CN113805200B - Anti-spoofing authentication method for satellite navigation signals - Google Patents

Abstract

The invention provides an anti-deception authentication method for satellite navigation signals, which combines a power monitoring technology with early-late gate measurement, simultaneously monitors received power and related function distortion under a Bayesian detection framework, and realizes effective detection of deception jamming. Under the Bayesian framework of hypothesis test, the invention obtains the optimal decision region by utilizing Monte Carlo experiments through four classifications, obtains the judged region by comparing the power value and early-late gate metric value of the received signal with each region, and obtains the detection reliability of various classifications by counting the judged region. Compared with the prior art, the method can greatly improve the detection reliability of different interferences.

Description

Anti-spoofing authentication method for satellite navigation signals

Technical Field

The invention relates to the field of global satellite navigation, in particular to a satellite signal authentication method, and in particular relates to the problem of interference detection of global satellite navigation signals.

Background

The satellite signal itself has weak signal strength when reaching the ground after being propagated in the atmosphere, and is more severely interfered in a complex electromagnetic environment. Therefore, detection of interference is particularly urgent. The disclosures of GNSS signals result in their susceptibility to counterfeiting. The receiver becomes the victim of a rogue attack in which a fake GNSS signal spoofs the receiver to report a misleading location or time.

Currently, receiver-autonomous, low-cost GNSS signal authentication techniques that do not require changing GNSS signal space are favored. But if operated alone for a certain characteristic, the detection performance is very unreliable, and in the application of the navigation system, a false alarm is often generated. And the existing combination of power and symmetry difference measures, for example, is insensitive to detection and unreliable in detection of deception jamming performance because only single-channel information is utilized; the combination of early-late gate metrics and ratio metrics is not effective in detecting high power fraud because no power metric value is introduced. Thus, the challenges of GNSS authentication techniques are also exposed, mainly in detecting whether spoofing is reliable.

Disclosure of Invention

In order to overcome the defects of the prior art, the invention provides an anti-spoofing authentication method for satellite navigation signals. In order to better solve the problem of deception jamming detection reliability, the invention provides an anti-deception authentication method for satellite navigation signals, which creatively combines a power monitoring technology with early-late gate measurement, thereby greatly reducing false alarm probability.

The invention combines the received power and early-late gate measurement, and simultaneously monitors the received power and related function distortion under the Bayesian detection framework, thereby realizing the effective detection of deception jamming. The invention has good detection performance and greatly improves the reliability of deception jamming detection.

The technical scheme adopted by the invention for solving the technical problems comprises the following steps:

step one: with the down-converted signals, under the condition of no related interference term, for the down-converted real GNSS signals S _A (t), the following complex baseband model is adopted:

Where P _A is the received power of the real signal in watts, D (t) is the navigation data with a value of ±1, t is the time in seconds, τ _A is the code offset in seconds, C _A (t) is the pseudorandom spreading code with a value of ±1, exp (j θ _A) is the carrier with a phase of θ _A, the navigation data D (t) can be ignored without loss of generality, let D (t) =1, and the interference signal S _J (t) is modeled as:

Where η=p _J/P_A is the power advantage of the interfering signal over the real signal, i.e. the ratio of the interfering power P _J to the real signal power P _A; τ _J and θ _J are the code offset and carrier phase of the interfering signal, respectively; the received noise S _N (t) is modeled as:

S_N(t)＝N(t)+M(t) (3)

The noise is the sum of thermal noise N (t) with constant spectral density N ₀ and multiple access interference M (t) with variable spectral density M ₀, and the complete received signal S (t) is modeled as follows:

S(t)＝S_A(t)+S_J(t)+S_N(t) (4)

Wherein S _A (t) is a true GNSS signal, S _J (t) is an interfering signal, S _N (t) is noise, and the scaling factor β (t) of the automatic gain control circuit is multiplied by S (t), so that the power of the scaled signal β (t) S (t) remains constant;

step two: the local code l (t, τ) is modeled as follows:

Where τ is any code phase delay in seconds, C _l (t) is the local code, equal to C _A (t); And/> Is an estimate of the code phase and carrier phase of the composite signal S (t);

And (3) correlating the beta (t) S (t) with the local code l (t, tau) to obtain two paths of data of I path I (tau) and Q path Q (tau), wherein the two paths of data are as follows:

