Method of kinematic ranging
View Patent ↗A method of kinematic ranging for finding the range R of a jammer moving on a trajectory involves measuring the bearing of the jammer and the rate of change thereof using an airborne detector radar at a first position ( 24 ), causing the airborne detector radar to carry out a manoeuvre such that is it displaced in the horizontal plane by a displacement having orthogonal components Δx, Δy, and measuring the bearing of the jammer at a second position subsequent to the manoeuvre. By making an appropriate choice for the components Δx, Δy, the range R may be found with a desired relative range accuracy, and the error in R may be minimized.
1. A method of kinematic ranging comprising the steps of:
(i) measuring a bearing al in azimuth of a jammer at a time t 1 with respect to a first position using an airborne radar detector located at a first position;
(ii) measuring a rate of change dα/dt of the bearing in azimuth of the jammer with respect to the first position using the airborne radar detector located at the first position;
(iii) causing the airborne radar detector to carry out a manoeuvre such that it is displaced to a second position by a horizontal displacement d having orthogonal components Δx, Δy in a time Δt=t 2 −t 1 and measuring a bearing α 2 in azimuth of the jammer at time t 2 with respect to the second position using the airborne radar detector located at the second position, where d=√{square root over (Δx 2 +Δy 2 )};
(iv) calculating a difference Δα in the bearing in azimuth of the jammer between the second and first positions;
wherein components Δx, Δy are calculated by the steps of
(a) choosing a desired relative range accuracy σ R /R for the method;
(b) obtaining an estimated range R est of the jammer from the second position at time t 2 ;
(c) finding d based on the relative range accuracy, the estimated range R est , the variance σ Δα 2 in Δα and the variance σ d 2 in d according to
σ
R
=
R
d
(
R
2
-
d
2
)
·
σ
Δ
α
2
+
σ
d
2
(d) calculating the components Δx, Δy of the displacement d according to
Δ x =cos(α 1 +{dot over (α)}·Δ t )· d
Δ y =−sin(α 1 +{dot over (α)}·Δ t )· d
wherein a range R of the jammer from the second position is calculated according to
R
=
d
sin
Δ
α
.
2. The method of claim 1 , further comprising the steps of:
(i) evaluating an angle Δβ 1 between a straight line joining the first position of the airborne detector radar and the position of the jammer at time t 2 , and a straight line defined by the components Δx, Δy;
(ii) evaluating an angle Δβ 2 between the straight line joining the first position of the airborne detector radar and the position of the jammer at time t 2 , and a straight line defined by the components −Δx, Δy;
(iii) if |Δβ 1 −π/2|≦|Δβ 2 −π/2| then choosing the manoeuvre of the airborne detector radar such that the airborne detector radar's displacement has components Δx, Δy and if |Δβ 1 −π/2|>|Δβ 2 −π/2| then choosing the manoeuvre of the airborne detector radar such that the airborne detector radar's displacement has components −Δx, Δy.
3. The method according to claim 1 , wherein a range of a second jammer is also determined, and wherein the method comprises the steps of:
(i) evaluating an angle Δβ 11 between a straight line joining the first position of the airborne detector radar and the position of the first jammer at time t 2 , and a straight line defined by the components Δx, Δy;
(ii) evaluating an angle Δβ 12 between a straight line joining the first position of the airborne detector radar and the position of the second jammer at time t 2 , and the straight line defined by the components Δx, Δy;
(iii) evaluating an angle Δβ 21 between the straight line joining the first position of the airborne detector radar and the position of the first jammer at time t 2 , and a straight line defined by the components −Δx, Δy;
(iv) evaluating an angle Δβ 22 between the straight line joining the first position of the airborne detector radar and the position of the second jammer at time t 2 , and the straight line defined by the components −x, −y;
(v) if |Δβ 11 +Δβ 12 −π|≦|Δβ 21 +Δβ 22 −π| then choosing the manoeuvre of the airborne detector radar such that the airborne detector radar's displacement has components Δx, Δy and if |Δβ 11 +Δβ 12 −π|>|Δβ 21 +Δβ 22 −π| then choosing the v of the airborne detector radar such that the airborne detector radar's displacement has components −Δx, Δy.