CN105652267B - A kind of passive radar maximum detectable range calculation method based on aspect - Google Patents

Abstract

A method for calculating the maximum detection distance of passive radar based on the target angle of view of the present invention comprises the following steps: 1. Establishing a bistatic radar system model composed of a GNSS launch satellite S, an airborne target T and a receiver R; 2. 1. Establish the calculation model of the GNSS reflection signal link, and obtain the correction formula of the square of the bistatic radar range product (R _r R _t ) ² ; 3. Establish the spatial geometric position relationship model of the bistatic radar based on the target viewing angle θ _r , and use the plane analysis method Obtain the R _t expression represented by R _r ; 4. Substitute the R _t expression into the correction formula of the bistatic radar distance product square (R _r R _t ) ² , and obtain the bistatic radar equation represented by R _r ; 5. Substitute The parameters involved are brought into the bistatic radar equation represented by R _r , and the maximum detection range (R _r ) _max of the receiver is solved.

Description

A Method for Calculating the Maximum Detection Range of Passive Radar Based on the Target Viewpoint

【Technical field】

The invention belongs to the field of satellite navigation and application, and in particular relates to a method for calculating the maximum detection distance of a passive radar based on a target perspective.

【Background technique】

Passive radar refers to the radar itself that does not emit electromagnetic wave signals, but only uses electromagnetic signals radiated by the target (external radiation) for target detection and tracking. The electromagnetic signal radiated by the target may be the signal emitted by the target itself, or it may be a third-party electromagnetic signal reflected by the target. Passive radar uses external radiation sources to detect targets, without a transmitter, and only needs a receiver to form a target detection system. From the perspective of the radar system, the transmitter and receiver of the system are configured in different places and belong to the dual (multi-base) radar. Compared with traditional radar technology, passive radar has the advantages of anti-stealth, anti-low-altitude attack, anti-reconnaissance, anti-jamming, etc., and has become an important field of radar research.

The signals emitted by the Global Navigation Satellite System (GNSS) are third-party electromagnetic signals, which have the advantages of high precision, all-time and all-weather, and have important applications in military, civilian and scientific research departments. However, the use of GNSS reflected signals to detect airborne targets is still in the exploratory stage internationally.

Using GNSS reflected signals to detect flying targets in the air requires receivers to receive and process GNSS direct and reflected signals. Receiver sensitivity refers to the lowest signal strength a receiver can receive and still function properly. When the strength of the reflected signal reaching the receiver just satisfies its sensitivity, its detection distance to the flying target is the maximum detection distance that the receiver can achieve. The maximum detection distance is one of the important indicators to measure the ability of passive radar system to detect flying targets in the air, and the acquisition of its solution method has very important practical significance.

【Content of invention】

The object of the present invention is: the present invention proposes a kind of passive radar maximum detection distance calculation method based on the target angle of view, by setting the sensitivity of the receiver, solve the maximum detection distance that the receiver can reach, so as to provide a new method for the passive radar system It provides an important basis for the evaluation of the detection capability of airborne targets.

Technical scheme of the present invention is:

The present invention is a method for calculating the maximum detection distance of passive radar based on the target angle of view, and its specific steps are as follows:

Step 1: Establish a bistatic radar system model consisting of GNSS satellite S, airborne target T and ground receiver R. The satellite signal transmitted by the GNSS satellite S reaches the ground receiver in two forms: one is directly to the ground receiver R, called direct signal; the other is reflected by the flying target T in the air and then reaches the ground receiver R, called for the reflected signal. Among them, the transmitting power of S is P _t , the transmitting antenna gain of S is G _t , the propagation distance from S to R is L, the propagation distance from S to T is R _t , the radar cross-sectional area of T is σ(β), and the distance from T to R is R t . The propagation distance of R is R _r , the equivalent area of R receiving antenna is A _r , and the gain of R receiving antenna is G _r ;

Step 2, establishing a GNSS reflection signal link calculation model. By calculating the reflected signal link, the correction formula of the square of the bistatic radar range product (R _r R _t ) ² is obtained;

Step 3, establish a bistatic radar spatial geometric position relationship model based on the target viewing angle θ _r . The target viewing angle θ _r is the target viewing angle of the receiving base. At this time, the two bases of GNSS signal transmission and reception and the air flight target can form a bistatic detection system plane, and the R _t expression expressed by R _r can be obtained by using the plane analysis method;

Step 4, Substitute the R _t expression represented by R _r in step 3 into the correction formula of the bistatic radar range product square (R _r R _t ) ² obtained in step 2, so as to obtain the bistatic radar represented by R _r radar equation;

Step 5, Substitute satellite transmit power, transmit antenna gain, receive antenna gain, GNSS signal wavelength, target radar cross-sectional area, receiver sensitivity, transmit loss, receive loss, transmit antenna pattern propagation factor and receive antenna propagation factor into step 4 In the obtained bistatic radar equation represented by R _r , the maximum detection range of the receiver (R _r ) _max is solved.

