Intelligent measurement positioning method based on three-point measurement method principle
By introducing an environment perception module and distributed collaborative algorithm, combining Kalman filtering and deep learning, the three-point measurement method is optimized, and the traditional three-point measurement method is solved, and efficient and accurate intelligent measurement positioning is achieved.
Patent Information
- Application Number
- CN202510678455.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-05-26
- Publication Date
- 2025-08-15
AI Technical Summary
The traditional three-point measurement method has shortcomings in efficiency, accuracy and operational convenience, especially in complex environments that are susceptible to human factors and external interference, resulting in an increase in measurement error.
Introducing an environment perception module and a distributed collaborative algorithm, combining Kalman filtering and deep learning, optimizing the measurement network through adaptive weight allocation and distributed collaborative algorithm, and designing intelligent measurement controllers to improve measurement accuracy and stability.
In complex environments, the measurement accuracy and efficiency are significantly improved, the calculation cost is reduced, and it is suitable for multi-scenario intelligent measurement tasks, achieving sub-millimeter-level positioning accuracy.
Smart Images
Figure CN120488948A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the field of measurement and positioning technology, and specifically relates to an intelligent measurement and positioning method based on the principle of a three-point measurement method. Background Art
[0002] In the development of measurement and positioning technology, the principle of three-point measurement has gradually attracted attention due to its unique advantages. The three-point measurement method is based on the principle of triangulation and determines the position of the target by measuring the distance or angle relationship between the target and three known position points. Compared with other measurement and positioning methods, the three-point measurement method has the potential for higher positioning accuracy in theory, because as long as the geometric relationship between the target and the three reference points can be accurately obtained, the target position can be determined more accurately through mathematical calculations. In addition, this method has strong adaptability to the environment and does not rely heavily on satellite signals like satellite positioning. It can also be tried in some environments where satellite signals are limited (such as underground spaces, tunnels or densely built-up areas), so it has a wide range of applications.
[0003] However, traditional measurement and positioning methods based on the three-point measurement method have significant shortcomings. These methods often rely on manual operation or complex and expensive professional equipment. Not only are they inefficient, they are also easily interfered with by human factors, resulting in increased measurement errors. For example, at a construction site, when using the traditional three-point measurement method for measurement and positioning, surveyors need to manually operate the measuring instrument to complete operations such as aiming and reading the measurement points. The entire process is time-consuming, and differences in the operating habits and skill levels of different surveyors may introduce varying degrees of measurement errors, thereby affecting the reliability and accuracy of the positioning results. Therefore, how to overcome the shortcomings of the traditional three-point measurement method in terms of efficiency, accuracy, and ease of operation has become an important issue that needs to be urgently addressed in the field of measurement and positioning technology. Summary of the Invention
[0004] The purpose of this invention is to provide an intelligent measurement and positioning method based on the principle of three-point measurement. By introducing an environmental perception module and a distributed collaborative algorithm, this method improves the measurement accuracy, efficiency, and robustness of the system in complex environments while reducing computational costs, making it suitable for intelligent measurement tasks in multiple scenarios.
[0005] The technical solution of the present invention is an intelligent measurement and positioning method based on the principle of three-point measurement, comprising the following steps:
[0006] Step 1: Construct a dynamic measurement network consisting of three reference nodes, including a main reference node and two auxiliary reference nodes, numbered 1, 2, and 3, and monitor external interference factors in real time through an environmental perception module;
[0007] Step 2: Construct the target position estimation error variable based on the measurement data of the dynamic measurement network and each reference node;
[0008] Step 3: Based on the target position estimation error variable, a Kalman filter algorithm is used to construct a virtual measurement model to obtain the optimal value of the first estimation accuracy function of the target position;
[0009] Step 4: Processing the optimal value of the first estimation accuracy function based on a deep learning method combined with a neural network, and designing an intelligent measurement controller of the master reference node, wherein the control law used by the intelligent measurement controller of the master reference node includes a master node optimal estimation law, an environmental interference compensation law, and a master node parameter update law;
[0010] Step 5: Based on the distributed collaborative algorithm, according to the optimal value of the first estimation accuracy function and in combination with least squares theory and neural network, a collaborative measurement controller of the auxiliary reference node is constructed, wherein the collaborative measurement controller of the auxiliary reference node includes a distributed estimator and a dynamic adjustment law;
[0011] Step 6: Based on the intelligent measurement controller of the primary reference node and the collaborative measurement controller of the auxiliary reference node, high-precision intelligent measurement and positioning of the target position are achieved.
