CN-121984479-A - Robust noise covariance estimation method based on iterative re-weighted least square

CN121984479ACN 121984479 ACN121984479 ACN 121984479ACN-121984479-A

Abstract

The invention relates to a robust noise covariance estimation method based on iterative re-weighting least square, which comprises the following steps of 1, constructing a state space model of a linear time-invariant system, acquiring measurement data in the operation process of the system, calculating an innovation sequence, estimating an observation vector formed by auto-covariance of the innovation sequence, 2, constructing a linear regression equation set of the innovation covariance and the noise covariance by utilizing the state space model of the system and steady-state Kalman gain based on the observation vector, 3, adopting an iterative re-weighting least square algorithm to acquire a robust noise covariance estimation value from the linear regression equation set, and 4, feeding the robust noise covariance estimation value back to a Kalman filter, and carrying out Kalman filter parameter updating and circulation to realize online self-adaption adjustment of noise statistical parameters. The invention obviously improves the robustness to the abnormal value on the noise statistic parameter estimation, and can still ensure the accuracy and stability of Kalman filtering in the environment containing noise and abnormal data.

Inventors

LI JIAHONG
ZHANG MENGMENG
DONG XUEPENG
LIU LEPING

Assignees

北京联合大学

Dates

Publication Date: 20260505
Application Date: 20260126

Claims (7)

1. A robust noise covariance estimation method based on iterative re-weighted least squares, comprising: Step 1, constructing a state space model of a linear time-invariant system, initializing a Kalman filter, acquiring measurement data in the running process of the system, calculating an innovation sequence, and estimating an observation vector formed by auto-covariance; step 2, based on the observation vector, constructing a linear regression equation set of the innovation covariance and the noise covariance by utilizing a system state space model and a steady-state Kalman gain; Step 3, adopting an iterative re-weighting least square algorithm to acquire a robust noise covariance estimation value for the linear regression equation set; And 4, feeding the robust noise covariance estimation value back to a Kalman filter, and carrying out Kalman filter parameter updating and circulation to realize on-line self-adaptive adjustment of noise statistical parameters.
2. The method for estimating robust noise covariance based on iterative re-weighted least squares according to claim 1, estimating an observation vector composed of its autocovariance comprising: Constructing a state space model of a linear time-invariant system, and initializing a Kalman filter state Initial covariance value Given process noise covariance And measuring noise covariance Is determined by the initial estimate of (a); acquiring measurement data during system operation by means of a sensor And calculating to obtain an innovation sequence by a prediction updating formula of Kalman filtering , wherein, In order to measure the matrix of the device, Is time of Predicting the obtained state by using the prior noise covariance; collecting a window with a preset length Is new information sequence data of (a) Calculating a sample estimate of the innovation auto-covariance of each order lag: stacking the auto-covariance estimates of all hysteresis orders in columns to form an observation vector: Wherein, the Is the first At the moment of time of day, In order to be a sequence of the innovation, Is an observation vector.
3. The method of iterative re-weighted least squares based robust noise covariance estimation according to claim 1, wherein the state space model is: Wherein, the In order to be in the state of the system, As the measurement data of the sensor(s), In the form of a state transition matrix, In order to observe the matrix, And The covariance matrix of the process noise and the measurement noise are respectively And 。
4. The method for estimating robust noise covariance based on iterative re-weighted least squares according to claim 1, wherein the set of linear regression equations is: Wherein, the For the corresponding matrix of coefficients, In order to include a vector of parameters to be estimated, For observing vectors 。
5. The method for robust noise covariance estimation based on iterative re-weighted least squares according to claim 1, wherein the steady state kalman gain is: Wherein, the Is the steady-state kalman gain of the device, Is the steady-state kalman gain of the device, For the transposition of the observation matrix, Is the observed noise covariance matrix.
6. The method of claim 1, wherein step 3, using an iterative re-weighted least squares algorithm to obtain a robust noise covariance estimate for the set of linear regression equations comprises: initializing, namely initializing all observed data weight initial values to be 1: Wherein the method comprises the steps of The total number of the strokes; The weight diagonal matrix representing step t, Representing the ith diagonal element thereof, initially set to a uniform weight, i.e Order-making Solving for an initial weighted least squares: ; Step 3.2. Calculating residual errors from the current estimate Calculating a residual vector: Each element of the residual Reflecting the first Deviation between the strip innovation covariance observation and the model predictive value; Step 3.3. Update weights, selecting Huber loss threshold The weights are updated according to the following rules: thereby constructing a new diagonal weight matrix ; Step 3.4. Solving the new estimate, after updating the weights, solving a new weighted least squares problem Obtaining a new noise covariance parameter estimation value; Step 3.5 iteration stop condition, let Repeating the steps 3.2-3.4 until any condition is satisfied, namely stopping 1) the small parameter change: 2) the cost function has small variation: 3) reaching the maximum iteration times And finally outputting a convergence result: Reconstructing the obtained robust noise covariance estimation value into a matrix form , 。
7. The method of iterative re-weighted least squares based robust noise covariance estimation according to claim 1, wherein performing kalman filter parameter updates and loops comprises: the obtained robust noise covariance estimation value 、 Feeding back to the Kalman filter, and updating the process noise and the measured noise parameters: and repeatedly executing the steps 1-3 according to every fixed step number or when the abnormal increase of the innovation variance is detected, and estimating and updating the covariance matrix of the process noise and the measurement noise in the state space model again by using the latest data window And And realizing the on-line self-adaptive adjustment of noise statistical parameters.