Wherein, the "establishing the GNSS reflection signal link calculation model" described in step 2 includes the following steps:

In step 2.1, the satellite signal is sent from the GNSS satellite, and the signal directly received by the receiver is called a direct signal, and the signal reflected by the target and then received by the receiver is called a reflected signal. Assuming that the GNSS reflection signal reaches the airborne target through the propagation distance of R _t after it is sent out, the expression of the power current density S _t at the airborne target is obtained;

Step 2.2, from the radar cross-sectional area σ(β) of the flying target in the air, the expression of the reflected signal power P at the target can be obtained;

Step 2.3, after the GNSS reflected signal reaches the target, it reaches the ground receiver R through the propagation distance of R _r , and the expression of the power flow density S _r of the target echo signal reaching the antenna of the receiving base is obtained;

Step 2.4, from the equivalent area A _r of the radar antenna of the receiving base, the expression of the target echo power P _r received by the receiving base is obtained, that is, the expression of the free space bistatic radar equation is obtained;

P _r = S _r A _r (4)

And because of

Among them, λ is the GNSS signal wavelength, G _r is the gain of the receiving antenna, then the formula (4) can be transformed into:

Combining formula (2), formula (3) and formula (6), the free space bistatic radar equation can be expressed as:

Step 2.5, convert the expression of the free space bistatic radar equation obtained in step 2.4 to obtain the expression of the square of the bistatic radar range product (R _r R _t ) ² ;

Step 2.6, considering the passive radar transmission loss L _T , reception loss L _R , the pattern propagation factor F _T of the transmitting antenna and the pattern propagation factor F _R of the receiving antenna, the square of the distance product of the bistatic radar (R _r R _t ) The modified formula of ² :

The two bases of GNSS signal transmission and reception and the air flying target constitute the plane of the bi-base detection system. In the triangle formed by S-R-T, the law of cosines can be obtained:

R _t ² ＝R _r ² +L ² -2R _r Lcos(π-θ _r ) (10)

Further sorting can be obtained:

R _t ² ＝R _r ² +L ² +2R _r Lcosθ _r (11)

Substituting formula (11) into formula (9) can get:

When the received power P _r of the receiver on the right side of formula (12) reaches the minimum value, the left side of the equation corresponds to the maximum detection distance R _r of the receiver, that is, when the GNSS reflected signal reaches the receiver sensitivity when it reaches the ground receiver, At this time, the distance between the receiver and the flying target in the air is the maximum detection distance of the receiver.

That is, formula (12) can be written as:

For a given GNSS signal source, its transmit power P _t , transmit antenna gain G _t and signal wavelength λ are all known; for a given airborne target, its radar cross-sectional area is known as σ(β); for For a given ground receiver, the receiving antenna gain G _r is known; when the GNSS direct signal reaches the ground receiver, according to the time delay information of the direct channel signal in the receiver, the distance L from the signal source to the receiver can be obtained, That is, L is known; the passive radar transmission loss L _T , reception loss L _R , the pattern propagation factor F _T of the transmitting antenna and the pattern propagation factor F _R of the receiving antenna are all known parameters; for a given ground receiving machine, the sensitivity of its receiver is known, that is, (P _r ) _min is known.

When the target angle of view θ _r is given, the maximum detection range (R _r ) _max corresponding to the receiver can be obtained by formula (13), and the maximum detection range calculation method is a method based on The calculation method of the maximum detection range of passive radar from the target perspective.

The advantages of the present invention are:

(1) The present invention analyzes the GNSS reflected signal link in detail by establishing a reflected signal link calculation model, and finally obtains the correction formula of the bistatic radar range product squared (R _r R _t ) ² , that is, in the reflected signal link During propagation, the relation expressions among P _r , R _t and R _r are obtained.

