The effect of the underlying sea surface on the angular measurements of the radar homing head

Protection of the Navy ships (NS) against anti-ship missiles (ASM) is a most crucial task faced by the anti-aircraft missile systems. Such missiles pose the greatest threat to the NS.

The anti-aircraft missile systems employ­ing externally guided anti-aircraft guided mis­siles (AAGM) are unable to ensure hitting of low-flying 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 low-flying 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 anti-aircraft missiles with active radar homing head when aiming at low-flying 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 anti-aircraft 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.

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 Vτ²,

h_β = ω_βVτ²

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 - closing-in 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 τ²,

h_β = DBET · DG V τ².

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.

Taken as the “determinant factor” is the difference

S₁τ₁ - S₂τ₂ .                                                           (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 S₁T₁, where τ₁ - time remaining to the kill point (see Fig. 3), is proportional to the product of ν_ρ⊥τ₁:

Here, V_⊥1 τ₁ produces miss h₁. Similarly, V_⊥2τ₂ produces miss h₂.

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).

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 fast-response 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

• root-mean-square 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 low-flying 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.