Ridge regression signal processing for position-fix navigation systems
First Claim
1. Apparatus for determining the position and velocity of a moving platform comprising:
- a radio navigation aid having at least three portions, two of which are distant from said platform and having a known position for providing to said platform a plurality of samples indicative of the position of said platform at respective times,a position estimator for receiving said plurality of samples for generating an estimate of position and velocity both with an unbiased estimator wherein the mean square error of the estimate is the variance and with a biased estimator and selecting said estimate of position and velocity from said biased estimator at times said geometry of said moving platform is substantially co-linear with said two distant portions of said radio navigation aid.
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Abstract
A position estimator for determining the position and velocity of a moving platform in cooperation with radio navigation aids is described incorporating an unbiased estimator, such as a least means square estimator, a biased estimator for determining the angle of inner section of the lines of position from the radio naviation aids for determining the liklihood of geometric dilution of precision (GDOP) and a switch for selecting the estimate of position and velocity from said biased estimator at first times and the unbiased estimator at second times. The invention overcomes the problem of accuracy degredation associated with a nearly collinear measurement geometry which causes the variance of the position estimates to be higly inflated.
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Citations
13 Claims
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1. Apparatus for determining the position and velocity of a moving platform comprising:
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a radio navigation aid having at least three portions, two of which are distant from said platform and having a known position for providing to said platform a plurality of samples indicative of the position of said platform at respective times, a position estimator for receiving said plurality of samples for generating an estimate of position and velocity both with an unbiased estimator wherein the mean square error of the estimate is the variance and with a biased estimator and selecting said estimate of position and velocity from said biased estimator at times said geometry of said moving platform is substantially co-linear with said two distant portions of said radio navigation aid. - View Dependent Claims (2, 3, 4, 5, 6, 7)
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8. Apparatus for determining the position and velocity of a moving platform in cooperation with at least two distant radio navigation aids spaced apart in distance by a predetermined amount comprising:
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means for receiving a plurality of samples from said radio navigation aids indicative of the position of said platform at respective times, means for determining the lines of position to each navigation aid and the angle of intersection of said lines of position at said platform, means for generating an estimate of position and velocity from said plurality of samples with an unbiased estimator wherein the mean square error of the estimate is the variance, means for generating an estimate of position and velocity with a biased estimator, and means for selecting said estimate of position and velocity from said biased estimator at times said angle of intersection of said lines of position are less than a first predetermined value or greater than a second predetermined value and for selecting said estimate of position and velocity from said unbiased estimator at other times. - View Dependent Claims (9, 10)
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11. A method for determining the position and velocity of a moving platform in cooperation with at least two distant radio navigation aids spaced apart in distance by a predetermined amount comprising the steps of:
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receiving a plurality of samples from said radio navigation aids indicative of the position of said platform at respective times, determining the lines of position to each navigation aid and the angle of intersection of said lines of position at said platform, generating an estimate of position and velocity from said plurality of samples with an unbiased estimator wherein the mean square error of the estimate is the variance, generating an estimate of position and velocity with a biased estimator, and selecting said estimate of position and velocity from siad biased estimator at times said angle of intersection of said lines of position are less than a first predetermined value or greater than a second predetermined value and for selecting said estimate of position and velocity from said unbiased estimator at other times. - View Dependent Claims (12)
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13. Apparatus for determining the position and velocity of a moving platform in a position-fix navigation system having known first and second transmitter locations at times the geometry of said transmitter locations with respect to the estimated position of the receiver on a moving platform is nearly collinear comprising:
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first means for receiving and storing a plurality of n samples indicative of range each spaced apart by an intersample time interval Δ
TS and occurring within time interval Δ
TM from each of said first and second transmitters having a known distance therebetween,second means for determining the initial position XO, YO of said platform from said plurality of n samples from each of said first and second transmitters where ##EQU50## where R01 is the distance to the first transmitter at time T1, R02 is the distance to the second transmitter at time T2, and XC1 is the position of said first transmitter, third means for determining ##EQU51## +10 where ##EQU52## fourth means for determining HTH where ##EQU53## +10 where A=cos2 74 1 +cos2 θ
2B=cosθ
1 sinθ
1 +cosθ
2 sinθ
2C=sin2 θ
1 +sin2 θ
2fifth means for determining HT H-1, sixth means for determining HT δ
R ##EQU54## seventh means for determining β
OLS where β
OLS =(HT H)-1 HT δ
R,eighth means for determining β
OLST,ninth means for selecting KOP where ##EQU55## +10where P is the number of variables and S2 is the sample standard deviation where ##EQU56## +10and tenth means for determining β
R where β
R =(HT H+KOP I)-1 HT δ
R to provide [δ
X, δ
Y, Vx, Vy ].
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Specification