A mobile robot positioning method based on RBF neural network assisted Kalman filtering
Patent Information
- Application Number
- CN202611241121.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-08-17
- Publication Date
- 2026-11-03
AI Technical Summary
Existing technologies for autonomous navigation of indoor mobile robots suffer from problems such as low state estimation accuracy, high computational complexity, and inability to distinguish the source of group values. In particular, the filter adjustment strategy is not accurate enough in non-Gaussian noise environments.
A two-layer radial basis function (RBF) neural network is used to assist Kalman filtering. By constructing a labeling network and a gain network, the source of outlier noise is identified and the Kalman gain is adaptively adjusted to distinguish between state noise and observation noise, thereby reducing computational complexity and improving filtering accuracy.
It achieves accurate state estimation of robots in non-Gaussian noise environments, reduces computational complexity, is suitable for deployment on resource-constrained embedded platforms, and improves the reliability of path planning and navigation.
Smart Images
Figure CN123028604A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of signal processing and state estimation technology, and relates to the technology of robot state estimation using neural network-assisted Kalman filtering. Specifically, it provides a mobile robot localization method based on RBF neural network-assisted Kalman filtering to solve the problem of autonomous navigation and path planning of indoor mobile robots in complex environments. Background Technology
[0002] Indoor mobile robots are widely used in intelligent manufacturing, intelligent logistics, and service robots. Reliable state estimation (including position, attitude, and velocity) is the foundation for robot path planning and navigation decisions, directly determining the system's safety and task execution accuracy. Indoor mobile robots rely on multi-source sensor fusion to achieve high-precision real-time state estimation during path planning and navigation decisions. However, factors such as non-line-of-sight occlusion, slippery surfaces, and dynamic obstacle interference in indoor environments cause sensor measurement data to exhibit non-Gaussian, heavy-tailed outlier noise characteristics, severely affecting the estimation accuracy of traditional Kalman filtering. Existing technical solutions have several shortcomings in addressing this issue.
[0003] 1) Existing model-driven methods rely on accurate statistical noise models;
[0004] Robust Kalman filtering methods based on M-estimation, information-theoretic learning, and variational Bayes are essentially model-driven methods. These methods require prior knowledge of the precise noise distribution model or the ability to make reasonable assumptions about the noise distribution. However, when mobile robots perform navigation tasks in indoor environments, sensors are affected by factors such as dynamic object occlusion and uncertain slippage, causing the statistical characteristics of their measurement noise to change dynamically over time, which cannot be accurately described by a single distribution with fixed parameters. Furthermore, the process noise covariance Q and measurement noise covariance R are usually unknown and difficult to obtain accurately. When the actual noise distribution deviates from the assumed model, the filtering performance degrades significantly.
[0005] 2) Existing data-driven methods have excessively high computational complexity;
[0006] KalmanNet and other methods employ deep recurrent neural networks such as gated recurrent units (GRUs), which have a large number of parameters, long training time, and high computational overhead during the inference stage. They are difficult to deploy on embedded platforms with limited onboard computing resources for mobile robots and cannot meet the needs of real-time path planning and navigation decision-making.
[0007] 3) Existing methods cannot distinguish the source of cluster values, leading to errors in path planning decisions;
[0008] Outliers in mobile robots can originate from two different physical causes. One is measurement noise outliers. UWB (Ultra-Wideband) is affected by occlusion from walls, moving objects, etc., leading to outlier observations in feature matching and causing a significant deviation between the observed robot position and the actual position. In this case, the filter should reduce the Kalman gain to suppress the impact of outlier observations on state estimation. The other is state noise outliers. During robot navigation, wheeled odometry can cause deviations between the motion model and the actual motion state due to robot slippage, making state prediction unreliable. In this case, the filter should increase the Kalman gain to place more trust in the observation data and quickly correct the prediction bias. In both cases, the filter's innovation (the difference between prediction and measurement) will be abnormally increased, but the required filtering strategies are completely opposite. Existing robust Kalman filtering methods fail to effectively distinguish whether the current anomaly originates from measurement noise or state noise when dealing with outliers, resulting in inaccurate filter adjustment strategies.
