recursive lagrangian total least squares estimator

Abstract

A recursive Lagrange total least squares estimator for estimating parameters of a physical system (100) considered as linear, such as a motor vehicle. An estimation device (110) includes a measurement unit (114) and an estimation unit (116), the measurement unit (114) being configured to acquire continuous input measurements A of the linear system. k and continuous output measurement value y k The estimation unit (116) is configured to recursively estimate one or more parameters x based on input and output measurements. k Estimating the recursion k+1 includes the following operations: (1), (2), (3), (4), (5), optionally (5'), (6), (7), where Q a,k and Q y,k The weighted matrix; δx k and P k For variables in the recursion; for instrumental variables related to the variables; Q z,k ΔA k K k λ is an internal variable; α is the regularization term, and λ is the forgetting parameter.

Description

Technical Field

[0001] This invention relates to the general field of parameter estimators in physical systems. Background Technology

[0002] More specifically, some parameters required for using actual physical systems may be unmeasurable or unmeasured, for example, to overcome the cost and complexity of integrating dedicated sensors (if available).

[0003] These unknown parameters can be estimated indirectly based on measurements of the physical system (typically input and output measurements).

[0004] Estimating unknown parameters is easier for linear physical systems (i.e., systems whose behavior is described by linear equations). Nonlinear physical systems can be reduced to linear systems through simplification. Therefore, many nonlinear physical systems are approximated as linear.

[0005] One class of linear system estimators (called OE (output error) estimators) is based on modeling the output error, which considers the error that exists only in the measurement of one side of the linear system equation (i.e., the output). These linear system estimators include, but are not limited to, recursive or non-recursive least squares estimators, linear Kalman filters, and recursive or non-recursive instrumental variable estimators.

[0006] It is known that if the input measurements are noisy, the OE estimator produces biased estimates. This is why a second type of linear system estimator (called the EIV (Variable Error) estimator) is preferred. Although more complex, these EIV estimators exhibit better performance. They are based on a modeling approach that considers errors in the measurements on both sides (input and output) of the linear system equations. Examples of this type of linear system estimator include the total Kalman filter, the total least squares (TLS) estimator, and the total instrumental variable estimator.

[0007] Some TLS estimators employ singular value decomposition (SVD) methods to solve the overall least squares problem. For example, the publication " Recursive Generalized Total Least Squares with Noise Covariance Estimation (Rhode S. et al., 2014) describes a recursive SVD TLS estimator.

[0008] Other TLS estimators are fewer in number and employ the Lagrange multiplier method. For example, the publication " An iterative solution of weighted total least-squares adjustment (Shen Y. et al., 2011) describes an iterative Lagrangian TLS estimator.

[0009] Recursive TLS estimators are preferred because they are capable of performing real-time estimation. Currently, only SVD-type recursive TLS estimators are known. Due to the nature of the SVD method, unlike the Lagrange multiplier method, it is difficult to use it with optimization / improvement tools from the classical least squares literature.

[0010] Therefore, it is necessary to overcome the above-mentioned shortcomings and improve the list of efficient recursive TLS estimators. Summary of the Invention

[0011] The purpose of this invention is to provide a recursive Lagrange TLS estimator for estimating one or more parameters of a linear physical system.

[0012] To this end, the inventors discovered that the iterative algorithm proposed by Shen Y. et al. can be cleverly transformed into a recursive algorithm. This results in a novel recursive Lagrangian TLS estimator that benefits from classical least-squares optimization techniques, such as forgetting factors, regularization, instrumental variables, and robustness to outliers.

[0013] In this context, the present invention relates to an estimation apparatus for estimating parameters of a physical system considered linear, comprising: A measurement unit configured to acquire continuous input measurement values ​​A from a linear system. k and continuous output measurement value y k , An estimation unit is configured to recursively estimate one or more parameters x of the physical system based on the input measurements and the output measurements. k The estimation of recursion (or recursive iteration) k+1 includes the following operations: (1) (2) (3) (4) (5) Optional (5') (6) (7) Where k is the recursive index; Q a,k and Q y,k The weighted matrix; δx k , and P k For variables in the recursion; For variables Related instrumental variables; Q z,k ΔAk K k α is the internally computed variable; α is the regularization term, and λ is the positive forgetting parameter less than or equal to 1.

[0014] Therefore, this device enables the acquisition of a recursive Lagrangian TLS estimator for real-time estimation of parameters of linear physical systems. Specifically, the number of operations in each recursion remains finite; the computational complexity is O(n^2). 2 ) magnitude.

[0015] This TLS estimator can be used in particular as a "virtual" sensor for parameters that are not directly measured.

[0016] It's important to note that λ=1 cancels any forgetting; α=0 cancels any regularization. Cancel any noise correction associated with the measurement signal.