Wherein Δτ _A is τ _A and And the difference of delta tau _J、Δθ_J and delta theta _A,/>, are obtained by the same methodAnd/>Two paths of Gaussian white noise are I, Q respectively; r (·) is a spreading code autocorrelation function, expressed as:

Where T _c is the spreading code single chip time period;

Step three: a bayesian multi-hypothesis testing framework is adopted to distinguish hypotheses, wherein each hypothesis type is H _i, I epsilon I, i= {0,1,2,3}, zero hypothesis H ₀ corresponds to a non-interference condition, and H _i, i=1, 2,3 respectively corresponds to multipath interference, deception interference and suppression interference;

The three relevant parameters, namely interference power dominance eta, interference and true signal spreading code offset delta tau = tau _J-τ_A and carrier phase offset delta theta = theta _J-θ_A, are selected, combined into a vector theta = [ eta, delta tau, delta theta ], and the vector theta is assumed to lie in a parameter space lambda which itself is divided into disjoint parameter sets And each parameter set is associated with its corresponding hypothesis H _i; thus, determining θ∈Λi is equivalent to selecting hypothesis H _i;

In the Bayesian formula of the composite hypothesis test problem, the vector θ is regarded as a random number, the probability density is w (θ), where pi _i is the prior probability that θ falls into Λ _i, and the conditional probability density for a given θ ε Λi, θ is expressed by w _i (θ):

There are two types of observations, namely, observed received power P and early-late gate metric m _ELP, which are associated with four hypotheses; combining the two observations into a vector z= [ m _ELP,P]^T, wherein the observation set of the vector z is Γ, and the conditional probability density distribution is p (z|theta);

The decision criterion δ (z) is used to divide Γ into disjoint decision regions Γ _i such that when z e Γ _i corresponds to the H _i hypothesis, i.e., Γ _i corresponds to H _i;

let C [ i, θ ] be the cost function when H _i is selected when θ∈Λ is the actual parameter vector, the cost function is closely related to the selection of θ, and the average cost of conditional risk is defined as:

Where E _θ represents the derivation of the expectation, the Bayesian risk r (δ) is defined as:

Finding the optimal decision criterion delta (z) minimizes the Bayesian risk r (delta), i.e. finding the optimal decision region Γ _i, I e I;

Step four: modeling the reception of M _S +1 real signals, each with an interference signal associated with it, the received signal S _C (t) is as follows:

Wherein S _Ai (t) is the i-th real signal, its associated interference is S _Ji (t), and N (t) is noise;

the observed power value P (dBW) is:

Wherein T is integration accumulated time, and T ₁ is time at any selected moment; the conditional probability density function of P meets the average value of Variance is/>In which,/>

Wherein Δθ _i and Δτ _i correspond to carrier phase offset and code phase offset between the ith interference and the corresponding real signal, respectively, P _Ai is the power value of the ith real signal, η _i is the ratio of the ith interference to the power of the ith real signal, W _P is the bandwidth of the power to be measured, N ₀ is the thermal noise spectral density, and σ _P is up to 0.5dB within the bandwidth of 2 MHZ;

for multiple access interference M (T), the density of multiple access interference is M ₀, expressed as:

wherein M _S is the number of real signals minus one, In relation to P _A, but in different cases with different values, where i=0 denotes the real signal and its interference, i=1,..m _s denotes the multiple access signal and its interference;

for the early-late gate metric value m _ELP:

where τ _d is the observation point position set for two data paths I (τ) and Q (τ), and tan ^-1 is the inverse tangent.

Combining the observed power value with the early-late gate metric value to obtain z= [ m _ELP,P]^T, wherein m _ELP and P are mutually independent;

Step five: acquiring a corresponding optimal decision area by utilizing a Monte Carlo experiment;

(1) For each I e I, the N _i parameter vector is modeled according to the w _i (θ) distribution, where N _i/N_p≈π_i, The first simulation vector extracted from w _i (θ) is denoted θ _li;

(2) For each θ _li, generate an N _M analog measurement; the mth simulation for a given θ _li measures z _mli, the total amount of samples generated by the simulation is N _PN_M;