(2) The present invention converts the spatial geometric position relationship between S, T and R into a bistatic plane by establishing a bistatic radar spatial geometric position relationship model based on the target perspective, and by introducing the target perspective θ _r , we get The relational expression between R _t and R _r is a method of expressing R _t by R _r and θ _r .

(3) The present invention finally _{obtains the radar equation expression related to P r ,} θ _r and R _r by expressing R _t by R r and θ _r . When the target echo power _Pr received by the receiving base in the expression is set as the receiver sensitivity, the calculated distance Rr from the airborne target T to the receiver _R is the maximum detection distance that the receiver can achieve, The calculation process is simple and clear, and easy to implement.

(4) The present invention proposes a method for calculating the maximum detection range of passive radar based on the target angle of view, and calculates the maximum detection range corresponding to the receiver through receiver sensitivity. It has strong practicability for the selection of the receiver model in the actual detection of flying targets in the air.

(5) The method for calculating the maximum detection distance proposed by the present invention is based on the detection of flying targets in the air by passive radar, which has strong concealment and good practicability.

【Description of drawings】

Figure 1 is a schematic diagram of the propagation path of the bistatic radar reflection satellite reflection signal.

Figure 2 is a schematic diagram of the geometric relationship of the bistatic radar.

Fig. 3 is a flow chart of the method for calculating the maximum detection range of passive radar based on the GNSS-R target perspective.

Fig. 4 is a flow chart of the reflection signal link calculation model.

The symbols in the figure are explained as follows:

S represents the GNSS transmitting satellite; P _t represents the transmit power of S; G _t represents the transmit antenna gain of S;

T represents the flying target in the air; R _t represents the propagation distance from S to T; R represents the ground receiver;

R _r represents the propagation distance from T to R; A _r represents the equivalent area of the receiving antenna of R; O represents the center of the earth;

G _r represents the receiving antenna gain of R; L represents the propagation distance from S to R, also known as the baseline;

θ _r is the included angle from the extension line of the baseline to the counterclockwise direction of R _r , that is, the target viewing angle of the receiving base.

【Detailed ways】

Embodiments of the present invention are further described below in conjunction with the accompanying drawings:

Figure 1 shows a schematic diagram of the propagation path of the bistatic radar reflection satellite reflection signal. In the bistatic radar system model composed of GNSS satellite S, air flying target T and ground receiver R, the satellite signal transmitted by GNSS satellite S reaches the ground receiver in two forms: one directly reaches the ground receiver R, It is called the direct signal; one is reflected by the air target T and then reaches the ground receiver R, which is called the reflected signal. Among them, the transmission power of S is P _t , the gain of transmitting antenna is G _t , the propagation distance from S to R is L, the propagation distance from S to T is R _t , the target radar cross-sectional area of T is σ(β), and the distance from T to R is R t . The propagation distance of R is R _r , the equivalent area of R receiving antenna is A _r , and the gain of R receiving antenna is G _r ;

Figure 2 shows a schematic diagram of the geometric relationship of the bistatic radar. The GNSS transmitting satellite S, the flying target T and the receiver R form a bistatic plane triangle, and the included angle between the extension line of the baseline L and the counterclockwise direction of R _r is θ _r .

Figure 3 shows the flow chart of the passive radar maximum detection range calculation method based on the GNSS-R target perspective, including the following steps:

Step 1, establishing a bistatic radar system model composed of a GNSS transmitting satellite S, an airborne target T and a receiver R;

Step 2, establishing a GNSS reflection signal link calculation model. By calculating the reflected signal link, the correction formula of the square of the bistatic radar range product (R _r R _t ) ² is obtained;

Step 3, establish a bistatic radar spatial geometric position relationship model based on the target viewing angle θ _r . The target viewing angle θ _r is the target viewing angle of the receiving base. At this time, the two bases of GNSS signal transmission and reception and the air flight target can form a bistatic detection system plane, and the R _t expression expressed by R _r can be obtained by using the plane analysis method;

Step 4, Substitute the R _t expression represented by R _r in step 3 into the correction formula of the bistatic radar range product square (R _r R _t ) ² obtained in step 2, so as to obtain the bistatic radar represented by R _r radar equation;

Step 5, Substitute satellite transmit power, transmit antenna gain, receive antenna gain, GNSS signal wavelength, target radar cross-sectional area, receiver sensitivity, transmit loss, receive loss, transmit antenna pattern propagation factor and receive antenna propagation factor into step 4 In the obtained bistatic radar equation represented by R _r , the maximum detection range of the receiver (R _r ) _max is solved.

