阅读说明：本技术 处理截断数据的卡尔曼滤波方法及滤波器 (Kalman filtering method and filter for processing truncated data ) 是由 高星 于 2021-08-16 设计创作，主要内容包括：本公开是关于数据处理技术领域,公开一种处理截断数据的卡尔曼滤波方法及滤波器。该处理截断数据的卡尔曼滤波方法包括：使用无迹卡尔曼滤波UKF算法计算待测系统的一步预测状态值和协方差；使用修正观测方程基于所述待测系统的一步预测状态值确定所述待测系统的预测观测值；基于所述待测系统的预测观测值和所述协方差确定所述待测系统的卡尔曼增益；基于所述卡尔曼增益对所述待测系统进行状态更新和测量值更新。(The disclosure relates to the technical field of data processing, and discloses a Kalman filtering method and a filter for processing truncated data. The Kalman filtering method for processing the truncated data comprises the following steps: calculating a one-step prediction state value and covariance of the system to be tested by using an unscented Kalman filtering UKF algorithm; determining a predicted observation value of the system to be tested based on the one-step predicted state value of the system to be tested by using a corrected observation equation; determining a Kalman gain of the system under test based on the predicted observation of the system under test and the covariance; and updating the state and the measured value of the system to be tested based on the Kalman gain.)

1. A kalman filtering method for processing truncated data, comprising:

calculating a one-step prediction state value and covariance of the system to be tested by using an unscented Kalman filtering UKF algorithm;

determining a predicted observation value of the system to be tested based on the one-step predicted state value of the system to be tested by using a corrected observation equation;

determining a Kalman gain of the system under test based on the predicted observation of the system under test and the covariance;

and updating the state and the measured value of the system to be tested based on the Kalman gain.

2. The method according to claim 1, wherein the calculating of the measurement observations of the system under test using Unscented Kalman Filter (UKF) algorithm comprises:

acquiring a plurality of first sampling points of a system to be tested by using unscented transformation, and calculating the weight of each first sampling point, wherein the weight comprises a mean weight and a covariance weight;

calculating a one-step prediction state value of each first sampling point;

and determining a one-step prediction state value and covariance of the system to be tested based on the one-step prediction state value of each first sampling point and the weight of each first sampling point.

3. The method of claim 2, wherein the weight of each of the first sample points is calculated according to the following equation:

in the formula:is a system state weight ofThe covariance weight is marked as the number of sampling points; parameter λ ═ a²(n + k) -n is a scaling parameter for reducing the total budget error, the selection of a controls the distribution state of sampling points, and k is a parameter to be selected; the candidate parameter beta is a non-negative weight coefficient.

4. The method of claim 2, wherein determining the one-step predicted state value and the covariance of the system under test based on the one-step predicted state value of each of the first sampling points and the weight of each of the first sampling points comprises:

calculating a one-step prediction state value of the system to be tested based on the one-step prediction state value of each first sampling point and the weight of each first sampling point by using the following formula:

in the formula:predicting a state value, ω, for a step of the system_m ⁽ⁱ⁾Is the weight of the ith sample point,predicting a state value for the ith sampling point by one step;

and calculating a covariance matrix of the system to be measured based on the one-step predicted state value of each first sampling point and the weight of each first sampling point by using the following formula:

in the formula: p_k|k-1Is the covariance matrix, omega, of the system under test_c ⁽ⁱ⁾Is the weight of the ith sample point,the state value is predicted for one step of the system,the state value is predicted for the one step at the ith sample point, and Q is a constant.

5. The method of claim 1, wherein determining the predicted observation of the system under test based on the one-step predicted state value and the covariance of the system under test using the modified observation equation comprises:

obtaining a plurality of second sampling points of the system to be tested by using unscented transformation on the one-step prediction state value of the system to be tested;

and determining a predicted observation value of the system to be tested based on the plurality of second sampling points by using a modified observation equation.

