Kalman filter robust to outlier and non-gaussian noise
The Kalman filter enhances performance in noisy environments by using exponentially weighted averages and covariances, adjusting Kalman gains based on likelihood ratios, to handle outliers and non-normal noise effectively.
Patent Information
- Authority / Receiving Office
- WO · WO
- Patent Type
- Applications
- Current Assignee / Owner
- Filing Date
- 2025-11-11
- Publication Date
- 2026-06-04
Smart Images
Figure KR2025018464_04062026_PF_FP_ABST
Abstract
Description
Kalman filter robust against outliers and irregular noise
[0001] The present invention relates to a Kalman filter, and more specifically, to a Kalman filter robust against outliers and irregular noise.
[0002] Kalman filters are utilized in various systems such as robots, computer vision, GPS, and radar.
[0003] Such Kalman filters exhibit optimal performance in situations where only normal noise is present, but performance degradation occurs in the presence of other noise or outliers. This invention aims to improve upon the shortcomings of such Kalman filters.
[0004] Furthermore, the Kalman filter was derived for situations where normal noise is added, and did not consider cases where other noise or outlier data exists.
[0005] In addition, although Kalman filters are applied in various vision systems, robots, and radar, performance degradation occurs with respect to various noises and outlier data present in the real world.
[0006] Therefore, although there are filters such as unscented Kalman filters and particle filters for non-normal noise situations, they are very complex and perform worse than conventional Kalman filters in normal noise conditions.
[0007] The present invention has been devised to solve the aforementioned problems, and the objective of the present invention is to provide a Kalman filter robust to outliers and irregular noise that can be applied wherever existing Kalman filters are used and can achieve excellent performance in situations where outlier data and irregular noise are present.
[0008] A filtering method using a Kalman filter robust to outliers and non-normal noise according to an embodiment of the present invention for achieving the above objective comprises: a step in which a system calculates a Kalman gain; a step in which a system calculates an estimated value based on the Kalman gain; a step in which a system calculates an error covariance by comparing and analyzing the predicted value and the measured value of the error covariance; a step in which a system calculates an exponentially weighted average and an exponentially weighted covariance for the estimated value; and a step in which a system incorporates the exponentially weighted average and the exponentially weighted covariance of the calculated estimated value into the next Kalman gain calculation.
[0009] And in the reflection step, once the exponentially weighted mean and exponentially weighted covariance of the estimates are calculated, the likelihood value of the normal distribution function for the exponentially weighted mean and exponentially weighted covariance can be calculated.
[0010] In addition, the reflecting step can calculate the likelihood ratio based on the calculated likelihood value once the likelihood value is calculated.
[0011] And in the reflection step, when calculating the likelihood ratio, the likelihood ratio can be calculated based on the median of the m most recently calculated likelihood values among the calculated likelihood values.
[0012] Additionally, in the reflection step, once the likelihood ratio is calculated, the calculated likelihood ratio can be reflected in the next Kalman gain calculation.
[0013] In addition, when data with outlier data or non-normal noise is input, the system can reduce the influence of outlier data or non-normal noise and improve the accuracy of the estimate by increasing the weight of the current time point as the current measurement value is similar to the existing estimate value, thereby allowing the calculated likelihood ratio value to have a relatively large influence on the estimate value to be calculated.
[0014] In addition, when data with outlier data or non-normal noise is input, the system can reduce the influence of the outlier data or non-normal noise and improve the accuracy of the estimate by decreasing the weight of the current time point as the similarity between the current measurement value and the existing estimate decreases, thereby allowing the calculated likelihood ratio value to have a relatively small influence on the estimate to be calculated.
[0015] And, the filtering method using a Kalman filter robust to outliers and non-normal noise according to the present embodiment may further include the step of, when an initial value is selected, the system predicting an estimated value and an error covariance.
[0016] In addition, the step of calculating the Kalman gain can calculate the Kalman gain based on the predicted value of the error covariance.