[0012] In the intelligent measurement and positioning method based on the three-point measurement principle, the environment perception module is used to collect data on external interference factors and dynamically adjust the measurement contribution of each reference node through an adaptive weight allocation algorithm. The expression of the adaptive weight allocation algorithm is:
[0013]
[0014] Among them, w i represents the weight of the i-th reference node, e i represents the measurement error of the i-th reference node, α is the adjustment factor used to balance the sensitivity of weight distribution, and e j represents the measurement error of the jth reference node.
[0015] In the aforementioned intelligent measurement and positioning method based on the three-point measurement principle, the expression of the Kalman filter algorithm is:
[0016]
[0017] in, represents the estimated target position at the kth moment, Represents the position value predicted based on the previous moment, K k is the Kalman gain, z k is the measurement value at the current moment, and H is the observation matrix.
[0018] In the aforementioned intelligent measurement and positioning method based on the principle of three-point measurement, the intelligent measurement controller of the main reference node further optimizes the optimal value of the first estimation accuracy function output by the Kalman filter algorithm through a neural network to improve the estimation accuracy.
[0019] In the aforementioned intelligent measurement and positioning method based on the principle of the three-point measurement method, the environmental interference compensation law compensates the measurement results according to the data collected by the environmental perception module to eliminate the influence of external interference.
[0020] In the aforementioned intelligent measurement and positioning method based on the principle of three-point measurement, the master node parameter update law continuously optimizes the parameters of the neural network through online learning to adapt to changes in the environment.
[0021] In the aforementioned intelligent measurement and positioning method based on the principle of the three-point measurement method, the distributed estimator in the collaborative measurement controller of the auxiliary reference node fits the measurement data through the least squares theory to improve the measurement accuracy.
[0022] In the aforementioned intelligent measurement and positioning method based on the three-point measurement principle, the dynamic adjustment law in the collaborative measurement controller of the auxiliary reference node dynamically adjusts the measurement strategy of the auxiliary reference node according to the estimation result of the main reference node to ensure the overall stability of the measurement network.
[0023] In the aforementioned intelligent measurement and positioning method based on the principle of three-point measurement, the primary reference node and the auxiliary reference node exchange information via a communication link to achieve cooperative working capability of the measurement network.
[0024] The aforementioned intelligent measurement and positioning method based on the principle of three-point measurement, the dynamic measurement network achieves efficient and accurate target position measurement and positioning in a complex environment through an adaptive weight distribution algorithm and a distributed collaborative algorithm.
[0025] Compared with the prior art, the present invention has the following beneficial effects:
[0026] 1. This invention uses a Kalman filter algorithm to construct a virtual measurement model and combines it with a neural network to perform dual optimization of the target position estimation error, effectively reducing the impact of random noise and systematic errors. Compared with the traditional three-point measurement method, it effectively improves positioning accuracy. The distributed estimator of the auxiliary reference node of the present invention fits the measurement data based on the least squares theory, further eliminating nonlinear errors through mathematical modeling, and ensuring the consistency of multi-node collaborative measurement.
[0027] 2. The environmental perception module of the present invention monitors external interference (such as temperature, electromagnetic interference, vibration, etc.) in real time and dynamically adjusts the measurement contribution of each node through an adaptive weight allocation algorithm. For example, when the error of a certain node increases due to environmental interference, its weight is automatically reduced to prevent the abnormality of a single node from affecting the overall result. The environmental interference compensation law of the present invention directly corrects the measurement results in real time based on the perception data, which can effectively offset most of the known environmental interference factors and improve stability in complex scenarios (such as underground tunnels and electromagnetic dense areas).
