CN112578410A - Evolution band-limited Gaussian noise interference algorithm for GPS based on LMS - Google Patents
Evolution band-limited Gaussian noise interference algorithm for GPS based on LMS Download PDFInfo
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Abstract
The invention relates to an evolutionary band-limited Gaussian noise interference algorithm for a GPS (global positioning system) based on LMS (least mean square), and an expression function x (nT) of an interference signal is determined; establishing an interference machine and a GPS receiver model; optimizing a flicker function r (nT) in the expression function x (nT) by adopting an evolutionary algorithm; the degree of influence of the interfering signal on the receiver is determined. The evolution band-limited Gaussian noise interference algorithm has more obvious interference effect than band-limited Gaussian noise interference when different interference amounts exist.
Description
Technical Field
The invention relates to the technical field of GPS signal interference, in particular to an evolutionary band-limited Gaussian noise interference algorithm for a GPS (Least mean square) based on LMS (Least mean square).
Background
A GPS receiver is an instrument that receives global positioning system satellite signals and determines the position of the ground space. The interference signal is a signal that impairs reception of a desired signal. Signal reception by an enemy GPS receiver may be opposed by signal interference.
Suppressive interference, electronic interference that obscures or completely masks the useful signal received by the hostile electronic device from proper operation. The traditional pressing type GPS jammer can not correctly decode a GPS receiver by transmitting an interference signal with higher power than a GPS signal. The zero setting GPS receiver uses an antenna array, and the self-adaptive algorithm is used for nulling the interference direction, so that the obvious anti-interference effect is achieved on the traditional suppression type interference mode.
Currently, most researchers are still working from the perspective of interfering with ordinary GPS receivers. In 58-62 pages of 58 th-62 th of book 15 of university of air force engineering (nature science edition), of mao hu et al in 2014, "gaussian noise interference parameter selection analysis with band limit for GPS military code signals", and in 257 th-267 pages of 4 th of book 24 of computer measurement and control, "wang jiao in 2016", a gaussian white noise interference optimum parameter selection strategy and a method for judging an optimum interference signal are respectively provided.
Prior to 2017, there were fewer interference studies with zeroed GPS. In a text of interference and anti-interference technology research on a satellite navigation receiver adopting an array antenna, Liyawei in 2017 provides a pulse interference method aiming at a zero GPS, relative time delay among a plurality of interferences is periodically adjusted, and a certain performance gain is obtained. However, no research result for improving the interference effect by the optimization algorithm is disclosed.
Disclosure of Invention
The invention aims to provide an evolutionary band-limited Gaussian noise interference algorithm for a GPS based on LMS, which can obviously improve the effect of signal interference.
The technical scheme for solving the technical problems is as follows:
an evolutionary band-limited gaussian noise interference algorithm for LMS-based GPS, comprising the steps of:
step 1: determining an expression function x (nT) of the interference signal;
step 2: establishing an interference machine and a GPS receiver model;
and step 3: optimizing a flicker function r (nT) in the expression function x (nT) by adopting an evolutionary algorithm;
and 4, step 4: the degree of influence of the interfering signal on the receiver is determined.
An evolutionary band-limited gaussian noise interference algorithm for LMS-based GPS, as described above, in step 1,
the complex field expression of the single interference signal x (nT) is shown as the following formula (1);
x(nT)＝r(nT)[f1(nT)cos(2πfcnT+β)+jf2(nT)sin(2πfcnT+β)] (1)
in the formula (1), fc1575.42MHz, representing the GPS L1 signal carrier frequency; β represents an initial phase; t1/fsRepresents a sampling period; f. ofsRepresents the sampling frequency; f. of1(nT)) and f2(nT) represents white gaussian noise after h (z) filtering; r (nt) represents a flicker function; n denotes a sample number, and j denotes an imaginary unit.