[0009] To address the aforementioned problems, this invention provides a mobile robot localization method based on RBF neural network-assisted Kalman filtering, which is suitable for autonomous navigation and path planning tasks of indoor mobile robots in complex environments. Summary of the Invention
[0010] The purpose of this invention is to provide a mobile robot localization method based on RBF neural network-assisted Kalman filtering, which solves the problems of low state estimation accuracy, high computational complexity, and inability to distinguish the source of outliers in the existing technology under non-Gaussian noise environment. This invention creatively constructs a two-layer radial basis function neural network to identify the source of outlier noise in real time and adaptively adjust the Kalman gain, thereby providing accurate and reliable state information for navigation and obstacle avoidance decision-making of indoor mobile robots.
[0011] To achieve the above objectives, the technical solution adopted by the present invention is as follows:
[0012] A mobile robot localization method based on RBF neural network-assisted Kalman filtering, characterized by the following steps:
[0013] Step 1: Start the mobile robot and obtain an initial state estimate with initial error;
[0014] Step 2: Update the wheel odometer and calculate the predicted state at the current time k. :
[0015] Step 3: Acquire the observation value at the current time k using the UWB module. Calculate new information : , The observation matrix;
[0016] Step 4: Transfer the new information Input a pre-trained two-layer radial basis function neural network to obtain the Kalman gain. ;
[0017] Step 5: Based on Kalman gain Update the state estimate of k at the current time step. ;
[0018] Step 6: Based on Kalman gain Update the covariance matrix at time k. .
[0019] Furthermore, in step 4, the two-layer radial basis function neural network consists of a labeling network and a gain network;
[0020] For the current time k, the input to the labeling network is the new information. The output is the state noise label parameter. With observation noise label parameters , This indicates that there are outliers in the state noise. This indicates that there are no outliers in the state noise. This indicates that there are outliers in the observation noise. This indicates that there are no outliers in the observed noise;
[0021] The input to the gain network is the new information. State noise marker parameters With observation noise label parameters The output is the Kalman gain. .
[0022] Furthermore, the number of RBF center points in the labeling network is set to 20, the RBF kernel function is a Gaussian function, and the kernel width is 0.5.
[0023] Furthermore, the number of RBF center points in the gain network is set to 40, the RBF kernel function is a Gaussian function, and the kernel width is 0.5.
[0024] Furthermore, in step 4, the training dataset for the two-layer radial basis function neural network is generated using the optimal Kalman filter (OKF) algorithm. Specifically, the process involves randomly generating state noise according to a Gaussian mixture model. and observation noise The sequence records the outlier labels at each time step; the OKF algorithm is run to obtain the new information at each time step. With ideal Kalman gain , will new information As input features, ideal Kalman gain The expected output constitutes the training dataset.
[0025] Furthermore, in step 4, the training loss of the two-layer radial basis function neural network is set as follows:
[0026] ,
[0027] in, For loss function, The number of training samples, This is the predicted output of a two-layer radial basis function neural network. This is the expected output.
[0028] Furthermore, in step 2, the predicted state at the current time k is represented as: , Here is the state transition matrix. This is the state estimate for k-1 at the previous time step.
[0029] Furthermore, in step 5, the state estimate for the current time k is expressed as: .
[0030] Furthermore, in step 6, the covariance matrix at the current time k is expressed as: , It is the identity matrix. Let be the prior error covariance matrix, representing the prediction error covariance of the state at time k based on the estimate at time k-1.
[0031] In terms of working principle, the Kalman gain is discontinuous and can be divided into three categories: 1) When there are no outliers, the Kalman gain tends to a steady-state value; 2) When there are outliers in the state noise, the process covariance increases, the Kalman gain increases, the prediction is unreliable, and it mainly relies on observation; 3) When there are outliers in the observation noise, the observation covariance increases, the Kalman gain decreases, the observation is unreliable, and it mainly relies on prediction. Based on this discovery, this invention transforms the learning task of the neural network from a regression problem to a classification problem. On the one hand, this invention uses a Gaussian mixture model to model noise and learns outlier patterns from data through an RBF neural network, thus avoiding the dependence of traditional model-driven methods on accurate noise priors. On the other hand, this invention uses a simple and computationally inexpensive RBF neural network to replace a deep recurrent neural network, with only a fraction of the parameters required by existing deep learning methods, resulting in fast inference speed and meeting the needs of real-time robot control. A two-layer network architecture is designed, with a first-layer labeling network used to identify the sources of outliers (measurement anomalies or state anomalies), and a second-layer gain network outputting the corresponding optimal Kalman gain based on the identification results, thus solving the fundamental defect of existing methods that cannot distinguish the sources of outliers.
