CN115051682A - Design method of variational iterative radar signal filter - Google Patents

Design method of variational iterative radar signal filter Download PDF

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CN115051682A
CN115051682A CN202210638423.0A CN202210638423A CN115051682A CN 115051682 A CN115051682 A CN 115051682A CN 202210638423 A CN202210638423 A CN 202210638423A CN 115051682 A CN115051682 A CN 115051682A
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马季容
王帅为
杨姝君
郑建强
马清华
苗昊春
王根
段辰璐
邓海鹏
梁益铭
李端松
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Xian Institute of Modern Control Technology
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Abstract

The invention belongs to the technical field of filter subsystems, and particularly relates to a variation iterative radar signal filter design method, which aims at the problem that process noise and measurement noise are unknown when a Kalman filtering is applied to a practical fire control radar system for state estimation, re-derivation solving is carried out under a variation Bayes framework, model refinement processing is carried out on the process noise and the measurement noise by introducing a new variable, an approximate posterior distribution updating formula of each variable is obtained according to an average field theory and a coordinate raising method, and a filter suitable for practical radar system application is finally designed. The invention provides a design method of a radar signal filter, which carries out closed-loop iterative processing on state estimation and parameter identification and repeatedly corrects the state estimation and the parameter identification, thereby improving the target state estimation precision.

Description

Design method of variational iterative radar signal filter
Technical Field
The invention belongs to the technical field of filter subsystems, and particularly relates to a design method of a variational iterative radar signal filter.
Background
In order to find and attack targets in a battlefield in time, the fire control system aims at the targets through the radar, and target information is resolved to realize fire attack. Due to the presence of measurement noise in radar, target state estimation is usually implemented by using kalman filtering. Kalman filtering is an unbiased optimal filter under the condition that model parameters are known, not only radar noise statistical characteristics are required, but also a target motion model and system disturbance statistical characteristics are required, the parameters in an actual system are often unknown and cannot be directly applied, and the filtering performance is reduced and even diverged due to the fact that the parameters are given simply according to experience. The state space is one of the commonly used modeling methods of an actual dynamic system, random quantities such as system disturbance are modeled as process noise, and sensor measurement errors are modeled as measurement noise. The variational Bayes algorithm is an algorithm which is approximate to the difficulty in solving probability distribution in the field of machine learning, is widely applied in the field of adaptive filtering, and can realize the joint optimization of a target state and model parameters. By modeling the target motion model as a combination of uniform linear motion and unknown system disturbance, the filtering problem of the actual fire control system is that the process noise and the measurement noise are unknown at the same time, and the filtering problem is limited by the assumption of conjugate prior distribution, and other variational-based adaptive filtering methods either only consider the unknown condition of the process noise or the measurement noise or consider offline smoothing processing, and do not conform to the actual application scene.
Disclosure of Invention
Technical problem to be solved
The technical problem to be solved by the invention is as follows: aiming at the problem that model parameters are unknown during filtering of an actual fire control radar system, refined modeling is carried out on process noise and measurement noise, and a design method of a radar signal filter is provided based on the thought of variational iteration, so that the estimation precision is improved.
(II) technical scheme
In order to solve the technical problem, the invention provides a design method of a variational iterative radar signal filter, which comprises the following steps:
step 1, acquiring fire control radar data at moment k, including target distance R k Angle of pitch epsilon k Azimuth angle beta k And obtaining the target three-dimensional position measurement y through coordinate conversion k ：
Figure BDA0003681427700000021
Step 2, initialization: at the moment k, acquiring a target state predicted value x according to the dynamic model k|k-1 Target state covariance prediction value P k|k-1 Introduction of covariance of variables P m,k Free parameter prediction value u of process noise covariance q,k|k-1 Process noise covariance matrix prediction value U q,k|k-1 And measuring the noise covariance free parameter predicted value u r,k|k-1 And measuring the noise covariance matrix predicted value U r,k|k-1 The calculation formula is as follows:
x k|k-1 ＝F k x k-1|k-1
Figure BDA0003681427700000022
Figure BDA0003681427700000023