(3) Dividing the two-dimensional observation space gamma into a large number of small rectangular units with uniform size; assuming that each cell belongs to a single decision region, so that all observation samples falling in the cells belonging to Γ _i are equivalently allocated to hypothesis H _i, I epsilon I, each cell is allocated to hypothesis H _i with the largest number of samples Γ in the cell, an initial partition of z _mli is created, the boundary is adjusted, each cell is guaranteed to belong to only one type, namely a certain type of sample point in the cell is the largest, all the cells are set to belong to the type, and each decision region Γ _i is in single communication;

(4) Adjusting the boundary area, and considering the allocation of a new decision area; as long as the resulting decision area remains single connected, the new assignment remains unchanged as long as the bayesian risk r (δ) is reduced; repeatedly changing the area of the boundary area, changing the area into the currently set area if the Bayesian risk is reduced, and keeping the original area until no boundary unit needs to be reassigned, wherein the unit assignment forms a final judgment area gamma _i at the moment, I epsilon I if the Bayesian risk is not reduced;

the bayesian risk r (δ) at this time is expressed as:

wherein the cost function C [ i, θ ] is defined as follows:

Writing the cost function to C _ij,C_ij represents the cost of selecting H _i when H _j is true; when i=j, cost C _ij =0, otherwise, cost C _ij =1; however, in a practical scenario, not all misclassifications will have the same cost, and the cost is set as follows:

Through the discussion of the previous parameters, modeling to generate sample points, carrying out small block division on the whole area, and obtaining an initial area by visual observation of the sample points; and then constantly replacing the assignment of the boundary region to minimize the Bayesian risk and obtain a final decision region, namely an optimal decision region.

After the optimal region is obtained, the sample point can be regenerated, the region to which the sample point belongs is known, and the determination is carried out in the optimal decision region by utilizing the power value and early-late gate metric value of the sample point, so as to re-determine which region the sample point belongs to; and a large number of samples are generated for experiments, and the probability obtained by comparing the determined belonging area with the original area is counted, so that the larger the probability is, the better the performance is.

In the third step, in order to find δ (z) of the optimal decision criterion, each parameter set Λi, I e I and condition distribution w _i (θ), I e I;

(1) H ₀ is free from interference;

In the absence of interference, the parameter set is defined as:

Λ₀＝{θ∈Λ∣η＝0} (12)

The three marginal distributions of w ₁ (x) are: w _η0 (x) is a dirac delta function, w _τ0 (x) and w _θ0 (x) are arbitrarily defined;

(2) H ₁ multipath;

in multipath situations, the parameter set is defined as:

Λ₁＝{θ∈Λ∣0<η＜1,0＜Δτ＜T_c} (13)

the three marginal distributions of w ₂ (x) are: w _η1 (x) is logarithmic distribution with a mean value of-21 dB and a standard deviation of 5dB, w _Δτ1(x)＝μ^-1e^-x/μ, x is more than or equal to 0, wherein mu is related to satellite pitch angle, and w _θ1 (x) is uniformly distributed on [0,2 pi);

(3) H ₂ deception jamming

In case of spoofing interference, the parameter set is defined as:

Λ₂＝{θ∈Λ∣1≤η,0＜|Δτ|＜T_c} (14)

The three marginal distributions of w ₂ (x) are: w _η2 (x) is a logarithmic distribution with a mean of 1dB and a standard deviation of 1dB, w _Δτ2 (x) is an exponential distribution with a parameter μ=120, w _θ2 (x) is uniformly distributed over [0,2 pi);

(4) H ₃ suppression type interference

In case of interference at compacting, the parameter set is defined as:

Λ₃＝{θ∈Λ∣1≤η,|Δτ|≥T_c} (15)

the three marginal distributions of w ₃ (x) are: w _η3 (x) is a dirac delta function, w _τ3 (x) and w _θ3 (x) are arbitrarily defined.

In the fourth step, the specific cases are as follows:

(1) In the case of no interference or only one multipath signal or only one spoofing interference, i.e., P _Ai＝P_A,i＝0,...,M_s and η _i＝0,i＝1,...,M_s; at this time, the liquid crystal display device,

(2) In the case of a jammer, i.e., each of the M _s +1 received signals is modeled as having a power P _A, and each signal is affected by an incoherent interference signal having a power ηp _A, at this point,

(3) In the case of spoofing, i.e. spoofing not only for real signals, but also for multiple access signals, at this point,

The invention has the beneficial effects that the received power and early-late gate measurement are innovatively combined, and under the Bayesian framework of hypothesis test, the optimal decision area is obtained by utilizing Monte Carlo experiments through four classifications. The decided areas can be obtained by comparing the power value and early-late gate metric value of the received signal with the respective areas. And obtaining the detection reliability of various classifications through statistics of the judged areas. Compared with the prior art, the method can greatly improve the detection reliability of different interferences.