[0032] In summary, this invention, by constructing a two-layer radial basis function neural network, can identify the source of outlier noise in real time and adaptively adjust the Kalman gain, providing accurate and reliable state information for the navigation and obstacle avoidance decisions of indoor mobile robots; specifically, it has the following advantages:
[0033] 1) This invention uses an RBF neural network, which has a small number of parameters, a training time of less than 1 minute (CPU), and a fast inference speed, making it suitable for deployment on resource-constrained embedded platforms such as drones and robots;
[0034] 2) This invention, through a two-layer network architecture, can identify whether outliers originate from state noise or observation noise, thereby employing targeted gain adjustment strategies to improve filtering accuracy;
[0035] 3) The performance of the present invention is superior to that of existing methods when the observation noise or state noise is non-Gaussian noise. Attached Figure Description
[0036] Figure 1 This is a diagram of the RBF two-layer neural network structure of the present invention.
[0037] Figure 2 This is a diagram showing the position mean square error test results in the first case of this invention.
[0038] Figure 3 This is a diagram showing the position mean square error test results in the second case of this invention.
[0039] Figure 4 This is a diagram showing the position mean square error test results in the third case of this invention.
[0040] Figure 5 This is a diagram showing the position mean square error test results in the fourth case of this invention. Detailed Implementation
[0041] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments.
[0042] This embodiment provides a mobile robot localization method based on RBF neural network-assisted Kalman filtering to solve the challenges of autonomous navigation and path planning for indoor mobile robots in complex environments, such as long-term navigation tasks like fetching a water glass from the kitchen and delivering it to the coffee table in the living room. The sensors carried by the indoor mobile robot include: 1) a wheeled odometry module, providing robot displacement increments with an update frequency of 50 Hz for state prediction; and 2) a UWB localization module, providing location information with an update frequency of 10 Hz for observation updates. When indoor mobile robots perform tasks in a residence, they often encounter two types of non-Gaussian noise sources: firstly, UWB signal obstruction caused by furniture and moving people, leading to deviations in ranging data and generating observation outliers; and secondly, slippage of the wheeled odometry module due to the smooth surface of the floor tiles, resulting in state outliers. To address these two issues, this embodiment constructs a two-layer radial basis function neural network, which can identify the source of outlier noise in real time and adaptively adjust the Kalman gain, thereby providing accurate and reliable state information for the navigation and obstacle avoidance decisions of the indoor mobile robot.
[0043] Considering the motion of an indoor mobile robot in a two-dimensional plane, this embodiment adopts a linear state-space model, represented as follows:
[0044] ,
[0045] in, Let k be the state vector (containing position and velocity). Let be the observation vector at time k;
[0046] The state transition matrix, using the CV model, is expressed as:
[0047] , The sampling period is ;
[0048] The observation matrix directly observes the positions of X and Y, and is represented as:
[0049] ;
[0050] State noise, To measure the noise, the non-Gaussian noise model is modeled as a Gaussian mixture model (GMM), represented as:
[0051] ,
[0052] in, Let be the probability of Gaussian noise occurring. This is the magnification factor for the covariance of outliers. ; This represents the probability that the state noise is Gaussian noise (i.e., the probability that the odometer is working properly). This represents the probability that the observation noise is Gaussian noise (i.e., the probability that the UWB is in line-of-sight mode). It represents the covariance amplification factor of the outlier value of the state noise (i.e., the factor by which the error suddenly increases when the odometer slips). This represents the covariance amplification factor of the observed noise outlier (i.e., the factor by which the ranging error suddenly increases when the UWB signal is blocked). Represents a normal distribution; and The nominal state noise covariance and the nominal observation noise covariance are known a priori. , , and All are identity matrices.
[0053] In this embodiment, outliers mainly originate from two physical conditions: 1) State anomaly, such as the wheeled odometer slipping on a smooth ceramic tile surface, causing a brief and sharp increase in the state noise covariance Q; 2) Measurement anomaly, such as the UWB being obstructed by walls, furniture, etc., causing a brief and sharp increase in the observation noise covariance R. Therefore, the above-mentioned Gaussian mixture model is used to model the noise, with specific parameters shown in Table 1. The first case represents the case where both state noise and measurement noise are Gaussian noise; the second case represents the case where the measurement noise is non-Gaussian noise while the state noise is Gaussian noise; the third case represents the case where the state noise is non-Gaussian noise while the measurement noise is Gaussian noise; and the fourth case represents the case where both state noise and measurement noise are non-Gaussian noise.
