CN114779642A - GNSS/INS tightly-combined deception detection method based on innovation robust estimation - Google Patents

GNSS/INS tightly-combined deception detection method based on innovation robust estimation Download PDF

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CN114779642A
CN114779642A CN202210458649.2A CN202210458649A CN114779642A CN 114779642 A CN114779642 A CN 114779642A CN 202210458649 A CN202210458649 A CN 202210458649A CN 114779642 A CN114779642 A CN 114779642A
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innovation
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柯晔
吕志伟
周玟龙
商向永
邓旭
周舒涵
张超
武文博
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Information Engineering University of PLA Strategic Support Force
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Abstract

The invention provides a GNSS/INS tight combination deception detection method based on innovation robust estimation, and belongs to the technical field of navigation system deception detection. When the existing cheating detection algorithm detects slowly-increasing slope type cheating interference, due to the fact that the cheating increasing speed is low, long-time accumulation is needed to reach a preset detection threshold value, and then the detection time is too long. When it is difficult to judge whether deception exists, the equivalent weight matrix is calculated according to the average normalized innovation vector and the upper and lower limit detection thresholds, then weight reduction processing is carried out through the equivalent weight matrix to obtain a new gain matrix, and the prior estimated state vector and the prior covariance estimated vector are optimized through the gain matrix, so that undetected deception interference is amplified at the moment of k +1, and the deception interference can reach the preset detection threshold through short time accumulation, thereby judging whether deception exists and shortening the deception detection time.

Description

GNSS/INS tightly-combined deception detection method based on innovation robust estimation
Technical Field
The invention relates to a GNSS/INS tight combination deception detection method based on innovation robust estimation, and belongs to the technical field of navigation system deception detection.
Background
In the prior art, an unmanned aerial vehicle generally adopts a combined navigation system of a global satellite navigation system and an inertial navigation system to perform navigation control. The combined Navigation System of a Global Navigation Satellite System (GNSS) and an Inertial Navigation System (INS) has the characteristics of complementary errors of the two, the GNSS can provide all-weather continuous Position, speed and Time (PVT) service in the Global range, the INS has the advantages of independent and continuous work, short-term anti-interference capability and the like, and the redundancy and reliability of the System are increased by combining the two. The GNSS/INS combined navigation can be divided into three combined modes of loose combination, tight combination and deep combination. And the tight combination is to combine the observed quantities such as pseudo range and pseudo range rate output by the GNSS receiver with the pseudo range and pseudo range rate obtained by the INS combined with ephemeris inverse calculation.
However, since the GNSS signal power is low and the structure is open, the GNSS service is susceptible to the deception jamming, and a third party may interfere with the motion of the drone by applying the deception jamming, at which time the flight trajectory of the drone deviates from the normal flight trajectory. However, when there is a deviation in the flight trajectory of the drone, it is difficult to determine whether it is caused by a problem in the drone itself or by a spoof disturbance applied by a third party. For this reason, real-time, fast, accurate spoof detection is necessary to ensure the reliability and integrity of the integrated navigation system.
Spoofing interference refers to the interference source producing a spoofed signal that is highly similar to the true signal or the forwarding of the true signal spoofing the target receiver forcing it to generate erroneous and potentially dangerous information. In the GNSS/INS integrated navigation system, a GNSS module locks deception signals and outputs wrong information, further influences the estimated value of state errors in a Kalman filtering measurement updating stage, outputs wrong navigation results, and simultaneously feeds back the wrong estimated value of the state errors to the INS through information fusion, finally influences the GNSS/INS integrated navigation system, so that the track of unmanned control equipment generates large deviation, and the safety of the equipment is possibly influenced.
The GNSS/INS tight combination deception detection method is mainly based on Kalman filtering innovation vectors as detection statistics, has the advantages of low cost, high efficiency, small calculated amount and the like, and is a hypothesis testing method with wide application. The method can be divided into a 'snapshot method' and a 'continuous method', wherein the snapshot method is used for forming test statistics by using an innovation vector at the current moment, is sensitive to step type deception interference, and cannot identify error measurement; the continuous method is to constitute the test statistic with the innovation vector in a period of time, and is sensitive to the slope deception jamming. However, these two methods have limitations, and when one of the channels is affected by the spoofing interference, the closed loop correction mechanism will affect the other channels to deviate from the normal new information value, so that the case of false alarm or miss alarm occurs. Therefore, the difficulty of deception jamming detection of the GNSS/INS integrated navigation system is the delay problem of the integrated navigation closed loop correction mechanism and the slowly increasing slope-type deception detection.
