A joint parameter estimation method and system based on an adaptive multiple model algorithm

Abstract

The application discloses a joint parameter estimation method and system based on an adaptive multi-model algorithm, and relates to the technical field of joint parameter estimation. The method comprises the following steps: obtaining a state estimation value and an error covariance estimation value of a filter at a current moment; obtaining a variance of a residual error according to an acceleration estimation value of the filter on a target at each moment; performing filtering according to the variance of the residual error to obtain a steady-state error of the filter at the current moment; obtaining a measurement sensitivity of the filter at the current moment according to a sum of innovation sequences of the filter at the current moment; obtaining a likelihood function value of the filter at the current moment based on the steady-state error of the filter at the current moment and the measurement sensitivity; and obtaining a fused state estimation value and an error covariance estimation value of all filters at the current moment based on the state estimation value, the error covariance estimation value and the likelihood function value of all filters at the current moment. The application can improve the precision of a joint parameter estimation result.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of joint parameter estimation, in particular to a joint parameter estimation method and system based on an adaptive multi-model algorithm. BACKGROUND

[0002] In the field of target tracking, a moving target and a radar for detection form a complex system, and a discrete form of a system equation of the complex system can be expressed as: wherein f(·) represents a state transition function; h(·) represents a measurement function; x k represents a system state quantity at a k moment, x k-1 represents a system state quantity at a k-1 moment, represents a system measurement, ζ k-1 represents a system parameter, which can be a characteristic parameter of target motion such as acceleration and turning angular velocity; w k and v k are process noise and measurement noise respectively, and both of them are white noise conforming to a Gaussian distribution, and variances are Q k and R k .

[0003] In the field of target tracking and motion information extraction, state estimation of a complex system formed by a moving target and a radar for detection is a widespread problem. For the estimation problem of the complex system, a plurality of filters can be used for estimation, and each filter represents a different system parameter mode. A typical method is an interactive multi-model method, however, this method needs to run a large number of models, and each model is allocated a certain model probability, and thus there is a problem of competition between models, resulting in low precision of parameter estimation. SUMMARY

[0004] The purpose of the present application is to provide a joint parameter estimation method and system based on an adaptive multi-model algorithm, which can improve the precision of joint parameter estimation results.

[0005] To achieve the above purpose, the present application provides the following solutions.

[0006] A joint parameter estimation method based on an adaptive multi-model algorithm, comprising:

[0007] At a current moment, for any filter, a Kalman filter is used to obtain a state estimation value of the filter at the current moment and an error covariance estimation value of the filter at the current moment according to a state estimation value of the filter at a previous moment and an error covariance estimation value of the filter at the previous moment; the state estimation value of the filter comprises an estimation value of a target position and an estimation value of a target velocity of the filter;

[0008] obtaining an average acceleration estimation value of the filter for the target at the current time according to the acceleration estimation values of the filter for the target at each time within a smoothing period, the last time in the each time being the current time;

[0009] obtaining a variance of a residual of the acceleration estimation value of the filter for the target at the current time according to the average acceleration estimation value of the filter for the target at the current time and the acceleration estimation value of the filter for the target at the current time;

[0010] filtering the variance of the residual of the acceleration estimation value of the filter for the target at the current time using a first low-pass filter to obtain a filtered variance of the residual of the acceleration estimation value of the filter for the target at the current time;

[0011] obtaining a steady-state error of the filter at the current time based on the filtered variance of the residual of the acceleration estimation value of the filter for the target at the current time;

[0012] filtering the sum of the innovation sequences of the filter at the current time using a second low-pass filter to obtain a filtered sum of the innovation sequences of the filter at the current time;

[0013] obtaining a measurement sensitivity of the filter at the current time according to the filtered sum of the innovation sequences of the filter at the current time;

[0014] obtaining a likelihood function value of the filter at the current time based on the steady-state error of the filter at the current time and the measurement sensitivity of the filter at the current time;

[0015] obtaining fused state estimation values of all the filters at the current time and fused error covariance estimation values of all the filters at the current time based on the state estimation values of all the filters at the current time, the error covariance estimation values of all the filters at the current time and the likelihood function values of all the filters at the current time.

[0016] Optionally, the obtaining the average acceleration estimation value of the filter for the target at the current time according to the acceleration estimation values of the filter for the target at each time within a smoothing period, the last time in the each time being the current time, specifically comprises:

[0017] obtaining the average acceleration estimation value of the filter for the target at the current time according to a formula wherein k represents the current time, i represents the i-th filter, l represents the l-th time, represents the average acceleration estimation value of the i-th filter for the target at the current time, μ represents a smoothing period, represents the acceleration estimation value of the i-th filter for the target at the l-th time.