Wherein, the "establishing the GNSS reflection signal link calculation model" described in step 2 includes the following steps:

In conjunction with Figure 4, the specific flow of the GNSS reflection signal link calculation model described in step 2 includes the following steps:

Step 1, the satellite signal is sent from the GNSS satellite, the signal directly received by the receiver is called a direct signal, and the signal reflected by the target and then received by the receiver is called a reflected signal. Assuming that the GNSS reflection signal reaches the airborne target through the propagation distance of R _t after it is sent out, the expression of the power current density S _t at the airborne target is obtained;

Step 2, from the target radar reflection cross-sectional area, the expression of the reflected signal power P at the flying target in the air can be obtained:

Step 3, after the GNSS reflected signal reaches the target, it reaches the ground receiver R through the propagation distance of R _r , and obtains the power flow density S _r expression of the target echo signal arriving at the antenna of the receiving base;

Step 4, from the equivalent area A _r of the radar antenna of the receiving base, the expression of the target echo power P _r received by the receiving base is obtained;

P _r = S _r A _r (4)

And because of

Among them, λ is the GNSS signal wavelength, G _r is the gain of the receiving antenna, then the formula (4) can be transformed into:

Combining formula (2), formula (3) and formula (6), the free space bistatic radar equation can be expressed as:

Step 5, convert the free-space bistatic radar equation expression obtained in step 4 to obtain the expression of the bistatic radar range product squared (R _r R _t ) ² :

Step 6, since the actual radar system always has various losses, considering the passive radar transmission loss L _T , reception loss L _R , the pattern propagation factor _FT of the transmitting antenna and the pattern propagation factor _FR of the receiving antenna, then The correction formula of the square of the bistatic radar range product (R _r R _t ) ² can be obtained:

The two bases of GNSS signal transmission and reception and the air flying target constitute the plane of the bi-base detection system. In the triangle formed by S-R-T, the law of cosines can be obtained:

R _t ² ＝R _r ² +L ² -2R _r Lcos(π-θ _r ) (10)

Further sorting can be obtained:

R _t ² ＝R _r ² +L ² +2R _r Lcosθ _r (11)

Substituting formula (11) into formula (9) can get:

It can be seen from mathematical knowledge that when the received power P _r of the receiver on the right side of the equation (12) reaches the minimum value, the left side of the equation corresponds to the maximum detection distance R _r of the receiver, that is, when the GNSS reflected signal reaches the ground receiver When the sensitivity of the receiver is high, the distance between the receiver and the flying target in the air is the maximum detection distance of the receiver.

That is, formula (12) can be written as:

For a given GNSS signal source, its transmit power P _t , transmit antenna gain G _t and signal wavelength λ are all known; for a given airborne target, its radar cross-sectional area is known as σ(β); for For a given ground receiver, the receiving antenna gain G _r is known; when the GNSS direct signal reaches the ground receiver, according to the time delay information of the direct channel signal in the receiver, the distance L from the signal source to the receiver can be obtained, That is, L is known; the passive radar transmission loss L _T , reception loss L _R , the pattern propagation factor F _T of the transmitting antenna and the pattern propagation factor F _R of the receiving antenna are all known parameters; for a given ground receiving machine, the sensitivity of its receiver is known, that is, (P _r ) _min is known.

When the target angle of view θ _r is given, the maximum detection range (R _r ) _max corresponding to the receiver can be obtained by formula (13), and the maximum detection range calculation method is a method based on The calculation method of the maximum detection range of passive radar from the target perspective.

Claims (3)

1. a kind of passive radar maximum detectable range calculation method based on aspect, it is characterised in that：It is as follows：

Step 1 using GNSS satellite S as radar signal station, using ground receiver R as signal receiving terminal, is established biradical Ground radar system realizes the detection to aerial target T；By the satellite-signal that GNSS satellite S emits, there are two types of form arrival ground Receiver：One kind is direct arrival ground receiver R, is known as direct signal；One kind be via airflight target T reflect after again Ground receiver R is reached, is known as reflected signal；Wherein, the transmission power of S is P_t, the transmitter antenna gain (dBi) G of S_t, the propagation of S to R Distance is L, and the propagation distance of S to T is R_t, the radar cross section of T is σ (β), and the propagation distance of T to R is R_r, R reception antennas etc. Effect area is A_r, R receiving antenna gains are G_r；

