CN116520380A - Dynamic target combined positioning method based on self-adaptive Kalman filtering - Google Patents
Dynamic target combined positioning method based on self-adaptive Kalman filtering Download PDFInfo
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Abstract
The invention discloses a dynamic target combined positioning method based on self-adaptive Kalman filtering, and belongs to the technical field of calculation, calculation or counting. The combined positioning method is used for two application scenes of a dynamic target in a linear state and a nonlinear state, on the basis of combined positioning of a global positioning system and ultra-wideband ranging information, an adaptive factor and dynamic window adjustment are introduced based on a covariance matching method, and an adaptive Kalman filtering combined positioning method fusing UWB and GPS is provided, and GPS single-point positioning is carried out based on a sliding window adaptive Kalman filtering method matched with covariance in a target linear motion state; and in a target nonlinear motion state, performing UWB/GPS combined positioning based on a self-adaptive unscented Kalman filtering method introducing a filtering divergence criterion. The invention improves the positioning precision and stability of the Kalman filtering method based on the fusion of UWB and GPS.
Description
Technical Field
The invention relates to a positioning technology in communication, in particular to a combined positioning scheme based on a dynamic target motion model and self-adaptive updating of real-time measurement data, discloses a dynamic combined positioning method based on self-adaptive Kalman filtering, and belongs to the technical field of calculation, calculation or counting.
Background
With the rise of industry 4.0, the internet of things has evolved rapidly, with the demand for location-based services (Location Based Services, LBS) growing more significantly. The LBS obtains the current position of the positioning equipment by using different positioning technologies, and provides information resources and basic services for the positioning equipment through the mobile Internet, so that intelligent positioning and tracking are realized. Under the background of industry 4.0, the requirements of people on the positioning and tracking of dynamic targets are higher and higher, so that the positioning and tracking technology of the dynamic targets in LBS has important research value.
When tracking and positioning a dynamic target, the pose information measurement value of the target needs to be obtained from a positioning sensor. The global navigation satellite system (Global Navigation Satellite System, GNSS) is an air-based radio navigation positioning system that can provide all-round, all-weather, all-time coordinate, velocity, time information. In the GNSS positioning system, the most widely used is a global positioning system (Global Positioning System, GPS) in a single-point positioning mode, which has low price and wide coverage range, but the positioning accuracy is not high, especially in the case of building shielding, the positioning accuracy is seriously reduced. Ultra Wide Band (UWB) is a wireless carrier communication technology, adopts nanosecond non-sine wave narrow pulse to transmit information, and provides centimeter-level positioning accuracy through a relatively low-power-consumption system, but has higher hardware cost and complex system, and cannot be used in a large area. The GPS is suitable for the conditions of simple motion state and low requirement on positioning precision, and has lower cost and wider coverage; for the conditions of complex motion state and higher positioning precision requirement, the GPS and UWB can be utilized for fusion positioning, and the positioning precision is improved on the premise of considering the cost.
At present, the difficulty of dynamic target tracking and positioning mainly lies in two points: firstly, uncertainty of a dynamic target motion model, namely a positioning system cannot accurately estimate a motion model of a positioned target; and the uncertainty of the dynamic target observation data, namely that the positioning system cannot accurately observe the pose information of the positioned target. The above two uncertainties result in model noise and metrology noise, respectively, in the positioning system. Therefore, the key point for improving the tracking and positioning accuracy of the dynamic target is to dynamically compensate the model noise error and reduce the influence of the measurement noise error. The dynamic target tracking and positioning method not only needs to meet higher positioning precision, but also ensures the real-time performance of filtering processing. The Kalman Filter (KF) algorithm has the characteristics of simple model, small data storage amount and the like, and is widely applied to dynamic target tracking and positioning.
The motion equation or the measurement equation of the dynamic target is divided into a linear type and a nonlinear type, so that the tracking and positioning of the dynamic target can be divided into a linear filtering problem and a nonlinear filtering problem. The KF algorithm combines with the least square method to propose a recursive optimal solution to the linear filtering problem based on the state space of the target. The optimal solution of the nonlinear filtering problem needs to be obtained through the conditional posterior probability by using an endless parameter, and in practical application, the optimal solution is obtained through sub-optimal approximation of the nonlinear problem. An extended kalman filter algorithm (Extended Kalman Filter, EKF) was developed based on a first order linearization truncation of the taylor expansion of the nonlinear function, ignoring Gao Jiexiang, and a linear approximation of the nonlinear function. An unscented kalman filter algorithm (Unscented Kalman Filter, UKF) was developed based on approximating the probability density distribution of the nonlinear function with a sampling strategy.
Since EKF is a first-order taylor expansion of a nonlinear function around a predicted value in a state space, when the degree of nonlinearity of a motion state of a target is high, a higher-order term of the taylor expansion cannot be ignored, and thus a system error is large. In addition, EKF requires derivation of Jacobian matrix of nonlinear function, which increases operation difficulty. The UKF approximates probability density distribution of a nonlinear function through a deterministic sampling strategy based on UT transformation, so that the calculation accuracy of nonlinear statistics reaches at least two orders, and the filtering accuracy is improved under the condition that the calculated amount is the same as the same order as an EKF algorithm.