6. The method of claim 5, wherein determining the predicted observation for the system under test based on the second plurality of sample points using the modified observation equation comprises:

calculating a predicted observation value of the system under test based on the plurality of second sampling points using the following observation equation:

Y_k＝p_k(h(x_k)+v_k)+(I_m×m-p_k)τ (38)

in the formula: y is_kAs observed measurements of the system, p_kIs a matrix of Bernoulli random variables, h (x)_k)+v_kIs the original observation equation of the system, (I)_m×m-p_k) τ is truncated gaussian noise.

7. The method of claim 1, wherein determining a Kalman gain of the system under test based on the predictive observations of the system under test and the covariance comprises:

determining a predictive measurement mean of the system under test based on the predictive observation of the system under test and the covariance;

determining a pre-measurement variance of the system to be tested based on the pre-measurement mean and the covariance of the system to be tested;

and determining the Kalman gain of the system to be tested based on the pre-measurement variance of the system to be tested.

8. The method of claim 7, wherein the predicted mean value of the system under test is determined based on the predicted observations of the system under test using the formula:

in the formula:as a predicted mean value, ω, of the system_m ⁽ⁱ⁾Is the mean weight of the ith sample point,is an observed measurement of the system;

determining a pre-measurement variance of the system under test based on the pre-measurement mean of the system under test using the following formula:

in the formula: p_yyIn order to pre-measure the variance of the measurements,is an observation of the systemThe magnitude of the signal is measured by the sensor,is the average of the pre-measurements of the system,to observe the expectation of noise, P_xyIn order to pre-measure the covariance,for the ith second sample point, the sample is,is the mean value of the state of the system, ω_c ⁽ⁱ⁾Is the covariance weight of the ith sample point.

9. The method of claim 1, wherein the performing state updates and measurement updates for the system under test based on the kalman gain comprises:

updating the state of the system under test based on the Kalman gain using the following formula:

and updating the measured value of the system to be measured based on the Kalman gain by using the following formula:

in the formula:in order to be a predictive state of the system,for the last predicted state of the system, K_kIn order to be the basis of the kalman gain,is a pre-measured value of the system,the last pre-measured value of the system; p_k|kFor the updated covariance matrix, P_k|k-1Is the covariance matrix of the system under test,is the pre-measured variance of the system.

10. A kalman filter, comprising:

one or more processors;

a memory for storing executable instructions of the transmitter;

wherein the one or more processors are configured to perform the Kalman filtering method of processing truncated data of any one of claims 1-9 via execution of the executable instructions.

Technical Field

The disclosure relates to the technical field of data processing, in particular to a Kalman filtering method and a filter for processing truncated data.

Background

Conventional linear filtering techniques are well established, however, the practical application environment often puts new requirements on the classical signal processing. What the comparison has to be of significance is the so-called truncated (Censored) data. Due to the limitation of sampling environment or insufficient processing capacity, data samples which need to be processed are often not complete, but are naturally or artificially truncated, so that precision loss or information loss is caused.

The existing filtering technology has the defects of poor stability and reliability when facing the data truncation problem of complex systems such as a nonlinear system and the like.

It is to be noted that the information disclosed in the above background section is only for enhancement of understanding of the background of the present disclosure, and thus may include information that does not constitute prior art known to those of ordinary skill in the art.

Disclosure of Invention

The present disclosure is directed to overcome the above-mentioned deficiencies in the prior art and to provide a kalman filtering method and filter for processing truncated data.

According to an aspect of the present disclosure, there is provided a kalman filtering method of processing truncated data, including:

calculating a one-step prediction state value and covariance of the system to be tested by using an unscented Kalman filtering UKF algorithm;

determining a predicted observation value of the system to be tested based on the one-step predicted state value of the system to be tested by using a corrected observation equation;

determining a Kalman gain of the system under test based on the predicted observation of the system under test and the covariance;

and updating the state and the measured value of the system to be tested based on the Kalman gain.

According to another aspect of the present disclosure, there is also provided a kalman filter, including:

one or more processors;

a memory for storing executable instructions of the transmitter;

wherein the one or more processors are configured to perform, via execution of the executable instructions, the Kalman filtering method of processing truncated data of any embodiment of the present disclosure.