Drawings

FIG. 1 is a sample graph produced by the present invention.

FIG. 2 is a graph of the optimal decision region produced by the present invention.

Detailed Description

The invention will be further described with reference to the drawings and examples.

Embodiments of the invention are as follows:

Step one:

The present invention uses down-converted signals. In the case of no fraud, for the down-converted real GNSS signal, the signal power is set to P _A = -156dBW, and the code offset τ _A of the real signal is set to 0, the carrier phase θ _A is set to 0, and D (t) = 1, resulting in the complex baseband model S _A (t) as follows:

where t is time in seconds and C _A (t) is a pseudorandom spreading code having a value of + -1, then the interfering signal S _J (t) can be modeled as:

Where η is the power dominance of the interfering signal over the real signal, τ _J and θ _J are the code and carrier phases of the interfering signal, respectively, and the received noise is modeled as:

S_N(t)＝N(t)+M(t) (25)

The noise is the sum of thermal noise N (t) with constant spectral density thermal noise spectral density N ₀ = -204dBW/Hz and multiple access interference M (t) with variable spectral density M0. The complete received signal S (t) model is as follows:

S(t)＝S_A(t)+S_J(t)+S_N(t) (26)

Wherein S _A (t) is a true GNSS signal, S _J (t) is an interference signal, and S _N (t) is noise. The scaling factor β (t) of the automatic gain control circuit is applied to S (t) such that the power in the scaled signal β (t) S (t) remains constant.

Step two:

The local code l (t, τ) is modeled as follows:

Where τ is any code phase delay in seconds, C _l (t) is the local code, typically equal to C _A (t). And/>Is an estimated value of the code phase and carrier phase of the composite signal S (t), and is set in step one, therefore/>And/>Is a value close to 0.

And (3) correlating the beta (t) S (t) with the local code l (t, tau) to obtain two paths of data of I path I (tau) and Q path Q (tau), wherein the two paths of data are as follows:

Wherein Δτ _J is τ _J and Delta theta _J is theta _J and/>Is a difference in (c). /(I)And/>And respectively is I, Q paths of Gaussian white noise. /(I)Is a spreading code autocorrelation function, expressed as:

Where T _c is the single chip time period of the spreading code, set to 10A ^-6 s.

Step three: a bayesian multiple hypothesis testing framework is employed to distinguish hypotheses, where H _i, I e I, i= {0,1,2,3}. Null hypothesis H ₀ corresponds to the no interference case and H _i, i=1, 2,3 correspond to multipath, spoofing, and squelch interference, respectively.

The signal model reveals three parameters related to the choice between hypotheses, namely the interference power dominance η, and the interference versus true signal spreading code offset and carrier phase offset Δτ=τ _J-τ_A＝τ_J and Δθ=θ _J-θ_A＝θ_J. Combining three parameters into a single vector θ= [ η, Δτ, Δθ ] is assumed to lie in a parameter space Λ, which itself is divided into disjoint parameter setsI e I, and each parameter set is associated with its corresponding hypothesis H _i. Thus, determining θ∈Λi is equivalent to selecting hypothesis H _i.

In the Bayesian formulation of the composite hypothesis testing problem, the parameter vector θ is considered as a random number θ. Its probability density w (θ) sets a priori probabilities of pi ₀＝0.6,π₁＝0.2,π₂＝0.05,π₃ =0.15, respectively.

The observation received power P and the early-late gate metric m _ELP are combined into a vector z= [ m _ELP,P]^T, the observation set of the vector z is Γ, and the conditional probability density distribution is P (z|θ).

There is then a decision criterion δ (z) for dividing Γ into disjoint decision regions Γ _i such that when z e Γ _i corresponds to the H _i hypothesis, i.e. Γ _i corresponds to H _i.

Let C [ i, θ ] be the cost function when H _i is selected when θ∈Λ is the actual parameter vector, set to:

To find delta (z) of the optimal decision criteria, each parameter set Λi, I e I and the condition distribution w _i (θ), I e I is defined as equations (12), (13), (14), (15).