[0018] Optionally, the variance of the residual of the acceleration estimation value of the filter for the target at the current time is calculated according to the average acceleration estimation value of the target at the current time and the acceleration estimation value of the target at the current time, and the variance of the residual of the acceleration estimation value of the filter for the target at the current time is calculated according to the formula

[0019] The variance of the residual of the acceleration estimation value of the filter for the target at the current time is calculated according to the formula The variance of the residual of the acceleration estimation value of the filter for the target at the current time is calculated according to the formula The variance of the residual of the acceleration estimation value of the filter for the target at the current time is calculated according to the formula The variance of the residual of the acceleration estimation value of the filter for the target at the current time is calculated according to the formula

[0020] Optionally, the variance of the residual of the filtered acceleration estimation value of the filter for the target at the current time is filtered using a first low-pass filter to obtain the variance of the residual of the filtered acceleration estimation value of the filter for the target at the current time, and the variance of the residual of the filtered acceleration estimation value of the filter for the target at the current time is calculated according to the formula

[0021] The variance of the residual of the filtered acceleration estimation value of the filter for the target at the current time is calculated according to the formula The variance of the residual of the filtered acceleration estimation value of the filter for the target at the current time is calculated according to the formula The variance of the residual of the filtered acceleration estimation value of the filter for the target at the current time is calculated according to the formula The variance of the residual of the filtered acceleration estimation value of the filter for the target at the current time is calculated according to the formula

[0022] Optionally, the steady-state error of the filter at the current time is obtained based on the variance of the residual of the filtered acceleration estimation value of the filter for the target at the current time, and the steady-state error of the filter at the current time is calculated according to the formula

[0023] The steady-state error of the filter at the current time is calculated according to the formula The steady-state error of the filter at the current time is calculated according to the formula The steady-state error of the filter at the current time is calculated according to the formula The expected range of g 1,k The steady-state error of the filter at the current time is calculated according to the formula 1,k The steady-state error of the filter at the current time is calculated according to the formula 1,k The steady-state error of the filter at the current time is calculated according to the formula 1,k The steady-state error of the filter at the current time is calculated according to the formula 1,k The steady-state error of the filter at the current time is calculated according to the formula

[0024] Optionally, the sum of the innovation sequences of the filtered filter at the current time is determined according to the formula The sum of the innovation sequences of the filtered filter at the current time is calculated according to the formula The sum of the innovation sequences of the filtered filter at the current time is calculated according to the formulam denotes a unit vector in m-dimension, H k denotes a measurement matrix, denotes the error covariance matrix of the i-th filter at the last time, R k denotes a measurement noise variance matrix, denotes the measurement value obtained at the current time, denotes the measurement prediction value of the i-th filter at the current time.

[0025] Optionally, the filtering of the sum of innovation sequences of the filter at the current time by using the second low-pass filter to obtain the sum of filtered innovation sequences of the filter at the current time comprises:

[0026] According to the formula obtain the sum of filtered innovation sequences of the filter at the current time, wherein, denotes the sum of filtered innovation sequences of the i-th filter at the current time, and τ2 denotes a tuning parameter of the second low-pass filter, is the sum of filtered innovation sequences of the i-th filter at the last time.

[0027] Optionally, the obtaining of the measurement sensitivity of the filter at the current time according to the sum of filtered innovation sequences of the filter at the current time comprises:

[0028] According to the formula calculate the measurement sensitivity of the filter at the current time, wherein, denotes the measurement sensitivity of the i-th filter at the current time, and β denotes a scaling parameter.

[0029] Optionally, the obtaining of the likelihood function value of the filter at the current time based on the steady-state error of the filter at the current time and the measurement sensitivity of the filter at the current time comprises:

[0030] According to the formula calculate the likelihood function value of the filter at the current time, wherein, denotes the likelihood function value of the i-th filter at the current time, exp() denotes an exponential function with a natural constant e as the base, and n denotes the total number of filters.

[0031] A joint parameter estimation system based on an adaptive multiple model algorithm comprises:

[0032] The state estimation value and error covariance estimation value calculation module is configured to, at the current time, obtain, for any filter, a state estimation value of the filter at the current time and an error covariance estimation value of the filter at the current time by using a Kalman filter according to a state estimation value of the filter at a previous time and an error covariance estimation value of the filter at the previous time; the state estimation value of the filter includes an estimation value of the filter for a target position and an estimation value of the filter for a target velocity;

[0033] The acceleration average estimation value calculation module is configured to obtain an acceleration average estimation value of the filter for a target at the current time according to acceleration estimation values of the filter for the target at each time within a smoothing period; a last time in the each time is the current time;

[0034] The variance calculation module of the residual of the acceleration estimation value is configured to obtain a variance of the residual of the acceleration estimation value of the filter for a target at the current time according to an acceleration average estimation value of the filter for the target at the current time and an acceleration estimation value of the filter for the target at the current time;

[0035] The first filtering module is configured to filter the variance of the residual of the acceleration estimation value of the filter for a target at the current time by using a first low-pass filter to obtain a filtered variance of the residual of the acceleration estimation value of the filter for the target at the current time;

[0036] The steady-state error calculation module is configured to obtain a steady-state error of the filter at the current time based on the filtered variance of the residual of the acceleration estimation value of the filter for a target at the current time;

[0037] The second filtering module is configured to filter the sum of innovation sequences of the filter at the current time by using a second low-pass filter to obtain a filtered sum of innovation sequences of the filter at the current time;

[0038] The measurement sensitivity calculation module is configured to obtain a measurement sensitivity of the filter at the current time according to the filtered sum of innovation sequences of the filter at the current time;

[0039] The likelihood function value calculation module is configured to obtain a likelihood function value of the filter at the current time based on the steady-state error of the filter at the current time and the measurement sensitivity of the filter at the current time;

[0040] The fusion module is configured to obtain fused state estimation values of all filters at the current time and fused error covariance estimation values of all filters at the current time based on the state estimation values of all filters at the current time, the error covariance estimation values of all filters at the current time, and the likelihood function values of all filters at the current time.