According to the filtering method, a UKF algorithm is used for a system to be tested to obtain a one-step prediction state value and covariance of the system to be tested, new sampling points of the system to be tested can be obtained on the basis of the one-step prediction state value, the sampling points are substituted into a correction observation equation provided by the method to obtain a prediction observation value of the system to be tested, then a Kalman gain of the system to be tested can be calculated according to the prediction observation value of the system to be tested and the covariance of the system to be tested, and then the Kalman gain is used to realize state updating and measurement value updating of the system to be tested. According to the method, the observation equation is corrected, truncation is integrated into the statistical characteristic of the corrected observation equation, noise is not Gaussian distribution any more, but is truncated Gaussian distribution, and therefore the observation value is also subjected to the truncated Gaussian distribution. Therefore, the method disclosed by the invention can be suitable for the nonlinear system and can effectively solve the data truncation problem of the nonlinear system.

It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the disclosure.

Drawings

The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the present disclosure and together with the description, serve to explain the principles of the disclosure. It is to be understood that the drawings in the following description are merely exemplary of the disclosure, and that other drawings may be derived from those drawings by one of ordinary skill in the art without the exercise of inventive faculty.

FIG. 1 is a flow chart of a Kalman filtering method of processing truncated data according to the present disclosure;

FIG. 2 is a schematic diagram of the principle of an unscented transformation;

FIG. 3 is a flow chart for calculating a one-step state prediction value and covariance of a system under test using the UKF algorithm;

FIG. 4 is a flow chart for determining a predictive observation for a system under test;

FIG. 5 is a flow chart of a method of Kalman gain determination;

FIG. 6 is a comparison graph of tracking position errors of a target by the filtering method of the present disclosure and a classical UKF filtering method;

FIG. 7 is a block diagram of the structure of the Kalman filter of the present disclosure.

Detailed Description

Example embodiments will now be described more fully with reference to the accompanying drawings. Example embodiments may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the concept of example embodiments to those skilled in the art. The same reference numerals in the drawings denote the same or similar structures, and thus their detailed description will be omitted. Furthermore, the drawings are merely schematic illustrations of the disclosure and are not necessarily drawn to scale.

Although relative terms, such as "upper" and "lower," may be used in this specification to describe one element of an icon relative to another, these terms are used in this specification for convenience only, e.g., in accordance with the orientation of the examples described in the figures. It will be understood that if the device of the figures is turned over, with its top and bottom reversed, elements described as "top" will be termed "bottom". When a structure is "on" another structure, it may mean that the structure is integrally formed with the other structure, or that the structure is "directly" disposed on the other structure, or that the structure is "indirectly" disposed on the other structure via another structure.

The terms "a," "an," "the," "said," and "at least one" are used to indicate the presence of one or more elements/components/etc.; the terms "comprising" and "having" are intended to be inclusive and mean that there may be additional elements/components/etc. other than the listed elements/components/etc.; the terms "first," "second," and "third," etc. are used merely as labels, and are not limiting on the number of their objects.

Since data truncation can be viewed as a special non-linearity, some non-linear recursive filters such as EKF, UKF, PF, etc. can be considered.

The EKF linearizes a nonlinear system near a working point, and the EKF is implemented by two points: firstly, linearly approximating the system near the working point; second, under linear system approximation, both the noise term and the state are treated as gaussian distributions, so that the state can be described by estimating their mean and covariance matrices, and the subsequent operation is the same as kalman filtering. Namely, the formula given by the EKF is consistent with Kalman, and a matrix after linearization is used for replacing a transfer matrix and an observation matrix of a Kalman filter. But because the observation equation has obvious discontinuity in the truncated region, there is no gradient at the discontinuity, and thus EKF cannot effectively deal with the truncated data problem.