u q,k|k-1 ＝ρ(u q,k-1|k-1 -n x -1)+n x +1
U q,k|k-1 ＝ρU q,k-1|k-1
u r,k|k-1 ＝ρ(u r,k-1|k-1 -n y -1)+n y +1
U r,k|k-1 ＝ρU r,k-1|k-1
wherein: f k Predicting arrays for state at time k, x k-1|k-1 Is the target state estimate at time k-1, P k-1|k-1 Is the target state covariance estimate, u, at time k-1 q,k-1|k-1 For the estimation of the free parameter of the process noise covariance at the time k-1, U q,k-1|k-1 Is an estimate of the covariance matrix of the process noise at time k-1, u r,k-1|k-1 For measuring noise covariance free parameter estimation value, U, at time k-1 r,k-1|k-1 Measuring the noise covariance matrix estimation value at k-1 moment, rho is attenuation factor, n x Representing the dimension of the state, n y Representing measurement dimension, (.) T Representing transposing the matrix;
adding a right upper corner mark i to each variable to represent the ith iteration result, initially setting i to be 0, and enabling the estimation values of all the variables in the 0 th iteration to be equal to the predicted values;
and 3, carrying out iterative optimization on the state and other parameters under a variational Bayes framework: the iteration time i is i +1, the ith iteration is as follows:
step 3a, updating according to a derivation formula to obtain a free parameter estimation value of the measured noise covariance
Figure BDA0003681427700000031
Sum-measure noise covariance matrix estimate
Figure BDA0003681427700000032
The formula is as follows:
Figure BDA0003681427700000033
Figure BDA0003681427700000034
wherein, y k For the measurement matrix at the time k, the time k is,
Figure BDA0003681427700000035
for the i-1 th iteration state estimate at time k,
Figure BDA0003681427700000036
for the i-1 th iteration state covariance estimate at time k, H k A k time measurement model;
step 3b, updating according to a derivation formula to obtain a process noise covariance free parameter estimation value
Figure BDA0003681427700000037
Sum-measure noise covariance matrix estimate
Figure BDA0003681427700000038
The formula is as follows:
Figure BDA0003681427700000039
Figure BDA00036814277000000310
wherein the content of the first and second substances,
Figure BDA00036814277000000311
introducing a variable estimated value for the i-1 st iteration at the k moment,
Figure BDA00036814277000000312
introducing variable covariance for the i-1 st iteration at the moment k;
step (ii) of3c, updating according to a derivation formula to obtain a target state estimation value
Figure BDA00036814277000000313
Covariance estimation of target state
Figure BDA00036814277000000314
The formula is as follows:
Figure BDA00036814277000000315
Figure BDA00036814277000000316
Figure BDA00036814277000000317
Figure BDA00036814277000000318
wherein A is k Is a first intermediate variable, B k Is a second intermediate variable, K x,k Updating Kalman Filter gain for the time k state, (. cndot.) -1 Representing an inversion matrix;
step 3d, updating according to a derivation formula to obtain an introduced variable state estimation value
Figure BDA00036814277000000319
And introducing a variable covariance estimate
Figure BDA00036814277000000320
The formula is as follows:
K m,k ＝A k (A k +P m,k ) -1
Figure BDA0003681427700000041
Figure BDA0003681427700000042
wherein, K m,k Introducing a variable update Kalman filtering gain for the moment k;
step 3e, iteration ending judgment: the difference between the state estimation values of the current iteration and the later iteration is smaller than a set threshold value delta x Or when the iteration times reach the preset maximum iteration times, outputting an estimation result, and otherwise, returning to the step 3;
and 4, step 4: recursion circulation: and (3) using the final target state estimation value at the moment k for missile control command resolving, enabling the time k to be k +1 and the iteration number i to be 0, and returning to the step 1 again.
Wherein the threshold value delta x ＝10 -4 。
Wherein the maximum number of iterations is 20.
(III) advantageous effects
Aiming at the problem of radar signal filtering in a fire control system, the invention carries out refined modeling on process noise and measurement noise and provides a variation iterative radar signal filter design method.
The method comprises the steps of modeling a target motion model into a combination of uniform linear motion and unknown system disturbance, designing a radar signal filter of an actual system, namely designing the filter under the condition that process noise and measurement noise are unknown, assuming that process noise covariance and measurement noise covariance both obey inverse Wishart distribution, introducing a new variable, and obtaining a target state, an introduced variable, a process noise covariance and a measurement noise covariance calculation method according to an average field theory and a coordinate rising method, thereby designing a variational iterative radar signal filter.
The classical Kalman filtering usually assumes that process noise and measurement noise are known, and the method provided by the invention considers the condition that model parameters in an actual fire control radar system are unknown, and provides a radar signal filter design method for state and parameter joint optimization based on the thought of variational iteration, so that the estimation precision is improved.