[0017] Meanwhile, a filtering system using a Kalman filter robust to outliers and non-normal noise according to another embodiment of the present invention comprises: a communication unit for acquiring a measurement value; and a processor for calculating a Kalman gain, calculating an estimated value based on the Kalman gain, calculating an error covariance by comparing and analyzing the predicted value and the measured value of the error covariance, calculating an exponentially weighted average and an exponentially weighted covariance for the estimated value, and reflecting the exponentially weighted average and the exponentially weighted covariance of the calculated estimated value in the next Kalman gain calculation.
[0018] Additionally, a filtering method using a Kalman filter robust to outliers and non-normal noise according to another embodiment of the present invention comprises: a step in which, when an initial value is selected, a system predicts an estimated value and an error covariance based on the selected initial value; a step in which the system calculates a Kalman gain based on the predicted value of the error covariance; a step in which the system calculates an estimated value based on the Kalman gain; a step in which the system calculates an exponentially weighted average and an exponentially weighted covariance for the estimated value; and a step in which the system incorporates the exponentially weighted average and the exponentially weighted covariance of the calculated estimated value into the next Kalman gain calculation.
[0019] A filtering system using a Kalman filter robust to outliers and non-normal noise according to another embodiment of the present invention comprises: a communication unit for acquiring a measurement value; and a processor that, when an initial value is selected, predicts an estimated value and an error covariance based on the selected initial value, calculates a Kalman gain based on the predicted value of the error covariance, calculates an estimated value based on the Kalman gain, calculates an exponentially weighted average and an exponentially weighted covariance for the estimated value, and incorporates the exponentially weighted average and the exponentially weighted covariance of the calculated estimated value into the next Kalman gain calculation.
[0020] As explained above, according to the embodiments of the present invention, superior performance compared to conventional Kalman filters can be achieved in situations where there is no normal noise.
[0021] In addition, according to embodiments of the present invention, robust performance can be achieved by reducing the influence of outlier data when it is present, and it is simpler than existing improved versions of Kalman filters, such as anechoic filters and particle filters, and can secure excellent performance in normal noise situations.
[0022] FIG. 1 is a drawing provided for the description of the configuration of a filtering system using a Kalman filter robust to outliers and irregular noise according to an embodiment of the present invention.
[0023] FIG. 2 is a flowchart provided for describing a filtering method using a Kalman filter robust to outliers and irregular noise according to an embodiment of the present invention.
[0024] FIG. 3 is a drawing provided to explain a filtering process using a Kalman filter robust to outliers and irregular noise according to an embodiment of the present invention.
[0025] FIG. 4 is a diagram illustrating a situation with added Cauchy noise, and
[0026] Figure 5 is a diagram illustrating the results of comparing the cumulative absolute error of the position in a Cauchy noise environment.
[0027] The present invention will be described in more detail below with reference to the drawings. To clearly explain the invention, parts unrelated to the description have been omitted from the drawings, and in the drawings, the width, length, thickness, etc., of the components may be exaggerated for convenience.
[0028] FIG. 1 is a diagram provided to describe the configuration of a filtering system using a Kalman filter robust to outliers and irregular noise according to one embodiment of the present invention.
[0029] A filtering system using a Kalman filter robust to outliers and non-normal noise according to the present embodiment (hereinafter collectively referred to as the 'system') can be applied wherever existing Kalman filters are used, and can provide a Kalman filter robust to outliers and non-normal noise that can achieve excellent performance in situations where outlier data and non-normal noise are present.
[0030] To this end, the system may include a communication unit (100), a processor (200), and a storage unit (300).
[0031] The communication unit (100) is equipped with a communication module connected to a network, and can acquire measurement data from various devices such as robots, computer vision, GPS, and radar.
[0032] The storage unit (300) is provided to store programs and data necessary for the operation of the processor (200).
[0033] The processor (200) can process all matters for performing a filtering operation using a Kalman filter according to the present embodiment on measurement data obtained through the communication unit (100).
[0034] Specifically, when an initial value of the Kalman filter is selected, the processor (200) predicts an estimated value and an error covariance based on the selected initial value, and can calculate a Kalman gain based on the predicted value of the error covariance.