The UKF abandons the traditional method of linearizing the nonlinear function, adopts a Kalman linear filtering frame, and uses Unscented Transformation (UT) to process the nonlinear transfer problem of mean value and covariance difference for a one-step prediction equation. The UKF algorithm is used for approximating the probability density distribution of a nonlinear function, and a series of determined samples are used for approximating the posterior probability density of the state instead of approximating the nonlinear function, and the derivation of a Jacobian matrix is not needed. The UKF does not ignore high-order terms, so the statistic of the nonlinear distribution has higher calculation precision. UKF, although a computationally less intensive method, is not robust when the measurements are close to the truncation region.

The PF adopts a method for describing the distribution by using a large number of sampling points, namely a process of continuous sampling, weight calculation and resampling, the more consistent the particles which are observed have about large weight, and the more weight is, the more easily the particles are acquired during resampling. PF is computationally much more costly than EKF and UKF because it requires the use of a set of weighted samples called particles to generate the posterior distribution. In addition, the discontinuity in the Tobit model means that a large number of particles are needed to fully model the system in the region, resulting in the number of particles required for sampling, which grows exponentially with the distribution, so that the problem of low dimension is limited, and the problem of high dimension is basically impossible.

In view of the above problems, the embodiments of the present disclosure provide a kalman filtering method for processing truncated data, which can be applied to a case where data truncation occurs in a nonlinear system. Fig. 1 is a flowchart illustrating a kalman filtering method for processing truncated data according to the present disclosure, which includes the following steps:

s110, calculating a one-step prediction state value and covariance of the system to be tested by using an unscented Kalman filtering UKF algorithm;

s120, determining a prediction observation value of the system to be tested based on the one-step prediction state value of the system to be tested by using a correction observation equation;

s130, determining Kalman gain of the system to be tested based on the prediction observation value and covariance of the system to be tested;

and S140, updating the state and the measured value of the system to be tested based on Kalman gain.

According to the filtering method, a UKF algorithm is used for a system to be tested to obtain a one-step prediction state value and covariance of the system to be tested, new sampling points of the system to be tested can be obtained on the basis of the one-step prediction state value, the sampling points are substituted into a correction observation equation provided by the method to obtain a prediction observation value of the system to be tested, then a Kalman gain of the system to be tested can be calculated according to the prediction observation value of the system to be tested and the covariance of the system to be tested, and then the Kalman gain is used to realize state updating and measurement value updating of the system to be tested. According to the method, the observation equation is corrected, truncation is integrated into the statistical characteristic of the corrected observation equation, noise is not Gaussian distribution any more, but is truncated Gaussian distribution, and therefore the observation value is also subjected to the truncated Gaussian distribution. Therefore, the method disclosed by the invention can be suitable for the nonlinear system and can effectively solve the data truncation problem of the nonlinear system. The steps in the present exemplary embodiment are specifically described below.

In step S110, a one-step predicted state value and covariance of the system under test are calculated by the existing UKF filtering algorithm. The system to be tested can be determined for the target object to be tracked, specifically according to the use scene. Unscented kalman filtering UKF is a nonlinear filtering method. It uses an unscented transform to handle the nonlinear transfer problem of mean and covariance. Fig. 2 is a schematic diagram illustrating the principle of the unscented transformation, the basic principle of which is: and selecting a plurality of sampling points, namely a Sigma point set, according to a certain rule by combining the original state distribution characteristics, so that the mean value and the covariance of the sampling points are equal to the mean value and the covariance of the original state distribution. And substituting the points into a nonlinear function to correspondingly obtain a nonlinear function value point set, and solving the mean value and the covariance after transformation through the point set. Therefore, the non-linear problem is simpler and more intuitive in processing due to the unscented transformation, and the better precision of the non-linear Kalman filter such as the EKF is kept. FIG. 3 shows the specific steps of calculating the one-step state prediction value and covariance of the system under test using the UKF algorithm, including:

s310, acquiring a plurality of first sampling points of the system to be tested by using unscented transformation, and calculating the weight of each first sampling point;

s320, calculating a one-step prediction state value of each first sampling point;

s330, determining a one-step prediction state value and covariance of the system to be tested based on the one-step prediction state value of each first sampling point and the weight of each first sampling point.