Drawings
FIG. 1 is a flow chart of a method for designing a radar signal filter with variational iteration.
FIG. 2 is a comparison graph of the 1000 Monte Carlo simulated target locations RMSE.
FIG. 3 is a comparison graph of 1000 Monte Carlo simulated target speeds RMSE.
Detailed Description
In order to make the objects, contents, and advantages of the present invention clearer, the following detailed description of the embodiments of the present invention will be made in conjunction with the accompanying drawings and examples.
In order to solve the above technical problem, the present invention provides a method for designing a radar signal filter with variational iteration, as shown in fig. 1, the method includes the following steps:
step 1, acquiring fire control radar data at moment k, including target distance R k Angle of pitch epsilon k Azimuthal angle beta k And obtaining the target three-dimensional position measurement y through coordinate conversion k ：
Figure BDA0003681427700000051
Step 2, initialization: at the moment k, a target state predicted value x is obtained according to the dynamic model k|k-1 Target state covariance prediction value P k|k-1 Introduction of covariance of variables P m,k Free parameter prediction value u of process noise covariance q,k|k-1 Prediction value U of process noise covariance scale matrix q,k|k-1 And measuring the noise covariance free parameter predicted value u r,k|k-1 And measuring the noise covariance matrix predicted value U r,k|k-1 The calculation formula is as follows:
x k|k-1 ＝F k x k-1|k-1
Figure BDA0003681427700000052
Figure BDA0003681427700000053
u q,k|k-1 ＝ρ(u q,k-1|k-1 -n x -1)+n x +1
U q,k|k-1 ＝ρU q,k-1|k-1
u r,k|k-1 ＝ρ(u r,k-1|k-1 -n y -1)+n y +1
U r,k|k-1 ＝ρU r,k-1|k-1
wherein: f k Predicting arrays for state at time k, x k-1|k-1 Is the target state estimate at time k-1, P k-1|k-1 Is an estimate of the covariance of the target state at time k-1, u q,k-1|k-1 Estimate of the free parameter of the process noise covariance for time k-1, U q,k-1|k-1 Is an estimate of the covariance matrix of the process noise at time k-1, u r,k-1|k-1 For measuring noise covariance free parameter estimation value, U, at time k-1 r,k-1|k-1 Measuring the noise covariance matrix estimation value at k-1 moment, rho is attenuation factor, n x Representing the dimension of the state, n y Representing measurement dimension, (.) T Representing transposing the matrix;
adding a right upper corner mark i to each variable to represent the ith iteration result, initially setting i to be 0, and enabling the estimation values of all the variables in the 0 th iteration to be equal to the predicted values;
and 3, carrying out iterative optimization on the state and other parameters under a variational Bayes framework: the iteration time i is i +1, the ith iteration is as follows:
step 3a, updating according to a derivation formula to obtain a free parameter estimation value of the measured noise covariance
Figure BDA0003681427700000061
Sum-measure noise covariance matrix estimate
Figure BDA0003681427700000062
The formula is as follows:
Figure BDA0003681427700000063
Figure BDA0003681427700000064
wherein, y k For the measurement matrix at the time k, the time k is,
Figure BDA0003681427700000065
for the i-1 th iteration state estimate at time k,
Figure BDA0003681427700000066
for the i-1 th iteration state covariance estimate at time k, H k A k time measurement model;
step 3b, updating according to a derivation formula to obtain a process noise covariance free parameter estimation value
Figure BDA0003681427700000067
Sum-measure noise covariance matrix estimate
Figure BDA0003681427700000068
The formula is as follows:
Figure BDA0003681427700000069
Figure BDA00036814277000000610
wherein the content of the first and second substances,
Figure BDA00036814277000000611
introducing a variable estimation value for the i-1 st iteration at the k moment,
Figure BDA00036814277000000612
introducing variable covariance for the i-1 st iteration at the moment k;
step (ii) of3c, updating according to a derivation formula to obtain a target state estimation value
Figure BDA00036814277000000613
Covariance estimation of target state
Figure BDA00036814277000000614
The formula is as follows:
Figure BDA00036814277000000615
Figure BDA00036814277000000616
Figure BDA00036814277000000617
Figure BDA00036814277000000618
wherein A is k Is a first intermediate variable, B k Is a second intermediate variable, K x,k Updating Kalman filter gain for time k state (·) -1 Representing an inversion matrix;
step 3d, updating according to a derivation formula to obtain an introduced variable state estimation value
Figure BDA0003681427700000071
And introducing a variable covariance estimate
Figure BDA0003681427700000072
The formula is as follows:
K m,k ＝A k (A k +P m,k ) -1
Figure BDA0003681427700000073
Figure BDA0003681427700000074
wherein, K m,k Introducing a variable update Kalman filtering gain for the moment k;
step 3e, iteration ending judgment: the difference between the state estimation values of the current iteration and the later iteration is smaller than a set threshold value delta x Or when the iteration times reach the preset maximum iteration times, outputting an estimation result, and otherwise, returning to the step 3;
and 4, step 4: recursion circulation: and (3) using the final target state estimation value at the moment k for missile control command resolving, enabling the time k to be k +1 and the iteration number i to be 0, and returning to the step 1 again.