In the above algorithm for the LMS-based GPS based evolutionary band-limited gaussian noise interference, in step 2, the process of establishing the jammer and GPS receiver models includes the following steps:
step 201: determining the arrangement mode of the jammer and the GPS receiver;
step 202: determining an expression function r (nT) of an array element receiving signal of a GPS receiver;
step 203: obtaining the optimal value W of the weight vector W by adopting an LMS algorithmopt；
Step 204: calculating directional diagram
In the above-mentioned LMS-based GPS evolutionary band-limited gaussian noise interference algorithm, in step 203, the LMS algorithm is adopted to obtain the optimal value W of the weight vector WoptComprises the following steps:
step 2031: calculating weighted average signals y (K) of the signals of the other array elements except the reference array element;
step 2032: calculating an error signal e (k);
step 2033: the LMS algorithm obtains a weight vector W by utilizing a steepest descent method;
step 2034: obtaining optimal weight vector W by using LMS algorithmopt。
In the above evolutionary band-limited gaussian noise interference algorithm for the LMS-based GPS, in step 3, the flicker function r (nt) in the expression function x (nt) is optimized by the evolutionary algorithm, and is implemented by optimizing the sequence a (k); the procedure for optimizing the a (k) sequence is as follows:
step 301: firstly, initializing parameters of an optimization algorithm;
step 302: for each population member, calculating a variation function updating gene of the gene mutation;
step 303: calculating a variation function updating gene of the cross variation;
step 304: calculating each member evaluation value scores;
step 305: the maximum value of all the evaluation values scores is calculated.
The scheme adopted by the invention has the beneficial effects that:
the invention relates to an evolutionary band-limited Gaussian noise interference algorithm for a GPS (global positioning system) based on LMS (least mean square), and an expression function x (nT) of an interference signal is determined; establishing an interference machine and a GPS receiver model; optimizing a flicker function r (nT) in the expression function x (nT) by adopting an evolutionary algorithm; the degree of influence of the interfering signal on the receiver is determined.
The invention optimizes the band-limited Gaussian noise interference flicker function through the evolutionary algorithm, thereby disturbing the convergence of the self-adaptive algorithm based on LMS in the GPS receiver, leading the average zero depth of the GPS receiver under the equal power to be lower and realizing better interference effect.
The evolution band-limited Gaussian noise interference algorithm has more obvious interference effect than band-limited Gaussian noise interference when different interference amounts exist.
Drawings
Fig. 1 is a schematic diagram of the distribution of jammers interfering with a GPS receiver according to the present invention.
Fig. 2 is a model of a zeroed GPS receiver of the present invention.
Fig. 3 is a schematic diagram of a seven-element uniform circular array according to the present invention.
Detailed Description
The principles and features of this invention are described below in conjunction with the following drawings, which are set forth by way of illustration only and are not intended to limit the scope of the invention.
As shown in fig. 1-3, an evolutionary band-limited gaussian noise interference algorithm for LMS-based GPS includes the following steps:
step 1: determining an expression function x (nT) of the interference signal;
step 2: establishing an interference machine and a GPS receiver model;
and step 3: optimizing a flicker function r (nT) in the expression function x (nT) by adopting an evolutionary algorithm;
and 4, step 4: the degree of influence of the interfering signal on the receiver is determined.
In the step 1, the step of processing the raw material,
the complex field expression of the single interference signal x (nT) is shown as the following formula (1);
x(nT)＝r(nT)[f1(nT)cos(2πfcnT+β)+jf2(nT)sin(2πfcnT+β)] (1)
in the formula (1), fc1575.42MHz, representing the GPS L1 signal carrier frequency; β represents an initial phase; t1/fsRepresents a sampling period; f. ofsRepresents the sampling frequency; f. of1(nT) and f2(nT) represents white gaussian noise after h (z) filtering; r (nt) represents a flicker function; n represents the sample point number, j represents the imaginary unit (j is the same as the common imaginary unit i);
fi(nT) (i ═ 1, 2) represents white gaussian noise after h (z) filtering.
The Z domain expression of H (Z) is:
the expression of the flicker function r (nt) is the following formula (2):
in the formula (2), function
Note Fa(0) 0. k is 0, 1, 2.; n denotes a sample point number.
In the step 2, the process of establishing the jammer and the GPS receiver model includes the following steps:
step 201: determining the arrangement mode of the jammer and the GPS receiver;
step 202: determining an expression function R (nT) of an array element receiving signal of a GPS receiver;
step 203: obtaining the optimal value W of the weight vector W by adopting an LMS algorithmopt；
Step 204: calculating directional diagram
In the evolution band-limited Gaussian noise interference algorithm, the sequence a (k) is optimized through the evolution algorithm, and then the flicker function r (nT) is optimized, so that a GPS receiver obtains smaller null in the interference direction.
To optimize the a (k) sequence, jammer and GPS receiver models need to be built. A typical jammer and receiver layout is shown in figure 1. Jammers are arranged in different directions of the GPS receiver. Fig. 1 shows six jammers arranged at different azimuth angles. Suppose that the jammer has N totalJA GPS receiver receives NJAn interfering signal.
Suppose that the GPS receiver array element receives a signal R (nT) composed of NsIndividual GPS signal, NJAn interference signal and an additive white Gaussian noise N (nT).