Aiming at the problem of a combined navigation closed loop correction mechanism, ZHANG Chuang and the like propose an improved detection algorithm based on robust estimation and a detection window, and the core idea is to select two appropriate threshold value calculation weight median factors, adaptively adjust a measured noise covariance matrix and reduce the weight of a deception interference measured value, so that a gain matrix is adaptively adjusted, when a single-path channel is subjected to slope interference of 0.5m/s, the improved algorithm shortens the detection time by 10s compared with the traditional algorithm, and the alarm leakage rate is reduced by 9%. The innovation rate robust estimation detection algorithm can effectively inhibit the influence of deception jamming on a state vector, improves the data utilization rate and the algorithm reliability, and maintains the slowly-increasing slope type deception jamming leakage rate and false alarm rate of a single-path channel at 0.1m/s within 4%. However, the two algorithms show that the detection time is too long and even the detection is not sensitive to slowly-increasing slope type deception jamming, particularly to deception jamming with the slope less than 0.1 m/s.
Aiming at the problem of slow-increasing slope type deception detection time delay, Bhatti and the like propose that the innovation rate is used for judging whether a GNSS measurement value is abnormal or not, and then Kalman filtering is adopted for estimating and normalizing the innovation rate in real time. Schui et al propose a spoofing signal detecting method of MEDLL, which can successfully detect and identify 2m/s of ramp spoofing, but the ramp slope is large, and it is difficult to apply to the slowly increasing 0.1m/s of ramp spoofing interference. In the last five years, some scholars research deception detection algorithms such as neural networks and support vector machines, but the algorithms are complex in calculation, weak in compatibility and high in cost.
In summary, when detecting slowly-increasing ramp-type deception jamming, the existing deception jamming detection algorithm has the defects of too long detection time, even insensitive detection, and high omission factor and false alarm rate, so that after the unmanned aerial vehicle flies for a long distance, whether deception jamming applied by a third party exists can be accurately judged, and the safety of the unmanned aerial vehicle in the flying process is seriously influenced.
Disclosure of Invention
The invention aims to provide a GNSS/INS tight combination deception detection method based on innovation robust estimation, which is used for solving the problem that the detection time is long when the existing deception jamming detection algorithm detects slowly-increasing slope type deception jamming.
In order to achieve the above object, the present invention provides a method for detecting tightly-combined GNSS/INS spoofing based on innovation robust estimation, which comprises the following steps:
s1, setting a detection window with the time length of L, and observing the GNSS/INS tight combination system in the detection window through an observation model to obtainAverage normalized innovation vector from k-L +1 to k time
Figure BDA0003619664690000031
And an innovation vector r at time kk(ii) a 1,2, wherein n is a visible satellite number;
s2, normalizing the innovation vector if averaged
Figure BDA0003619664690000032
Absolute value of the ith element in
Figure BDA0003619664690000033
Greater than a preset upper limit detection threshold Td2Then normalizing the innovation vector with the average
Figure BDA0003619664690000034
Spoofing exists in the GNSS measured value corresponding to the ith element; if it is
Figure BDA0003619664690000035
Less than a predetermined lower detection threshold Td1Then normalizing the innovation vector with the average
Figure BDA0003619664690000036
No spoofing exists on the GNSS measured value corresponding to the ith element; if it is
Figure BDA0003619664690000037
Greater than Td1And is less than Td2Then according to
Figure BDA0003619664690000038
Td1、Td2And the observed noise covariance matrix R of the observation modelkCalculating an equivalent weight matrix Wk；
S3, observation model H according to k timekA priori covariance estimation vector Pk -And an equivalent weight matrix WkCalculating a gain matrix
Figure BDA0003619664690000039
Gain matrix according to k time
Figure BDA00036196646900000310
Innovation vector rkAnd a priori estimate state vector
Figure BDA00036196646900000311
Calculating a posteriori estimated state vector at time k
Figure BDA00036196646900000312
Observation model H according to the k timekGain matrix
Figure BDA00036196646900000313
Sum prior covariance estimate vector Pk -Calculating the posterior estimated covariance vector P at time kk +；
S4, estimating the state vector according to the posterior of k time at k +1 time
Figure BDA00036196646900000314
Sum a posteriori estimation of covariance vector Pk +Respectively calculating prior estimation state vectors at k +1 moment
Figure BDA0003619664690000041
Sum prior covariance estimate vector
Figure BDA0003619664690000042
Estimating state vector a priori from time k +1
Figure BDA0003619664690000043
Sum prior covariance estimate vector
Figure BDA0003619664690000044
Combining the observation vector Z at the time k +1k+1Calculating the average normalized innovation vector from k-L to k +1, and further according to Td1And Td2Spoof detection at time k +1 is performed.
