The effect of the underlying sea surface on the angular measurements of the radar homing head
Abstract
Keywords
For citation:
Mizrokhi V.Ya. The effect of the underlying sea surface on the angular measurements of the radar homing head. Journal of «Almaz – Antey» Air and Space Defence Corporation. 2019;(4):1923. https://doi.org/10.38013/25420542201941923
Protection of the Navy ships (NS) against antiship missiles (ASM) is a most crucial task faced by the antiaircraft missile systems. Such missiles pose the greatest threat to the NS.
The antiaircraft missile systems employing externally guided antiaircraft guided missiles (AAGM) are unable to ensure hitting of lowflying ASM with the required probability. It is only through the use of radar guidance on the final flight leg that a possibility appears to fulfil the task of hitting the ASM flying low over the sea surface with the required probability.
When using radar guidance for interception of lowflying targets, it is important to determine the effect of the underlying sea surface on the angular measurements taken by the active radar homing head (ARHH).
The problem of the effect of the underlying sea surface on the radar head angular measurements during homing on targets flying low over the sea surface has been considered in many publications, in particular, in the papers by this author: “Opredeleniye dalnosti uglovogo raz resheniya radiolokatsionnoi golovkoi samonave deniya nizkoletyaschikh nad morem tselei” (Ra diotekhnika, 2001, No. 12); “Building of control algorithms for antiaircraft missiles with active radar homing head when aiming at lowflying targets at the underlying sea surface” (Polyot, 2015, No. 10).
In M. Skolnik’s Radar Handbook [1], section 8.7 “Theories of Sea Clutter”, it is pointed out that creating a sufficiently realistic model of the sea has proved to be a very difficult task.
In the present paper the author, while agreeing with M. Skolnik’s opinion, does not attempt to build a radar model of the sea but rather is up to building a model of the effect of the underlying sea surface on the angular measurements of the radar homing head.
This task was solved on the basis of the analysis of real experiments by one of the antiaircraft guided missiles with ARHH when homing on targets flying low over the sea surface. The results of the real experiments are given below.
The analysis was performed using telemetric records of angular deviations of the target’s line of sight from the ARHH antenna radiation pattern axis in that plane where they were the greatest: del_eps_pf del_bet_pf (in the vertical and horizontal planes) or DEYMS, DEZMS (in the inclined planes).
Angular deviations of the target’s line of sight from the ARHH antenna radiation pattern axis depending on time remaining to the kill point τ are shown in Fig. 1. Angular deviations of the target’s line of sight from the ARHH antenna radiation pattern axis were measured in two coordinate systems (Fig. 2). The designations in Fig. 2 correspond to those given in Fig. 1.
Fig. 2. Angular deviations of target’s line of sight from ARHH antenna radiation pattern axis
Based on the results of the analysis of real experiments with the investigated missile, a “Model of the effect of the underlying sea surface on the angular measurements of an active radar homing head” was built.
Angular deviations of the ARHH antenna radiation pattern axis from the direction to target are proportional to the effected miss, which follows from the known geometrical relationships.
The miss value equals to
h_{ε}= ω_{ε }Vτ^{2},
h_{β} = ω_{β}Vτ^{2}
where h_{ε}, h_{β}  misses by axes ε and β, respectively;
ω_{ε}, ω_{β}  line of sight angular velocity projections on the axes (ε, β);
V  closingin relative velocity modulus;
τ  flight time to the kill point.
Angular velocities of the line of sight are linked to angular deviations of the ARHH antenna axis from the direction to target DEPS, DBET by relationships
ω_{ε} = DEPS ⋅ DG,
ω_{β} = DBET · DG,
where DG  ARHH Q factor.
Hence, miss projections on the respective axes are expressed through the respective projections of the ARHH antenna axis angular deviations by the relationships:
h_{ε} = DEPS · DG V τ^{2},
h_{β }= DBET · DG V τ^{2}.
Fig. 3 shows a typical pattern of missile guidance to target on the final flight leg before the kill point (τ = 0), given in the form of a curve of target’s line of sight angular deviations from the ARHH antenna radiation pattern axis.
Fig. 3. Curve of target’s line of sight angular deviations: S_{1}, S_{2}  areas under respective curve segments
Taken as the “determinant factor” is the difference
S_{1}τ_{1}  S_{2}τ_{2 }. (I)
The implication behind the “determinant factor” consists in the following.