Step four: a received signal model for M _S = 7 is built as follows:

Wherein S _Ai (t) is the i-th real signal, its associated interference is S _Ji (t), and N (t) is noise.

The integration time at the power calculation is set to 0.1s, and the observed power value P (dBW) is:

Wherein t ₁ is the selected arbitrary time. Setting the conditional probability density mean square error sigma _P =0.4dB of P, wherein the conditional probability density function of P meets the average value as Variance is/>In which,/>And the bandwidth W _P of the power to be measured is set to 2MHz.

Wherein Δθ _i and Δτ _i correspond to the carrier phase offset and the code phase offset, respectively, between the ith interference and the corresponding real signal.

For multiple access interference M (T), its density is M ₀, expressed as:

For H ₀ and H ₁: H₂：/>H₃：/>

If the reference observation point τ _d is set to 0.5T _c, the early-late gate metric value m _ELP is:

wherein tan ^-1 represents the inverse tangent.

Step five: and obtaining a corresponding optimal decision area by using a Monte Carlo experiment.

Setting N _P to 100000 and N _M to 20, 200000 sample points were generated by Monte Carlo experiments. As shown in fig. 1, a range area 1"+" indicates a non-interfering signal sample point, a range area 3"O" indicates a multi-path signal sample point, a range area 4"×" indicates a spoofed interfering signal sample point, and a range area 1"Δ" indicates a suppressed interfering signal sample point.

The initial decision region is approximately acquired by the sample points of fig. 1. And optimizing the region boundary by using the following formula to obtain an optimal region.

Wherein, N _i, I ε I is obtained by prior probability and N _M.

The optimal decision area is obtained through simulation as shown in fig. 2, wherein the '①' area represents a non-interference decision area, the '②' area represents a multipath interference decision area, the '③' area represents a spoofing interference decision area, and the '④' area represents a suppression interference decision area.

The effect of the invention can be further illustrated by a simulated evaluation of the optimal region. The simulation results are shown in table 1:

Wherein table 1 is a classification matrix table generated using the optimal decision region of the present invention. The horizontal direction represents the region to which the real sample belongs, and the vertical direction represents the decided region. Consistent across and across indicates that the decision is correct, e.g., 89.34% of the probability that a point of spoofing is past the decision region is determined to be spoofing. The degree of reliability of detection of each kind of interference can be seen from the data shown in the figure.

Claims (3)

1. The anti-spoofing authentication method for the satellite navigation signal is characterized by comprising the following steps of:

step one: with the down-converted signals, under the condition of no related interference term, for the down-converted real GNSS signals S _A (t), the following complex baseband model is adopted:

Where P _A is the received power of the real signal in watts, D (t) is the navigation data with a value of ±1, t is the time in seconds, τ _A is the code offset in seconds, C _A (t) is the pseudorandom spreading code with a value of ±1, exp (j θ _A) is the carrier with a phase of θ _A, the navigation data D (t) can be ignored without loss of generality, let D (t) =1, and the interference signal S _J (t) is modeled as:

Where η=p _J/P_A is the power advantage of the interfering signal over the real signal, i.e. the ratio of the interfering power P _J to the real signal power P _A; τ _J and θ _J are the code offset and carrier phase of the interfering signal, respectively; the received noise S _N (t) is modeled as:

S_N(t)＝N(t)+M(t) (3)

The noise is the sum of thermal noise N (t) with constant spectral density N ₀ and multiple access interference M (t) with variable spectral density M ₀, and the complete received signal S (t) is modeled as follows:

S(t)＝S_A(t)+S_J(t)+S_N(t) (4)

Wherein S _A (t) is a true GNSS signal, S _J (t) is an interfering signal, S _N (t) is noise, and the scaling factor β (t) of the automatic gain control circuit is multiplied by S (t), so that the power of the scaled signal β (t) S (t) remains constant;

step two: the local code l (t, τ) is modeled as follows:

Where τ is any code phase delay in seconds, C _l (t) is the local code, equal to C _A (t); And/> Is an estimate of the code phase and carrier phase of the composite signal S (t);

And (3) correlating the beta (t) S (t) with the local code l (t, tau) to obtain two paths of data of I path I (tau) and Q path Q (tau), wherein the two paths of data are as follows:

Wherein Δτ _A is τ _A and And the difference of delta tau _J、Δθ_J and delta theta _A,/>, are obtained by the same methodAnd/>Two paths of Gaussian white noise are I, Q respectively; r (·) is a spreading code autocorrelation function, expressed as:

Where T _c is the spreading code single chip time period;

Step three: a bayesian multi-hypothesis testing framework is adopted to distinguish hypotheses, wherein each hypothesis type is H _i, I epsilon I, i= {0,1,2,3}, zero hypothesis H ₀ corresponds to a non-interference condition, and H _i, i=1, 2,3 respectively corresponds to multipath interference, deception interference and suppression interference;

The three relevant parameters, namely interference power dominance eta, interference and true signal spreading code offset delta tau = tau _J-τ_A and carrier phase offset delta theta = theta _J-θ_A, are selected, combined into a vector theta = [ eta, delta tau, delta theta ], and the vector theta is assumed to lie in a parameter space lambda which itself is divided into disjoint parameter sets I e I, and each parameter set is associated with its corresponding hypothesis H _i; thus, determining θ∈Λi is equivalent to selecting hypothesis H _i;

In the Bayesian formula of the composite hypothesis test problem, the vector θ is regarded as a random number, the probability density is w (θ), where pi _i is the prior probability that θ falls into Λ _i, and the conditional probability density for a given θ ε Λi, θ is expressed by w _i (θ):

There are two types of observations, namely, observed received power P and early-late gate metric m _ELP, which are associated with four hypotheses; combining the two observations into a vector z= [ m _ELP,P]^T, wherein the observation set of the vector z is Γ, and the conditional probability density distribution is p (z|theta);

The decision criterion δ (z) is used to divide Γ into disjoint decision regions Γ _i such that when z e Γ _i corresponds to the H _i hypothesis, i.e., Γ _i corresponds to H _i;

let C [ i, θ ] be the cost function when H _i is selected when θ∈Λ is the actual parameter vector, the cost function is closely related to the selection of θ, and the average cost of conditional risk is defined as:

Where E _θ represents the derivation of the expectation, the Bayesian risk r (δ) is defined as:

Finding the optimal decision criterion delta (z) minimizes the Bayesian risk r (delta), i.e. finding the optimal decision region Γ _i, I e I;

Step four: modeling the reception of M _S +1 real signals, each with an interference signal associated with it, the received signal S _C (t) is as follows:

Wherein S _Ai (t) is the i-th real signal, its associated interference is S _Ji (t), and N (t) is noise;

the observed power value P (dBW) is:

Wherein T is integration accumulated time, and T ₁ is time at any selected moment; the conditional probability density function of P meets the average value of Variance is/>In which,/>

Wherein Δθ _i and Δτ _i correspond to carrier phase offset and code phase offset between the ith interference and the corresponding real signal, respectively, P _Ai is the power value of the ith real signal, η _i is the ratio of the ith interference to the power of the ith real signal, W _P is the bandwidth of the power to be measured, N ₀ is the thermal noise spectral density, and σ _P is up to 0.5dB within the bandwidth of 2 MHZ;

for multiple access interference M (T), the density of multiple access interference is M ₀, expressed as:

wherein M _S is the number of real signals minus one, In relation to P _A, but in different cases with different values, where i=0 denotes the real signal and its interference, i=1,..m _s denotes the multiple access signal and its interference;

for the early-late gate metric value m _ELP:

Wherein τ _d is the observation point position set on the two paths of data of the I path I (τ) and the Q path Q (τ), and tan ^-1 represents the inverse tangent;

Combining the observed power value with the early-late gate metric value to obtain z= [ m _ELP,P]^T, wherein m _ELP and P are mutually independent;

Step five: acquiring a corresponding optimal decision area by utilizing a Monte Carlo experiment;

(1) For each I e I, the N _i parameter vector is modeled according to the w _i (θ) distribution, where N _i/N_p≈π_i, The first simulation vector extracted from w _i (θ) is denoted θ _li;

(2) For each θ _li, generate an N _M analog measurement; the mth simulation for a given θ _li measures z _mli, the total amount of samples generated by the simulation is N _PN_M;

