Abstract

An automatic tracking apparatus based on a pulsed laser and characterized by space and time quantifications is presented. Taking into account the statistical nature of the returns, we have been able to optimize the tracking system control functions and to increase their performance.

© 1972 Optical Society of America

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References

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  1. M. Staron, La Recherche Aérospatiale, No. 133, 29 (1969).
  2. R. Moreau, “Automatic aiming system for laser range-finders.” AGARD Conference Proceedings, vol. 50, October1969.
  3. G. Seguin, “On an Optimal Solution for Automatic Tracking from Sampled and Quantified data,” Doctorate thesis Orsay, France (December1969).
  4. M. Athans, IEEE Trans. Automatic Control AC-11, 580 (1966).
    [CrossRef]

1969 (2)

M. Staron, La Recherche Aérospatiale, No. 133, 29 (1969).

R. Moreau, “Automatic aiming system for laser range-finders.” AGARD Conference Proceedings, vol. 50, October1969.

1966 (1)

M. Athans, IEEE Trans. Automatic Control AC-11, 580 (1966).
[CrossRef]

Athans, M.

M. Athans, IEEE Trans. Automatic Control AC-11, 580 (1966).
[CrossRef]

Moreau, R.

R. Moreau, “Automatic aiming system for laser range-finders.” AGARD Conference Proceedings, vol. 50, October1969.

Seguin, G.

G. Seguin, “On an Optimal Solution for Automatic Tracking from Sampled and Quantified data,” Doctorate thesis Orsay, France (December1969).

Staron, M.

M. Staron, La Recherche Aérospatiale, No. 133, 29 (1969).

AGARD Conference Proceedings (1)

R. Moreau, “Automatic aiming system for laser range-finders.” AGARD Conference Proceedings, vol. 50, October1969.

IEEE Trans. Automatic Control (1)

M. Athans, IEEE Trans. Automatic Control AC-11, 580 (1966).
[CrossRef]

La Recherche Aérospatiale (1)

M. Staron, La Recherche Aérospatiale, No. 133, 29 (1969).

Other (1)

G. Seguin, “On an Optimal Solution for Automatic Tracking from Sampled and Quantified data,” Doctorate thesis Orsay, France (December1969).

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Figures (11)

Fig. 1
Fig. 1

Block diagram.

Fig. 2
Fig. 2

Tracking turret.

Fig. 3
Fig. 3

Five areas of the telescope field.

Fig. 4
Fig. 4

Telescope and ecartometry device.

Fig. 5
Fig. 5

Block diagram for single axis of an idealized tracking device.

Fig. 6
Fig. 6

Slant distance as a function of time for an aircraft.

Fig. 7
Fig. 7

Evolution of the target in the telescope field.

Fig. 8
Fig. 8

Example 1: angular distribution.

Fig. 9
Fig. 9

Example 2: autocorrelation function.

Fig. 10
Fig. 10

Example 3: prediction.

Fig. 11
Fig. 11

Example 4: spectral density.

Tables (2)

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Table I Interpretation Subprogram

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Table II Over-all Optimization

Equations (14)

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E ( t ) = E 0 + v t ;
= E - S ;
K / p ( p + a ) ;
S ¨ + a S ˙ = K u .
1 = error value , 2 = ˙ error velocity ; }
˙ 1 = 2 , ˙ 2 = a 2 + a v - K u . }
1 ( n + 1 ) - 1 ( n ) = a 1 2 ( n ) + a 2 U ( n ) , 2 ( n + 1 ) - 2 ( n ) = a 0 2 ( n ) + a 0 U ( n ) , }
U ( n ) = ( K / a ) u ( n ) - v , 1 ( n ) = 1 ( t ) for t = n T , 2 ( n ) = 2 ( t ) for t = n T , u ( n ) = u ( t ) for n T t < ( n + 1 ) T , a 0 = exp ( - a T ) - 1 , a 1 = [ 1 - exp ( - a T ) ] / a , a 2 = [ 1 - a T - exp ( - a T ) ] / a ,
J = n = 0 N - 1 1 2 ( n + 1 ) .
u ( n ) = ( a / K ) [ U ( n ) + v ] = ( a / K ) ( - { [ 1 ( n ) + a 1 2 ( n ) ] / a 2 } + v ) .
φ ( i ) = ϕ ( i ) ϕ ( o )             and             ϕ ( i ) = 1 N - i j = 1 N - i 1 ( j ) 1 ( j + i ) ;
φ ^ ( i ) = ϕ ^ ( i ) ϕ ^ ( o )             and             ϕ ^ ( i ) = 1 N - i j = 1 N - i ^ 1 ( j ) ^ 1 ( j + i ) ;
φ * ( τ ) = ( e - 3 τ + e - 3 τ 2 ) / 2 ,
S D ( ω ) = [ 3 / ( 3 2 + ω 2 ) ] + ( π / 6 ) exp ( - ω 2 / 36 ) .

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