[0035] And the processor (200) can calculate an estimate based on the Kalman gain and calculate an exponentially weighted average and an exponentially weighted covariance for the estimate.
[0036] Afterward, the processor (200) can incorporate the exponentially weighted average and exponentially weighted covariance of the calculated estimates into the next Kalman gain calculation.
[0037] Specifically, the processor (200) calculates the likelihood value of a normal distribution function for the exponentially weighted average and exponentially weighted covariance of the estimated values when the exponentially weighted average and exponentially weighted covariance are calculated, and calculates the likelihood ratio based on the calculated likelihood value and can reflect the calculated likelihood ratio in the next Kalman gain calculation.
[0038] At this time, the processor (200) can reduce the influence of outlier data or non-normal noise and improve the accuracy of the estimate by making the calculated likelihood ratio value have a relatively large influence on the estimate value to be calculated, when outlier data or non-normal noise is added to the data input.
[0039] Here, the processor (200) can increase the weight of the current time point as the current time point measurement is similar to the existing estimate, so that the calculated likelihood ratio value has a relatively large influence on the estimate to be calculated.
[0040] That is, the processor (200) can increase the weight of the current time point as the current time point measurement value is similar to the existing estimate value, so that the calculated likelihood ratio value has a relatively large influence on the estimate value to be calculated.
[0041] Additionally, the processor (200) can reduce the influence of outlier data or non-normal noise and improve the accuracy of the estimate when outlier data or non-normal noise is added to data input by making the calculated likelihood ratio value have a relatively small influence on the estimate to be calculated.
[0042] In this case, the processor (200) can reduce the weight of the current time point as the similarity between the current time point measurement and the existing estimate decreases, so that the calculated likelihood ratio value has a relatively small influence on the estimate to be calculated.
[0043] FIG. 2 is a flowchart provided to explain a filtering method using a Kalman filter robust to outliers and irregular noise according to one embodiment of the present invention, and FIG. 3 is a drawing provided to explain a filtering process using a Kalman filter robust to outliers and irregular noise according to one embodiment of the present invention.
[0044] The filtering method using a Kalman filter robust to outliers and irregular noise according to the present embodiment can be executed by the system described above with reference to FIG. 1.
[0045] Referring to FIGS. 2 and 3, when an initial value is selected (S210), the system predicts an estimated value and an error covariance based on the selected initial value (S220), and based on the predicted value of the error covariance, a Kalman gain (K K ) can be calculated (S230).
[0046] Here, the initial value is the initial estimate ( It may include ) and covariance (P0).
[0047] Subsequently, the system, Kalman gain (K K Estimated value based on ) Calculate ) (S240), and compare and analyze the predicted and measured values of the error covariance to determine the error covariance (P k ) can be calculated (S250).
[0048] Additionally, the system calculates the exponentially weighted average and exponentially weighted covariance of the estimates (S260), and can incorporate the calculated exponentially weighted average and exponentially weighted covariance of the estimates into the next Kalman gain calculation (S270).
[0049] Specifically, the system, the estimated value ( When the exponentially weighted average and exponentially weighted covariance of ) are calculated, the likelihood value of the normal distribution function for the exponentially weighted average and exponentially weighted covariance is calculated, and when the likelihood value is calculated, the likelihood ratio is calculated based on the calculated likelihood value, and the calculated likelihood ratio can be reflected in the next Kalman gain calculation.
[0050] Referring to Figure 3, A represents the state-space equation representing the system, Q is the system error, and R is the sensor error.
[0051] In the case of conventional Kalman filters, Q and R are fixed values during the design phase and do not change once the system is in operation. Therefore, they have the disadvantage of being unable to adapt to environmental changes.
[0052] β represents the likelihood ratio, and in conventional Kalman filters, the value of β is fixed at 1.
[0053] The system according to the present embodiment may calculate and use the mean and covariance of the Kalman filter output using an exponentially weighted average and covariance method. This is intended to increase the reflection ratio of recent data and reduce the influence of past data, thereby enabling the system to operate well even in environments that change over time.