The filtering accuracy of the linear KF algorithm and the nonlinear UKF algorithm depends on the accuracy of the state model and the measurement data, and accurate estimation of the statistical properties of the model noise and the measurement noise, namely, the covariance matrix Q of the model noise and the covariance matrix R of the measurement noise. Typical KF algorithm and UKF algorithm generally obtain statistical characteristics of noise through comprehensive analysis of a large number of experiments in advance, and fix Q, R matrix to a certain fixed value. However, when the typical KF algorithm or the typical UKF algorithm is applied to dynamic target tracking and positioning, the statistical characteristics of model noise and measurement noise are affected by the change of the target motion state, so that the uncertainty of the Q, R matrix is increased, the filtering precision is reduced, and even the filter diverges.
The self-adaptive filtering is a filtering method with the functions of adjusting system parameters in real time, reducing error influence and inhibiting filter divergence. Adaptive filtering methods are very diverse. The Sage-Husa self-adaptive filtering algorithm obtains an estimated value of a state quantity based on an observation sequence, and calculates a mean value and a covariance matrix of model noise and measurement noise according to a maximum posterior estimation principle. An improved self-adaptive UKF algorithm can be obtained by using an improved Sage-Husa suboptimal unbiased maximum posterior estimator and introducing a self-adaptive attenuation factor to correct prediction error covariance. On the basis of an evanescent filtering algorithm, researchers introduce a filter convergence criterion, and select a proper forgetting factor so that the actual error is smaller than the theoretical error. There are also few studies to introduce maximum likelihood criteria based on the adaptive estimation based on innovation and the adaptive estimation method based on multiple models, and to adjust the kalman gain coefficient of the filter in real time. In addition, researchers improve the UKF algorithm from the angles of self-adaptive adjustment process noise and measurement noise as well as correction of Kalman gain, propose a self-adaptive Kalman filtering algorithm based on a covariance matching method, introduce a sliding window with fixed width to update a Q, R matrix, and improve the robustness of the algorithm. However, the existing Sage-Husa adaptive filtering algorithm can only estimate R when Q is known or estimate Q when R is known, and because most adaptive algorithms do not introduce a filter divergence criterion and have certain filter divergence possibility, the positioning accuracy of the existing Sage-Husa adaptive filtering algorithm still has room for improvement.
Based on the above study, the key to improving the positioning accuracy of the dynamic target by the kalman filter algorithm is to reduce the estimation error caused by the uncertainty of the Q, R matrix. The present invention aims to provide a dynamic combined positioning method based on adaptive kalman filtering to overcome the above-mentioned drawbacks.
Disclosure of Invention
The invention aims to overcome the defects of the background art, and provides a dynamic combination positioning method based on self-adaptive Kalman filtering on the basis of the research of self-adaptive filtering, which aims to improve the response precision of the Kalman filtering on a dynamic target and effectively inhibit the divergence of the filter, and solves the technical problems of how to improve the positioning precision of the dynamic target tracking positioning method and ensure the real-time performance of filtering processing.
The invention adopts the following technical scheme for realizing the purposes of the invention: the dynamic target combined positioning method based on the adaptive Kalman filtering is characterized by comprising the following steps of:
step 1, judging the motion state of a course angle according to the course angle of a dynamic target, entering step 2 when the dynamic target is in a linear motion state, and entering step 3 when the dynamic target is in a nonlinear motion state;
step 2, performing single-point positioning on the dynamic target by adopting a sliding window self-adaptive Kalman filtering algorithm based on covariance matching;
and 3, fusing UWB measurement data and GPS measurement data to construct a measurement vector, establishing a state space model in a nonlinear motion state, and adopting a self-adaptive unscented Kalman filtering algorithm which introduces two filtering divergence criteria based on covariance matching to carry out combined positioning on a dynamic target.
As a further optimization scheme of the dynamic target combined positioning method based on the adaptive Kalman filtering, the specific method for judging the motion state of the course angle according to the dynamic target course angle in step 1 is as follows: when the course angle change of the dynamic target is smaller than or equal to a threshold value, judging that the dynamic target is in a linear motion state; and when the course angle change of the dynamic target is larger than the threshold value, judging that the dynamic target is in a nonlinear motion state.
As a still further optimization scheme of the dynamic target combined positioning method based on the self-adaptive Kalman filtering, the concrete method for carrying out single-point positioning on the dynamic target by adopting a sliding window self-adaptive Kalman filtering algorithm based on covariance matching in the step 2 is as follows:
step 2-1, initializing a dynamic target state vector and an error covariance matrix;
step 2-2, prior estimation of the predicted dynamic target state vector at time kPrior estimation P of predictive k-moment error covariance matrix (k|k-1) ；
Step 2-3, obtaining an innovation error sequence epsilon at k moment based on a covariance matching method k Covariance matrix C of (2) k The k moment is self-adaptive to the factor alpha k Estimating K moment Kalman gain coefficient K after introducing K moment innovation error sequence covariance matrix k Calculating a k-moment innovation error sequence covariance matrix C meeting an optimal filter theory k Adaptive factor alpha at time k k Estimating a k+1 moment sliding window according to the distance between the k moment innovation error sequence and the mean value of the previous k-1 moment residual error sequence, and updating a k moment self-adaptive factor alpha according to the estimated k moment sliding window k ；
Step 2-4, the k-time adaptive factor alpha updated according to step 2-3 k Step 2-3, the estimated K moment Kalman gain factor K k And carrying out state prediction and measurement updating on the dynamic target.