[0041] According to the specific embodiments of the present application, the following technical effects are disclosed:

[0042] According to the present application, the average acceleration estimation value of the filter for the target at the current time is obtained according to the acceleration estimation value of the filter for the target at each time within a smooth period; the variance of the residual of the acceleration estimation value of the filter for the target at the current time is obtained according to the average acceleration estimation value of the filter for the target at the current time and the acceleration estimation value of the filter for the target at the current time; the variance of the residual of the filtered acceleration estimation value of the filter for the target at the current time is obtained by filtering the variance of the residual of the acceleration estimation value of the filter for the target at the current time using a first low-pass filter; the steady-state error of the filter at the current time is obtained based on the variance of the residual of the filtered acceleration estimation value of the filter for the target at the current time; the sum of the innovation sequences of the filter at the current time is filtered using a second low-pass filter to obtain the sum of the innovation sequences of the filtered filter at the current time; the measurement sensitivity of the filter at the current time is obtained according to the sum of the innovation sequences of the filtered filter at the current time; and the likelihood function value of the filter at the current time is obtained based on the steady-state error of the filter at the current time and the measurement sensitivity of the filter at the current time, which combines the new likelihood function and takes into account the steady-state tracking error and tracking flexibility of the system, and can solve the parameter estimation problem of the complex system with parameter mutation and the high-precision tracking problem of the target. BRIEF DESCRIPTION OF DRAWINGS

[0043] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed in the embodiments will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0044] Figure 1 The flowchart of the joint parameter estimation method based on the adaptive multi-model algorithm provided by the embodiments of the present application is shown in Figure 1.

[0045] Figure 2 The simulation scene diagram is shown in Figure 2.

[0046] Figure 3 The position estimation error comparison diagram is shown in Figure 3.

[0047] Figure 4 The velocity estimation error comparison diagram is shown in Figure 4.

[0048] Figure 5 The X-direction acceleration estimation result comparison diagram is shown in Figure 5.

[0049] Figure 6 The Y-direction acceleration estimation result comparison diagram is shown in Figure 6. DETAILED DESCRIPTION

[0050] The technical solutions in the embodiments of the present application will be apparently and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all the other embodiments obtained by a person of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0051] In order to make the above objectives, characteristics and advantages of the present application more obvious and easy to understand, the present application will be further described in detail below with reference to the drawings and specific embodiments.

[0052] The embodiment of the present application provides a joint parameter estimation method based on an adaptive multiple model algorithm. The joint parameter estimation method based on the adaptive multiple model algorithm mainly has three parts: parallel filtering (step 101), likelihood function calculation (steps 102 to 108), and result fusion (step 109), as shown in the figure. Figure 1 The method comprises the following steps.

[0053] Step 101: At the current time, for any filter, a Kalman filter is used to obtain a state estimation value of the filter at the current time and an error covariance estimation value of the filter at the current time according to a state estimation value of the filter at the last time and an error covariance estimation value of the filter at the last time; the state estimation value of the filter comprises an estimation value of the filter for a target position and an estimation value of the filter for a target speed, wherein the target is a target moving in a complex system composed of a radar for detection.

[0054] Step 102: An average estimation value of the filter for the target acceleration at the current time is obtained according to the estimation values of the filter for the target acceleration at each time in a smoothing period; the last time in the each time is the current time.

[0055] Step 103: A variance of a residual of the estimation value of the filter for the target acceleration at the current time is obtained according to the average estimation value of the filter for the target acceleration at the current time and the estimation value of the filter for the target acceleration at the current time.

[0056] Step 104: A first low-pass filter is used to filter the variance of the residual of the estimation value of the filter for the target acceleration at the current time to obtain a filtered variance of the residual of the estimation value of the filter for the target acceleration at the current time.

[0057] Step 105: A steady-state error of the filter at the current time is obtained based on the filtered variance of the residual of the estimation value of the filter for the target acceleration at the current time.

[0058] Step 106: filtering the sum of the innovation sequences of the filter at the current time using a second low-pass filter to obtain the sum of the filtered innovation sequences of the filter at the current time.

[0059] Step 107: obtaining the measurement sensitivity of the filter at the current time according to the sum of the filtered innovation sequences of the filter at the current time.

[0060] Step 108: obtaining the likelihood function value of the filter at the current time based on the steady-state error of the filter at the current time and the measurement sensitivity of the filter at the current time.

[0061] Step 109: obtaining the fused state estimation value of all the filters at the current time and the fused error covariance estimation value of all the filters at the current time based on the state estimation values of all the filters at the current time, the error covariance estimation values of all the filters at the current time and the likelihood function values of all the filters at the current time.