[0017] Accordingly, an estimation method for estimating parameters of a physical system considered linear includes the following steps: - Obtain continuous input measurement A from a linear system k and continuous output measurement value y k , Based on the input and output measurements, one or more parameters x of the physical system are recursively estimated. k The estimation of recursion k+1 includes the following operations: (1) (2) (3) (4) (5) Optional (5') (6) (7) .

[0018] Optional features of the embodiments are defined in the appended claims. Some of these features are explained hereinafter with reference to the apparatus; however, they can be converted into method features.

[0019] In one implementation, Q a,k and Q y,k These are the input and output measurement error or noise covariance matrices, respectively. This arrangement allows for the consideration of heterogeneous noise distributions in the input and output data.

[0020] In one particular implementation, Q a,kand Q y,k It is an evolution matrix, and the estimation unit has a matrix estimation subunit, which is configured to determine matrix Q for each recursive iteration based on the input measurement value and the output measurement value, respectively. a,k and Q y,k This improves the estimation of unknown parameters.

[0021] Of course, a pre-defined (and therefore constant from one recurrence to another) matrix Q can also be used. a,k and Q y,k For example, such matrices are determined based on the specifications of the sensors used in the test and / or measurement units before recursive iterations.

[0022] In one implementation, λ is 1, and / or α is 0, and / or for This allows some optimization tools derived from literature on classical least squares to be disabled.

[0023] In another implementation, the forgetting parameter λ is strictly less than 1, and / or the regularization term α is strictly positive and less than 1, and / or the instrumental variable... for , where a is a positive integer. Therefore, one or more optimization tools are enabled.

[0024] In one embodiment, the measurement unit includes a preprocessing subunit for preprocessing measurement values ​​acquired from one or more sensors to generate continuous input measurement values ​​A. k and output measurement value y k The preprocessing subunit is configured to perform at least one of the following operations: - Time alignment of input or output measurements is performed by interpolating and / or downsampling the acquired measurements, and - Select a portion of the measured values ​​to generate continuous input measured values ​​A. k and output measurement value y k The choice depends on the accompanying behavior of the physical system.

[0025] Time alignment reduces the risk of error bias inherent when using non-accompanied measurements together.

[0026] Partial selection allows for the exclusion of measurements that may introduce errors, particularly those caused by conditions that do not conform to the linearization assumptions of the physical system.

[0027] These preprocessing operations lead to improvements in the estimation.

[0028] In one implementation, the physical system is a vehicle, and in some cases, only measurements associated with the vehicle's linear motion are selected. In practice, a linear model of the vehicle can be envisioned for linear motion. The acquired measurements allow for the determination of the nature of the accompanying motion (linear or non-linear). The yaw rate can be calculated for each iteration. The yaw rate is compared to a threshold that defines the boundary between the range of linear motion and the range of non-linear motion.

[0029] This invention has a variety of applications. In one embodiment, the physical system is a vehicle, and the one or more parameters include the mass of the vehicle. Therefore, a preferred application is estimating the mass of a vehicle (typically a land-based motor vehicle) without the need for dedicated sensors.

[0030] In this configuration, the measuring unit can be connected to sensors used to measure the vehicle's engine torque, longitudinal acceleration, and the angular velocities of the engine and wheels to determine the vehicle's longitudinal velocity and gear ratio. These measurements enable the invention to recursively estimate the mass of a vehicle (i.e., a linear system derived from force balance according to Newton's second law).

[0031] As an illustration, estimating the vehicle's mass allows for the determination of the vertical load borne by each tire. This information, in turn, can be used to accurately estimate tire wear, tire grip, and tire rolling resistance during use, enabling appropriate actions to be taken.

[0032] For example, understanding the total load of a vehicle can be used to better predict the driving range of an electric vehicle (EV) battery, whose transport load can vary significantly over time. This can then provide improved routes for EVs to charging stations, optimizing battery usage and degradation.

[0033] Other vehicle applications include estimating the effective rolling radius of tires, vehicle center of gravity, aerodynamic coefficients, tire grip, tire wear, tire load, tire stiffness (Kx, Dz), and vehicle speed. Similar applications exist in fields such as aviation, aerospace, and geodesy, to name just a few.

[0034] At least a portion of the method according to the invention can be executed by a computer. Therefore, the invention can take the form of a fully hardware implementation, a fully software implementation (including microprograms, resident software, microcode, etc.), or an implementation combining software and hardware aspects (all of which are collectively referred to herein as "circuit," "module," or "system"). Furthermore, the invention can take the form of a computer program product contained in any non-transitory recording medium, having computer-readable program code for performing the described methods.

