International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B1. Istanbul 2004 
Z(AV,., ), 
(M^ Ya = d 
At that value AV,;, is determined by the following expression 
AV = 0.5 (Af) ois À 
min 
Where (Af, us is minimal quantization step of oscillator 
frequency changes; AV, is corresponding quantization step of 
velocity changes; À is radiation wave-length. 
Simultaneously, value of oscillator tuning frequency is 
calculated that will be used for the next line in a distance 
calculation loop 
(V, ) = (Ve ) + (A V et à 
Thus, output of algorithms of a velocity calculation loop were 
values of change of oscillator frequency (Afj4)«;, value of 
velocity which will be compensated by oscillator on the next 
line (V,,).,, and value of predicted vehicle velocity (Vey) j., on 
the next line. Value (4/54) ; - , goes to radio-frequency module, 
values V, and (V,,) ;.| go to the distance calculation loop. 
Processing in a distance calculation loop. 
Let's consider how distance calculation loop operates. The loop 
operates in the rate of measurements arrival. I.e. calculation of 
distance to probed surface is carried out right after current time 
delay measurement arrives and before the next measurement 
arrives. 
Input of a distance measurement loop algorithms are values of a 
+ 
: = 
delay times / je] - 
To do calculation in distance measurement loop the value of the 
. ~ + V . - . 
correction of delay time (f ) is required. It is connected to 
incomplete compensation of velocity by oscillator and is 
determined for each element of a scanning line as: 
f (ur 
ext 
cosa : cos B — Tum ju yk. (10) 
Where V; is value of velocity compensated by oscillator; 
k= (2 “Ty )/(AF - A) is constant of proportionality. 
Slant-distance in an element of the image depending on linear 
FM section is determined as: 
—{+ v 
D uc = um uf ) : e 
—/+ . : : s : = 
Where {el is delay time in an element of the image; [^ is the 
correction of the delay time, calculated by expression (10) 
which follows from (6) and (7); c - velocity of light. 
Horizontal distance is: 
D=D, 
incl 
cosa - cos B 
88 
Where a and B are viewing angles of a scanning beam. 
The horizontal distance R reduced to a motionless point at the 
moment of the beginning of formation of the image, is 
c 
calculated as 
ReD+lV ce Uum-l trf4.:0)» 
Where V 
true 
scanning line period, m is number of the current line of the 
image, Tq. iS linear FM half-cycle, n - number of the current 
element in the line. 
is vehicle horizontal velocity, 7,,, is the 
Output of distance measurement loop algorithms is the image in 
which each pixel represents value of the reduced horizontal 
distance up to a corresponding point of a scene. 
The block diagram of algorithms of distance and velocity 
determination by the suggested method is displayed on fig. 2. 
Algorithms are adapted for realization on computational 
structure of conveyor type that provides an opportunity to carry 
out calculations in real time. 
Preprocessing algorithms simulation 
At use of an offered method of distance measurement according 
to expressions (6) and (7) distance measurement error is 
determined by two components: errors of pulse-delay time 
measurement and an error of extrapolated vehicle velocity 
determination, i.e. 
  
85 - [p 56 eraty) (n 
Where, p = c/2 p 2 c/2 and k 2 2. r,, yr - 2). At that 
8 (£j) is determined according to (3). 
As a performance criterion at mathematical simulation the 
absolute maximum error of slant-distance measurement (AD max) 
determined by vehicle own velocity determination errors was 
accepted. 
pr. : 
AD ux 7 Max ———À—.AV; - COS@ - cos B 
A NF n 
. . . s : > tl 
where AV; is vehicle own velocity determination error for j^ 
scanning line (/ 7 1—128). 
Vehicle velocity was modelled by slowly varying functions of 
time. At simulating the structure of algorithms, factors k, and ka 
ratio, a method of velocity extrapolation were varied. 
Mathematical simulation has allowed to reveal dependence of 
the maximal distance error AD, on values of factors K, and 4». 
This dependence has the expressed minimum (fig. 3). At that 
the best result was AD. = 0.8 m at 4, 7 0.41 and k, = 0.59. As 
the error of velocity determination is formed as a result of 
influence of many random factors it is possible to consider that 
it has normal distribution. Then standard deviation of the 
distance error originated in the inaccuracy of velocity 
determination, will make 6D(V) € ADq4,,/3. At the values of 
factors k| and k,, specified above, transitional period duration 
did not exceed 35-40 lines of scanning. 
  
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