[0062] In actual applications, the state estimation value of the filter at the current time and the error covariance estimation value of the filter at the current time are obtained by using the Kalman filter according to the state estimation value of the filter at the previous time and the error covariance estimation value of the filter at the previous time, which is a parallel filtering step, and each filter uses the estimation result at the previous time As an input value, the process noise Q (i) and the system measurement value are combined. According to the formula the filtering estimation is performed, and finally the corresponding state estimation value under the process noise is obtained, wherein KF(·) represents the Kalman filtering function, Q (i) represents the process noise of the i-th filter, represents the state estimation value and the error covariance estimation value of the i-th filter at the previous time, respectively, represents the measurement residual, the measurement residual covariance, the state estimation value and the error covariance estimation value output by the i-th filter at the k-th time, respectively.

[0063] For the i-th filter, the to-be-estimated parameter is estimated together with the state vector . Further, the problem is converted into an estimation problem of a complex system, wherein and are to be estimated. In the multi-model estimation method, different intensities of process noise are used for each filter. Therefore, the parameters of the filter are averaged in a smooth time period, that is, the average estimation value of the acceleration of the target by the filter at the current time is obtained according to the acceleration estimation values of the target by the filter at each time in a smooth period, and specifically includes:

[0064] According to the formula The average estimation of the target acceleration of the filter at the current time is calculated, wherein k represents the current time, i represents the i th filter, and l represents the l th time, is the average estimation result, is the smoothing estimation of each filter, represents the average estimation of the target acceleration of the i th filter at the current time, and μ represents a smoothing period, represents the estimation of the target acceleration of the i th filter at the l th time. Assuming that the process noise satisfies a Gaussian distribution: w k ~ N (0, Q k ), if the smoothing time period μ is long enough, it can be assumed that that is, the parameter average estimation results of the filters are the same.

[0065] In practical applications, the variance of the residual of the estimation of the target acceleration of the filter at the current time obtained according to the average estimation of the target acceleration of the filter at the current time and the estimation of the target acceleration of the filter at the current time is specifically: comprising:

[0066] According to the formula The variance of the residual of the estimation of the target acceleration of the filter at the current time is calculated, wherein represents the variance of the residual of the estimation of the target acceleration of the i th filter at the current time, and can be used to evaluate the noise intensity in the estimation result, represents the estimation of the target acceleration of the i th filter at the current time, and the superscript T represents the transpose operation.

[0067] In practical applications, the variance of the residual of the estimation of the target acceleration of the filter at the current time is filtered by using a first low-pass filter to obtain the variance of the residual of the estimation of the target acceleration of the filter at the current time, specifically: comprising:

[0068] According to the formula The variance of the residual of the estimation of the target acceleration of the filter at the current time is calculated, wherein k-1 represents the last time, represents the variance of the residual of the estimation of the target acceleration of the i th filter at the current time, and τ1 represents a tuning parameter of the first low-pass filter, represents the variance of the residual of the estimation of the target acceleration of the i th filter at the last time.

[0069] In practical applications, the steady-state error of the filter at the current time is obtained based on the variance of the residual of the estimation of the target acceleration of the filter at the current time, specifically: comprising:

[0070] According to the formula the steady-state error of the filter at the current time is calculated, wherein, denotes the steady-state error of the i-th filter at the current time, the expected range of is [b, a], b and a are the normalized lower limit and the normalized upper limit, the lower limit can be simply taken as b = 0, g 1,k denotes a set composed of the variances of the residuals of the filtered acceleration estimation values of all filters on the target at the current time, max(g 1,k ) denotes the maximum value taken from g 1,k , and min(g 1,k ) denotes the minimum value taken from g 1,k .

[0071] In actual applications, the sum of the innovation sequences of the filtered filters at the current time is determined according to the formula , wherein, denotes the sum of the innovation sequences of the i-th filtered filter at the current time, 1 m denotes an m-dimensional unit vector, H k denotes a measurement matrix, which can be obtained by taking the Jacobian matrix of the measurement function h(·), and the calculation formula is: , that is, the partial derivative of the measurement function at x k , x k denotes the position of the target at the k-th time; denotes the error covariance matrix estimated by the i-th filter at the previous time, R k denotes a measurement noise variance matrix, is the innovation, that is, the measurement value obtained at the current time, denotes the measurement prediction value of the i-th filter at the current time, and the expression is: , wherein, denotes the state estimation result of the filter i at the k-th time.

[0072] In actual applications, the sum of the innovation sequences of the filtered filters at the current time is filtered by using the second low-pass filter to obtain the sum of the innovation sequences of the filtered filters at the current time, and the specific process includes:

[0073] According to the formula , the sum of the innovation sequences of the filtered filters at the current time is obtained, wherein, denotes the sum of the innovation sequences of the i-th filtered filter at the current time, τ2 denotes the tuning parameter of the second low-pass filter, which is the tuning parameter of the low-pass effect, is the sum of the innovation sequences of the i-th filtered filter at the previous time.

[0074] In practical applications, the measurement sensitivity of the filter at the current time is obtained according to the sum of the innovation sequences of the filter at the current time after filtering, and specifically comprises:

[0075] According to the formula , the measurement sensitivity of the filter at the current time is calculated, wherein is the scaled measurement sensitivity of the filter, represents the measurement sensitivity of the i th filter at the current time, and β represents a scaling parameter.