The GPS antenna array selects more uniform circular arrays. Fig. 3 is a seven-array uniform circular array. Selecting the central array element as the reference array element, and assuming the reference array element to receive the signal x0(t) the expression is:
where A (t) is the signal amplitude,
is the initial phase of the signal.
The model structure of the zero-setting GPS receiver is shown in fig. 2, signals received by M antenna array elements obtain an optimal weight W through an LMS-based adaptive algorithm, and the signals obtained through weighting of the optimal weight W are demodulated through a GPS receiver to obtain GPS information. And calculating the directional diagram G through the optimal weight W. The directional null depth from the interference signal in the directional diagram is much larger than in the other directions. The influence degree of the interference signal on the receiver can be evaluated through the null depth of the directional diagram.
Assuming that M array elements except the array element at the center of circle in the uniform circular array of M array elements are respectively expressed as [ x ]1(t)，x2(t)，...，xM-1(t)]The propagation time delay between M-1 array elements and the reference array element is [ tau [ tau ] ]1，τ2，...，τM-1]. Considering that for the narrowband signal a (t- τ) ≈ a (t), the array element received signal may be denoted as X ═ Ax0(t) of (d). Wherein X ═ X0(t)，x1(t)，...，xM-1(t)]T，
A is called a steering vector. Where j is an imaginary unit and ω represents angular frequency.
For the seven-array-element uniform circular array, the radius of the array element is half wavelength, namely r is lambda/2, and the guide vector of the seven-array element can be obtained
The respective expressions are as follows (3):
in the formula (3), theta is a signal pitch angle,
for azimuth of the signal, e.g. diagram3, respectively. j denotes an imaginary unit.
The GPS receiver array element receiving signal R (nT) is expressed as the following formula (4):
in the formula (4), the reaction mixture is,
a steering vector representing the ith GPS signal, AjA steering vector, S, representing the jth interfering signali(nT) denotes the received signal of the i-th GPS signal at the reference array element, Jj(nT) represents the received signal of the jth interference signal in the reference array element, and N (nT) represents additive white Gaussian noise. Here, j is a number of the interference signal, and is different from j in the imaginary unit expressed by the above equations (1) and (3). Since the units of imaginary numbers are commonly denoted by the letter i or j, they are also commonly used in summing functions
The manner of representation of (c). Therefore, in the case where the conventional expression is used for both cases, j represents a different meaning. But the person skilled in the art should easily recognize the representation of the serial number j and the representation of the imaginary unit j.
In step 203, an LMS algorithm is used to obtain an optimal value W of the weight vector WoptComprises the following steps:
step 2031: calculating weighted average signals y (k) of the signals of the other array elements except the reference array element;
step 2032: calculating an error signal e (k);
step 2033: the LMS algorithm obtains a weight vector W by utilizing a steepest descent method;
step 2034: obtaining optimal weight vector W by using LMS algorithmopt。
The LMS algorithm minimizes the mean square error of the filtered output signal from the desired signal. In the null GPS, a reference array element output signal is used as an expected signal d (k), that is, d (k) x0(k) In that respect And weighted average y (k) of signals of the rest array elements except the reference array element is used as a filtering output signal.
y(k)＝WTX(k) (5)
In formula (5), x (k) ═ x1(k)，x2(k)，...，xM-1(k)]TThe weight vector W is ═ W1，w2，...，wM-1]T。
The error signal e (k) is calculated by the following equation (6).
e(k)＝d(k)-y(k) (6)
In equation (6), the desired signal d (k) is the reference array element output signal, and y (k) is the filtered output signal.
The LMS algorithm obtains a weight vector by using the steepest descent method according to the formula (7) below.
In equation (7), μ represents an iteration step.
Representing the gradient and E the mathematical expectation. k is 0, 1, 2.
The LMS algorithm obtains the optimal weight Wopt＝[W1 W2 ... WM-1]TThen, the array element weight can be represented by the following formula (8).
W＝[1，-W1，-W2，...，-WM-1]T (8)
In the formula (8), M represents the number of array elements, and the number of array elements is 7 in fig. 3.
Directional diagram
Are represented by the following formula (9).
In the formula (9), abs is a function for calculating an absolute value.
In the step 3, the flicker function R (nT) in the expression function x (nT) is optimized by adopting an evolutionary algorithm, and the optimization is realized by optimizing a (k) sequence; the procedure for optimizing the a (k) sequence is as follows:
step 301: firstly, initializing parameters of an optimization algorithm;
step 302: for each population member, calculating a variation function updating gene of the gene mutation;
step 303: calculating a variation function updating gene of the cross variation;
step 304: calculating each member evaluation value scores;
step 305: the maximum value of all the evaluation values scores is calculated.