[0028] 3. The intelligent measurement controller of the master reference node of the present invention integrates the master node's optimal estimation law and parameter update law. It continuously optimizes neural network parameters through online learning, adapting to environmental changes without manual intervention and reducing manual debugging costs. The auxiliary reference nodes of the present invention interact with the master node in real time through a dynamic adjustment law. They automatically optimize the measurement strategy based on the master node's estimation results, ensuring the coordinated efficiency of the entire dynamic measurement network and significantly shortening measurement time compared to traditional methods.
[0029] 4. The lightweight controller designed based on a distributed collaborative algorithm eliminates the need for expensive specialized equipment and can be implemented using common intelligent sensor nodes, reducing hardware costs. The system architecture supports multi-node expansion, significantly improving flexibility by simply adding auxiliary nodes via communication links to accommodate measurement needs in larger or more complex scenarios. BRIEF DESCRIPTION OF THE DRAWINGS
[0030] Figure 1 A schematic flow chart of an intelligent measurement and positioning method based on the three-point measurement principle in an embodiment of the present invention is shown.
[0031] Figure 2 A schematic structural diagram of a dynamic measurement network in an embodiment of the present invention is shown, including the distribution relationship between a main reference node and two auxiliary reference nodes.
[0032] Figure 3 A schematic diagram of the recursive update process of the Kalman filter algorithm in an embodiment of the present invention is shown, showing the optimization steps of the target position estimate.
[0033] Figure 4 A schematic diagram of a control mechanism for the coordinated operation of a primary reference node and an auxiliary reference node in an embodiment of the present invention is shown, demonstrating an application scenario of a distributed collaborative algorithm. DETAILED DESCRIPTION
[0034] The present invention will be further described below with reference to the accompanying drawings and examples, but they are not intended to limit the present invention.
[0035] Example: An intelligent measurement and positioning method based on the principle of three-point measurement method, the core of which is to achieve high-precision target position measurement and positioning in complex environments through the combination of dynamic measurement network, Kalman filter algorithm, adaptive weight distribution algorithm and deep learning and distributed collaborative algorithm. Figures 1 to 4 , describe the specific implementation methods of the present invention in detail.
[0036] like Figure 1 As shown, the following steps are included:
[0037] Step 1: Construct a dynamic measurement network consisting of three reference nodes. The dynamic measurement network includes a main reference node and two auxiliary reference nodes, numbered 1, 2, and 3 respectively, and monitor external interference factors in real time through the environment perception module, such as Figure 2 As shown;
[0038] In this step, the main reference node is responsible for making the optimal estimate of the target position and designing the corresponding intelligent measurement controller; the auxiliary reference node ensures the stability and accuracy of the measurement network through a distributed collaborative algorithm. In practical applications, such as in industrial automation scenarios, these reference nodes can be deployed in different locations on the factory floor to cover the entire measurement area. In order to cope with interference factors in complex environments, each reference node is equipped with an environmental perception module for real-time monitoring of external interference, such as temperature changes, electromagnetic noise, etc. The data collected by the environmental perception module is processed and input into the adaptive weight allocation algorithm for dynamically adjusting the measurement contribution of each reference node. The expression of the adaptive weight allocation algorithm is:
[0039]
[0040] Among them, w i represents the weight of the i-th reference node, e i represents the measurement error of the i-th reference node, α is the adjustment factor used to balance the sensitivity of weight distribution, and e j represents the measurement error of the jth reference node.
[0041] This formula allows the system to dynamically adjust the weight of each node based on its measurement error, ensuring the stability and reliability of the measurement network in complex environments. For example, if a reference node's measurement error increases due to environmental interference, its weight will be reduced accordingly, while the weights of other nodes will be increased to maintain overall measurement accuracy.
[0042] Step 2: Construct the target position estimation error variable based on the measurement data of the dynamic measurement network and the reference node.
[0043] This process is completed by collecting the measurement values of each reference node and calculating the deviation between it and the true target position. Assuming that the true coordinates of the target position are (x, y)(x, y), and the measurement values of the reference nodes are (x1, y1), (x2, y2) and (x3, y3)(x3, y3), the target position estimation error variable can be expressed as:
[0044]
[0045] Where i represents the i-th reference node. By calculating the error variable of each node, the system can quantify the accuracy level of the current measurement result, providing a basis for subsequent optimization steps.