[0054] Table 1. Parameters of the non-Gaussian noise model
[0055]
[0056] Based on this, this embodiment constructs a two-layer radial basis function (RBF) neural network to identify the source of outlier noise in real time and adaptively adjust the Kalman gain; the two-layer radial basis function (RBF) neural network is as follows: Figure 1 As shown, the two-layer RBF network structure consists of a marker network and a gain network, respectively.
[0057] For the current time k, the input to the labeling network is the new information. Defined as: , To predict the state, The observation matrix is generated by the labeling network, which outputs state noise labeling parameters. With observation noise label parameters , This indicates that there are outliers in the state noise. This indicates that there are no outliers in the state noise. This indicates that there are outliers in the observation noise. This indicates that there are no outliers in the observation noise; furthermore, the number of RBF center points in the labeling network can be determined according to the problem complexity. In this embodiment, 20 are used, and the RBF kernel function is a Gaussian function with a kernel width of 0.5.
[0058] The input to the gain network is the new information. State noise marker parameters With observation noise label parameters The output is the Kalman gain. Furthermore, the number of RBF center points in the gain network is set to 40, the RBF kernel function is a Gaussian function, and the kernel width is 0.5.
[0059] For the aforementioned two-layer radial basis function (RBF) neural network, this embodiment employs the optimal Kalman filter (OKF) algorithm to generate training data. To cover all possible operating scenarios in a home environment, 200 independent trajectories are generated, each containing 300 time steps. The trajectories simulate typical item search paths in a home, including actions such as traversing multiple rooms, bypassing furniture, and entering narrow spaces. In each trajectory, the occurrence time and type of outliers are randomly generated according to the aforementioned probabilities, and the initial state of each trajectory is set to... The specific process is as follows: setting system parameters As shown in Table 1; state noise is randomly generated according to the Gaussian mixture model. and observation noise The sequence records the outlier labels at each time step; the OKF algorithm is run to obtain the new information at each time step. With ideal Kalman gain , will new information As input features, ideal Kalman gain As the expected output, it constitutes the training dataset;
[0060] Furthermore, the specific process of the Optimal Kalman Filter (OKF) algorithm is as follows:
[0061] Assuming the time of outlier occurrence is known, i.e. the type of outlier is known prior to the observation noise or state noise, the OKF algorithm can be used to generate the ideal Kalman gain.
[0062] Predicted status: ;
[0063] Predicted covariance: If outliers exist in the state noise, then Otherwise, it means that there are outliers in the observation noise. ;
[0064] Calculate the Kalman gain: If outliers exist in the state noise, then Otherwise, it means that there are outliers in the observation noise. ;
[0065] Status Update: ;
[0066] Covariance update: .
[0067] Based on the above training dataset, this embodiment uses gradient descent to train a two-layer radial basis function (RBF) neural network, with the loss function set as follows:
[0068] ,
[0069] in, For loss function, The number of training samples, This is the predicted output of a two-layer radial basis function neural network. The expected output;
[0070] This embodiment uses the Adam optimizer, sets the learning rate to 0.01, and trains 50 times to complete the training of a two-layer radial basis function neural network.
[0071] Based on the trained two-layer radial basis function neural network described above, the specific steps of the mobile robot localization method based on RBF neural network-assisted Kalman filtering in this embodiment are as follows:
[0072] Step 1: Start the mobile robot and obtain an initial state estimate with initial error. ;
[0073] Step 2: Update the wheel odometer and calculate the predicted state at the current time k. : , Here is the state transition matrix. This is the state estimate for time k-1 at the previous time step;
[0074] Step 3: Acquire the observation value at the current time k using the UWB module. Calculate new information : , The observation matrix;
[0075] Step 4: Transfer the new information Input a trained two-layer radial basis function neural network to obtain the Kalman gain. ;
[0076] Step 5: Based on Kalman gain Update the state estimate of k at the current time step. : ;
[0077] Step 6: Based on Kalman gain Update the covariance matrix at time k. : , for The identity matrix, Let be the prior error covariance matrix, representing the prediction error covariance of the state at time k based on the estimate at time k-1;
[0078] Step 7: Estimate the state at the current time k. Input the navigation planning module to guide the mobile robot to the target area and complete the item search and delivery.