The evolution band-limited Gaussian noise interference algorithm optimizes the sequence a (k) through the evolution algorithm, and further optimizes the flicker function, so that the GPS receiver obtains smaller nulls in the interference direction.
1. Initialization: selecting a GPS signal number NsNumber of interfering signals NJLength of signal L, number of elements M of GPS receiver, initial signal parameter signal carrier frequency fcAnd a sampling frequency fs. Initializing the pitch angle theta and azimuth angle of each GPS signal and interference signal
And the weight W is initialized, the population member number N and the gene length N of the evolutionary algorithm parameters are initializedgInterval of genetic variation [ L, E]Maximum number of iterations NloopCrossover rate α, number of evaluation cycles NtInitializing the Gene a of each population Memberi(j，n)(1≤i≤NJ，1≤j≤NJ，1≤n≤Ng) The best assessment max _ score and corresponding gene max _ a, etc. are initialized.
The following steps 2-5 require a cycle of NloopNext, the process is carried out.
2. For each member, calculating a mutation function Mutate (a (j, n)) updating gene of gene mutation;
the gene update program is as follows:
for i＝1：N
for j＝1：NJ
k1＝randi(1，Ng/2)*2-1
k2＝randi(1，Ng/2)*2
αi(j，k1)＝randi(L，E)
αi(j，k2)＝randi(L，E)
end
end
wherein randi (A, B) represents a random integer within the interval [ A, B ].
3. Calculating a variation function Cross (a (j, n), alpha) updating gene of the Cross variation;
the calculation procedure is as follows:
for k＝1：αN
i1＝randi(1，N)
i2＝randi(1，N)
i3＝randi(1，Ng/2)
swap(αi1(1：NJ，i3：i3+Ng/2-1)，αi2(1：NJ，i3：i3+Ng/2-1))
end
wherein swap (A, B) represents swaps A and B.
4. Calculating each member evaluation value scores ═ Score (a (j, n));
the calculation procedure is as follows:
for i＝1：N
for j＝1：Nt
calculating the received signal matrix R (nT) (see equation 4 above)
Taking R (nT) as a first action expected signal d (k), and taking the rest actions X (k)
Computing W by LMS Algorithmopt(calculated by the above equation 5, the above equation 6, the above equation 7)
Calculating directional diagram
(see equation 8 above, equation 9 above)
Calculating an interference direction average null
Wherein
(1≤j≤NJ) Are the interference signal pitch and azimuth angles.
end
score(i)＝mean(s)
end
5. The scores maximum is calculated and the correspondence a (j, n) is recorded.
The calculation procedure is as follows:
[max，I]＝max(scores)
if max_score＜max
max_α＝αI
end
wherein the Mutate function takes random values within the range of values for the random positions of a (k). The Cross function Cross swaps the members of the α N, swaps half of the data and swaps randomly. The Score function firstly calculates an interference signal, and then calculates an optimal weight W through an LMS algorithmoptThen return to the directional diagram
Depth of null in the direction of the interfering signal.
The performance difference between the band-limited Gaussian noise interference algorithm and the traditional band-limited Gaussian noise interference algorithm is compared and evolved through simulation experiments. Number of interference signals N in experimentjAnd respectively testing 1-6 samples, wherein the zero depth is the average value of 100 groups of sample data. The other parameters are: the array element number M is 7; the radius r of the antenna array is lambda/2; sampling rate fs3.2 GHz; the length of single sample data is 10000; the number Ns of GPS signals is 1; the pitch angle of the GPS signal is 70, and the azimuth angle is 10; the interference signal has a pitch angle of 70 and an azimuth angle of 7040, 70, 100, 150, 250, and 320; the S/N ratio is-30 dB; the dry-to-noise ratio J/N is 30 dB. The results of the experiment are shown in table 1.