Description

Robust noise covariance estimation method based on iterative re-weighted least square Technical Field The invention relates to the technical field of signal processing and automatic control, in particular to a robust noise covariance estimation method based on iterative re-weighting least square. Background The kalman filter has optimal performance in linear gaussian system state estimation. In practical applications, however, the statistical properties (covariance) of the process noise and the measurement noise are often unknown or vary over time. Incorrect setting of the noise covariance can significantly impair the filtering effect, leading to increased state estimation bias and even filter divergence. To solve this problem, scholars at home and abroad propose various methods for estimating noise covariance by using historical data, including bayesian estimation, maximum Likelihood Estimation (MLE), covariance matching, minimum and maximum methods, subspace identification, correlation function methods, and the like. The correlation function method is widely focused because of moderate computational complexity and no special assumption on a noise model. Mehra and Belanger originally proposed a three-step noise statistics estimation method based on the autocorrelation of the innovation sequence, followed by the development of an Autocovariance Least Squares (ALS) method for single-step completion estimation. The ALS method can estimate the process noise and measure the noise covariance simultaneously by constructing a linear equation set between the innovation sequence auto-covariance and the noise covariance and solving by least square, and is applied to a plurality of actual systems. However, most of the above methods default to the observation noise approximately satisfying the gaussian distribution, and do not consider the outlier (outlier) influence caused by the sensor malfunction or external disturbance. In practical systems, abnormal values often occur, such as transient impact on a sensor, packet loss of communication data, or strong interference signals in the environment, which can cause abnormal samples in a new information sequence, which deviate significantly from the main data distribution. These outliers can disrupt the gaussian noise assumption of the kalman filter, causing severe bias or variance expansion of the filtering results. In particular, when estimating the noise covariance using the least squares principle, even a small amount of outlier data may dominate the cost function, resulting in the estimated Q, R deviating from the true value, which in turn degrades the filter performance. In response to the above problems, researchers have developed a variety of robust kalman filter algorithms (ORKF) to enhance the tolerance of filters to outliers. From the method, the method mainly comprises a first parameter self-adaptive method, namely, assuming that noise distribution is in a certain thick tail form, counteracting abnormal value influence by introducing prior distribution, for example, using a heavy tail model such as Gaussian mixture prior or Student-t distribution and the like to enhance robustness, a second non-parameter method, namely, not directly assuming specific distribution, reducing abnormal value influence by utilizing an information theory or statistical means, for example, a filtering method based on related entropy, and a third robust filtering energized by an M estimation theory. The M estimation method reduces the influence function corresponding to the abnormal residual error by selecting a non-square robust cost function, thereby inhibiting the interference of the outlier to the estimation. Typical practices include the weighted least squares (WLMS) method of introducing weight-reducing outlier contributions to the residual, the Least Absolute Deviation (LAD) method employing L1 norms, and the piecewise functions proposed by Huber and their modified loss functions for filtering weighting, etc. The robust filtering method ensures that the filtering residual error is not led by an abnormal value to a certain extent, and improves the anti-interference capability of state estimation. However, the robust method generally adopts a fixed-form influence function, which is determined by a selected loss function and an adjustment parameter, and when the abnormal value distribution characteristics are inconsistent with a preset assumption, performance degradation may occur, so that the robust method is difficult to adaptively adjust for different types of outliers. For example, the Huber function requires a preset threshold, and a fixed threshold may not achieve optimal results when the abnormal noise ratio or amplitude exceeds the expected value. To overcome the limitation of the fixed influence function, an iterative re-weighted least squares (IRLS) algorithm is provided in the field of robust statistics. IRLS approximates the optimal p-norm minimization solution by contin