Existing spoof detection algorithmsWhen the slowly increasing slope type deception jamming is detected, because the deception increasing rate is low, the preset detection threshold value can be reached only after long-time accumulation, and then the deception jamming is detected, and the detection time is too long. The invention designs a detection window with the time length of L, observes a GNSS/ISN tight combination navigation system through an observation model in the detection window to obtain an average normalized innovation vector from k-L +1 to k and an innovation vector from k, and judges whether deception exists or not by combining preset upper and lower limit detection thresholds. And when the cheating is difficult to judge, calculating an equivalent weight matrix according to the average normalized innovation vector and the upper and lower limit detection thresholds. And performing weight reduction processing through the equivalent weight matrix to obtain a new gain matrix, and performing posterior estimation on the prior estimation state vector and the prior covariance estimation vector at the moment k through the gain matrix to obtain a posterior estimation state vector and a posterior covariance estimation vector. At the moment of k +1, calculating the prior state vector and the prior covariance estimation vector at the moment of k +1 through the posterior estimation state vector and the posterior covariance estimation vector at the moment of k, combining the observation vector at the moment of k +1 and the average normalized innovation vector from k-L to the moment of k +1, and further according to Td1And Td2And carrying out fraud detection at the moment k +1 until the fraud detection is finished. Aiming at the slowly increasing slope type deception, the invention carries out the weight reduction treatment through the equivalent weight matrix and amplifies the undetected deception interference, thereby leading the deception interference to reach the preset detection threshold value through the short time accumulation, judging whether the deception exists or not and shortening the deception detection time.
Further, in the above method, the gain matrix is calculated in step S2 by the following formula:
Figure BDA0003619664690000045
in the formula (I), the compound is shown in the specification,
Figure BDA0003619664690000046
denotes the gain matrix, HkRepresenting an observation model, Pk -Representing a priori covariance estimate vector, WkRepresenting an equivalent weight matrix.
The gain matrix is calculated according to the equivalent weight matrix by providing a specific set of formulas, which is convenient for the implementation of the invention.
Further, in the above method, the equivalence weight matrix W is calculated in step S2 by the following formulak：
Figure BDA0003619664690000051
Figure BDA0003619664690000052
In the formula (I), the compound is shown in the specification,
Figure BDA0003619664690000053
represents the equivalence weight matrix WkThe (i) th element of (a),
Figure BDA0003619664690000054
representing the observed noise covariance matrix RkThe ith element of (2), wiIs the intermediate variable(s) of the variable,
Figure BDA0003619664690000055
representing an average normalized innovation vector
Figure BDA0003619664690000056
The ith element of (1), Td1Indicating a preset lower detection threshold, Td2Representing a preset upper detection threshold.
A set of specific formulas is provided to calculate the intermediate variable according to the average normalized innovation vector and the upper and lower limit detection thresholds, and then the equivalent weight matrix is calculated according to the intermediate variable and the observation noise covariance matrix, which facilitates the implementation of the present invention.
Further, in the above method, the a posteriori estimated state vector is calculated by the following formula in step S2
Figure BDA0003619664690000057
Figure BDA0003619664690000058
In the formula (I), the compound is shown in the specification,
Figure BDA0003619664690000059
representing the a priori estimated state vector of the state,
Figure BDA00036196646900000510
representing a gain matrix, rkRepresenting an innovation vector.
And a group of specific formulas is provided to optimize the prior estimation state vector according to the gain matrix, so that the posterior estimation state vector is obtained for deception detection at the next moment, the real-time performance of the state vector is better, and the implementation is convenient.
Further, in the above method, the a priori estimated state vector at the time k +1 is calculated in step S3 by the following formula
Figure BDA00036196646900000511
Figure BDA00036196646900000512
In the formula (I), the compound is shown in the specification,
Figure BDA00036196646900000513
a state transition matrix is represented that represents the state transition,
Figure BDA00036196646900000514
representing the a posteriori estimated state vector at time k.
A group of specific formulas are provided for calculating the prior estimation state vector at the k +1 moment according to the posterior estimation state vector at the k moment, so that the implementation of the invention is facilitated.
Further, in the above method, the step S2 is calculated by the following formulaA posteriori estimated covariance vector Pk +：
Figure BDA0003619664690000061
In the formula, I represents a unit vector,
Figure BDA0003619664690000062
represents a gain matrix, HkRepresenting an observation model, Pk -The a priori covariance estimate vector is represented.
A group of specific formulas is provided to optimize the prior estimation covariance vector according to the gain matrix, so that the posterior estimation covariance vector is obtained for deception detection at the next moment, the real-time performance of the covariance vector is better, and the implementation is convenient.
Further, in the above method, the prior covariance estimation vector at the time k +1 is calculated in step S3 by the following formula
Figure BDA0003619664690000063
Figure BDA0003619664690000064
In the formula (I), the compound is shown in the specification,
Figure BDA0003619664690000065
representing a state transition matrix, Pk +Representing the a posteriori estimated covariance vector at time k, qkRepresenting the system noise covariance matrix.
A specific set of formulas is provided to calculate the a priori estimated covariance vector at time k +1 from the a posteriori estimated covariance vector at time k, facilitating the implementation of the present invention.