[0035] Tangible or non-transitory media may include storage media, such as hard disk drives, magnetic tape devices, or semiconductor storage devices. Attached Figure Description

[0036] Other objects, features, and advantages of the invention will become apparent from the following description, which is provided only by way of non-limiting example and with reference to the accompanying drawings, wherein: Figure 1 A physical system, considered to be linear, is shown for implementing the present invention; Figure 2 The steps of the estimation method for estimating parameters of a physical system, according to the implementation scheme, are illustrated using a flowchart. Figure 3 A flowchart illustrates the more detailed steps of the estimation method for estimating physical system parameters according to the implementation scheme; Figure 4 A physical system of the type of motor vehicle is shown, whose linear behavior is defined by Newton's second law; Figure 5 The estimation method is shown in Figure 4 Applications in the system; and Figure 6 The computer hardware architecture of the estimated system or apparatus according to the implementation scheme is shown. Detailed Implementation

[0037] One aspect of estimation theory focuses on linear systems, which can be physical systems whose behavior is inherently linear, or physical systems whose behavior can be reduced to linear behavior through approximation or simplification.

[0038] Figure 1 The diagram illustrates a physical system 100 considered linear, meaning its behavior conforms to the linear system equation y=Ax. The dimensions n and m of vectors x and y depend on the physical system under consideration. The matrix A has a dimension of m*n.

[0039] The following description Figure 4 The example illustrates a motor vehicle as a linear physical system. In this example, n=3, m=1.

[0040] Some parameters of a physical system are not measurable or cannot be directly obtained from other measurements. These parameters (usually the parameters that form a vector x) can be estimated.

[0041] For this purpose, system 100 includes an estimation device 110 for estimating parameters of a physical system and a processing unit 120 configured to operate the physical system 100 using one or more parameters estimated by the device 110.

[0042] According to the present invention, the estimation device 110 operates recursively to estimate one or more unknown parameters x. Hereinafter, the index "k" indicates recursion or recursive iteration "k".

[0043] Processing unit 120 can process the obtained estimated value x k Perform calculations to obtain values ​​for specific parameters used in decision-making.

[0044] As an illustration, the device 110 estimates the mass of the electric vehicle so that the processing unit 120 can calculate the total load of the vehicle, thereby activating or enabling a specific driving mode to conserve battery power.

[0045] Although the processing unit 120 is shown as embedded in system 100, it can also be located externally. In this case, the estimates generated by device 110 (and any other measurements obtained) can be transmitted to the external unit 120 via wired (e.g., Ethernet) or wireless (e.g., WiFi network or Bluetooth link – trade name) means. For example, the processing unit 120 can be implemented in a remote processing server that manages a fleet of vehicles and sends back instructions to the vehicles.

[0046] Similarly, although the estimation device 110 is shown as embedded in the system 100, it may be located externally, meaning that the measurement sensor is located outside the system 100 being monitored.

[0047] The estimation device 110 has one or more sensors 112, a measurement unit 114 and an estimation unit 116.

[0048] Sensor 112 is configured to acquire measured values ​​or "observations" o(t) from physical system 100 over time t. The sensor can be embedded within the physical system being monitored. Figure 4 In this example, the onboard torque meter measures the vehicle's engine torque, the accelerometer measures the vehicle's longitudinal acceleration, and the gyroscope measures the angular velocity of the engine and wheels. Besides this example, any type of sensor can be used.

[0049] For the unknown parameter x k For each recursive k in the estimation, measurement unit 114 obtains continuous input measurements A from the linear system. k and continuous output measurement value y k .

[0050] Measured value A k and y k All or part of it can correspond to the acquired measurement value o(t) transmitted by sensor 112. However, it will be clear from the example described below that the measurement value A k and y kPart of it is obtained by processing the acquired measurement value o(t).

[0051] Therefore, the measurement unit 114 may have a preprocessing subunit 115.

[0052] Measured value A k and y k The input is provided to the estimation unit 116. The estimation unit utilizes a Lagrange TLS-type recursive estimator. Based on input measurement value A k and output measurement value y k Recursively estimate the parameter x k .

[0053] According to one embodiment of the present invention, the recursive scheme of the estimator includes the following recursive k+1 calculation operations: (1) (2) (3) (4) (5) (6) (7) Q a,k and Q y,k It is a weighted matrix. Q a,k and Q y,k This allows us to take into account the heterogeneous noise distribution on the input and output data.

[0054] In one implementation, Q a,k and Q y,k These are the input and output measurement error (or noise) covariance matrices, respectively.

[0055] These matrices can be preset, i.e., fixed in different recursions, in which case the index "k" can be omitted. Then, these matrices can be determined before the estimation operation of estimator 116, typically through a series of tests and / or by utilizing the technical specifications of the sensor 160 involved.