Step 2 establishes GNSS reflected signal link calculation models；By carrying out reflected signal link calculation, biradical land mine is obtained Up to distance product square (R_rR_t)²Amendment type；

Step 3 is established based on aspect θ_rBistatic radar space geometry position relationship model；Aspect θ_rTo receive The aspect in base；GNSS signal transmitting-receiving one bistatic detection system in two bases and airflight target configuration is put down at this time Face is obtained using two dimensional analysis method by R_rThe R of expression_tExpression formula；

Step 4, by step 3 by R_rThe R of expression_tExpression formula is updated to the bistatic radar distance product obtained in step 2 Square (R_rR_t)²Amendment type, so as to obtain by R_rThe bistatic radar equation of expression；

Step 5, by satellite launch power, transmitter antenna gain (dBi), receiving antenna gain, GNSS signal wavelength, target RCS Product, receiver sensitivity, launch loss receive loss, transmitting antenna directional diagram propagation factor and reception antenna propagation factor generation Enter to step 4 obtain by R_rIn the bistatic radar equation of expression, so as to calculate receiver maximum detectable range (R_r)_max。

2. a kind of passive radar maximum detectable range calculation method based on aspect according to claim 1, special Sign is：

Wherein, the GNSS reflected signal link calculation models of establishing described in step 2 comprise the following steps：

Step 2.1, satellite-signal is sent from GNSS satellite, is directly received machine received signal and is known as direct signal, through target Machine received signal is received after reflection again and is known as reflected signal；If GNSS reflected signals send after by R_tPropagation distance arrive Up to airflight target, power flow density S at airflight target is obtained_tExpression formula；

<mrow> <msub> <mi>S</mi> <mi>t</mi> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>P</mi> <mi>t</mi> </msub> <msub> <mi>G</mi> <mi>t</mi> </msub> </mrow> <mrow> <mn>4</mn> <msup> <msub> <mi>&amp;pi;R</mi> <mi>t</mi> </msub> <mn>2</mn> </msup> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>

Step 2.2, by the radar cross section σ (β) of airflight target, the expression formula of reflection signal power P at target is obtained；

<mrow> <mi>&amp;sigma;</mi> <mrow> <mo>(</mo> <mi>&amp;beta;</mi> <mo>)</mo> </mrow> <mi>P</mi> <mo>=</mo> <msub> <mi>S</mi> <mi>t</mi> </msub> <mi>&amp;sigma;</mi> <mrow> <mo>(</mo> <mi>&amp;beta;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <msub> <mi>P</mi> <mi>t</mi> </msub> <msub> <mi>G</mi> <mi>t</mi> </msub> <mi>&amp;sigma;</mi> <mrow> <mo>(</mo> <mi>&amp;beta;</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mn>4</mn> <msup> <msub> <mi>&amp;pi;R</mi> <mi>t</mi> </msub> <mn>2</mn> </msup> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>

Step 2.3, after GNSS reflected signals reach target, then through R_rPropagation distance reach ground receiver R, obtain target return Ripple signal reaches the power flow density S received at base antenna_rExpression formula；

<mrow> <msub> <mi>S</mi> <mi>r</mi> </msub> <mo>=</mo> <mfrac> <mi>P</mi> <mrow> <mn>4</mn> <msup> <msub> <mi>&amp;pi;R</mi> <mi>r</mi> </msub> <mn>2</mn> </msup> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>

Step 2.4, by receiving base radar antenna equivalent area A_r, obtain receiving the target echo power P that base receives_r's Expression formula is to get having arrived free space bistatic radar equation expression formula；

P_r=S_rA_r (4)

And due to

<mrow> <msub> <mi>A</mi> <mi>r</mi> </msub> <mo>=</mo> <mfrac> <msup> <mi>&amp;lambda;</mi> <mn>2</mn> </msup> <mrow> <mn>4</mn> <mi>&amp;pi;</mi> </mrow> </mfrac> <msub> <mi>G</mi> <mi>r</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>

Wherein, λ be GNSS signal wavelength, G_rFor receiving antenna gain, then formula (4) turns to：