As a still further optimization scheme of the dynamic target combined positioning method based on the self-adaptive Kalman filtering, the specific method for combined positioning of the dynamic target by adopting the self-adaptive unscented Kalman filtering algorithm which introduces two filtering divergence criteria based on covariance matching in the step 3 comprises the following steps:
step 3-1, initializing a dynamic target state vector and an error covariance matrix;
step 3-2, carrying out first UT conversion on the state vector prediction result of the dynamic target at the moment k, constructing a Sigma point set, and predicting the state vector of the dynamic target at the moment k+1 according to the first-order statistical characteristic weight coefficient and the second-order statistical characteristic weight coefficient of the Sigma point setk+1 time error covariance matrix P (k+1|k )；
Step 3-3, predicting the state vector of the dynamic target at the time k+1 in step 3-2Performing UT conversion for the second time, obtaining an updated Sigma point set, and predicting the measurement vector +.>Auto-covariance matrix of dynamic target measurement vector at time k+1>Cross covariance matrix of dynamic target measurement vector at time k+1>Kalman gain K at time k+1 k+1 According to the Kalman gain K at time k+1 k+1 Filtering and updating;
step 3-4, introducing two filtering divergence criteria, and updating covariance matrix R of measuring noise at k+1 moment k+1 ：
Updating covariance matrix R of k+1 moment measurement noise when k moment innovation error sequence meets first filtering divergence criterion k+1 Covariance matrix R for measuring noise at k time k ，
When the k moment innovation error sequence does not meet the first filter divergence criterion but meets the second filter divergence criterion, measuring a covariance matrix R of noise at the k+1 moment k+1 Assigning infinity and applying the Kalman gain K at time k+1 k+1 Assigning 0, performing state prediction only on the dynamic target state vector,
estimating a covariance matrix R of the k+1 moment measurement noise based on the k moment sliding window and the previous k moment innovation error sequence when the k moment innovation error sequence meets a second filtering divergence criterion k+1 Covariance matrix R of noise measured according to k+1 time k+1 And carrying out state prediction and measurement correction on the dynamic target state vector.
As a oneStill further optimizing scheme of dynamic target combined positioning method based on self-adaptive Kalman filtering, wherein k moment innovation error sequence covariance matrix C meeting optimal filter theory in step 2-3 k Is C k ＝HP k|k-1 H T +α k R k K-moment self-adaptive factor alpha meeting optimal filter theory k Is thatWhere H is the measurement matrix and tr is the trace-taking operation.
As a still further optimization scheme of the dynamic target combined positioning method based on the adaptive Kalman filtering, the step 2-3 predicts the expression of the k+1 moment sliding window as follows according to the distance between the k moment innovation error sequence and the previous k-1 moment residual sequence mean valueWherein N is k 、N k+1 The window size is k time and k+1 time epsilon k (j) Innovative sequence for the j-th measurement dimension at time k,>for the average modulus of the information sequence of the jth measurement dimension at the previous k-1 moment, L is the measurement dimension of the measurement vector, [ #]The numerical value is rounded.
As a still further optimization scheme of the dynamic target combined positioning method based on the adaptive Kalman filtering, the steps 2-3 update the k moment adaptive factor alpha according to the estimated k moment sliding window k The expression of (2) isWherein C is k-j And the covariance matrix of the innovation error sequence at the moment k-j.
As a still further optimization scheme of the dynamic target combined positioning method based on the adaptive Kalman filtering, the first filtering divergence criterion is thatDelta is a control coefficient, and delta is more than or equal to 1.
As a still further optimization scheme of the dynamic target combined positioning method based on the adaptive Kalman filtering, the second filtering divergence criterion is that
As a still further optimization scheme of the dynamic target combined positioning method based on the adaptive Kalman filtering, the steps 3-4 estimate a covariance matrix R of the measurement noise at the k+1 moment based on a k moment sliding window and a previous k moment innovation error sequence k+1 The expression of (2) is:wherein ε k-i For the k-i moment innovation error sequence, n is the dimension of the dynamic target state vector, ++>For the second order statistical characteristic weight coefficient of the mu th Sigma point, χ μ,(k+1) Mu Sigma point at time k+1, h (x) is the measurement function.
The invention adopts the technical scheme and has the following beneficial effects:
(1) The invention provides an improved adaptive factor alpha for weakening measurement errors k The method can improve the sudden maneuver tracking precision of the dynamic target in real time according to the noise condition of the current environment of the system, overcomes the defect that a fixed value alpha in the traditional algorithm is difficult to consider under different maneuver environments, can more accurately position the dynamic target by the self-adaptive Kalman filtering method based on dynamic window adjustment, reduces positioning errors, and can meet the positioning requirement of high precision.
(2) The self-adaptive unscented Kalman filtering method provided by the invention effectively filters abnormal measurement values by introducing two filtering divergence criteria, and iteratively calculates a covariance matrix R of measurement noise of a dynamic sliding window based on an innovation error k Greatly reduces the divergence possibility of the filter and improves the self-adaptive unscented Kalman filtering methodReliability and tracking speed for dynamic target state change, and positioning accuracy is improved.
Drawings
Fig. 1 is a flowchart of an overall scheme of a dynamic combined positioning method based on adaptive kalman filtering.
Fig. 2 is a flow chart of the adaptive AKF method according to the present invention.
Fig. 3 is a flow chart of the adaptive AUKF method according to the present invention.
Fig. 4 is a flowchart of the adaptive AUKF method prediction covariance matrix according to the present invention.
Fig. 5 is a flowchart of updating a posterior covariance matrix according to the adaptive AUKF method of the present invention.
FIG. 6 is a real trace of a dynamic object in an embodiment of the present invention.