[0056] In implementations that provide more accurate estimates, matrix Q a,k and Q y,k These are evolution matrices, meaning they are re-evaluated or recalculated for each new recursion k. In this case, they are also provided as input to the aforementioned recursion scheme. Therefore, estimation unit 116 can have a matrix estimation subunit 117. This unit 117, for each recursion iteration, estimates the matrix based on the input measurement A.k and output measurement value y k Determine matrix Q a,k and Q y,k .

[0057] Matrix Q a,k and Q y,k It can be completely recalculated on each iteration, or it can be updated in a manner similar to recalculation.

[0058] The variable δx of estimator 116 k , and P k It refers to variables passed between recursions, that is, variables that are passed from one recursion to another. In the Lagrange TLS method, δx k It is parameter x k The estimate of incremental correction between two iterations, This takes into account the prediction residual matrix ΔA k (Below) A k The correction matrix, P k It is the noise covariance matrix.

[0059] Q z,k ΔA k K k These are internally calculated variables.

[0060] λ is a positive forgetting parameter (or factor) less than or equal to 1. This parameter can be adjusted by the operator of device 110. This forgetting factor, present in operations 4 and 5 of the estimator, is used to exponentially forget past data, thereby giving greater importance to newer estimates. The smaller the parameter λ, the more important the forgetting.

[0061] In addition to forgetting old information, the parameter λ can converge to the true parameter faster when the parameter initialization is poor, and smooth the parameter estimate when the system is damaged by excessive noise.

[0062] For applications that do not forget old measurements in continuous recursion, λ is set to 1. For applications that involve forgetting, λ can be set to a value strictly between 0 and 1.

[0063] The recursive scheme of the estimator can be regarded as a function The first four parameters of the function are the parameters to be estimated and three recursive variables, while the last four parameters come from the input and output observations.

[0064] Therefore, estimation unit 116 generates an estimate x for processing unit 120 during the recursion k. k .

[0065] Therefore, the estimation device 110 can be regarded as a virtual sensor.

[0066] The appendix below shows that these recursive computation operations correspond to the Lagrange total least squares estimator.

[0067] Figure 2 The flowchart illustrates the steps of an estimation method for estimating parameters of a physical system considered linear. This method is specifically performed by the aforementioned estimation device 110.

[0068] In the initial step 200, the recursive estimator is initialized. This step involves initializing the values ​​of the variables used for the first recursion (k=1), specifically the parameter x0 and the inter-recursion variable δx0. 、P0.

[0069] In one implementation, x0 is set to a reasonable value for the corresponding unknown parameter. "Reasonable value" is understood to mean any value within the expected range of values ​​for the parameter in question. For illustrative purposes, refer to... Figure 4 For example, the vehicle's mass is set to 1000 kg.

[0070] δx0 is initialized to the zero vector. It is initialized to a zero matrix.

[0071] The covariance matrix P0 is then initialized to po.Id, where Id is the identity matrix, and p o It is the variance factor, whose value can be set to the square of the maximum uncertainty associated with parameter x.

[0072] Initial step 200 can also be used to retrieve computational parameters, such as the forgetting factor λ and the weighting matrix Q. a Q y (If they are preset). These calculation parameters can be stored in the memory of the estimation device 110.

[0073] Step 210 involves the estimation device 110 obtaining continuous input measurement values ​​A. k and continuous output measurement value y k .

[0074] In this step, sensor 112 acquires the measured value o(t) and transmits it to measurement unit 114, which extracts the input and output measured values ​​of the linear model for each new recursion k. The acquired measured value o(t) can also be preprocessed to generate the input and output measured values ​​of the linear model, for example, when the sensor does not directly acquire these input and output measured values.

[0075] These input measurements A are used for the next iteration. k and output measurement value yk The result is transmitted to estimation unit 116. In step 220, estimation unit 116 estimates one or more parameters x used for recursively calculating k by performing the above calculation operations. k .

[0076] Thus, the estimated parameter x is obtained. k Parameter x k It is transmitted to the processing unit 120 in step 230.

[0077] Then, step 240 involves incrementing the recursion counter k, and then looping back to step 210 to perform the next recursion.

[0078] The recursion frequency can be defined by the operator of the estimation device 110. Figure 4 In the example of the vehicle, the recursion cycle, ranging from 10 milliseconds (ms) to 500 ms, is compatible with off-the-shelf sensors and real-time operation.

[0079] Figure 3 A flowchart illustrates the more detailed steps of the estimation method for estimating parameters of a linear physical system according to the implementation scheme. This method is still performed by the estimation device 110.

[0080] Initialize the recursive estimator Step 200 remains unchanged.

[0081] Obtain input measurement value A k and output measurement value y k Step 210 includes a sub-step 212 of obtaining the measurement value o(t) and a sub-step 214 of preprocessing the obtained measurement value.

[0082] For example, acquiring the measured value o(t)212 includes acquiring the measurement performed by sensor 112.