TABLE 1 nulling depth contrast for bandlimited Gaussian noise interference Algorithm and Algorithm of the present invention
| Number of disturbances | Band limited gaussian noise | Evolutionary | Performance gain | |
| 1 | 48.85dB | 43.07dB | 5.78dB | |
| 2 | 48.66dB | 42.97dB | 5.69dB | |
| 3 | 50.11dB | 44.52dB | 5.59dB | |
| 4 | 47.60dB | 41.94dB | 5.66dB | |
| 5 | 41.59dB | 32.83dB | 8.76dB | |
| 6 | 29.81dB | 20.04dB | 9.77dB |
From table 1, it can be seen that the null depth of the conventional band-limited gaussian noise algorithm in the interference direction is kept stable when the interference amount is 1-4, and the null depth is obviously improved when the interference amount is 5-6. The depth of null of the evolutionary band-limited gaussian noise interference algorithm has similar conclusions at different interference quantities. Compared with the traditional band-limited Gaussian noise interference algorithm, the performance gain of the evolved band-limited Gaussian noise interference algorithm is about 5-9 dB, and the performance difference is increased along with the increase of the interference quantity.
The zero setting GPS based on the LMS algorithm provides an interference algorithm for optimizing a flicker function through an evolutionary algorithm, and the performance of the algorithm is analyzed through the depth of interference zero-trap. The algorithm better disturbs the convergence of LMS through an optimized flicker function, obtains better performance gain, and has performance obviously superior to that of a band-limited Gaussian noise interference algorithm.
The invention optimizes the band-limited Gaussian noise interference flicker function through the evolutionary algorithm, thereby disturbing the convergence of the self-adaptive algorithm based on LMS in the GPS receiver, leading the average zero depth of the GPS receiver under the equal power to be lower and realizing better interference effect. Simulation experiment results show that the interference algorithm has more obvious interference effect than band-limited Gaussian noise interference when the interference amount is different.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential attributes thereof. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.
Furthermore, it should be understood that although the present description refers to embodiments, not every embodiment may contain only a single embodiment, and such description is for clarity only, and those skilled in the art should integrate the description, and the embodiments may be combined as appropriate to form other embodiments understood by those skilled in the art.
Claims (5)
1. An evolutionary band-limited gaussian noise interference algorithm for LMS-based GPS, comprising the steps of:
step 1: determining an expression function x (nT) of the interference signal;
step 2: establishing an interference machine and a GPS receiver model;
and step 3: optimizing a flicker function r (nT) in the expression function x (nT) by adopting an evolutionary algorithm;
and 4, step 4: the degree of influence of the interfering signal on the receiver is determined.
2. An evolutionary band-limited gaussian noise interference algorithm for LMS-based GPS according to claim 1, characterized in that: in the step 1, the step of processing the raw material,
the complex field expression of the single interference signal x (nT) is shown as the following formula (1);
x(nT)＝r(nT)[f1(nT)cos(2πfcnT+β)+jf2(nT)sin(2πfcnT+β)] (1)
in the formula (1), fc＝1575.42MHz, representing the GPS L1 signal carrier frequency; β represents an initial phase; t1/fsRepresents a sampling period; f. ofsRepresents the sampling frequency; f. of1(nT)) and f2(nT) represents white gaussian noise after h (z) filtering; r (nt) represents a flicker function; n denotes a sample number, and j denotes an imaginary unit.
3. An evolutionary band-limited gaussian noise interference algorithm for LMS-based GPS according to claim 1, characterized in that: in the step 2, the process of establishing the jammer and the GPS receiver model includes the following steps:
step 201: determining the arrangement mode of the jammer and the GPS receiver;
step 202: determining an expression function r (nT) of an array element receiving signal of a GPS receiver;
step 203: obtaining the optimal value of the weight vector W by adopting an LMS algorithm
Step 204: calculating directional diagram
4. An evolutionary band-limited gaussian noise interference algorithm for LMS-based GPS according to claim 3, characterized in that: in step 203, an LMS algorithm is used to obtain an optimal value W of the weight vector WoptComprises the following steps:
step 2031: calculating weighted average signals y (k) of the signals of the other array elements except the reference array element;
step 2032: calculating an error signal e (k);
step 2033: the LMS algorithm obtains a weight vector W by utilizing a steepest descent method;
step 2034: obtaining optimal weight vector W by using LMS algorithmopt。
5. An evolutionary band-limited gaussian noise interference algorithm for LMS-based GPS according to claim 1, characterized in that: in the step 3, the flicker function r (nT) in the expression function x (nT) is optimized by adopting an evolutionary algorithm, and the optimization is realized by optimizing a (K) sequence; the procedure for optimizing the a (K) sequence is as follows:
step 301: firstly, initializing parameters of an optimization algorithm;
step 302: for each population member, calculating a variation function updating gene of the gene mutation;
step 303: calculating a variation function updating gene of the cross variation;
step 304: calculating each member evaluation value scores;
step 305: the maximum value of all the evaluation values scores is calculated.
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