Further, in the above method, the innovation vector r is calculated in step S2 by the following formulakAnd its covariance matrix Vk：
Figure BDA0003619664690000066
Figure BDA0003619664690000067
In the formula, ZkRepresents an observation vector, HkA model of the observation is represented by,
Figure BDA0003619664690000068
a priori estimated state vector, P, representing time kk -A priori covariance estimate vector, R, representing time kkRepresenting the observed noise covariance matrix.
A group of formulas is provided for calculating the innovation vector and the covariance matrix thereof, the calculation is simple, and the implementation of the invention is convenient.
Drawings
FIG. 1 is a block diagram of a GNSS/INS tight combination spoofing detection method based on innovation robust estimation in an embodiment of the method of the present invention;
FIG. 2 is a schematic view of a simulated flight trajectory in an embodiment of the method of the present invention;
fig. 3(a) is a simulation result of a snapshot under jump spoofing in an embodiment of the method of the present invention;
FIG. 3(b) is a simulation result of a continuous method under step-wise spoofing in an embodiment of the method of the present invention;
fig. 4(a) is a simulation result of a slope-type deception snapshot method in an embodiment of the method of the present invention;
fig. 4(b) is a simulation result of the continuous method under the slope-type spoofing in the embodiment of the method of the present invention;
FIG. 5(a) is a simulation result of a continuous method under a slope type deception of 0.1m/s in the method embodiment of the present invention;
FIG. 5(b) is a simulation result of a continuous method based on innovation robust estimation under the slope-type deception of 0.1m/s in the method embodiment of the present invention;
FIG. 6(a) is a simulation result of a continuous method based on innovation robust estimation under a slope-type deception of 0.1m/s in the method embodiment of the present invention;
FIG. 6(b) is a simulation result of a GNSS/INS tight combined spoofing detection method based on innovation tolerance estimation under the sloping spoofing of 0.1m/s in the method embodiment of the present invention;
fig. 7 is a schematic diagram showing comparison of simulation results of a continuous method based on innovation robust estimation and a GNSS/INS tightly-combined spoofing detection method based on innovation robust estimation under the condition that a ramp type spoofing of 0.1m/s is applied to a channel 6 in the method embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments.
The method comprises the following steps:
the tight combination GNSS/INS deception detection method based on innovation tolerance estimation, disclosed by the invention, is shown in figure 1 and comprises the following steps:
1. the tight combination navigation system based on the GNSS/INS uses the GNSS pseudo range and pseudo range rate as input, and in closed loop correction, the estimated position, speed and attitude error is fed back to the INS processor by each filtering iteration, and the solution of the INS is corrected. The 17-dimensional state vector X of the Extended Kalman Filter (EKF) is expressed as:
Figure BDA0003619664690000071
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003619664690000072
δ v and δ r are attitude, velocity and position vectors of the INS estimation error, respectively, baAnd bgAccelerometer and gyro zero bias, respectively, of inertial sensors, bclkAnd
Figure BDA00036196646900000814
GNSS clock error and clock drift, respectively.
At time k, an observation vector Z is obtained that is the difference between the GNSS observation and the INS predictionk. Direction of observationQuantity ZkCan be expressed as:
Figure BDA0003619664690000081
in the formula (I), the compound is shown in the specification,
Figure BDA0003619664690000082
and
Figure BDA0003619664690000083
respectively representing GNSS observed pseudoranges and observed pseudorange rates,
Figure BDA0003619664690000084
and
Figure BDA0003619664690000085
respectively representing the INS predicted pseudorange and the predicted pseudorange rate, and n represents the number of visible satellites.
2. And in the real-time updating stage of the Kalman filter, the observation vector is updated in real time. The real-time update comprises a time update phase and a measurement update phase.
In the time updating stage, the prior estimation state vector at the k moment is obtained by carrying out prior estimation on the state vector and the covariance of the GNSS/INS tight combination system
Figure BDA0003619664690000086
Sum prior covariance estimate vector Pk -。
Figure BDA0003619664690000087
Figure BDA0003619664690000088
In the formula, symbol "Λ" represents an estimated value, superscript "-" represents a prior estimate, "+" represents a posterior estimate, and superscript "T" represents the transpose of the matrix.
Figure BDA0003619664690000089
Represents the a priori estimated state vector at time k,
Figure BDA00036196646900000810
representing the a posteriori estimated state vector at time k-1,
Figure BDA00036196646900000811
representing a state transition matrix; p isk -The prior error covariance matrix for the instant k is represented,
Figure BDA00036196646900000812
representing the covariance matrix of the posterior errors at time k-1, qk-1Representing the system noise covariance matrix. A priori estimated state vector
Figure BDA00036196646900000813
Sum prior covariance estimate vector Pk -The initial value of (2) is obtained from the 17-dimensional state vector X at the initial time, and in general, the initial velocity is 0, that is, the initial velocities in the north, east, and ground directions are all 0. In a simulation experiment, the numerical values of the position, the attitude, the accelerometer and the gyroscope are generally 0, and can be determined according to the actual situation of a field in other different scenes. The rest of the states are also determined according to the actual situation on site.