[0076] In practical applications, the likelihood function value of the filter at the current time is obtained based on the steady-state error of the filter at the current time and the measurement sensitivity of the filter at the current time, and specifically comprises:

[0077] According to the new likelihood function formula , the likelihood function value of the filter at the current time is calculated, which represents the accuracy of the to-be-estimated parameters and the state vector , and is composed of two parts and . The exponential weighting method commonly used in adaptive filtering is used to weight and to obtain a new likelihood function, wherein represents the likelihood function value of the i th filter at the current time, exp() represents an exponential function with natural constant e as the base, and n represents the total number of filters.

[0078] In practical applications, the fused state estimation value of all filters at the current time and the fused error covariance estimation value of all filters at the current time are obtained based on the state estimation values of all filters at the current time, the error covariance estimation values of all filters at the current time, and the likelihood function values of all filters at the current time, and specifically comprise:

[0079] The fused state estimation value of all filters at the current time is obtained according to the state estimation values of all filters at the current time and the likelihood function values of all filters at the current time.

[0080] The fused error covariance estimation value of all filters at the current time is obtained based on the error covariance estimation values of all filters at the current time, the state estimation values of all filters at the current time, the fused state estimation values of all filters at the current time, and the likelihood function values of all filters at the current time.

[0081] In practical applications, the fused state estimation value of all filters at the current time is obtained according to the state estimation values of all filters at the current time and the likelihood function values of all filters at the current time, and specifically comprises: according to the formula Calculate the state estimation value of all filters after fusion at the current time, wherein, The state estimation value of all filters after fusion at the current time is represented as, The state estimation value of the jth filter at the current time is represented as, The likelihood function value of the jth filter at the current time is represented as.

[0082] In practical applications, the error covariance estimation value of all filters at the current time, the state estimation value of all filters at the current time, the state estimation value of all filters after fusion at the current time, and the likelihood function value of all filters at the current time obtain the error covariance estimation value of all filters after fusion at the current time, and specifically comprise: according to formula Calculate the error covariance estimation value of all filters after fusion at the current time, wherein, P k|k The error covariance estimation value of all filters after fusion at the current time is represented as, The error covariance estimation value of the jth filter at the current time is represented as.

[0083] The state space expansion method is adopted in the application, the system parameters are taken as state variables for estimation, and the expanded state variables are: [x k ζ k ] T Then, different process noises with different intensities are given to each filter to represent different steady-state tracking accuracy and tracking flexibility of the system. Finally, a new likelihood function is used to calculate the weight of estimation fusion, and any interaction between filters is not required, and even if there are only two filters, the algorithm can ensure steady-state accuracy and fast parameter tracking.

[0084] The design principle of the new likelihood function of the application is as follows:

[0085] Steady-state error Part: formula (2) represents fitting a constant to the estimation value of each filter in a smooth period, and then using formula (3) to calculate the deviation from the value to obtain However, when is directly used as the input of the likelihood function, there are two problems. First, since the estimation error of the dynamic system with random noise, may have mutations. In this case, sudden changes in weights are also observed. Second, for each filter, the input value of the exponential function should fall within the expected range.

[0086] For the first problem, formula (4) can be used to filter , and a more smooth estimation value can be obtained to prevent mutations. For the second problem, it is assumed that If the expected range is [b, a], then the form of the steady-state error can be modified to obtain the result shown in equation (5). Finally, the form of the first component of the new likelihood function is shown in equation (6), which characterizes the steady-state error. Its physical meaning is that the estimated value deviates from the average value. The degree of noise. When the process noise intensity of the filter is high, The value is also larger (closer to the upper limit a), and because The likelihood of this filter is smaller. Conversely, when the process noise intensity of the filter is small, If the value of b is smaller (closer to the lower limit b), the filter's estimation result is more likely.

[0087] Measurement sensitivity Part: Usually, in the use of Before the output shows a sudden change in the estimated parameters, it should be low-pass filtered according to formula (7). When the estimated parameters remain unchanged, the normalized innovation sequence after low-pass filtering satisfies a normal distribution, i.e., En k ~N(0,1). When the estimated parameters change suddenly, it will increase / decrease, and the magnitude of the change depends on the sensitivity of the filter. Therefore, if the filter has strong process noise and can quickly capture new parameters, then... The level of change is relatively low. When the process noise of the filter is strong enough, it may not even be observed. This change. Therefore, It can be used to measure the sensitivity of a filter. Unlike steady-state error, the sensitivity of a filter is lower for filters with weaker process noise. A higher value indicates a lower value, and vice versa. Furthermore, before using it as input to the exponential function, it should be adjusted according to formula (8). Scaling is performed. b, β, and a cannot be arbitrarily chosen. Let b = 0; here, the tuning parameters are defined as... The switching sensitivity between models is determined. The appropriate model should be selected based on the application, especially considering the process noise intensity of each filter. Equation (8) gives the likelihood function. The second component Its physical meaning is the accuracy of the filter's tracking of parameters when the parameters change. It refers to the estimation likelihood of a filter with low process noise covariance when the estimated parameters change. Will reduce ( It will increase because On the other hand, for filters with high process noise and covariance, due to There will be no significant changes, so the estimation results of these filters are likely to be more accurate.