Wherein the threshold value delta x ＝10 -4 。
Wherein the maximum number of iterations is 20.
Example 1
In this embodiment, as shown in fig. 1, a flowchart of a method for designing a radar signal filter based on variational iteration according to the present invention is shown, and details of implementation of each part are as follows:
1. description of the problem
Consider a linear markov system as follows,
x k ＝F k x k-1 +w k
y k ＝H k x k +v k
wherein x is k Representing the target state vector at time k, y k Indicating sensor measurements, F k And H k Is a known state transition matrix and measurement equation. Process noise w k And the measurement noise v k Is zero mean, covariance Q k And R k Unknown slowly varying white gaussian noise.
When solving under a Bayesian framework, the objective of the above problem is to solve a joint posterior distribution p (x) k ,Q k ,R k |y 1:k-1 ) The method can be carried out by the following two steps,
a prediction step:
p(x k ,Q k ,R k |y 1:k-1 )＝p(x k |y 1:k-1 ,Q k ,R k )p(Q k |y 1:k-1 )p(R k |y 1:k-1 ).
and (3) updating:
p(x k ,Q k ,R k |y 1:k )∝p(y k |x k ,Q k ,R k )p(x k ,Q k ,R k |y 1:k-1 ).
as can be seen from the framework of kalman filtering,
Figure BDA0003681427700000081
Figure BDA0003681427700000082
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003681427700000083
which represents a gaussian distribution of the intensity of the light,
x k|k-1 ＝F k x k-1|k-1
Figure BDA0003681427700000084
for Q k And R k In order to obtain an analytical solution that is easy to solve, it is desirable that the posterior distribution has the same form as the prior distribution, so that conjugate prior modeling needs to be performed on two variables. From the above equation, it can be seen that the likelihood functions of both obey the Gaussian distribution, except that R k Is the covariance part of the Gaussian distribution, Q k Is only one component of the gaussian covariance. Since the inverse Wishart distribution is a conjugate prior distribution of multidimensional gaussian distribution with covariance as parameter, consider by introducing a new variable m k ，
Figure BDA0003681427700000085
Wherein the content of the first and second substances,
Figure BDA0003681427700000086
therefore, consider a priori modeling with an inverse Wishart distribution as follows,
p(Q k |y 1:k-1 )＝IW(Q k |u q,k|k-1 ,U q,k|k-1 )
p(R k |y 1:k-1 )＝IW(R k |u r,k|k-1 ,U r,k|k-1 )
wherein IW (-) represents the inverse Wishart distribution, and has two parameters of a free parameter and a scale matrix, and the dynamic model thereof adopts a common heuristic dynamic system, which is not detailed here. Meanwhile, the process noise and the measurement noise covariance at the initial moment are also considered to be subjected to inverse Wishart distribution and are called nominal noise.
2. Variational Bayes solution
Due to the introduction of a new variable m k Solving the state estimation problem under the conditions of unknown process and unknown measurement noise under the variational Bayes framework is to calculate the combined posterior probability distribution p (x) k ,m k ,Q k ,R k |y 1:k ) Based on the mean field theory, approximating this distribution with a distribution q is as follows,
p(x k ,m k ,Q k ,R k |y 1:k )≈q(x k ,m k ,Q k ,R k )≈q(x k )q(m k )q(Q k )q(R k )
the KL divergence may be used to measure the similarity of two distributions,
Figure BDA0003681427700000091
as can be seen from the above derivation, minimizing KL divergence can be translatedTo maximize the lower bound of confidence
Figure BDA0003681427700000092
The updating formula of the approximate posterior probability of each variable can be deduced by a coordinate ascending method as follows,
Figure BDA0003681427700000093
Figure BDA0003681427700000094
Figure BDA0003681427700000095
Figure BDA0003681427700000096
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003681427700000097
the expected value represented by the q distribution, and oc represents a proportional relationship.