FIG. 7 is a measurement trace at a high signal-to-noise ratio in an embodiment of the invention.
FIG. 8 is a measurement trace at low signal-to-noise ratio in an embodiment of the invention.
Fig. 9 is a positioning trace at a high signal-to-noise ratio in an embodiment of the invention.
FIG. 10 is a positioning trace at low signal-to-noise ratio in an embodiment of the present invention.
Fig. 11 shows euclidean distance errors at high signal-to-noise ratios in an embodiment of the invention.
Fig. 12 shows euclidean distance errors at low signal-to-noise ratios in an embodiment of the invention.
Detailed Description
The technical scheme of the invention is further described in detail below with reference to the accompanying drawings and examples.
As shown in FIG. 1, the method for positioning the dynamic target combination based on the adaptive Kalman filtering specifically comprises the following sequential steps.
Firstly, judging that a dynamic target is in a linear motion state or a nonlinear motion state based on a course angle: when the course angle of the dynamic target keeps stable or slightly changed, judging that the dynamic target is in a linear motion state, and turning to the second step; when the course angle of the dynamic target changes greatly, the dynamic target is judged to be in a nonlinear motion state, and the step III is changed.
Secondly, positioning a dynamic target in a linear motion state by adopting an AKF-based single-point positioning method, wherein the positioning method specifically comprises the following steps of: the single-point GPS measurement result is filtered by using a KF algorithm, so that the problem of low single-point GPS positioning accuracy is solved, and the single-point positioning accuracy is improved by adopting a sliding window self-adaptive Kalman filtering (Adaptive Kalman Filter, AKF) method based on covariance matching on the premise of effectively saving cost.
Step three, for a dynamic target in a turning nonlinear motion state, positioning by adopting an AUKF-based combined positioning method, wherein the method specifically comprises the following steps: based on UKF, an improved self-adaptive unscented Kalman filtering (Adaptive Unscented Kalman Filter, AUKF) method is adopted by fusing UWB and GPS measurement data, two filtering divergence criteria are introduced in the method, and the measurement data are preprocessed and then combined and positioned, so that the tracking and positioning accuracy of a dynamic target is improved.
When the heading angle of the dynamic object remains stable or slightly changed (less than or equal to 2 °/s), it is considered to be in linear motion. The state space model of the linear state is constructed as follows:
consider a linear discrete time dynamic system:
X k ＝FX k-1 +W k-1 (1)
Z k ＝HX k +V k (2)
in the formulas (1) to (2), X k N×1-dimensional state vector, Z, which is a dynamic target at time k k The m x 1 measurement vector is the dynamic target at the moment k, and F and H are the state transition matrix and the measurement matrix respectively. W (W) k-1 And V k The uncorrelated zero-mean random Gaussian white noise sequence respectively represents k moment model noise and k moment measurement noise, namely:
its covariance matrix is:
in the formula (4), W i For i moment model noise, Q k 、R k Covariance matrix of k moment model noise, covariance matrix of k moment measurement noise, delta i The impulse function value at time i.
The motion model of the linear motion state generally adopts a uniform acceleration linear motion (Constant Acceleration, CA) model, and according to the kinematic analysis, the state vector of the dynamic target is generally set as:
X k ＝[x k y k v xk v yk a xk a yk ] T (5)
in the formula (5), x k 、v xk 、a xk The position coordinates, the speed, the acceleration and the y of the dynamic target along the X axis at the moment k respectively k 、v yk 、a yk The position coordinates, the speed and the acceleration of the dynamic target along the Y axis at k are respectively shown.
The state transition matrix F of the system is:
in equation (6), Δt is the time difference between time k+1 and time k.
Considering that the dynamic target tracking and positioning method is most concerned about the position coordinates of the target and has certain requirements on filtering instantaneity, the vector measurement is simplified into Z k ＝[x k y k ] T The simplified measurement matrix H is:
the traditional KF scheme steps are as follows:
P (k|k-1) ＝FP (k-1|k-1) F T +Q k-1 (9)
K k ＝P (k|k-1) H T *[HP (k|k-1) H T +R k ] (10)
P (k|k) ＝(I-K (k) H)P (k|k-1) (12)
in the formulas (8) to (12),is an a priori estimate of the dynamic target pose state at time k,/>Is a posterior estimation of the dynamic target pose state at time k. P (P) (k|k-1) Is the prior estimation of the k moment error covariance matrix, P (k|k) Is the posterior estimation of the K moment error covariance matrix, K (k) Is the kalman gain. Covariance matrix R for measuring noise in a recursive optimization process k Updating in real time, and calculating the k moment innovation sequence epsilon by introducing a covariance matching method k Covariance matrix C of (2) k 。
Covariance matching method the covariance matching method includes adaptive estimation based on Innovation-based Adaptive Estimation (IAE) and adaptive estimation based on Residual error (Residual-based Adaptive Estimation, RAE). The innovation error sequence of the IAE and the residual sequence of the RAE are defined as follows:
substituting formula (2) into formula (13) to obtain a covariance matching formula:
taking the variance of the two sides of the formula (15), taking the orthogonality of the measurement errors and the model errors into consideration of the formulas (3) and (4) to obtain an innovation error sequence epsilon at the moment k k Covariance matrix C of (2) k The method comprises the following steps:
the core of the adaptive Kalman filtering is to adapt the adaptive factor alpha k Introducing an innovation covariance matrix C k Thereby updating the measurement noise covariance matrix R in real time k Attenuating the effect of measurement noise, rewrites equation (16) to:
C k ′＝HP k|k-1 H T +α k R k (17)
substituting equation (17) into equation (10) to obtain an adaptive kalman gain coefficient:
K k ＝P (k|k-1) H T *[HP (k|k-1) H T +α k R k ]＝P (k|k-1) H T (C′ k ) -1 (18)
according to the optimal filter theory, the adaptation factor satisfies the following equation:
P k|k-1 H T -K k C k ＝0 (19)
the combined formula (18) and the formula (19) are obtained:
P k|k-1 H T -[P k|k-1 H T (C′ k ) -1 )]C k ＝0 (20)
simplifying to obtain:
I-(C′ k ) -1 C k ＝0 (21)
namely:
C k ＝C′ k (22)
substituting formula (17) into formula (22):
C k ＝HP k|k-1 H T +α k R k (23)
simultaneously taking traces from two sides of the formula (23) to obtain an adaptive factor alpha k ：
Introducing dynamic window adjustment to the formula (24), and using the innovation error sequence defined by the formula (13) as a judgment standard for evaluating the state change of the system. The change of the noise of the positioning system can directly influence the magnitude and the change condition of the modulus of the innovation sequence, so that the magnitude N of the estimation window is dynamically adjusted by utilizing the distance between the innovation sequence at the k moment and the mean value of the innovation sequence at the previous k-1 moment as follows:
in the formula (25), N k 、N k+1 For a window size of k time, k +1 time,is the average modulus value epsilon of the jth measurement dimension innovation sequence at the previous k-1 moment k (j) An innovation sequence of the j-th measurement dimension at the k moment, L is the measurement dimension of the measurement vector, []Is the rounding of the values.
The adaptive factors that introduce dynamic window estimation are:
in consideration of practical application, alpha k It is required to be 1 or more, and therefore:
in summary, a flowchart of the adaptive kalman filtering method based on dynamic window adjustment is shown in fig. 2. When the motion model of the dynamic target is judged to be in a nonlinear motion state based on the course angle, namely, the course angle change rate is more than 2 degrees/s, the pose model of the dynamic target is complex, and the accurate estimation of the pose model is often difficult by a single measurement means. The defects of a single sensor can be made up by information fusion of multiple sensors through a KF algorithm, so that the nonlinear motion pose can be accurately estimated.
Consider a nonlinear discrete-time dynamic system:
X k ＝f(X k-1 )+W k-1 (28)
Z k ＝h(X k )+V k (29)
in the formulas (28) to (29), X k N×1-dimensional state vector, Z, which is a dynamic target at time k k The m multiplied by 1 measurement vector is a dynamic target at the moment k, and f and h are a state transfer function and a measurement function respectively, wherein f is a nonlinear function. W (W) k-1 And V k The zero-mean random Gaussian white noise sequence is uncorrelated and represents k-moment model noise and k-moment measurement noise respectively. The covariance matrix is:
when the dynamic target is in a nonlinear motion state, a constant turning rate and speed motion (ConstantTurn Rate and Velocity, CTRV) model is adopted, and real-time measurement data of the dynamic target is obtained through GPS and UWB.
According to the kinematic analysis, using the CTRV model, the state vector of the dynamic object is generally set as:
X k ＝[x k y k θ k v k ] T (31)
in the formula (31), x k 、y k The position coordinates of the dynamic target along the X, Y axis at the time k, theta k Is the course angle of the dynamic target at the moment k, v k Is the velocity of the dynamic target at time k.
The state transfer function f (·) of the system is:
in the formula (32), delta t is the time difference between k+1 time and k time, X (delta t) is the pose offset of the dynamic target passing time interval delta t, f (·) is the dynamic pose state update equation, v (t) is the linear velocity of the dynamic target at t time, X (t) and y (t) are the position coordinates of the object to be measured at t time along X, Y axis respectively,the position coordinate of the dynamic object along the X axis, the position coordinate along the Y axis, the course angle and the offset of the linear speed at the time interval delta t are respectively, and w is the angular speed of the dynamic object.
Measurement vector Z k ＝[x k y k θ k v k ] T The position coordinates (x, y) of the dynamic target are obtained by UWB acquisition and calculation, and the course angle theta and the linear speed v of the dynamic target are obtained by GPS message analysis. The simplified measurement function h is:
after a state space model in a nonlinear motion state is established, a filtering divergence basis based on a covariance matching method is introduced into a traditional UKF scheme, and a covariance matrix R of measurement noise is adjusted in real time k 。
The traditional UKF scheme steps are as follows:
(1) Initialization of
In the formula (34), the amino acid sequence of the compound,is estimated initial value of the pose state of the dynamic target, P 0 Is the estimated covariance matrix initial value.
(2) Constructing Sigma Point sets
The most widely used of the Sigma point sampling strategies currently available is the centrosymmetric sampling strategy. The calculation formula for constructing the center sampling Sigma point is as follows:
in the formula (35), χ 0,k Is the 0 th Sigma point, χ at time k μ,k Is the mu-th Sigma point at time k, lambda is the scale factor, lambda=alpha 2 (n+kappa) -n, n is the dimension of the dynamic target state vector at time k shown in formula (31), alpha (n+kappa) represents a variable controlling the distance of Sigma points from the mean of the dynamic target state vector,representing matrix root->Is shown in column mu. First-order statistical property weight coefficient of Sigma point 0->And mu th Sigma point first order statistical property weight coefficient +.>Mu th Sigma point second order statistical property weight coefficient +.>The following are provided:
in the formula (36), beta is a non-negative weight coefficient to be selected, beta is more than or equal to 0, and Gaussian distribution generally takes 2.