[0088] The present application provides an embodiment to verify the effectiveness of the above method:

[0089] The expected model augmentation method (EMA) is a multi-model estimation method that can effectively deal with the problem of parameter mutation. Therefore, in this embodiment, the joint parameter estimation method based on adaptive multi-model algorithm (JPE-IMM) proposed in the present application and the expected model augmentation method are simulated and compared in the context of maneuvering target tracking problem. Thus, the superiority of the proposed method in the case of parameter mutation is verified.

[0090] Assuming that the acceleration of the maneuvering target is constantly changing, the acceleration can be regarded as an unknown parameter of the system, and the joint parameter estimation method based on adaptive multi-model algorithm proposed in the present application is used for tracking. When the acceleration is used as a system parameter to be estimated, the state equation of the target is:

[0091] Formula In the formula, is the state quantity at time k, which respectively represents the position and velocity of the target at time k; a k-1 is the acceleration at time k-1; Δ is the simulation step. If the acceleration is expanded into the state quantity, the state quantity of the target is Specifically, the position, velocity and acceleration of the target at time k, the state equation of formula (12) can be extended as: Where, w k is the process noise. In addition, the measurement equation is written as: Where, y k represents the measurement. In this simulation, the measurement of the target position x k .

[0092] In this simulation, the initial state of the target is [0m 300m / s 0m 300m / s], the simulation duration is 350s, the simulation step is 1s, and the acceleration setting during the maneuvering process is shown in Table 1:

[0093] Table 1 Simulation scene parameters

[0094]

[0095] The simulation scene generated thereby is shown in Figure 2 :

[0096] 1. Simulation parameter setting

[0097] In this embodiment, the joint parameter estimation method based on adaptive multi-model algorithm and the EMA method are both set with 7 filters for simulation, and the simulation step T=1s. The EMA method adopts the target motion model represented by formula (12), and the acceleration settings of each filter are as follows:

[0098]

[0099] In the joint parameter estimation method based on adaptive multi-model algorithm, each filter adopts the model shown in formula (13), the difference is that the process noise variance matrix Q of each filter is different. Let the unified expression of Q be: Wherein, qq is a coefficient for controlling the process noise variance matrix of different filters, and qq of the seven filters is respectively taken as 0.01, 0.030, 0.07, 0.1, 0.4, 0.7 and 1. The measurement accuracy of the system is σ=50m, so the variance matrix of the measurement noise is:

[0100] Other parameter settings in the simulation process are shown in Table 2

[0101] Table 2 Simulation parameter table

[0102]

[0103]

[0104] 2. Simulation results

[0105] Figures 3 to 6 The simulation comparison results of the algorithm proposed in the application and the expected mode expansion algorithm (EMA) are given. It can be seen that the position estimation accuracy and the speed estimation accuracy of the joint parameter estimation method based on the adaptive multi-model algorithm are higher than those of the EMA method as a whole, especially the position estimation accuracy, and the joint parameter estimation method based on the adaptive multi-model algorithm has obvious improvement compared with the EMA method.

[0106] At t=120s and t=240s, due to the sudden change of acceleration, the position estimation error and the speed estimation error of the two algorithms are increased, but the position estimation error of the joint parameter estimation method based on the adaptive multi-model algorithm has a smaller increase.

[0107] Figure 5 and Figure 6The tracking result of acceleration is given, and it can be seen that the estimation accuracy of the joint parameter estimation method based on the adaptive multiple model algorithm is obviously better than that of the EMA method. The reason is that in the EMA algorithm, the estimation of the parameter is mainly to weight and sum the model parameters of each filter by using the model probability. Due to the competition problem between models, even if the acceleration at a moment completely matches a certain model in the model set, the matching degree of the multiple model as a whole is reduced due to the fact that other models also allocate a certain model probability, and finally the estimation accuracy is reduced. The joint parameter estimation method based on the adaptive multiple model algorithm expands the estimated parameters into the state quantity, and estimates by using the Kalman filter, so that the estimation accuracy is higher. The application expands the estimated parameters into the state space, and distinguishes different models by the process noise intensity. In addition, considering the steady-state performance and dynamic response ability of the filter tracking, a new likelihood function is defined to fuse the multiple model estimation results. The final simulation result shows that the proposed algorithm not only ensures the steady-state estimation accuracy, but also realizes accurate estimation of the sudden change parameter.

[0108] The application further provides a joint parameter estimation system based on an adaptive multiple model algorithm corresponding to the method, and the system comprises:

[0109] A state estimation value and error covariance estimation value calculation module of a filter at a current moment is configured to, at the current moment, obtain, for any filter, a state estimation value of the filter at the current moment and an error covariance estimation value of the filter at the current moment by using a Kalman filter according to a state estimation value of the filter at a previous moment and an error covariance estimation value of the filter at the previous moment; the state estimation value of the filter comprises an estimation value of the filter for a target position and an estimation value of the filter for a target velocity.

[0110] An acceleration average estimation value calculation module is configured to obtain an acceleration average estimation value of the filter for a target at the current moment according to acceleration estimation values of the filter for the target at each moment in a smoothing period; the last moment in the each moment is the current moment.

[0111] A variance calculation module of a residual error of an acceleration estimation value is configured to obtain a variance of a residual error of an acceleration estimation value of the filter for a target at the current moment according to an acceleration average estimation value of the filter for the target at the current moment and an acceleration estimation value of the filter for the target at the current moment.