In step S310, a set of sigma points, i.e. a plurality of first sampling points, is obtained through the UT transformation, and a weight of each first sampling point is calculated, where the weight includes a state mean weight and a covariance weight of the system under test. In this exemplary embodiment, a proportional symmetric sampling method with better performance may be adopted to perform UT transformation to obtain a sigma point set of the system under test. If n is the dimension of the state vector, 2n +1 sigma sampling points can be obtained as follows:

in the formula:is the ith first sampling point;is the state mean of the system; i is the number of columns of the matrix;is the square root of the matrixColumn i.

And calculating the weight of each sigma sampling point of the system to be measured based on the following formula, wherein the weight of each sigma sampling point is used for calculating the Kalman gain of the system in the subsequent steps. The weight of each sigma sampling point in the step comprises a system state weight and a covariance weight, and the calculation formula is as follows:

in the formula:is a system state weight ofThe covariance weight is marked as the number of sampling points; parameter λ ═ a²(n + k) -n is a scaling parameter for reducing the total budget error, the selection of a controls the distribution state of sampling points, and k is a parameter to be selected; the candidate parameter beta is a non-negative weight coefficient.

In step S320, a one-step predicted state value of each first sampling point is calculated to predict a next state of the system through the one-step predicted state values of the sigma point set. The one-step predicted state value for each first sample point can be expressed as:

in the formula:in order to predict the state value in one step,for the last state value, f (-) is the state update function of the system.

In step S330, a predicted value and covariance of the state of the system under test are further determined. Specifically, the one-step predicted state value of the system to be measured can be calculated based on the one-step predicted state value of each first sampling point and the weight of each first sampling point through the following formula:

in the formula:predicting a state value, ω, for a step of the system_m ⁽ⁱ⁾Is the weight of the ith sample point,the state values are predicted for one step at the ith sample point.

And calculating a covariance matrix of the system to be measured based on the one-step predicted state value of each first sampling point and the weight of each first sampling point by using the following formula:

in the formula: p_k|k-1Is the covariance matrix, omega, of the system under test_c ⁽ⁱ⁾Is the weight of the ith sample point,the state value is predicted for one step of the system,the state value is predicted for the one step at the ith sample point, and Q is a constant.

After the steps S310 to S330, the one-step state prediction of the system to be tested is realized according to the UKF algorithm, so that a basis is provided for the system state updating in the subsequent steps.

In step S120, on the basis of one-step prediction of the system state, a new sigma point set, that is, a plurality of second sampling points, is obtained through UT transformation, and then the plurality of second sampling points are substituted into the modified observation equation provided in the present disclosure to obtain the predicted observation value of the system to be measured, which is equivalent to that the measurement observation value is used in kalman filtering in this step to obtain the predicted observation value. It is worth noting that the problem of data truncation of a nonlinear system can be effectively solved by using the corrected observation equation through correcting the observation equation of the system, and the function extension of the existing UKF filtering algorithm is realized. FIG. 4 shows a flow diagram for determining a predictive observation for a system under test, comprising:

s410, acquiring a plurality of second sampling points of the system to be tested by using unscented transformation on the one-step prediction state value of the system to be tested;

and S420, determining a prediction observation value of the system to be measured based on the plurality of second sampling points by using the corrected observation equation.

In step S410, the UT transform is used to re-sample the obtained one-step predicted state of the system under test, so as to obtain a new sigma point set, i.e. a plurality of second sampling points. It should be understood that, in this step, a plurality of second sampling points may also be obtained by using a proportional-symmetric sampling method with better sampling performance. The resulting plurality of second sample points may be represented by:

in the formula:is the ith second sampling point;a state average value predicted for one step of the system; i is the number of columns of the matrix;is the square root of the matrixColumn i.

In step S420, specifically, a plurality of second sampling points generated in step S410 are substituted into the modified observation equation provided in the present disclosure to obtain a predicted observation value of the system under test.