(3) Calculating a one-step prediction matrix and a covariance matrix of the k moment:
χ μ,(k+1|k) ＝f(χ μ,(k|k) )μ＝0,1,2...2n (37)
in the formulae (37) to (38),a priori estimation matrix for the state vector of the dynamic target at time k+1, P (k+1|k) For the prior estimation of the k+1 moment error covariance matrix, χ μ,(k|k) Mu-th Sigma point, χ, estimated a priori for time k μ,(k+1|k) Mu. Sigma point estimated for the posterior at time k.
(4) And obtaining a new Sigma point set and a measurement vector by utilizing UT conversion for the second time:
(5) Calculating a covariance matrix of system prediction:
in the formulae (41) to (42),for the moment k+1, measure vector +.>Is>For the state vector at time k+1 +.>And k+1 moment measurement vector->Is a cross covariance matrix of (a) is provided.
(6) Calculating a Kalman gain matrix:
(7) And (5) filtering and updating:
aiming at the problem that a nonlinear filtering algorithm is easily disturbed by an abnormal measurement value, and a typical UKF is easily diverged, a filtering divergence basis based on a covariance matching method is introduced.
When the calculated prediction error is far smaller than the actual estimation error, the judgment filter is in a divergent state, and the divergent condition is as follows:
in the formula (46), ε k An innovation error defined by the formula (13) represents a real estimation error at the moment k;represents the theoretical estimated error at time k; and delta is an adjustable control coefficient (delta is more than or equal to 1), and when the actual estimation error is larger than delta times of the theoretical estimation error, the filter is judged to be in a divergent state, namely the error between the estimated value and the actual value is overlarge. In practical use, the->Often difficult to obtain, and the covariance matrix of the measurement values +.>Can be expressed as the expected value of the sum of squares of the measurement residuals, so equation (46) can be rewritten as:
in addition, in the nonlinear motion state, the equivalent measurement error is larger or the model error is larger, namely the innovation error epsilon k When the error is large, the filter generates a large estimation error in the measurement correction stage, at this time, the measurement error cannot be well reduced by performing self-adaptive update on R, and a second divergence criterion is introduced for filtering abnormal measurement values:
|ε k |＞ξ (48)
in equation (48), ζ is a preset filter threshold. When the innovation is error epsilon k When the modulus value of (a) is larger than the threshold value xi, the measurement noise covariance matrix R is set to infinity, and the Kalman gain K influenced by R tends to 0 at the moment, namely, only state model prediction is performed at the moment, measurement correction is not performed, so that the interference of the abnormal measurement value on the filter is reduced. When the innovation is error epsilon k When the model value is smaller than the threshold value xi, namely, the model error is lower and the measurement accuracy is higher, the state model prediction and the measurement correction are simultaneously carried out.
A sliding window-based R matrix adaptive calculation method is introduced to UKF. Dynamic adjustment of estimated Window size N As shown in equation (25), the dynamic adjustment of R is accomplished by utilizing a plurality of previous time innovation errors ε k For R at the next moment k+1 And (3) recursion:
the self-adaptive unscented Kalman filtering method provided by the invention effectively filters the abnormal measurement value by introducing two filtering divergence criteria; and based on the innovation error, a covariance matrix R of the measurement noise of the dynamic sliding window is designed k The formula is iterated. Two introduced filtering divergence criteria are adopted, whether the filter is in a divergence state is judged firstly, and when the filter is in the divergence state, a smaller R is used k The convergence speed of the filter is increased, and the divergence degree of the filter is reduced. When the filter is in a steady state, a threshold value xi is used for judging whether the modulus value of the innovation error is too large, and when the error modulus value exceeds the threshold value xi, the error modulus value is considered to be an abnormal measurement value, so that R is k+1 =0, so that the kalman gain tends to infinity, i.e. the a priori estimates of the states are not corrected from the measured values. When the error modulus value is less than or equal to the threshold value xi, the error modulus value is considered as a normal measurement value, and R is recalculated through a dynamic sliding window of the innovation sequence k+1 The filtering precision is further improved by measuring the prior estimated value of the value correction state. The flow chart of the adaptive unscented Kalman filtering method based on dynamic window adjustment is shown in FIG. 3. Details of the prediction module in fig. 3 are shown in fig. 4, and details of the measurement update module are shown in fig. 5.
(3) Final example performance analysis:
the dynamic target combined positioning method based on the self-adaptive Kalman filtering provided by the invention is compared with the traditional Kalman filtering positioning method and the self-adaptive Kalman filtering positioning method without a sliding window, simulation performance is compared, simulation parameters are set as shown in a table 1, and average errors of simulation results are shown in a table 2.