[0079] The beneficial effects of the present invention will be described in detail below with reference to simulation tests. During the test, there were 50 test trajectories, each with a length of 400 steps. The initial state was set to... The initial estimation error is a standard deviation of 0.3. To more intuitively demonstrate the advantages of this invention (labeled RBF-KF), traditional KF, BIKF, AORKF, and MCKF algorithms are used as comparative examples. Figure 2 The figure shows the position mean square error test results in the first case. As can be seen from the figure, the performance of this invention is basically overlapping with that of traditional KF and KalmanNet, and the mean square error reaches the theoretical optimal value; Figure 3 The figure shows the position mean square error test results in the second case. As can be seen from the figure, the mean square error of the present invention is significantly better than that of other algorithms; for example Figure 4 The figure shows the position mean square error test results in the third case. As can be seen from the figure, the mean square error of this invention is also superior to several other algorithms; for example... Figure 5 The figure shows the position mean square error test results in the fourth case. As can be seen from the figure, the mean square error of the present invention is significantly better than that of the other algorithms.
[0080] In summary, this invention provides a mobile robot localization method based on RBF neural network-assisted Kalman filtering. The constructed two-layer radial basis function neural network can identify the source of outlier noise in real time and adaptively adjust the Kalman gain, thereby providing accurate and reliable state information for the navigation and obstacle avoidance decisions of indoor mobile robots.
[0081] The above description is merely a specific embodiment of the present invention. Any feature disclosed in this specification may be replaced by other equivalent or similar features unless otherwise specified. All disclosed features, or steps in all methods or processes, may be combined in any way except for mutually exclusive features and / or steps.
Claims
1. A mobile robot localization method based on RBF neural network-assisted Kalman filtering, characterized in that, Includes the following steps: Step 1: Start the mobile robot and obtain an initial state estimate with initial error; Step 2: Update the wheel odometer and calculate the predicted state at the current time k. : Step 3: Acquire the observation value at the current time k using the UWB module. Calculate new information : , The observation matrix; Step 4: Transfer the new information Input a pre-trained two-layer radial basis function neural network to obtain the Kalman gain. ; Step 5: Based on Kalman gain Update the state estimate of k at the current time step ; Step 6: Based on Kalman gain Update the covariance matrix at time k. .
2. The mobile robot localization method based on RBF neural network-assisted Kalman filtering according to claim 1, characterized in that, In step 4, the two-layer radial basis function neural network consists of a labeling network and a gain network; For the current time k, the input to the labeling network is the new information. The output is the state noise label parameter. With observation noise label parameters , This indicates that there are outliers in the state noise. This indicates that there are no outliers in the state noise. This indicates that there are outliers in the observation noise. This indicates that there are no outliers in the observed noise; The input to the gain network is the new information. State noise marker parameters With observation noise label parameters The output is the Kalman gain. .
3. The mobile robot localization method based on RBF neural network-assisted Kalman filtering according to claim 2, characterized in that, The number of RBF center points in the labeling network is set to 20, the RBF kernel function is a Gaussian function, and the kernel width is 0.
5.
4. The mobile robot localization method based on RBF neural network-assisted Kalman filtering according to claim 2, characterized in that, The number of RBF center points in the gain network is set to 40, the RBF kernel function is a Gaussian function, and the kernel width is 0.
5.
5. The mobile robot localization method based on RBF neural network-assisted Kalman filtering according to claim 2, characterized in that, The training dataset for the two-layer radial basis function neural network is generated using the optimal Kalman filter (OKF) algorithm. Specifically, the state noise is randomly generated according to the Gaussian mixture model. and observation noise The sequence records the outlier labels at each time step; the OKF algorithm is run to obtain the new information at each time step. With ideal Kalman gain , will new information As input features, ideal Kalman gain The expected output constitutes the training dataset.
6. The mobile robot localization method based on RBF neural network-assisted Kalman filtering according to claim 2, characterized in that, The training loss of a two-layer radial basis function neural network is set as follows: ， in, For loss function, The number of training samples, This is the predicted output of a two-layer radial basis function neural network. This is the expected output.
7. The mobile robot localization method based on RBF neural network-assisted Kalman filtering according to claim 1, characterized in that, In step 2, the predicted state at the current time k is represented as: , Here is the state transition matrix. This is the state estimate for k-1 at the previous time step.
8. The mobile robot localization method based on RBF neural network-assisted Kalman filtering according to claim 1, characterized in that, In step 5, the state estimate for the current time k is expressed as: .
9. The mobile robot localization method based on RBF neural network-assisted Kalman filtering according to claim 1, characterized in that, In step 6, the covariance matrix at the current time k is expressed as: , It is the identity matrix. Let be the prior error covariance matrix.