[0083] Depending on the sensor used, the acquired measurements may have different sampling frequencies and / or may not be time-synchronized (e.g., accurate to milliseconds).

[0084] This is why these acquired measurements o(t) can be preprocessed in step 214.

[0085] In one implementation, preprocessing includes time alignment of the input or output measurements. The purpose of step 2140 is to ensure that the input measurement A to be provided to estimator 116... k and output measurement value y k Corresponding to the same time point, to reduce estimation bias.

[0086] When the acquired measurement values ​​o(t) are not synchronized, preprocessing may include: interpolating the acquired measurement values, for example, at the time (t) corresponding to the recursive k. k Linear interpolation is performed between two available measurements o(t1) and o(t2) on both sides (time t1 and time t2). Typically, the preprocessed measurements o... k Corresponding to o(t1) + [o(t2) + o(t1)] * [(t k -t1) / (t2-t1)].

[0087] If the sampling frequency is greater than the recursion frequency, especially if the ratio is greater than 2, preprocessing may include downsampling the acquired measurements (e.g., equal to the ratio between the two frequencies mentioned above).

[0088] Interpolation and downsampling can be combined to provide preprocessed acquired measurements. k In particular, downsampling is advantageously performed before interpolation.

[0089] In one implementation, preprocessing includes based on the acquired measurement value o(t) (advantageously, the preprocessed measurement value o). k Calculate one or more input measurements A k and / or output measurement value y k 2142. The objective is to convert the acquired data into useful data related to the linear system y=Ax.

[0090] This sub-step 2142 is used to generate an input measurement value A that cannot be directly obtained by sensor 112. k and output measurement value y k In the following discussion Figure 4 In the example, step 2142 is used to calculate the longitudinal speed of the vehicle based on the acquired wheel angular velocity measurements (considering the radius of the wheel), and to calculate the transmission efficiency of the vehicle based on the acquired engine and wheel angular velocity measurements.

[0091] In another embodiment, preprocessing includes partially selecting the measured values ​​2144 to generate continuous input measured values ​​A. k and output measurement value y k The purpose of this partial selection is to exclude irrelevant measurements, such as those that contradict the conditions or assumptions that allow the physical system to be considered linear. Therefore, this partial selection depends on the accompanying (i.e., concurrent) behavior of the physical system with the measurements in question.

[0092] Partial selection 2144 can be for the measurement value o(t) acquired from sensor 112 or for the preprocessed measurement value o from sub-step 2140. kPerform, or (as shown in the figure) for the input measurement value A obtained directly from sensor 112 (large arrow in the figure) and / or from sub-step 2140 and / or from calculation 2142. k and output measurement value y k The process is carried out. As a result, a subset of the measured values ​​is eventually able to be transmitted to the input of estimation step 220.

[0093] The selection criteria are determined in sub-step 2146 and applied in selection sub-step 2144.

[0094] For example, sub-step 2146 depends on the acquired measurement value o(t) (which may be preprocessed, o k ).

[0095] exist Figure 4 In the example, the selection criterion is the vehicle's yaw rate value. For example, substep 2146 is based on time t. k The yaw rate k is calculated by the speed difference between the rear wheels. As a variation, substep 2146 can obtain the yaw rate from dedicated sensor 112.

[0096] When the vehicle is not traveling in a straight line, the measured values ​​(obtained o(t), o) k Or input / output A k y k This will be excluded. This leads to the selection of a measurement accompanied by a low yaw rate, typically below a threshold, such as 0.5 radians per second, preferably 0.1 radians per second.

[0097] The preprocessing operations (2140, 2142, 2144) described above can be performed in combination as in the example. As a variation, only one or both preprocessing operations can be performed.

[0098] Then, enter the measurement value A. k and output measurement value y k The input is provided to the estimation step 220.

[0099] When the weighting matrix Q is not preset a,k and Q y,k At this point, optional sub-step 222 is executed. In this case, the weighting matrix Q... a,k and Q y,k Based on input measurement value A k and output measurement value y k Make an estimate.

[0100] Typically, the input noise covariance matrix Q a,k It can be based on the input measurement value A k Updates are performed, thus allowing for recursive evaluation. Similarly, the output noise covariance matrix Q... y,kIt can be based on the output measurement value y k Updates are performed, so evaluations can be performed recursively.

[0101] When matrix Q a,k and Q y,k When available, they are related to the input measurement value A. k and output measurement value y k Together they are provided as input to the recursive estimation algorithm 224 described.

[0102] Thus, the estimated parameter x is obtained. k Parameter x k In step 230, it is transmitted to processing unit 120. Then, step 240 involves incrementing the recursion counter k, and then looping back to step 210 to perform the next recursion.

[0103] Figure 4 The physical system of the type of motor vehicle is shown, whose behavior, defined by Newton's second law (balance of forces), can be reduced to linear behavior by some simplifying assumptions (e.g., zero wind speed).