Table 1 simulation parameters
Table 2 method euclidean distance average error unit: m is m
| Low signal to noise ratio | High signal to noise ratio | |
| Typical method | 1.100781 | 0.324015 |
| Adaptive method 1 | 0.768326 | 0.27294 |
| The method of the invention | 0.405906 | 0.152158 |
It can be seen from fig. 6, 9 and 10 that, under the condition of low signal-to-noise ratio or high signal-to-noise ratio of the measured value, the combined positioning method provided by the invention better fits the real track compared with the typical kalman filtering method and the self-adaptive kalman method 1 without sliding window, which indicates that the method provided by the invention can better inhibit errors, the error value of the positioning result is smaller, the positioning accuracy and the track smoothness are improved, and the dynamic target can be tracked and positioned more accurately. Typical methods often rely highly on accurate estimation of noise statistics, which makes it difficult to correct the system model by measurement values when the noise variance is large, i.e. the noise variation is frequent; since the measurement noise covariance matrix is not updated, the influence of the new measurement value in measurement correction is smaller and smaller along with the progress of iteration, and the divergence of a filter or the reduction of the filtering precision is easy to cause. Although the adaptive method 1 introduces adaptive adjustment, a dynamic sliding window is not used, when the system is in a steady state, the current moment data is still only processed, and the historical residual sequence is not considered, so that the historical residual sequence is easily affected by some abnormal measurement values, and the filtering precision is lower than that of the improved adaptive positioning method proposed herein.
As can be seen from fig. 7 to fig. 10, the combined positioning method provided by the invention can carry out filtering smoothing on the high-precision and low-precision position coordinate measurement values, can accurately model the motion state of the dynamic target through the sensor, effectively filters abnormal measurement values, corrects the measurement values through the prior estimation value of the motion model, thereby effectively improving the positioning precision, and the track map obtained by the combined positioning method provided by the invention is obviously more fit with the real track than the measurement values, so that the influence of the deviation of the measurement values and the characteristic change of measurement noise on filtering noise reduction stability can be restrained by the positioning method provided by the invention, namely, the effective measurement data information is furthest reserved on the premise of efficiently and accurately eliminating error data.
11, 12 and Table 2, it can be seen that, under the condition of low signal-to-noise ratio of the measured value, the improved adaptive Kalman filtering combined positioning method provided by the invention has the advantages that compared with a typical Kalman filtering positioning system, the positioning accuracy is improved by 63.13%, and compared with an adaptive Kalman filtering positioning system without a sliding window, the positioning accuracy is improved by 30.20%; under the condition of high signal-to-noise ratio of the measured value, the improved self-adaptive Kalman filter combined positioning method provided by the invention has the advantages that compared with a typical Kalman filter positioning system, the positioning accuracy is improved by 53.04%, and compared with a self-adaptive Kalman filter positioning system without a sliding window, the positioning accuracy is improved by 44.25%. The filtering processing data of the improved self-adaptive positioning method provided by the invention is closer to the real position coordinates, and the superiority and universality of the method are proved.
(4) Conclusion:
aiming at the linear motion state and the nonlinear motion state of a dynamic target, the invention respectively provides an improved self-adaptive Kalman single-point positioning method and an improved unscented Kalman combined positioning method. Both calculate the size of dynamic sliding window according to the innovation error, estimate the measurement noise covariance matrix in real time, and are self-adaptive adjustment methods based on covariance matching method. Aiming at the problems that a nonlinear filter is easier to diverge and has lower precision, the invention introduces two filter divergence criteria in the improved unscented Kalman combined positioning method, eliminates error data and avoids affecting the noise reduction effect; and the tolerance degree of the filter to errors can be dynamically adjusted by changing the threshold value, so that the universality and the stability of the filter are improved. Simulation results show that the fusion positioning method provided by the invention can restrain the influence of measurement value deviation and system noise characteristic unknown on filtering noise reduction stability under the conditions of unknown measured noise characteristic and complex noise characteristic, and can realize more accurate positioning effect on dynamic targets.
The above specific embodiments and examples are specific support for the technical idea proposed by the present invention, and the scope of protection of the present invention is not limited thereby, and any equivalent changes or equivalent modifications made on the basis of the technical scheme according to the technical idea proposed by the present invention still belong to the scope of protection of the technical scheme of the present invention.
Claims (10)
1. The dynamic target combined positioning method based on the adaptive Kalman filtering is characterized by comprising the following steps of:
step 1, judging the motion state of a course angle according to the course angle of a dynamic target, entering step 2 when the dynamic target is in a linear motion state, and entering step 3 when the dynamic target is in a nonlinear motion state;
step 2, performing single-point positioning on the dynamic target by adopting a sliding window self-adaptive Kalman filtering algorithm based on covariance matching;
and 3, fusing UWB measurement data and GPS measurement data to construct a measurement vector, establishing a state space model in a nonlinear motion state, and adopting a self-adaptive unscented Kalman filtering algorithm which introduces two filtering divergence criteria based on covariance matching to carry out combined positioning on a dynamic target.
2. The method for positioning a dynamic target combination based on adaptive kalman filtering according to claim 1, wherein the specific method for determining the motion state of the heading angle according to the heading angle of the dynamic target in step 1 is as follows: when the course angle change of the dynamic target is smaller than or equal to a threshold value, judging that the dynamic target is in a linear motion state; and when the course angle change of the dynamic target is larger than the threshold value, judging that the dynamic target is in a nonlinear motion state.