The control command invoking missile acceleration W_{pl}, is proportional to the homing head radiation pattern angular deviations from the target’s line of sight, i. e., del_eps_pf del_bet_pf:
The product of missile acceleration by its lasting time interval is proportional to the produced missile speed component, normal to the line of sight:
Product S_{1}T_{1}, where τ_{1}  time remaining to the kill point (see Fig. 3), is proportional to the product of ν_{ρ⊥}τ_{1}:
Here, V_{⊥}_{1} τ_{1} produces miss h_{1}. Similarly, V_{⊥}_{2}τ_{2} produces miss h_{2}.
These relationships clarify the implication behind the “determinant factor”, which consists in that it is proportional to the resulting miss:
The magnitudes of misses effected under the experiments are given in the table in the relative form (related to the magnitude of the greatest miss effected).
Results of the experiments of homing on a lowflying target and “determinant factor” value
Experiment No. 
Target flight altitude, m 
S_{1}τ_{1}  S_{2}τ_{2} 


1 
232 
0,052800 
1,000 
2 
50 
0,011000 
0,208 
3 
200 
0,016200 
0,396 
4 
83 
0,022500 
0,438 
5 
290 
0,026500 
0,497 
6 
250 
0,024000 
0,466 
7 
68 
0,026000 
0,498 
8 
50 
0,041400 
0,863 
9 
300 
0,005760 
0,122 
10 
200 
0,042800 
0,859 
11 
75 
0,001837 
0,030 
Let us represent relative magnitudes of the misses effected under the experiments in their dependence on the “determinant factor”, with their approximation function drawn.
The approximation function has the view
For an optimal control algorithm, the relative miss magnitude is linked to the “determinant factor” by the relationship
The absolute magnitudes of the effected misses depend not only on the “determinant factor” but also on fast response of the stabilisation system and control algorithm.
The AAGM used in the experiments have a fastresponse stabilisation system but their control algorithm is not optimal.
A graphic representation of these functions (6), (7) and the magnitudes of relative misses effected in the launches are given in Fig. 4.
The telemetry data of the experiments have enabled to determine statistical characteristics of a miss:
 mathematical expectation of a relative miss
 rootmeansquare of a relative miss
Using dependence (6), it has made it possible to proceed to statistical characteristics of the “determinant factor”:
Expression (10) is essentially a model of the effect of the underlying sea surface on the homing accuracy.
For an optimal control algorithm, the dependence of a relative miss on the “determinant factor” is expressed by relationship (7), with the statistical estimates of the homing accuracy making:
The dependence of a relative miss on the “determinant factor” (Fig. 4) makes it possible to determine the notion of “strong” and “weak” effect of the underlying sea surface on the ARHH angular measurements and, as a result, on the accuracy of homing on the lowflying targets.
If we take as a criterion of “strong” water effect the magnitude of the “determinant factor” causing a relative miss , it will mean that a “strong” water effect is manifested at the “determinant factor” magnitude exceeding 0.01, i. e., corresponding to
In this way, the materials dwelt upon in this paper, pertaining to the analysis of experiments with AAGM having an active radar homing head, when homing on targets flying low over the sea surface, have made it possible to reveal a factor determining the effect of the underlying sea surface on the ARHH angular measurements and, as a result, on the homing accuracy, namely, the “determinant factor”.
This has enabled to build a statistical model of the effect of the underlying sea surface on the angular measurements of an active radar homing head and develop recommendations for building a control algorithm.
References
1. Справочник по радиолокации / под ред. М. Скольника. М.: Советское радио, 1976.
About the Author
V. Ya. MizrokhiRussian Federation
Mizrokhi Vladimir Yakovlevich – Doctor of Engineering Sciences, Professor, Advisor to the General Designer. Science research interests: antiaircraft missile control, flight dynamics of antiaircraft guided missiles.
Khimki, Moscow Region
For citation:
Mizrokhi V.Ya. The effect of the underlying sea surface on the angular measurements of the radar homing head. Journal of «Almaz – Antey» Air and Space Defence Corporation. 2019;(4):1923. https://doi.org/10.38013/25420542201941923