Then through the observation matrix HkA priori estimated state vector
Figure BDA0003619664690000091
A priori covariance estimation vector Pk -And the observed noise covariance matrix RkCalculating an innovation vector rkAnd its covariance matrix Vk。
Innovation vector rkAnd its covariance matrix VkCan be expressed as:
Figure BDA0003619664690000092
Figure BDA0003619664690000093
then, according to the innovation vector rkAnd its covariance matrix VkCalculating a normalized innovation vector omegai. Normalized innovation vector omegaiThe ith element in (b) is calculated by the following formula:
Figure BDA0003619664690000094
in the formula (I), the compound is shown in the specification,
Figure BDA0003619664690000095
the ith value of the innovation vector at the k moment (i is 1, …, n is the number of visible satellites),
Figure BDA0003619664690000096
at time k
Figure BDA0003619664690000097
Covariance of (c), ωiThe i-th innovation value after the normalization of the k time can reflect the i-th GNSS measurement value error.
3. Defining a detection window as L, and averaging normalized innovation vectors at all times in the detection window to obtain average normalized innovation from k-L +1 time to k time
Figure BDA0003619664690000098
The ith element in
Figure BDA0003619664690000099
Calculated by the following formula:
Figure BDA00036196646900000910
4. judging GNS according to the average normalized innovationS whether there is spoofing in the measurement. Setting Td2To check the threshold, Td1＝0.5Td2。
The detection criteria for spoofing interference are:
Figure BDA00036196646900000911
when the average normalized innovation satisfies
Figure BDA00036196646900000912
It is difficult to determine whether spoofing exists, and in this case, the gain matrix K is adjustedkUpdating, and then adopting the updated gain matrix to carry out deception detection.
5. In the measurement updating stage, weight reduction processing is carried out by using an IGG-3 equivalent weight function according to the average normalization information, and an equivalent weight matrix W is calculatedk. The equivalence weight matrix can be expressed as:
Figure BDA0003619664690000101
Figure BDA0003619664690000102
in the formula (I), the compound is shown in the specification,
Figure BDA0003619664690000103
represents the equivalence weight matrix WkThe (i) th element of (a),
Figure BDA0003619664690000104
representing the observed noise covariance matrix RkThe ith element of (1).
Calculation of w by IGG-3 equivalent weight functioniThe IGG-3 equivalence weight function is:
Figure BDA0003619664690000105
in the formula (I), the compound is shown in the specification,
Figure BDA0003619664690000106
for average normalized innovation, w, of corresponding ith GNSS measurementiFor the equivalence weight corresponding to the ith GNSS measurement, wiIs a non-zero value.
6. According to an equivalent weight matrix WkComputing a new gain matrix
Figure BDA0003619664690000107
Thereby realizing the gain matrix KkThe update of (2). The calculation formula is as follows:
Figure BDA0003619664690000108
according to a gain matrix
Figure BDA0003619664690000109
Innovation vector rkAnd updated gain matrix
Figure BDA00036196646900001010
Calculating a posteriori estimated state vector at time k
Figure BDA00036196646900001011
Figure BDA00036196646900001012
An a posteriori estimated covariance vector P at time k is also calculatedk +。
Figure BDA00036196646900001013
In the formula, I is a unit vector.
And then, finishing the cheating detection process at the moment k, returning to the step 1 at the moment k +1, and estimating the state vector according to the posteriori at the moment k
Figure BDA0003619664690000111
Sum a posteriori estimated covariance vector Pk +Respectively calculating prior estimation state vectors at k +1 moment
Figure BDA0003619664690000112
Sum prior covariance estimate vector
Figure BDA0003619664690000113
Combining the observation vector Z at the time k +1k+1And (4) carrying out deception detection, thereby amplifying undetected deception interference at the moment of k +1 and achieving the purposes of rapid detection and detection time reduction.
Calculating the prior estimation state vector at the k +1 moment by the following formula
Figure BDA0003619664690000114
Figure BDA0003619664690000115
In the formula (I), the compound is shown in the specification,
Figure BDA0003619664690000116
a state transition matrix is represented that represents the state transition,
Figure BDA0003619664690000117
representing the a posteriori estimated state vector at time k.
Calculating the prior covariance estimation vector at time k +1 by the following formula
Figure BDA0003619664690000118
Figure BDA0003619664690000119
In the formula (I), the compound is shown in the specification,
Figure BDA00036196646900001110
indicating a stateTransition matrix, Pk +Representing the a posteriori estimated covariance vector at time k, qkRepresenting the system noise covariance matrix.
In order to verify the beneficial effects of the invention, the snapshot method (M1), the continuous method (M2), the continuous method based on innovation robust estimation (M3) and the GNSS/INS tight combination spoofing detection method based on innovation robust estimation (M4) are compared.