2.1 State estimation results
According to the above formula, there are
Figure BDA0003681427700000101
Order to
Figure BDA0003681427700000102
As may be derived from the kalman filter derivation process,
Figure BDA0003681427700000103
Figure BDA0003681427700000104
P k|k ＝A k -K x,k H k A k
wherein, K x,k Representing the filter gain.
2.2 introducing variable estimation results
According to the above formula, there are
Figure BDA0003681427700000105
Similar to the state estimation, the update formula can be derived as,
K m,k ＝A k (A k +P m,k ) -1
m k|k ＝x k|k-1 +K m,k (x k|k -x k|k-1 )
P m,k|k ＝P m,k -K m,k P m,k
wherein, K m,k Is the filter gain.
2.3 Process noise covariance identification
According to the above formula, there are
Figure BDA0003681427700000111
Wherein the content of the first and second substances,
Figure BDA0003681427700000112
it can be seen that Q k The posterior probability of (c) is still subject to the inverse Wishart distribution IW (Q) k |u q,k|k ,U q,k|k ) The parameters are as follows,
u q,k|k ＝u q,k|k-1 +1
U q,k|k ＝U q,k|k-1 +C k
2.4 measurement of noise covariance identification results
According to the above formula, there are
Figure BDA0003681427700000113
Wherein the content of the first and second substances,
Figure BDA0003681427700000121
and Q k Similarly, the posterior probability still obeys the inverse Wishart distribution IW (R) k |u r,k|k ,U r,k|k ) The parameters are as follows,
u r,k|k ＝u r,k|k-1 +1
U r,k|k ＝U r,k|k-1 +D k
4. iterative end determination
And if the iteration estimation results of the target state before and after twice are smaller than a preset threshold value, or the current iteration times reach the preset maximum iteration times, exiting the iteration.
Figure BDA0003681427700000122
Or i is not less than i max
Wherein, delta x ∈[0,1]Iteration termination threshold for target state, i max Is a preset maximum number of iterations.
Example 2
This embodiment describes a design method of a variational iterative radar signal filter, which performs conjugate prior modeling on process noise and measurement noise covariance by introducing a new variable. The method decomposes the approximate posterior probability of each variable based on the average field hypothesis under the framework of variational Bayes, deduces the update formula of the posterior probability of each variable according to a coordinate ascending method, and iteratively solves each variable under a closed-loop framework.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.

Claims (10)

1. A design method of a variational iterative radar signal filter is characterized by comprising the following steps:
step 1, acquiring fire control radar data at moment k, including target distance R k Angle of pitch epsilon k Azimuthal angle beta k And obtaining the target three-dimensional position measurement y through coordinate conversion k ：
Figure FDA0003681427690000011
Step 2, initialization: at the moment k, a target state predicted value x is obtained according to the dynamic model k|k-1 Target state covariance prediction value P k|k-1 Introduction of covariance of variables P m,k Free parameter prediction value u of process noise covariance q,k|k-1 Process noise covariance matrix prediction value U q,k|k-1 And measuring the noise covariance free parameter predicted value u r,k|k-1 And measuring the noise covariance matrix predicted value U r,k|k-1 The calculation formula is as follows:
x k|k-1 ＝F k x k-1|k-1
Figure FDA0003681427690000012
Figure FDA0003681427690000013
u q,k|k-1 ＝ρ(u q,k-1|k-1 -n x -1)+n x +1
U q,k|k-1 ＝ρU q,k-1|k-1
u r,k|k-1 ＝ρ(u r,k-1|k-1 -n y -1)+n y +1
U r,k|k-1 ＝ρU r,k-1|k-1
wherein: f k Predicting arrays for state at time k, x k-1|k-1 Is an estimate of the target state at time k-1, P k-1|k-1 Is an estimate of the covariance of the target state at time k-1, u q,k-1|k-1 For the estimation of the free parameter of the process noise covariance at the time k-1, U q,k-1|k-1 Estimate of the covariance matrix of the process noise at time k-1, u r,k-1|k-1 For measuring noise covariance free parameter estimation value, U, at time k-1 r,k-1|k-1 Measuring noise covariance matrix estimation value at k-1 moment, rho is attenuation factor, n x Representing the dimension of the state, n y Representing measurement dimension, (.) T Representing transposing the matrix;
adding a right upper corner mark i to each variable to represent the ith iteration result, initially setting i to be 0, and enabling the estimation values of all the variables in the 0 th iteration to be equal to the predicted values;
and 3, carrying out iterative optimization on the state and other parameters under a variational Bayes framework: the iteration time i is i +1, the ith iteration is as follows:
step 3a, updating according to a derivation formula to obtain a free parameter estimation value of the measured noise covariance
Figure FDA0003681427690000021
Sum-measure noise covariance matrix estimate
Figure FDA0003681427690000022
The formula is as follows:
Figure FDA0003681427690000023
Figure FDA0003681427690000024
wherein, y k For the measurement matrix at the time k, the time k is,
Figure FDA0003681427690000025
for the i-1 th iteration state estimate at time k,
Figure FDA0003681427690000026
for the i-1 th iteration state covariance estimate at time k, H k A k time measurement model;
step 3b, updating according to a derivation formula to obtain a process noise covariance free parameter estimation value
Figure FDA0003681427690000027
Sum-measure noise covariance matrix estimate
Figure FDA0003681427690000028
The formula is as follows:
Figure FDA0003681427690000029
Figure FDA00036814276900000210
wherein the content of the first and second substances,
Figure FDA00036814276900000211
introducing a variable estimation value for the i-1 st iteration at the k moment,
Figure FDA00036814276900000212
introducing variable covariance for the i-1 st iteration at the moment k;
step 3c, updating according to a derivation formula to obtain a target state estimation value
Figure FDA00036814276900000213
Covariance estimation of target state
Figure FDA00036814276900000214
The formula is as follows:
Figure FDA00036814276900000215
Figure FDA00036814276900000216
Figure FDA00036814276900000217
Figure FDA00036814276900000218
wherein A is k Is a first intermediate variable, B k Is a second intermediate variable, K x,k Updating Kalman filter gain for time k state (·) -1 Representing an inversion matrix;
step 3d, updating according to a derivation formula to obtain an introduced variable state estimation value
Figure FDA00036814276900000219
And introducing a variable covariance estimate
Figure FDA00036814276900000220
The formula is as follows:
K m,k ＝A k (A k +P m,k ) -1
Figure FDA0003681427690000031
Figure FDA0003681427690000032
wherein, K m,k Introducing a variable update Kalman filtering gain for the moment k;
step 3e, iteration ending judgment: the difference between the state estimation values of the current iteration and the later iteration is smaller than a set threshold value delta x Or when the iteration times reach the preset maximum iteration times, outputting an estimation result, and otherwise, returning to the step 3;
and 4, step 4: recursion circulation: and (3) using the final target state estimation value at the moment k for missile control command resolving, enabling the time k to be k +1 and the iteration number i to be 0, and returning to the step 1 again.
2. The method of claim 1, wherein the threshold δ is a function of a number of the iterative radar signal filters x ＝10 -4 。
3. The method of claim 1, wherein the maximum number of iterations is 20.
4. The method of claim 1, wherein F is k And predicting the matrix for the state at the moment k.
5. The method of claim 1, wherein x is k-1|k-1 Is the estimated value of the target state at the k-1 moment.
6. The method of claim 1, wherein P is the number of variables k-1|k-1 Is the target state covariance estimate at time k-1.
7. The method of claim 1, wherein the method comprises applying a variable iteration of a radar signal filter design，u q,k-1|k-1 Is the process noise covariance free parameter estimate at time k-1.
8. The method of claim 1, wherein U is the number of basis functions for the design of the iterative radar signal filter q,k-1|k-1 Is the process noise covariance matrix estimated value at the k-1 moment.
9. The method of claim 1, wherein u is the number of points in the design of the iterative radar signal filter r,k-1|k-1 The noise covariance free parameter estimate is measured at time k-1.
10. The method of claim 1, wherein U is the number of basis functions for the design of the iterative radar signal filter r,k-1|k-1 The noise covariance matrix estimate is measured at time k-1.
CN202210638423.0A 2022-06-07 2022-06-07 Design method of variational iterative radar signal filter Pending CN115051682A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115333506A (en) * 2022-10-17 2022-11-11 杭州光粒科技有限公司 Signal processing method, device, equipment and readable storage medium

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115333506A (en) * 2022-10-17 2022-11-11 杭州光粒科技有限公司 Signal processing method, device, equipment and readable storage medium
CN115333506B (en) * 2022-10-17 2023-05-02 杭州光粒科技有限公司 Signal processing method, device, equipment and readable storage medium

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