After introducing the basic equation of the UKF algorithm to the Tobit model of the left truncation type, the nonlinear system can be expressed as follows:

thus, the modified observation equation of the present disclosure can be expressed as:

Y_k＝p_k(h(x_k)+v_k)+(I_m×m-p_k)τ (38)

in the formula: y is_kAs observed measurements of the system, p_kIs a matrix of Bernoulli random variables, h (x)_k)+v_kIs the original observation equation of the system, (I)_m×m-p_k) τ is truncated gaussian noise.

After substituting the second sampling point into the modified observation equation (38), an expression for calculating the predicted observation value of the system under test can be obtained as follows:

in the formula:as observed measurements of the system, p_kIs a matrix of bernoulli random variables,is the original observation equation of the system, (I)_m×m-p_k) τ is truncated gaussian noise.

The derivation of the modified observation equation in this disclosure is described below. The basic equation for kalman filtering is:

the state equation is as follows: x is the number of_k＝f(x_k-1)+w_k-1 (2)

The observation equation: y is_k＝h(x_k)+v_k (3)

Where x is the state value, y is the measured value, and the corner mark k represents the recursion order (or temporal order); f (-) is a state update function, h (-) is an observation function; w is the state noise obeying a zero mean gaussian distribution with variance Q, and v is the observation noise obeying a zero mean gaussian distribution with variance R.

When the problem of truncating data is faced, the problem can be solved by introducing a Tobit model. For convenience of expression, only the left truncated Tobit model will be described below, and other Tobit types can be derived by analogy with the left truncated Tobit model. The general description of the Tobit model of the left truncation type is as follows:

wherein the content of the first and second substances,is an observed value without truncation, y_tIs the true observation that is truncated, and τ is the data truncation threshold, the value of which is determined by the specific environment.

It can be seen that truncation caused by the Tobit model is a unique non-linear type, with zero slope in the truncation region and a discontinuity at the truncation point. After the Tobit model is introduced into a basic equation of Kalman filtering, a new equation set is obtained as follows:

the state equation is as follows: x is the number of_k＝f(x_k-1)+w_k-1 (6)

The observation equation:

tobit model of left truncation type:

due to the data truncation, the observed noise in the truncation region no longer follows the Gaussian distribution, and the state value determines the occurrence of the truncation phenomenonAnd thus noise is correlated with the state value. In the case of data truncation, against the assumption that the noise of kalman filtering is independent of the state value, processing truncated data directly using a kalman filter will no longer be unbiased. The Kalman filtering may be modified by an observation equation according to the Tobit model, specifically to represent the truncation measure y_k∈R^m×1Introducing a Bernoulli random variable matrix p_k∈R^m×mWherein:

based on the formulas (6) to (9), a modified observation equation of kalman filtering can be obtained:

y_k＝p_k(h(x_k)+v_k)+(I_m×m-p_k)τ (10)

applying the modified observation equation shown in equation (10) to the nonlinear system shown in equation (17) can obtain the modified observation equation of the nonlinear system shown in equation (38).

The observation value is subjected to the truncated Gaussian distribution, so that the observation value can be used for processing the truncated data.

In step S130, to determine the kalman gain of the system under test, fig. 5 shows a flowchart of the method for determining the kalman gain, which includes:

s510, determining a prediction average value of the system to be tested based on the prediction observation value and the covariance of the system to be tested;

s520, determining the prediction variance of the system to be tested based on the prediction mean value and the covariance of the system to be tested;

s530, determining Kalman gain of the system to be tested based on the pre-measurement variance of the system to be tested.

In step S510, the predicted average value of the system under test may be calculated according to the following formula:

in the formula:as a predicted mean value, ω, of the system_m ⁽ⁱ⁾Is the mean weight of the ith sample point,is an observed measurement of the system.