[0054] As mentioned above, once the corresponding mean and covariance are obtained, the system uses them to calculate the likelihood (L) of the normal distribution function. k It can be used for calculations.
[0055] Since the Kalman filter assumes normal noise, it means determining how well new data matches existing data from the perspective of normal noise.
[0056] Specifically, when the system calculates the likelihood ratio (β), the calculated likelihood (L k The median of the m most recently calculated likelihood values among the values (M k The likelihood ratio (β), which is the ratio to the median value based on ), can be calculated.
[0057] In other words, the system utilizes the likelihood ratio (β) value during the next Kalman gain calculation to allow the Kalman gain to change, thereby providing a Kalman filter that is more robust against outliers and non-normal noise than when using a conventional Kalman filter.
[0058] Here, the likelihood ratio (β) value according to the present embodiment can be such that when the measurement data is similar to the existing data, the weight of the current data increases, thereby significantly influencing the estimated value, and conversely, when the measurement data at the current time is less similar to the existing data, the β value decreases, thereby reflecting the predicted value of the previous stage more significantly than the current data.
[0059] Based on this principle, when outlier data or data with added non-normal noise is input, its impact can be reduced and the accuracy of the estimate can be improved.
[0060] Figure 4 is a diagram illustrating a situation where Cauchy noise is added.
[0061] In Figure 4, an example of comparing performance is shown by depicting a situation where non-normal noise or outlier data is added.
[0062] The system can estimate the coordinates of an object moving along an ∞ shape along the solid line of Fig. 4.
[0063] In Figure 4, measurement data with added Cauchy noise is indicated by dots to depict data with added non-normal noise or outliers, and in this case, the estimate of the conventional Kalman filter is indicated by a dotted line. Additionally, the result filtered through the system is shown as a dashed line.
[0064] As illustrated in Figure 4, it can be seen that the estimation results of the Kalman filter fluctuate significantly depending on the noise. On the other hand, the technology of the present invention is robust against noise, and it can be confirmed that more stable estimation is possible than that of the conventional Kalman filter.
[0065] Figure 5 is a diagram illustrating the results of comparing the cumulative absolute error of position in a Cauchy noise environment.
[0066] Referring to Fig. 5, the solid line represents the simple measurement value, the dotted line represents the Kalman filter, and the dashed line represents the result filtered through the system.
[0067] As illustrated in Fig. 5, when the measured value has a large error due to noise, the performance of the Kalman filter deteriorates. It can be confirmed that the filtered result through this system effectively suppresses noise, resulting in a very small cumulative error and excellent performance.
[0068] So far, a filtering system and method using a Kalman filter robust against outliers and irregular noise have been described in detail with preferred embodiments.
[0069] According to embodiments of the present invention, in situations where there is no normal noise, it can have superior performance compared to conventional Kalman filters.
[0070] In addition, according to embodiments of the present invention, robust performance can be achieved by reducing the influence of outlier data when it is present, and it is simpler than existing improved versions of Kalman filters, such as anechoic filters and particle filters, and can secure excellent performance in normal noise situations.
[0071] Meanwhile, it goes without saying that the technical concept of the present invention may also be applied to a computer-readable recording medium containing a computer program that enables the device and method according to the present embodiment to perform their functions. Furthermore, the technical concept according to various embodiments of the present invention may be implemented in the form of computer-readable code recorded on a computer-readable recording medium. A computer-readable recording medium may be any data storage device that can be read by a computer and store data. For example, a computer-readable recording medium may be a ROM, RAM, CD-ROM, magnetic tape, floppy disk, optical disk, hard disk drive, etc. Additionally, computer-readable code or a program stored on a computer-readable recording medium may be transmitted through a network connected between computers.
[0072] Furthermore, although preferred embodiments of the present invention have been illustrated and described above, the present invention is not limited to the specific embodiments described above. Various modifications are possible by those skilled in the art without departing from the essence of the invention as claimed in the claims, and such modifications should not be understood individually from the technical spirit or perspective of the present invention.