[0104] The forces involved include: Inertial force F inertie Its value is (m+m) e )a x Where m is the mass of the vehicle, m e It is the equivalent mass of the rotating component. Traction force F tract Its value is , among which, T mot γ is the engine torque, η is the gear ratio, and γ is the transmission ratio. motrice This refers to the mechanical or drive transmission efficiency (typically fixed between 0.95 and 0.99), r roue That is the radius of the wheel. For engine braking, the traction force may be negative. In this case, the traction force is the braking force. Aerodynamic or drag F aero Its value is , where ρ air It is the ambient air density, ν x It is the longitudinal speed of the vehicle, ν vent It is the longitudinal wind speed, A f It is the vehicle's frontal area, C d It is the vehicle's aerodynamic coefficient. Rolling resistance F roll Its value is mgC rr .cos(θ), where g is the gravitational constant, C rr Here, θ is the rolling resistance coefficient, and θ is the slope angle. Gravity F gravIts value is mgsin(θ).

[0105] Force balance yields F inertie =F tract +F aero +F roll +F grav Therefore, the following linear model is derived: ,Right now y = A = x = .

[0106] In this linear system, the values ​​of vector y and matrix A are fixed and known values ​​(e.g., g), or values ​​that can be measured using sensors.

[0107] The goal is to acquire the vehicle's mass *m* in real time without using dedicated sensors. Similarly, the drag coefficient *C* can be obtained in real time. rr and C d (A) f and (Known).

[0108] Therefore, it can be applied Figure 2 and Figure 3 The method. Figure 5 The method is shown in Figure 4 Applications in the system.

[0109] The same reference numerals in the figures correspond to the same steps / substeps.

[0110] The vehicle's onboard sensor 112 obtains the engine torque T. mot (t), longitudinal acceleration a x (t) and the angular velocities of the engine and wheels (t) and The measured values ​​of (t) are transmitted to the measurement unit 114 via the vehicle's CAN (Controller Area Network) bus.

[0111] In step 2146, the preprocessing unit 115 calculates the yaw rate ψ(t) at a predetermined preprocessing frequency.

[0112] In step 2140, for example by downsampling and / or interpolation as described above, the various measured values ​​T are... mot (t), a x (t) (t), (t) and data ψ(t) with the time t for recursion k k Perform time alignment.

[0113] In step 2142, angular velocity is used , Calculate the transmission ratio γ.

[0114] angular velocity Used to calculate the longitudinal speed ν of the vehicle x,k .

[0115] Based on the calculated yaw rate ψ k For the preprocessed measurement value T mot,k a x,k and the calculated measured values ​​γ, ν x,k Select option 2144 to retain only the measurements and data associated with the vehicle's linear motion.

[0116] In optional step 222, the transmitted measurement value / data T is processed. mot,k a x,k ,γ,ν x,k To determine the noise covariance matrix Q a,k and Q y,k .

[0117] In step 224, by the estimator Using these six data points (other input data (r) roue η motrice (g) is a fixed value to obtain the unknown parameter x. k The estimated values ​​are, here, the mass m and the drag coefficient C. rr and C d The estimated value (A) f and ρ air (Known).

[0118] As mentioned above, the estimator Optimization / improvement tools derived from literature on classical least squares can be utilized. The forgetting parameter λ has been introduced into the scheme proposed above.

[0119] In these tools, regularization avoids numerical instability in the matrix inversion operation (4). In fact, this numerical instability can lead to problems with the covariance matrix P. k The covariance matrix P diverges, leading to overall divergence in the estimator. Therefore, a regularization term α (either zero to cancel any regularization or positive) is introduced in the additional operation (5') to correct the covariance matrix P. k : : (1) (2) (3) (4) (5) (5') (6) (7) α is typically less than 1 to achieve fine regularization; for example, α = 0.1.

[0120] Another tool is known by the name "instrumental variable". This correction avoids biased estimations when the measurement noise is correlated with the measurement signal in one way or another. In fact, if there is a correlation between the noise and the signal, it may not be sufficient to establish this estimator. One of the assumptions made is additive noise. An instrumental variable ζ is introduced into operation (4). k And calculate for each new recursion. Select these instrumental variables and replace them with appropriate input values ​​to eliminate the aforementioned correlations, thereby improving the accuracy of the estimator. Instrumental variable ζ k With variables Strong correlation, usually ζ k It is the matrix of the previous recursion. For example, ζ k+1 = or .

[0121] The example below includes the forgetting factor λ, the regularization term α, and the instrumental variable ζ. k Of course, these different tools can be used individually.