In step S520, the pre-measurement variance of the system under test, including the pre-measurement variance P, can be calculated by_yyAnd a pre-measurement covariance P_xyAnd:

in the formula: p_yyIn order to pre-measure the variance of the measurements,in order to be an observed measurement of the system,is a predicted mean value of the system, P_xyIn order to pre-measure the covariance,for the ith second sample point, the sample is,is the mean value of the states, ω, of the system_c ⁽ⁱ⁾Is the covariance weight of the ith sample point.

The above formula(26) In (1),to observe the expectation of noise, where p_kIs a Bernoulli random variable, v_k∈R^m×1Is zero mean Gaussian white noise, and the covariance is R ∈ R^m×mIt is assumed that the state noise and the observation noise of the process are independent of each other, the state noise and the observation noise are independent of each other, and the state noise and the observation noise are also independent of each other in time. The bernoulli random variable can be calculated according to the following formula:

E(p_k(l) Is the probability that the true observation falls into the non-truncated region, assuming that the observation noise is in an opposite angle form, there are:

it should be noted that, in step S520, based on the UKF algorithm, the correction of the statistical properties of the measurement observed value and the observed noise covariance is realized by introducing the Tobit model, and the change of the statistical properties of the observed noise can be approximately equivalent to the noise multiplied by a "truncated observation matrix". Therefore, the real value can be well converged by using the information existing in the truncation value, the estimation performance is improved, and the state estimation can be well improved by including the truncation information in the model.

In obtaining the covariance P of the pre-measurement_xySum variance P_yyThen, in step S530, the kalman gain of the system under test may be calculated according to the following formula:

after obtaining the kalman gain, in step S140, the state of the system under test may be updated according to the following formula:

and updating the measured value of the system to be measured based on Kalman gain by using the following formula:

in the formula:in order to be a predictive state of the system,for the last predicted state of the system, K_kIs the gain of the karman, and is,is a pre-measured value of the system,the last pre-measured value of the system; p_k|kFor the updated covariance matrix, P_k|k-1Is the covariance matrix, P, of the system under test_ykykIs the pre-measured variance of the system.

The filtering method provided by the disclosure can show better performance than that of a classical UKF in the problem of target tracking with a limited detection range, is less influenced by a strong nonlinearity and a truncation region, and can keep better tracking capability on a target. The application effect of the filtering method of the present disclosure is further described below with reference to a specific example.

Illustratively, in a radar tracking example, particle M is assumed to have a uniform acceleration motion in two dimensions x-y. Available vector of its position, velocity and acceleration at a certain moment kAnd (4) showing. The motion in both the horizontal direction (x-axis direction) and the vertical direction (y-axis direction) has additive system noise w (k), and the motion state equation of the mass point under the cartesian coordinate system is:

X(k+1)＝ΦX(k)+W(k) (31)

in the formula:

assuming that the radar with the coordinate position at the origin tracks the mass point M, the radar can effectively detect the range of the target as a circular region with a radius D. The distance between the radar and the mass point M is denoted r_kThe angle of mass point M relative to the radar isIn actual measurement, the radar has additive measurement noise V (k), and in a coordinate system taking the radar as a center, an observation equation is as follows:

the measured values are:

in the simulation, the radar detection range D is assumed to be 5200m, and the system noise W (k) has a covariance matrix Q_kV (k) has a covariance matrix R_kRespectively as follows:

w, V, the observation times N is 120 and the sampling time T is 0.5 s. Initial state X (0) ═ 1000; 4500; 40; 150; 2; -10]^TThe initial state covariance matrix is:

fig. 6 shows the comparison of the tracking position error of the filtering method of the present disclosure with the tracking position error of the classical UKF filtering method for a target, in which the abscissa represents the number of observations and the ordinate represents the distance deviation, the first curve 701 is the tracking curve of the filtering method of the present disclosure for a target, the second curve 702 is the tracking curve of the classical UKF filtering method for a target, which can be obtained from simulation results, when the filtering algorithm provided by the present disclosure is used to track a target with a limited detection range, it can still maintain a relatively good tracking ability near a truncation region with a relatively strong nonlinear ratio, which is less affected by the nonlinearity and the truncation region, the tracking deviation of which is not more than 25m at the truncation region, whereas the traditional UKF filtering method shows an obvious instability near a truncation region with a relatively strong nonlinear ratio, the tracking deviation of which is 90m at the maximum in the truncation region, and exhibit significant instability. In addition, when the target is tracked by using the filtering algorithm disclosed by the invention, the tracking result of the target each time is superior to the tracking result of the classic UKF filtering method. It can be seen that the filtering method provided by the present disclosure has better performance in detecting range-limited target tracking.