Claims
1. The step in which the system calculates the Kalman gain; A step in which the system calculates an estimate based on Kalman gain; A step in which the system calculates the error covariance by comparing and analyzing the predicted and measured values of the error covariance; The system calculates an exponentially weighted average and an exponentially weighted covariance for the estimates; and A filtering method using a Kalman filter robust to outliers and non-normal noise, comprising the step of the system incorporating the exponentially weighted average and exponentially weighted covariance of the calculated estimates into the next Kalman gain calculation.
2. In Claim 1, The reflective stage is A filtering method using a Kalman filter robust to outliers and non-normal noise, characterized by calculating the likelihood value of a normal distribution function for the exponentially weighted average and exponentially weighted covariance of the estimated values when the exponentially weighted average and exponentially weighted covariance are calculated.
3. In Claim 2, The reflective stage is A filtering method using a Kalman filter robust to outliers and non-normal noise, characterized by calculating a likelihood ratio based on the calculated likelihood value once the likelihood value is calculated.
4. In Claim 3, The reflective stage is A filtering method using a Kalman filter robust to outliers and non-normal noise, characterized by calculating the likelihood ratio based on the median of the m most recently calculated likelihood values among the calculated likelihood values.
5. In Claim 3, The reflective stage is A filtering method using a Kalman filter robust to outliers and non-normal noise, characterized by reflecting the calculated likelihood ratio in the next Kalman gain calculation when the likelihood ratio is calculated.
6. In Claim 5, The system, A filtering method using a Kalman filter robust to outliers and non-normal noise, characterized by increasing the weight of the current time point as the current time point measurement value is similar to the existing estimate value when outlier data or non-normal noise is input, in order to reduce the influence of outlier data or non-normal noise and improve the accuracy of the estimate value, so that the calculated likelihood ratio value has a relatively large influence on the estimate value to be calculated.
7. In Claim 5, The system, A filtering method using a Kalman filter robust to outliers and non-normal noise, characterized by reducing the influence of outlier data or non-normal noise and improving the accuracy of the estimate when data with added outlier data or non-normal noise is input, such that the weight of the current time point decreases as the similarity between the current time point measurement value and the existing estimate value decreases, thereby causing the calculated likelihood ratio value to have a relatively small influence on the estimate value to be calculated.
8. In Claim 1, A filtering method using a Kalman filter robust to outliers and non-normal noise, characterized by further including the step of, once an initial value is selected, the system predicting the estimated value and the error covariance.
9. In Claim 8, The step of calculating Kalman gain is, A filtering method using a Kalman filter robust to outliers and non-normal noise, characterized by calculating Kalman gain based on the predicted value of the error covariance.
10. A communication unit for acquiring a measurement value; A filtering system using a Kalman filter robust to outliers and non-normal noise, comprising: a processor that calculates a Kalman gain, calculates an estimate based on the Kalman gain, calculates the error covariance by comparing and analyzing the predicted and measured values of the error covariance, calculates an exponentially weighted average and an exponentially weighted covariance for the estimate, and incorporates the calculated exponentially weighted average and exponentially weighted covariance of the estimate into the next Kalman gain calculation.
11. A step in which, when an initial value is selected, the system predicts an estimated value and an error covariance based on the selected initial value; A step in which the system calculates Kalman gain based on the predicted value of the error covariance; A step in which the system calculates an estimate based on Kalman gain; The system calculates an exponentially weighted average and an exponentially weighted covariance for the estimates; and A filtering method using a Kalman filter robust to outliers and non-normal noise, comprising the step of the system incorporating the exponentially weighted average and exponentially weighted covariance of the calculated estimates into the next Kalman gain calculation.
12. A communication unit for acquiring a measurement value; and A filtering system using a Kalman filter robust to outliers and non-normal noise, comprising: a processor that, when an initial value is selected, predicts an estimated value and an error covariance based on the selected initial value, calculates a Kalman gain based on the predicted value of the error covariance, calculates an estimated value based on the Kalman gain, calculates an exponentially weighted average and an exponentially weighted covariance for the estimated value, and incorporates the exponentially weighted average and the exponentially weighted covariance of the calculated estimated value into the next Kalman gain calculation.