3. The method for positioning a dynamic target combination based on adaptive kalman filtering according to claim 2, wherein the specific method for performing single-point positioning on the dynamic target by adopting a sliding window adaptive kalman filtering algorithm based on covariance matching in step 2 is as follows:
step 2-1, initializing a dynamic target state vector and an error covariance matrix;
step 2-2, prior estimation of the predicted dynamic target state vector at time kPrior estimation P of predictive k-moment error covariance matrix (k|k-1) ；
Step 2-3, obtaining an innovation error sequence epsilon at k moment based on a covariance matching method k Covariance matrix C of (2) k The k moment is self-adaptive to the factor alpha k Estimating K moment Kalman gain coefficient K after introducing K moment innovation error sequence covariance matrix k Calculating a k-moment innovation error sequence covariance matrix C meeting an optimal filter theory k Adaptive factor alpha at time k k According to the mean value of k moment innovation error sequence and previous k-1 moment residual error sequenceThe distance of the k+1 moment sliding window is estimated, and the k moment self-adaptive factor alpha is updated according to the estimated k moment sliding window k ；
Step 2-4, the k-time adaptive factor alpha updated according to step 2-3 k Step 2-3, the estimated K moment Kalman gain factor K k And carrying out state prediction and measurement updating on the dynamic target.
4. The method for combined positioning of dynamic targets based on adaptive kalman filtering according to claim 3, wherein the specific method for combined positioning of dynamic targets by adopting an adaptive unscented kalman filtering algorithm introducing two filtering divergence criteria based on covariance matching in the step 3 is as follows:
step 3-1, initializing a dynamic target state vector and an error covariance matrix;
step 3-2, carrying out first UT conversion on the state vector prediction result of the dynamic target at the moment k, constructing a Sigma point set, and predicting the state vector of the dynamic target at the moment k+1 according to the first-order statistical characteristic weight coefficient and the second-order statistical characteristic weight coefficient of the Sigma point setk+1 time error covariance matrix P (k+1|k) ；
Step 3-3, predicting the state vector of the dynamic target at the time k+1 in step 3-2Performing UT conversion for the second time, obtaining an updated Sigma point set, and predicting the measurement vector +.>Auto-covariance matrix of dynamic target measurement vector at time k+1>Cross covariance matrix of dynamic target measurement vector at time k+1>Kalman gain K at time k+1 k+1 According to the Kalman gain K at time k+1 k+1 Filtering and updating;
step 3-4, introducing two filtering divergence criteria, and updating covariance matrix R of measuring noise at k+1 moment k+1 ：
Updating covariance matrix R of k+1 moment measurement noise when k moment innovation error sequence meets first filtering divergence criterion k+1 Covariance matrix R for measuring noise at k time k ，
When the k moment innovation error sequence does not meet the first filter divergence criterion but meets the second filter divergence criterion, measuring a covariance matrix R of noise at the k+1 moment k+1 Assigning infinity and applying the Kalman gain K at time k+1 k+1 Assigning 0, performing state prediction only on the dynamic target state vector,
estimating a covariance matrix R of the k+1 moment measurement noise based on the k moment sliding window and the previous k moment innovation error sequence when the k moment innovation error sequence meets a second filtering divergence criterion k+1 Covariance matrix R of noise measured according to k+1 time k+1 And carrying out state prediction and measurement correction on the dynamic target state vector.
5. The method for positioning a dynamic target combination based on adaptive Kalman filtering according to claim 4, wherein the k moment innovation error sequence covariance matrix C satisfying the optimal filter theory in the step 2-3 k Is C k ＝HP k|k-1 H T +α k R k K-moment self-adaptive factor alpha meeting optimal filter theory k Is thatWhere H is the measurement matrix and tr is the trace-taking operation.
6. An adaptive Kalman filtering-based dynamic objective according to claim 5The mark combination positioning method is characterized in that the step 2-3 predicts the expression of a k+1 moment sliding window according to the distance between the k moment innovation error sequence and the mean value of the previous k-1 moment residual error sequence as followsWherein N is k 、N k+1 The window size is k time and k+1 time epsilon k (j) Innovative sequence for the j-th measurement dimension at time k,>for the average modulus of the information sequence of the jth measurement dimension at the previous k-1 moment, L is the measurement dimension of the measurement vector, [ #]The numerical value is rounded.
7. The method for combining and positioning dynamic targets based on adaptive Kalman filtering according to claim 6, wherein the steps 2-3 update the k-time adaptive factor alpha according to the estimated k-time sliding window k The expression of (2) isWherein C is k-j And the covariance matrix of the innovation error sequence at the moment k-j.
8. The method for combining and positioning dynamic targets based on adaptive Kalman filtering according to claim 7, wherein the first filter divergence criterion isDelta is a control coefficient, and delta is more than or equal to 1.
9. The method for dynamic target combined positioning based on adaptive Kalman filtering according to claim 8, wherein the second filter divergence criterion is
10. The method for combining and positioning dynamic targets based on adaptive Kalman filtering according to claim 9, wherein the steps 3-4 estimate covariance matrix R of measured noise at k+1 time based on k time sliding window and previous k time innovation error sequence k+1 The expression of (2) is:
wherein ε k-i For the k-i moment innovation error sequence, n is the dimension of the dynamic target state vector, ++>For the second order statistical characteristic weight coefficient of the mu th Sigma point, χ μ,(k+1) Mu Sigma point at time k+1, h (x) is the measurement function.
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| CN117990112A (en) * | 2024-04-03 | 2024-05-07 | 中国人民解放军海军工程大学 | Unmanned aerial vehicle photoelectric platform target positioning method based on robust unscented Kalman filtering |
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| CN117375471B (en) * | 2023-12-08 | 2024-03-12 | 浙江大学 | Permanent magnet motor moment of inertia and load torque identification method and system |
| CN117990112A (en) * | 2024-04-03 | 2024-05-07 | 中国人民解放军海军工程大学 | Unmanned aerial vehicle photoelectric platform target positioning method based on robust unscented Kalman filtering |
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