[0122] The adjusted recursive scheme is as follows: : (1) (2) (3) (4) (5) (5') (6) (7) Another tool is known by the name "Huber Outlier Weighting". It is used to mitigate the negative impact that the presence of outliers can have on recursive estimation. Indeed, the presence of outliers or anomalies in input or output measurements often degrades the performance of the estimator. The Huber weighting function is introduced at the beginning of the recursive scheme in operations denoted as (0) and (0'), and then used in operation (4) to compute the matrix variable K. The parameter ξ is adjusted by the operator. As mentioned above, although all the tools presented are combined in this example, they can also be used individually.

[0123] The adjusted recursive scheme is as follows: : (0) (1) (2) (3) (4) (5) (5') (6) (7) The tool variants involve multiple forgetting factors.

[0124] The forgetting factor λ can be set individually for each parameter of the vector x to be estimated. Therefore, multiple forgetting factors can be represented as λ. i , i is a vector x={x i The parameter x in} i The indexes enable the assignment of individual forgetting levels for each estimated parameter.

[0125] The forgetting factor λ can also be evolutionary, with its value adjusted from one recursion to another. Thus, multiple forgetting factors can be represented as λ. k They are used to respond to parameters that change over time.

[0126] These two properties can also be combined. Therefore, multiple forgetting factors can be represented as λ. k,i It is also represented as ∧. k ={λ k,i}

[0127] They are introduced at the beginning of the recursive scheme in the operation denoted as (0), and then used in operations (4) and (5), where matrices K and P are calculated coefficient by coefficient: : (0) (0'') (0') (1) (2) (3) (5) (5') (6) (7) Figure 6 The computer hardware architecture of system 100 or estimation device 110 according to the implementation scheme is shown.

[0128] Device 600 includes a communication bus 601, which is preferably connected to: - One or more central processing units 602, for example, one or more CPU processors and / or one or more microprocessors; - ROM and / or hard disk and / or flash memory type storage memory 603, which is used to store computer programs intended to perform all or part of the above operations; -RAM or even video RAM (VRAM) type random access memory 604, which is used to store the executable code of a computer program and registers suitable for recording the variables and parameters required for its execution; - Communication interface 605, which is connected to a network (e.g., CAN bus or WiFi network) to communicate with external devices (e.g., external sensor 112 or processing unit 120); - One or more I / O inputs / outputs 606 that enable an operator to interact with a computer program for configuring and operating both. Typically, the inputs / outputs may include a screen serving as a graphical interface with the operator and capable of displaying values ​​of unknown parameters, and / or speakers for displaying audio content, and / or a keyboard or any other pointing device enabling operator interaction; and - One or more sensors 112 as described above, if they are physically integrated in device 600.

[0129] Preferably, the communication bus 601 ensures communication and interoperability between the various elements included in or connected to the device 600. The representation of the bus is not limiting, and in particular, the central processing unit can be used to transmit instructions directly or through another element of the computing device to any element of the computing device 600.

[0130] Executable code stored in memory 603 can be received via communication interface 605 through a communication network and stored therein before execution. Alternatively, the executable code can be loaded from a remote server into volatile memory 604 for direct execution instead of being stored in non-volatile memory 603.

[0131] The central processing unit 602 is preferably adapted to control and manage the execution of instruction or software code portions of one or more computer programs. When powered on, one or more programs stored in non-volatile memory 603 or a remote server are transferred / loaded into random access memory 604, which then contains executable code for one or more programs, as well as registers for storing variables and parameters required to execute the present invention.

[0132] Of course, the present invention is by no means limited to the above-described variant embodiments, and those skilled in the art are particularly able to separate or freely combine the above features, or replace their equivalent features.

[0133] appendix The linear system under consideration is always y=Ax.

[0134] The aforementioned publication by Shen Y. et al. provides an iterative overall least squares estimator.

[0135] Consider the following symbol: W y It is a positive symmetric weighting matrix (e.g., output measurement noise covariance), W a It is a positive symmetric weighted matrix (e.g., input measurement noise covariance). Regarding iteration, the following notation is used: for the updated parameter, x （i+1） =x （i） +δx （i+1） For the corrected input matrix, A （i） =A-ΔA （i） For the corrected output vector, 。 operator Corresponding to the Kronecker product, I m It is an m*m dimensional identity matrix (where m is the dimension of y).

[0136] The explanation by Shen Y. et al. (including formulas 14, 15a, and 15b) yielded the following iterative process: (Equation 1) (Equation 2) To transition from an iterative estimator to a recursive estimator, the input measurement A and the output measurement y are divided into two groups: (Equation 3) and .

[0137] Similarly, and .

[0138] The components of equation 1 can be written as: (Equation 4) Consider the following lemma: (A+BCD) -1 =A -1 –A -1 B(C) -1 +DA -1 B) -1 DA -1 , The first expression of equation 4 is given by the following: (Equation 5) in, .