Designing 3 GNSS/INS combined navigation deception detection experimental scenes, (1) comparing the detection effects of M1 and M2 when the 1-path channel is subjected to different degrees of step-type and slope-type pseudo range deviations; (2) when the 1-path channel is subjected to slope pseudo range deviation, comparing the detection effects of M2 and M3; (3) when the 1-path channel is subjected to the slope type pseudo range deviation, the detection effects of M3 and M4 are compared.
1. And setting parameters. The experimental parameter setting of the GNSS/INS tight combination comprises the following steps: simulated flight path data, deception scenes and parameters of three sensors of GNSS, IMU and Kalman. As shown in figure 2 and tables 1 and 2, respectively.
Table 1 spoofed scene setting
Figure BDA00036196646900001111
Figure BDA0003619664690000121
TABLE 2 simulation parameters
Figure BDA0003619664690000122
2. And (6) analyzing the result. (1) Scene 1: the detection capabilities of M1 and M2 were compared by varying degrees of stepwise or ramped pseudorange bias spoofing interference at channel 1.
Two sets of experiments were set up, with 50m, 20m and 10m step pseudorange bias values applied to channel 1 (i.e., visible satellite 1) of the first set of experiments, respectively, for spoofing durations of 350s to 550 s. Fig. 3(a) is a graph of the simulation result of M1, and fig. 3(b) is a graph of the simulation result of M2, as can be seen from fig. 3(a) and 3 (b): 1) fig. 3(a) shows that M1 can immediately detect the application of 50M and 20M of step spoofing to channel 1, both at 0s, and the detection of 10M of step spoofing is not valid; 2) fig. 3(b) shows that M2 detects the detection time of 10s, 10s and 10s when detecting the step spoofing of 50M, 20M and 10M applied to channel 1. Comparing fig. 3(a) and fig. 3(b), it can be seen that the detection time of M2 is prolonged by 10s on average compared with that of M1, but M2 can detect all spoofing situations, proving that the detection performance of M2 is better than that of M1.
Ramped pseudo-range bias values of 0.5m/s, 0.2m/s and 0.1m/s were applied to channel 1 (i.e., satellite 1) of the second set of experiments, respectively. Fig. 4(a) is a graph of the simulation result of M1, and fig. 4(b) is a graph of the simulation result of M2, as can be seen from fig. 4(a) and 4 (b): 1) fig. 4(a) shows that when M1 detects the application of the ramped spoofs of 0.5M/s and 0.2M/s to channel 1, the detection time is 44s and 135s, respectively, and the ramped spoof detection for 0.1M/s is invalid; 2) fig. 4(b) shows that M2 has detection times of 20s, 50s and 100s when detecting the application of ramp spoofing of 0.5M/s, 0.2M/s and 0.1M/s to channel 1. As can be seen by comparing fig. 4(a) and fig. 4(b), the detection time of M2 is respectively shortened by 24s, 85s and 100s compared with that of M1, and is shortened by 67s on average, so that M2 has better detection efficiency and detection performance when dealing with ramp-type spoofing.
The comparison results are combined to obtain: when the channel 1 is subjected to jump cheating, the detection time of M2 is prolonged by 10s compared with that of M1 on average, but the detection performance of M2 is better; when the channel 1 is subjected to slope cheating, the detection time of M2 is respectively shortened by 54.5%, 63% and 100% compared with that of M1, the average detection time is shortened by 72.5%, and the detection performance of M2 is better. Therefore, the detection efficiency and detection performance of M2 are better than those of M1.
(2) Scene 2: channel 1 is set to be subjected to spoofing interference of a slope pseudo range deviation value of 0.1M/s, and the detection capabilities of M2 and M3 are compared, so that the effect of robust estimation in restraining the normal channel from deviating from a normal value due to spoofing interference is verified.
Applying a ramp spoofing pseudorange bias of 0.1M/s to channel 1, wherein FIG. 5(a) is a graph of M1 simulation results, FIG. 5(b) is a graph of M2 simulation results, and FIG. 5(a) and FIG. 5(b) can be taken fromIt is seen that: 1) fig. 5(a) shows that M2 has a detection time of 100s when detecting channel 1 as spoofed, but channels 3, 4 and 5 are all affected by spoofing interference of different programs, causing their innovation to deviate from the normal value, where channel 4 even exceeds threshold Td2A false alarm condition occurs; 2) fig. 5(b) shows that M3 has a detection time of 100s when detecting channel 1 being spoofed, and the innovation values of the remaining channels are not deviated, which proves that the robust estimation effectively attenuates the influence of spoofing interference causing other channels. However, it can also be seen that the M3 method does not shorten the detection time.