[0112] A first filtering module is configured to filter the variance of the residual error of the acceleration estimation value of the filter for the target at the current moment by using a first low-pass filter to obtain a filtered variance of the residual error of the acceleration estimation value of the filter for the target at the current moment.

[0113] A steady-state error calculation module is configured to obtain a steady-state error of the filter at the current moment based on a variance of a residual of an estimated acceleration of the target filtered by the filter at the current moment.

[0114] A second filtering module is configured to filter the sum of the innovation sequences of the filter at the current moment using a second low-pass filter to obtain a filtered sum of the innovation sequences of the filter at the current moment.

[0115] A measurement sensitivity calculation module is configured to obtain a measurement sensitivity of the filter at the current moment based on the filtered sum of the innovation sequences of the filter at the current moment.

[0116] A likelihood function value calculation module is configured to obtain a likelihood function value of the filter at the current moment based on the steady-state error of the filter at the current moment and the measurement sensitivity of the filter at the current moment.

[0117] A fusion module is configured to obtain a fused state estimation value of all the filters at the current moment and a fused error covariance estimation value of all the filters at the current moment based on the state estimation values of all the filters at the current moment, the error covariance estimation values of all the filters at the current moment and the likelihood function values of all the filters at the current moment.

[0118] The present application combines a new likelihood function, takes into account the steady-state tracking error and tracking flexibility of the system, and can solve the parameter estimation problem of a complex system with parameter mutation and the high-precision tracking problem of a target.

[0119] The embodiments in the specification are described in a progressive manner, and each embodiment focuses on the difference from other embodiments, and the same or similar parts of each embodiment can be referred to each other. For the system disclosed by the embodiments, since it corresponds to the method disclosed by the embodiments, the description is relatively simple, and the related parts can be referred to the method part.

[0120] The principles and implementation manners of the present application are described by using specific examples in this paper, and the above embodiment description is only used to help understand the method of the present application and its core idea; at the same time, for those skilled in the art, according to the idea of the present application, the specific implementation manner and application range will be changed. In conclusion, the content of the specification should not be understood as a limitation of the present application.

Claims

1. A method of joint parameter estimation based on an adaptive multiple model algorithm, characterized in that, The method comprises the following steps: At the current time, for any filter, a Kalman filter is used to obtain a state estimation value of the filter at the current time and an error covariance estimation value of the filter at the current time according to a state estimation value of the filter at the previous time and an error covariance estimation value of the filter at the previous time; the state estimation value of the filter comprises an estimation value of the filter for a target position and an estimation value of the filter for a target velocity; An average estimation value of the filter for the target acceleration at the current time is obtained according to the estimation values of the filter for the target acceleration at each time within a smoothing period; the last time in the each time is the current time; A variance of a residual of the estimation value of the filter for the target acceleration at the current time is obtained according to the average estimation value of the filter for the target acceleration at the current time and the estimation value of the filter for the target acceleration at the current time; The variance of the residual of the estimation value of the filter for the target acceleration at the current time is filtered by using a first low-pass filter to obtain a filtered variance of the residual of the estimation value of the filter for the target acceleration at the current time; The steady-state error of the filter at the current time is obtained based on the filtered variance of the residual of the estimation value of the filter for the target acceleration at the current time; The sum of the innovation sequences of the filter at the current time is filtered by using a second low-pass filter to obtain a filtered sum of the innovation sequences of the filter at the current time; The measurement sensitivity of the filter at the current time is obtained according to the filtered sum of the innovation sequences of the filter at the current time; The likelihood function value of the filter at the current time is obtained based on the steady-state error of the filter at the current time and the measurement sensitivity of the filter at the current time; The fused state estimation value of all the filters at the current time and the fused error covariance estimation value of all the filters at the current time are obtained based on the state estimation values of all the filters at the current time, the error covariance estimation values of all the filters at the current time and the likelihood function values of all the filters at the current time.

2. The joint parameter estimation method based on an adaptive multiple model algorithm according to claim 1, characterized in that, The average estimation value of the filter for the target acceleration at the current time is obtained according to the estimation values of the filter for the target acceleration at each time within a smoothing period, specifically comprising: According to the formula The average acceleration estimate of the target by the filter at the current time is calculated, where k represents the current time, i represents the i-th filter, and l represents the l-th time, represents the average acceleration estimate of the target by the i-th filter at the current time, and μ represents a smoothing period, represents the acceleration estimate of the target by the i-th filter at the l-th time.

3. The joint parameter estimation method based on an adaptive multiple model algorithm according to claim 2, characterized in that, The variance of the residual of the estimation value of the filter for the target acceleration at the current time is obtained according to the average estimation value of the filter for the target acceleration at the current time and the estimation value of the filter for the target acceleration at the current time, specifically comprising: According to the formula calculating a variance of a residual of the acceleration estimate of the target by the filter at the current time, denotes the variance of the residual of the acceleration estimate of the target by the i-th filter at the current time, denotes the acceleration estimate of the target by the i-th filter at the current time, the upper index T denotes the transposition operation.