[0139] Combining the expressions from equations 4 and 5 into equation 1, we get: Right now, because We got Right now, (Equation 6) Similarly, we obtain: (Equation 7) By considering the additional measurement value AN+1 y N+1 The two sets of consecutive iterative measurements are then correlated in the following way, allowing the iteration index "i" to be removed and replaced with the recursive index "k": as well as In the context of each iterative data collection, the Kronecker product ( The noise covariance matrix W can be simplified to x. Therefore, the noise covariance matrix W Z It can be written as: (Equation 8) .

[0140] From equation 2, we can derive: (Equation 9) in By introducing a gain matrix: (Equation 10) , The recursive parameter and the increment of the recursive parameter can be written as: (Equation 11) as well as Furthermore, Equation 5 enables the rewriting of the covariance matrix P: (Equation 12) Finally, by adopting the reasonable assumption of zero-mean Gaussian noise on both the input and output measurements, the random characteristics of the random error can be characterized as follows: in, and .

[0141] By setting Q=W -1 estimator This is thus formed by equations 8 to 12.

Claims

1. An estimation apparatus (110) for estimating parameters of a physical system (100) considered linear, comprising: - Measurement unit (114), configured to acquire continuous input measurement values ​​A from a linear system. k and continuous output measurement value y k , - An estimation unit (116) configured to recursively estimate one or more parameters x of the physical system based on the input and output measurements using a Lagrange total least squares estimator. k The estimation recursion k+1 of the Lagrange total least squares estimator includes the following operations: (1) (2) (3) (4) (5) Optional (5') (6) (7) Where k is the recursive index; Q a,k and Q y,k The weighted matrix; δx k , and P k For variables in the recursion; For variables Related instrumental variables; Q z,k ΔA k K k α is the internally computed variable; α is the regularization term, and λ is the positive forgetting parameter less than or equal to 1.

2. The apparatus (110) according to claim 1, wherein, Q a,k and Q y,k These are the input and output measurement error or noise covariance matrices, respectively.

3. The apparatus (110) according to claim 1 or 2, wherein, Q a,k and Q y,k The evolution matrix is ​​an estimation unit (116) with a matrix estimation subunit (117) configured to determine matrix Q for each recursive iteration based on the input measurement and the output measurement, respectively. a,k and Q y,k .

4. The apparatus (110) according to any one of claims 1 to 3, wherein, The forgetting parameter λ is 1, and / or the regularization term α is 0, and / or the instrumental variable is 0. for .

5. The apparatus (110) according to any one of claims 1 to 3, wherein, The forgetting parameter λ is strictly less than 1, and / or the regularization term α is strictly positive and less than 1, and / or the instrumental variable. for , where a is a positive integer.

6. The apparatus (110) according to any one of the preceding claims, wherein, The measurement unit (114) includes a preprocessing subunit (115) for preprocessing measurement values ​​acquired from one or more sensors (112) to generate continuous input measurement values ​​A. k and output measurement value y k The preprocessing subunit is configured to perform at least one of the following operations: - Time alignment of input or output measurements is performed by interpolating and / or downsampling the acquired measurements, and - Select a portion of the measured values ​​to generate continuous input measured values ​​A. k and output measurement value y k The choice depends on the accompanying behavior of the physical system.

7. The apparatus (110) according to the preceding claim, wherein, The physical system (110) is a vehicle, and only measurements associated with the linear motion of the vehicle are selected in part.

8. The apparatus (110) according to any one of the preceding claims, wherein, The physical system (100) is a vehicle, and the one or more parameters include the mass of the vehicle.

9. The apparatus (110) according to the preceding claim, wherein, The measuring unit (114) is connected to a device for measuring the engine torque (T) of a vehicle. mot ), longitudinal acceleration of the vehicle (a x ) and the engine's angular velocity ( ) and the angular velocity of the wheel ( The sensor (112) is used to determine the longitudinal speed (v) of the vehicle. x ) and transmission ratio (γ).

10. An estimation method for estimating parameters of a physical system (100) considered linear, executed by a computer, and comprising the following steps: - Acquire (210) continuous input measurements A from a linear system using one or more sensors. k and continuous output measurement value y k , - Using a Lagrange total least squares estimator, based on the input and output measurements, one or more parameters x of the physical system are recursively estimated (220). k The estimation recursion k+1 of the Lagrange total least squares estimator includes the following operations: (1) (2) (3) (4) (5) Optional (5') (6) (7) Where k is the recursive index; Q a,k and Q y,k The weighted matrix; δx k , and P k For variables in the recursion; For variables Related instrumental variables; Q z,k ΔA k K k α is the internally computed variable; α is the regularization term, and λ is the positive forgetting parameter less than or equal to 1.

11. A computer program product comprising a non-transitory recording medium having computer-readable program code for performing the method according to the preceding claim.

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