To further illustrate the advantages of M3, table 3 shows a 100-cycle monte carlo simulation scenario under scenario 2. Here, "+" indicates a channel interfered by deception, and will not be described in detail later.
TABLE 3 Experimental 2 Monte Carlo simulation results
Figure BDA0003619664690000141
(3) Scene 3: aiming at the limitation of M3 on small slope type deception detection in scene 2, particularly the problem that the slope type deception detection time is long and is less than 0.1M/s, two groups of experiments are set in scene 3, and the detection capabilities of M3 and M4 are compared.
The first set of experiments: applying a ramped pseudorange bias value of 0.1M/s to channel 1, fig. 6(a) is a graph of the simulation results for M3, fig. 6(b) is a graph of the simulation results for M4, as can be seen in fig. 6(a) and 6 (b): 1) fig. 6(a) shows that M3 has a detection time of 100s when detecting channel 1 is deceived, and the remaining channels are normal; 2) fig. 6 shows that M4 has a detection time of 70s when detecting channel 1 spoofing, which is 30s shorter than M3.
The second set of experiments: a ramp pseudo range offset value of 0.1m/s is applied to channel 6, as can be seen in fig. 7: the detection time of M3 when the detection channel 6 is deceived is 110s, while the detection time of M4 when the detection channel 6 is deceived is 60s, and the detection time of M4 is shortened by 50s relative to that of M3. Two sets of experiments show that the detection algorithm of M4 is superior to M3 when processing slowly increasing ramp type deception detection.
To better illustrate that M4 outperforms M3, table 4 shows the monte carlo simulation case for 100 cycles under scenario 3.
TABLE 4 Experimental 3 Monte Carlo simulation results
Figure BDA0003619664690000142
As can be seen in conjunction with fig. 6(a), 6(b), 7 and table 4: 1) when the channel 1 is subjected to the ramp type cheating of 0.1M/s, the detection time of M4 is shortened by 30 percent compared with that of M3; when applying a ramp spoofing of 0.1m/s to the channel 6, the detection time is shortened by 45.5%. In conjunction with the spoof detection cases of channel 1 and channel 6, it can be seen that: the detection time of M4 is shortened by 37.8% on average compared with that of M3. 2) For the omission factor, both M3 and M4 were 0%. For channel 3, channel 4 and channel 5, the false alarm rates using M3 were 8%, 6% and 0, respectively; the false alarm rates of M4 are respectively 2%, 0 and 0, and the false alarm rates of M4 compared with M3 are respectively reduced by 6%, 6% and 0, and are reduced by 4% on average. It can be verified that M4 can shorten the detection time and improve the detection performance when dealing with slowly increasing ramped spoofing interference.
In conclusion, the invention optimizes the innovation detection amount by adjusting the pseudo-range parameters, and further improves the detection processing capability of the slow-growth deception jamming. Simulation results show that when slowly-increasing deception jamming is detected, the detection time is averagely shortened by 37.8%, the missed detection rate is maintained at 0, and the false alarm rate is averagely maintained within 0.7%. Compared with the traditional algorithm, the method has the advantages of fast detection and low false alarm rate when detecting the slowly-increasing slope type deception jamming, and has important significance in the application field of civil and military unmanned aerial vehicles.

Claims (8)

1. A tight combination GNSS/INS spoofing detection method based on innovation robust estimation is characterized by comprising the following steps:
s1, setting a detection window with the time length of L, observing the GNSS/INS tight combination system in the detection window through an observation model to obtain an average normalized innovation vector from k-L +1 to k
Figure FDA0003619664680000011
And an innovation vector r at time kk(ii) a 1,2, wherein n is a visible satellite number;
s2, normalizing the innovation vector if averaged
Figure FDA0003619664680000012
Absolute value of the ith element in
Figure FDA0003619664680000013
Greater than a preset upper limit detection threshold Td2Then normalizing the innovation vector with the average
Figure FDA0003619664680000014
Spoofing exists in the GNSS measured value corresponding to the ith element; if it is
Figure FDA0003619664680000015
Less than a predetermined lower detection threshold Td1Then normalizing the innovation vector with the average
Figure FDA0003619664680000016
There is no spoofing of GNSS measurements corresponding to the ith element; if it is
Figure FDA0003619664680000017
Greater than Td1And is less than Td2Then according to
Figure FDA0003619664680000018
Td1、Td2And the observed noise covariance matrix R of the observation modelkCalculating an equivalent weight matrix Wk；
S3, observing model H according to k timekPrior covariance estimate vector
Figure FDA0003619664680000019
And an equivalent weight matrix WkCalculating a gain matrix
Figure FDA00036196646800000110
Gain matrix according to k time
Figure FDA00036196646800000111
Innovation vector rkAnd a priori estimate state vector
Figure FDA00036196646800000112
Calculating a posteriori estimated state vector at time k
Figure FDA00036196646800000113
Observation model H according to the k timekGain matrix
Figure FDA00036196646800000114
Sum prior covariance estimate vector
Figure FDA00036196646800000115
Calculating a posteriori estimated covariance vector at time k
Figure FDA00036196646800000116
S4, estimating the state vector according to the posterior of k time at k +1 time
Figure FDA00036196646800000117
Sum a posteriori estimated covariance vector
Figure FDA00036196646800000118
Respectively calculating prior estimation state vectors at the k +1 moment
Figure FDA00036196646800000119
Sum prior covariance estimate vector
Figure FDA00036196646800000120
Estimating state vector a priori from time k +1
Figure FDA00036196646800000121
Sum prior covariance estimate vector
Figure FDA00036196646800000122
Combining the observation vector Z at the time k +1k+1Calculating the average normalized innovation vector from k-L to k +1, and further according to Td1And Td2Spoof detection at time k +1 is performed.