In addition, in an exemplary embodiment of the present disclosure, a kalman filter capable of implementing the above method is also provided.

A kalman filter 900 according to this embodiment of the present invention is described below with reference to fig. 7. The kalman filter 900 shown in fig. 7 is merely an example, and should not place any limitation on the function and scope of use of an embodiment of the present invention.

As shown in fig. 7, the kalman filter 900 is in the form of a general purpose computing device. The components of the kalman filter 900 may include, but are not limited to: the at least one processing unit 910, the at least one storage unit 920, a bus 930 connecting different system components (including the storage unit 920 and the processing unit 910), and a display unit 940.

Wherein the storage unit stores program code that may be executed by the processing unit 910 to cause the processing unit 910 to perform the steps according to various exemplary embodiments of the present invention described in the above section "exemplary method" of the present specification.

The storage unit 920 may include readable media in the form of volatile memory units, such as a random access memory unit (RAM)921 and/or a cache memory unit 922, and may further include a read only memory unit (ROM) 923.

Storage unit 920 may also include a program/utility 924 having a set (at least one) of program modules 925, such program modules 925 including, but not limited to: an operating system, one or more application programs, other program modules, and program data, each of which, or some combination thereof, may comprise an implementation of a network environment.

Bus 930 can be any of several types of bus structures including a memory unit bus or memory unit controller, a peripheral bus, an accelerated graphics port, a processing unit, or a local bus using any of a variety of bus architectures.

The kalman filter 900 may also be in communication with one or more external devices 1100 (e.g., a keyboard, a pointing device, a bluetooth device, etc.), with one or more devices that enable a user to interact with the kalman filter 900, and/or with any device (e.g., a router, a modem, etc.) that enables the kalman filter 900 to communicate with one or more other computing devices. Such communication may occur via input/output (I/O) interface 950. Also, the kalman filter 900 may also communicate with one or more networks (e.g., a Local Area Network (LAN), a Wide Area Network (WAN), and/or a public network, such as the internet) via a network adapter 960. As shown, the network adapter 940 communicates with the other modules of the kalman filter 900 over a bus 930. It should be appreciated that, although not shown in the figures, other hardware and/or software modules may be used in conjunction with the kalman filter 900, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage systems, among others.

Through the above description of the embodiments, those skilled in the art will readily understand that the exemplary embodiments described herein may be implemented by software, or by a combination of software and necessary hardware. Therefore, the technical solution according to the embodiments of the present disclosure may be embodied in the form of a software product, which may be stored in a non-volatile storage medium (which may be a CD-ROM, a usb disk, a removable hard disk, etc.) or on a network, and includes several instructions to enable a computing device (which may be a personal computer, a server, a terminal device, or a network device, etc.) to execute the method according to the embodiments of the present disclosure.

It should be noted that although the various steps of the kalman filtering method of processing truncated data in the present disclosure are depicted in the drawings in a particular order, this does not require or imply that the steps must be performed in this particular order, or that all of the depicted steps must be performed, to achieve the desired results. Additionally or alternatively, certain steps may be omitted, multiple steps combined into one step execution, and/or one step broken down into multiple step executions, etc.

Other embodiments of the disclosure will be apparent to those skilled in the art from consideration of the specification and practice of the disclosure disclosed herein. This application is intended to cover any variations, uses, or adaptations of the disclosure following, in general, the principles of the disclosure and including such departures from the present disclosure as come within known or customary practice within the art to which the disclosure pertains. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the disclosure being indicated by the following claims.