

“…The third section presents an overview of various methods and formulas which have been proposed in the span of the last 25 years, from the direct and inverse solutions of Bowring (1984) up to the vector solutions for azimuths of Earle (2008). The third section presents an overview of various methods and formulas which have been proposed in the span of the last 25 years, from the direct and inverse solutions of Bowring (1984) up to the vector solutions for azimuths of Earle (2008).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

New Algorithm for Great Elliptic Sailing (GES)

Pallikaris

Latsas

2009

J. Navigation

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An analytical method and algorithm for great elliptic sailing (GES) calculations is presented. The method solves the complete GES problem calculating not only the great elliptic arc distance, but also other elements of the sailing such as the geodetic coordinates of intermediate points along the great elliptic arc. The proposed formulas provide extremely high accuracies and are straightforward to be exploited immediately in the development of navigational software, without the requirement to use advanced numerical methods. Their validity and effectiveness have been verified with numerical tests and comparisons to extremely accurate geodetic methods for the direct and inverse geodetic problem.

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“…Vector solutions for great ellipses, azimuth angles and the intersection of two circle of equal altitude on spheroids are presented in [4][5][6]. The intersection of two geodesic paths on the sphere or the ellipsoid are calculated and approximated in [15,17].…”

Section: Introductionmentioning

confidence: 99%

Circle Approximations on Spheroids

2011

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We present an approximation method for geodesic circles on a spheroid. Our approximation curve is the intersection of two spheroids whose axes are parallel, and it interpolates four points of the geodesic circle. Our approximation method has two merits. One is that the approximation curve can be obtained algebraically, and the other is that the approximation error is very small. For example, our approximation of a circle of radius 1000 km on the Earth has error 1·13 cm or less. We analyze the error of our approximation using the Hausdorff distance and confirm it by a geodesic distance computation.K E Y WO R D S 1. geodesic circle.2. spheroid. 3. geodesic distance. 4. geodesic path.

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Vector Solutions for Azimuth

Cited by 6 publications

References 1 publication

Optimized Bias Estimation Model for Mobile Radar Error Registration

Optimized Bias Estimation Model for Mobile Radar Error Registration

New Algorithm for Great Elliptic Sailing (GES)

Circle Approximations on Spheroids

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