2. The method for detecting GNSS/INS tightly-combined spoofing based on innovation immunity difference estimation as claimed in claim 1, wherein the gain matrix is calculated in step S2 by the following formula:
Figure FDA0003619664680000021
in the formula (I), the compound is shown in the specification,
Figure FDA0003619664680000022
represents a gain matrix, HkA model of the observation is represented by,
Figure FDA0003619664680000023
representing a priori covariance estimate vector, WkRepresenting an equivalent weight matrix.
3. The method for detecting tightly-combined GNSS/INS spoofing based on innovation robust estimation as claimed in claim 2, wherein the equivalence weight matrix W is calculated in step S2 according to the following formulak：
Figure FDA0003619664680000024
Figure FDA0003619664680000025
In the formula (I), the compound is shown in the specification,
Figure FDA0003619664680000026
represents an equivalence weight matrix WkThe (i) th element of (2),
Figure FDA0003619664680000027
representing the observed noise covariance matrix RkThe ith element of (1), wiIs a function of the intermediate variable(s),
Figure FDA0003619664680000028
representing an average normalized innovation vector
Figure FDA0003619664680000029
The ith element of (1) M, Td1Indicating a preset lower detection threshold, Td2Representing a preset upper detection threshold.
4. The GNSS/INS tightly-combined spoofing detection method based on innovation immunity difference estimation as claimed in claim 1 or 2, wherein the a posteriori estimated state vector is calculated by the following formula in step S2
Figure FDA00036196646800000210
Figure FDA00036196646800000211
In the formula (I), the compound is shown in the specification,
Figure FDA00036196646800000212
representing the a priori estimated state vector of the state,
Figure FDA00036196646800000213
express increaseA benefit matrix rkRepresenting an innovation vector.
5. The GNSS/INS tightly-combined spoofing detection method based on innovation robust estimation as claimed in claim 4, wherein the prior estimation state vector at the time k +1 is calculated by the following formula in step S3
Figure FDA00036196646800000214
Figure FDA00036196646800000215
In the formula (I), the compound is shown in the specification,
Figure FDA00036196646800000216
a state transition matrix is represented that represents the state transition,
Figure FDA00036196646800000217
representing the a posteriori estimated state vector at time k.
6. The method for detecting tightly-combined GNSS/INS spoofing based on innovation robust estimation as claimed in claim 1 or 2, wherein the posterior estimation covariance vector is calculated by the following formula in step S2
Figure FDA0003619664680000031
Figure FDA0003619664680000032
In the formula, I represents a unit vector,
Figure FDA0003619664680000033
represents a gain matrix, HkA model of the observation is represented by,
Figure FDA0003619664680000034
representing the a priori covariance estimate vector.
7. The GNSS/INS tightly-combined spoofing detection method based on innovation robust estimation as claimed in claim 6, wherein the prior covariance estimation vector at time k +1 is calculated by the following formula in step S3
Figure FDA0003619664680000035
Figure FDA0003619664680000036
In the formula (I), the compound is shown in the specification,
Figure FDA0003619664680000037
a state transition matrix is represented that represents the state transition,
Figure FDA0003619664680000038
representing the a posteriori estimated covariance vector at time k, qkRepresenting the system noise covariance matrix.
8. The method for detecting tightly-combined GNSS/INS spoofing based on innovation immunity difference estimation as claimed in claim 1 or 2, wherein the innovation vector r is calculated by the following formula in step S2kAnd its covariance matrix Vk：
Figure FDA0003619664680000039
Figure FDA00036196646800000310
In the formula, ZkRepresents an observation vector, HkA model of the observation is represented by,
Figure FDA00036196646800000311
represents the a priori estimated state vector at time k,
Figure FDA00036196646800000312
a priori covariance estimate vector, R, representing time kkRepresenting the observed noise covariance matrix.
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Cited By (1)

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Publication number Priority date Publication date Assignee Title
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116931004A (en) * 2023-09-18 2023-10-24 南开大学 GNSS slowly-varying deception detection method based on weighted Kalman gain

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