<mrow> <msub> <mi>P</mi> <mi>r</mi> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>S</mi> <mi>r</mi> </msub> <msub> <mi>G</mi> <mi>r</mi> </msub> <msup> <mi>&amp;lambda;</mi> <mn>2</mn> </msup> </mrow> <mrow> <mn>4</mn> <mi>&amp;pi;</mi> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>

Combinatorial formula (2), formula (3) and formula (6) obtain free space bistatic radar equation expression：

<mrow> <msub> <mi>P</mi> <mi>r</mi> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>P</mi> <mi>t</mi> </msub> <msub> <mi>G</mi> <mi>t</mi> </msub> <msub> <mi>G</mi> <mi>r</mi> </msub> <msup> <mi>&amp;lambda;</mi> <mn>2</mn> </msup> <mi>&amp;sigma;</mi> <mrow> <mo>(</mo> <mi>&amp;beta;</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msup> <mrow> <mo>(</mo> <mn>4</mn> <mi>&amp;pi;</mi> <mo>)</mo> </mrow> <mn>3</mn> </msup> <msup> <msub> <mi>R</mi> <mi>t</mi> </msub> <mn>2</mn> </msup> <msup> <msub> <mi>R</mi> <mi>r</mi> </msub> <mn>2</mn> </msup> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>

Step 2.5, the free space bistatic radar equation expression formula transition form that will be obtained in step 2.4, obtains bistatic Distance by radar accumulates square (R_rR_t)²Expression formula；

<mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>R</mi> <mi>r</mi> </msub> <msub> <mi>R</mi> <mi>t</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>=</mo> <mfrac> <mrow> <msub> <mi>P</mi> <mi>t</mi> </msub> <msub> <mi>G</mi> <mi>t</mi> </msub> <msub> <mi>G</mi> <mi>r</mi> </msub> <msup> <mi>&amp;lambda;</mi> <mn>2</mn> </msup> <mi>&amp;sigma;</mi> <mrow> <mo>(</mo> <mi>&amp;beta;</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msup> <mrow> <mo>(</mo> <mn>4</mn> <mi>&amp;pi;</mi> <mo>)</mo> </mrow> <mn>3</mn> </msup> <msub> <mi>P</mi> <mi>r</mi> </msub> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>

Step 2.6, it is contemplated that passive radar launch loss L_T, receive loss L_R, transmitting antenna directional diagram propagation factor F_TAnd The directional diagram propagation factor F of reception antenna_R, obtain bistatic radar distance product square (R_rR_t)²Amendment type：

<mrow> <msup> <mrow> <mo>(</mo> <msub> <mi>R</mi> <mi>r</mi> </msub> <msub> <mi>R</mi> <mi>t</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>=</mo> <mfrac> <mrow> <msub> <mi>P</mi> <mi>t</mi> </msub> <msub> <mi>G</mi> <mi>t</mi> </msub> <msub> <mi>G</mi> <mi>r</mi> </msub> <msup> <mi>&amp;lambda;</mi> <mn>2</mn> </msup> <mi>&amp;sigma;</mi> <mrow> <mo>(</mo> <mi>&amp;beta;</mi> <mo>)</mo> </mrow> <msup> <msub> <mi>F</mi> <mi>T</mi> </msub> <mn>2</mn> </msup> <msup> <msub> <mi>F</mi> <mi>R</mi> </msub> <mn>2</mn> </msup> </mrow> <mrow> <msup> <mrow> <mo>(</mo> <mn>4</mn> <mi>&amp;pi;</mi> <mo>)</mo> </mrow> <mn>3</mn> </msup> <msub> <mi>P</mi> <mi>r</mi> </msub> <msub> <mi>L</mi> <mi>T</mi> </msub> <msub> <mi>L</mi> <mi>R</mi> </msub> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>

GNSS signal receives and dispatches two bases and airflight target configuration bistatic detection System planes, in the triangle of S-R-T compositions In shape, obtained using the cosine law：

R_t ²=R_r ²+L²-2R_rLcos(π-θ_r) (10)

It further arranges and obtains：

R_t ²=R_r ²+L²+2R_rLcosθ_r (11)