(3) Dividing the two-dimensional observation space gamma into a large number of small rectangular units with uniform size; each cell belongs to a single judging area, so that all observation samples falling in the cells belonging to the gamma _i are equivalently allocated to the hypothesis H _i, I epsilon I, each cell is allocated to the hypothesis H _i with the maximum number of samples gamma in the cell, an initial partition of z _mli is created, the boundary is adjusted, each cell is guaranteed to belong to only one type, namely a certain type of sample point in the cell is the most, all the cells are set to belong to the type, and each judging area gamma _i is communicated singly;

(4) As long as the resulting decision area remains single connected, the new assignment remains unchanged as long as the bayesian risk r (δ) is reduced; repeatedly changing the area of the boundary area, changing the area into the currently set area if the Bayesian risk is reduced, and keeping the original area until no boundary unit needs to be reassigned, wherein the unit assignment forms a final judgment area gamma _i at the moment, I epsilon I if the Bayesian risk is not reduced;

the bayesian risk r (δ) at this time is expressed as:

wherein the cost function C [ i, θ ] is defined as follows:

Writing the cost function to C _ij,C_ij represents the cost of selecting H _i when H _j is true; when i=j, cost C _ij =0, otherwise, cost C _ij =1; however, in a practical scenario, not all misclassifications will have the same cost, and the cost is set as follows:

Modeling to generate sample points, performing small block division on the whole area, and visually obtaining an initial area by using the sample points; the assignment of the boundary region is replaced continuously, so that the Bayesian risk is minimum, and a final decision region, namely an optimal decision region, is obtained;

After the optimal region is obtained, the sample point can be regenerated, the region to which the sample point belongs is known, and the determination is carried out in the optimal decision region by utilizing the power value and early-late gate metric value of the sample point, so as to re-determine which region the sample point belongs to; and a large number of samples are generated for experiments, and the probability obtained by comparing the determined belonging area with the original area is counted, so that the larger the probability is, the better the performance is.

2. The satellite navigation signal anti-spoofing authentication method of claim 1, wherein:

In the third step, in order to find δ (z) of the optimal decision criterion, each parameter set Λi, I e I and condition distribution w _i (θ), I e I;

(1) H ₀ is free from interference;

In the absence of interference, the parameter set is defined as:

Λ₀＝{θ∈Λ∣η＝0} (12)

The three marginal distributions of w ₁ (x) are: w _η0 (x) is a dirac delta function, w _τ0 (x) and w _θ0 (x) are arbitrarily defined;

(2) H ₁ multipath;

in multipath situations, the parameter set is defined as:

Λ₁＝{θ∈Λ∣0<η＜1,0＜Δτ＜T_c} (13)

the three marginal distributions of w ₂ (x) are: w _η1 (x) is logarithmic distribution with a mean value of-21 dB and a standard deviation of 5dB, w _Δτ1(x)＝μ^-1e^-x/μ, x is more than or equal to 0, wherein mu is related to satellite pitch angle, and w _θ1 (x) is uniformly distributed on [0,2 pi);

(3) H ₂ deception jamming

In case of spoofing interference, the parameter set is defined as:

Λ₂＝{θ∈Λ∣1≤η,0＜|Δτ|＜T_c} (14)

The three marginal distributions of w ₂ (x) are: w _η2 (x) is a logarithmic distribution with a mean of 1dB and a standard deviation of 1dB, w _Δτ2 (x) is an exponential distribution with a parameter μ=120, w _θ2 (x) is uniformly distributed over [0,2 pi);

(4) H ₃ suppression type interference

In case of interference at compacting, the parameter set is defined as:

Λ₃＝{θ∈Λ∣1≤η,|Δτ|≥T_c} (15)

the three marginal distributions of w ₃ (x) are: w _η3 (x) is a dirac delta function, w _τ3 (x) and w _θ3 (x) are arbitrarily defined.

3. The satellite navigation signal anti-spoofing authentication method of claim 1, wherein:

in the fourth step, the specific cases are as follows:

(1) In the case of no interference or only one multipath signal or only one spoofing interference, i.e., P _Ai＝P_A,i＝0,...,M_s and η _i＝0,i＝1,...,M_s; at this time, the liquid crystal display device,

(2) In the case of a jammer, i.e., each of the M _s +1 received signals is modeled as having a power P _A, and each signal is affected by an incoherent interference signal having a power ηp _A, at this point,

(3) In the case of spoofing, i.e. spoofing not only for real signals, but also for multiple access signals, at this point,