4. The method of joint parameter estimation based on adaptive multiple model algorithm according to claim 3, characterized in that, The filtered variance of the residual of the estimation value of the filter for the target acceleration at the current time is obtained by filtering the variance of the residual of the estimation value of the filter for the target acceleration at the current time by using a first low-pass filter, specifically comprising: According to the formula calculating a variance of a residual of the filtered acceleration estimate of the target by the filter at the current time, where k-1 represents the previous time, represents the variance of the residual of the filtered acceleration estimate of the target by the i-th filter at the current time, and τ1 represents a tuning parameter of the first low-pass filter, represents the variance of the residual of the filtered acceleration estimate of the target by the i-th filter at the previous time.

5. The method of joint parameter estimation based on adaptive multiple model algorithm according to claim 4, characterized in that, The steady-state error of the filter at the current time is obtained based on the filtered variance of the residual of the estimation value of the filter for the target acceleration at the current time, specifically comprising: According to the formula the steady state error of the filter at the current time is calculated, wherein denotes the steady state error of the i-th filter at the current time, the desired range of g 1,k denotes the set consisting of the variances of the residuals of all filtered filters from the target's acceleration estimate at the current time, max(g 1,k ) denotes the maximum value taken from g 1,k , min(g 1,k ) denotes the minimum value taken from g 1,k .

6. The method of joint parameter estimation based on an adaptive multiple model algorithm according to claim 5, characterized in that The sum of the innovation sequences of the filters filtered at the current time is determined according to the formula wherein denotes the sum of the innovation sequences of the i-th filter filtered at the current time, 1 m denotes a unit vector in m dimensions, H k denotes a measurement matrix, denotes the error covariance matrix of the i-th filter estimated at the previous time, R k denotes a measurement noise variance matrix, denotes the measurement values obtained at the current time, denotes the measurement prediction of the i-th filter at the current time.

7. The method of joint parameter estimation based on an adaptive multiple model algorithm according to claim 6, characterized in that The filtered sum of the innovation sequences of the filter at the current time is obtained by filtering the sum of the innovation sequences of the filter at the current time by using a second low-pass filter, specifically comprising: According to the formula the sum of the innovation sequences of the filters filtered at the current time is obtained, wherein the sum of the innovation sequences of the i-th filter filtered at the current time is represented, and τ2 represents the tuning parameter of the second low-pass filter, is the sum of the innovation sequences of the i-th filter filtered at the last time.

8. The method of joint parameter estimation based on an adaptive multiple model algorithm according to claim 7, characterized in that, The measurement sensitivity of the filter at the current moment is obtained according to the sum of the innovation sequences of the filter after filtering at the current moment, and specifically comprises: The measurement sensitivity of the filter at the current time is calculated according to the formula wherein denotes the measurement sensitivity of the i-th filter at the current time, and β denotes a scaling parameter.

9. The method of joint parameter estimation based on an adaptive multiple model algorithm according to claim 8, characterized in that, The likelihood function value of the filter at the current moment is obtained based on the steady-state error of the filter at the current moment and the measurement sensitivity of the filter at the current moment, and specifically comprises: According to the formula The likelihood function value of the filter at the current time is calculated, wherein, represents the likelihood function value of the i-th filter at the current time, exp() represents the exponential function with the natural constant e as the base, and n represents the total number of filters.

10. A joint parameter estimation system based on an adaptive multiple model algorithm, characterized in that Comprise: The state estimation value and error covariance estimation value calculation module of the filter at the current moment is used to obtain the state estimation value and error covariance estimation value of the filter at the current moment at the current moment for any filter, using the Kalman filter according to the state estimation value of the filter at the last moment and the error covariance estimation value of the filter at the last moment; The state estimation value of the filter comprises the estimation value of the target position and the estimation value of the target velocity; The acceleration average estimation value calculation module is used to obtain the average acceleration estimation value of the target of the filter at the current moment according to the acceleration estimation value of the target of the filter at each moment in a smoothing period; The last moment in the each moment is the current moment; The acceleration estimation value residual variance calculation module is used to obtain the acceleration estimation value residual variance of the target of the filter at the current moment according to the average acceleration estimation value of the target of the filter at the current moment and the acceleration estimation value of the target of the filter at the current moment; The first filtering module is used to filter the acceleration estimation value residual variance of the target of the filter at the current moment using the first low-pass filter to obtain the acceleration estimation value residual variance of the target of the filter at the current moment after filtering; The steady-state error calculation module is used to obtain the steady-state error of the filter at the current moment based on the acceleration estimation value residual variance of the target of the filter at the current moment after filtering; The second filtering module is used to filter the sum of the innovation sequences of the filter at the current moment using the second low-pass filter to obtain the sum of the innovation sequences of the filter at the current moment after filtering; The measurement sensitivity calculation module is used to obtain the measurement sensitivity of the filter at the current moment according to the sum of the innovation sequences of the filter at the current moment after filtering; The likelihood function value calculation module is used to obtain the likelihood function value of the filter at the current moment based on the steady-state error of the filter at the current moment and the measurement sensitivity of the filter at the current moment; The fusion module is used to obtain the state estimation value and error covariance estimation value of all filters after fusion at the current moment based on the state estimation value of all filters at the current moment, the error covariance estimation value of all filters at the current moment and the likelihood function value of all filters at the current moment.

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