Formula (11) is substituted into formula (9) to obtain：

<mrow> <msup> <msub> <mi>R</mi> <mi>r</mi> </msub> <mn>2</mn> </msup> <mo>*</mo> <mrow> <mo>(</mo> <msup> <msub> <mi>R</mi> <mi>r</mi> </msub> <mn>2</mn> </msup> <mo>+</mo> <msup> <mi>L</mi> <mn>2</mn> </msup> <mo>+</mo> <mn>2</mn> <msub> <mi>R</mi> <mi>r</mi> </msub> <msub> <mi>Lcos&amp;theta;</mi> <mi>r</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <msub> <mi>P</mi> <mi>t</mi> </msub> <msub> <mi>G</mi> <mi>t</mi> </msub> <msub> <mi>G</mi> <mi>r</mi> </msub> <msup> <mi>&amp;lambda;</mi> <mn>2</mn> </msup> <mi>&amp;sigma;</mi> <mrow> <mo>(</mo> <mi>&amp;beta;</mi> <mo>)</mo> </mrow> <msup> <msub> <mi>F</mi> <mi>T</mi> </msub> <mn>2</mn> </msup> <msup> <msub> <mi>F</mi> <mi>R</mi> </msub> <mn>2</mn> </msup> </mrow> <mrow> <msup> <mrow> <mo>(</mo> <mn>4</mn> <mi>&amp;pi;</mi> <mo>)</mo> </mrow> <mn>3</mn> </msup> <msub> <mi>P</mi> <mi>r</mi> </msub> <msub> <mi>L</mi> <mi>T</mi> </msub> <msub> <mi>L</mi> <mi>R</mi> </msub> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> </mrow>

Receiver on the right side of formula (12) equation receives power P_rWhen reaching minimum value, this receiver is corresponded on the left of equation Maximum detectable range R_r, i.e., when GNSS reflected signals reach ground receiver when reaching receiver sensitivity, at this time receiver with The distance of airflight target is the detection range of receiver maximum therefore；

I.e. formula (12) is written as：

<mrow> <msub> <msup> <mrow> <mo>(</mo> <msub> <mi>R</mi> <mi>r</mi> </msub> <mo>)</mo> </mrow> <mn>4</mn> </msup> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>+</mo> <mn>2</mn> <mi>L</mi> <msub> <msup> <mrow> <mo>(</mo> <msub> <mi>R</mi> <mi>r</mi> </msub> <mo>)</mo> </mrow> <mn>3</mn> </msup> <mi>max</mi> </msub> <msub> <mi>cos&amp;theta;</mi> <mi>r</mi> </msub> <mo>+</mo> <msup> <mi>L</mi> <mn>2</mn> </msup> <msub> <msup> <mrow> <mo>(</mo> <msub> <mi>R</mi> <mi>r</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>P</mi> <mi>t</mi> </msub> <msub> <mi>G</mi> <mi>t</mi> </msub> <msub> <mi>G</mi> <mi>r</mi> </msub> <msup> <mi>&amp;lambda;</mi> <mn>2</mn> </msup> <mi>&amp;sigma;</mi> <mrow> <mo>(</mo> <mi>&amp;beta;</mi> <mo>)</mo> </mrow> <msup> <msub> <mi>F</mi> <mi>T</mi> </msub> <mn>2</mn> </msup> <msup> <msub> <mi>F</mi> <mi>R</mi> </msub> <mn>2</mn> </msup> </mrow> <mrow> <msup> <mrow> <mo>(</mo> <mn>4</mn> <mi>&amp;pi;</mi> <mo>)</mo> </mrow> <mn>3</mn> </msup> <msub> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mi>r</mi> </msub> <mo>)</mo> </mrow> <mi>min</mi> </msub> <msub> <mi>L</mi> <mi>T</mi> </msub> <msub> <mi>L</mi> <mi>R</mi> </msub> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> <mo>.</mo> </mrow>

3. a kind of passive radar maximum detectable range calculation method based on aspect according to claim 2, special Sign is：For given GNSS signal source, transmission power P_t, transmitter antenna gain (dBi) G_tIt is known with signal wavelength lambda；It is right In given airflight target, radar cross section is that σ (β) is known；For given ground receiver, reception antenna Gain G_rTo be known；After the direct signal of GNSS reaches ground receiver, believed according to direct projection channel signal time delay in receiver Breath, the distance L of signal source to receiver can be asked, i.e. L is known；Passive radar launch loss L_T, receive loss L_R, transmitting antenna Directional diagram propagation factor F_TAnd the directional diagram propagation factor F of reception antenna_RIt is known parameters；It is connect for given ground Receipts machine, the sensitivity of receiver is knowable, i.e. (P_r)_minIt is known.