[0046] Step 3: Based on the target position estimation error variable, a virtual measurement model is constructed using the Kalman filter algorithm to obtain the optimal value of the first estimation accuracy function of the target position, such as Figure 3 shown.
[0047] In this step, the core idea of the Kalman filter algorithm is to gradually reduce the impact of measurement noise on the estimation results through recursive updates, thereby improving positioning accuracy. Its mathematical expression is:
[0048]
[0049] in, represents the estimated target position at the kth moment, Represents the position value predicted based on the previous moment, K k is the Kalman gain, z k is the measurement value at the current moment, and H is the observation matrix.
[0050] The recursive update process of the Kalman filter algorithm consists of a prediction phase and a correction phase. In the prediction phase, the system predicts the current target position based on the state estimate from the previous moment. In the correction phase, the system uses the current measurement value to correct the prediction, resulting in a more accurate estimate. For example, in autonomous driving scenarios, the vehicle's position information may be affected by sensor noise. The Kalman filter algorithm can effectively suppress this noise and improve the accuracy of position estimation.
[0051] Step 4: Based on the deep learning method, the optimal value of the first estimation accuracy function is processed in combination with the neural network to design an intelligent measurement controller for the main reference node.
[0052] In this step, the control laws used by the intelligent measurement controller of the main reference node include the main node optimal estimation law, the environmental interference compensation law, and the main node parameter update law. The main node optimal estimation law further optimizes the first estimation accuracy function output by the Kalman filter algorithm through a neural network to improve the estimation accuracy. The environmental interference compensation law compensates the measurement results based on the data collected by the environmental perception module to eliminate the influence of external interference. For example, in the UAV positioning task, changes in wind speed may cause measurement errors. Through the environmental interference compensation law, the system can adjust the measurement value in real time to ensure positioning accuracy. The main node parameter update law continuously optimizes the parameters of the neural network through online learning to adapt to changes in the environment. The training process of the neural network adopts the backpropagation algorithm. The loss function is defined as the mean square error between the estimated value and the true value. The loss function is minimized by the gradient descent method to improve the estimation accuracy.
[0053] Step 5: Based on the distributed collaborative algorithm, according to the optimal value of the first estimation accuracy function, and combining the least squares theory with the neural network, a collaborative measurement controller of the auxiliary reference node is constructed.
[0054] In this step, the collaborative measurement controller of the auxiliary reference node includes a distributed estimator and a dynamic adjustment law. The distributed estimator fits the measurement data through the least squares theory to improve the measurement accuracy. The dynamic adjustment law dynamically adjusts the measurement strategy of the auxiliary reference node according to the estimation results of the main reference node to ensure the overall stability of the measurement network. For example, in a multi-robot collaborative scenario, the auxiliary reference node can adjust its own measurement frequency or measurement range according to the estimation results of the main reference node, thereby improving the overall measurement efficiency. The core idea of the distributed collaborative algorithm is to achieve efficient completion of measurement tasks through information sharing and coordination between nodes. Figure 4 As shown, the main reference node and the auxiliary reference node exchange information through a communication link to ensure the collaborative working capability of the measurement network.
[0055] Step 6: The intelligent measurement controller of the primary reference node and the collaborative measurement controller of the auxiliary reference node achieve high-precision intelligent measurement and positioning of the target location. In practical applications, such as in intelligent warehousing systems, the primary reference node is responsible for optimally estimating the location of the goods, while the auxiliary reference nodes ensure the stability and accuracy of the measurement network through distributed collaborative algorithms.
[0056] Through the above steps, the system can efficiently and accurately complete the task of positioning the target in complex environments, providing an innovative solution for intelligent measurement in multiple scenarios. The entire process of this invention begins with the construction of a dynamic measurement network, and then goes through the construction of target position estimation error variables, the optimization of the Kalman filter algorithm, the processing of deep learning methods, and the application of distributed collaborative algorithms, ultimately achieving high-precision target position measurement and positioning.
[0057] To better enable relevant personnel in this technical field to fully understand and implement the present invention, the following is a specific implementation case applied to an industrial automation scenario (factory workshop parts positioning), combining the technical solution in the specification with the actual scenario to illustrate the application process and effects of the present invention in detail:
[0058] Application scenarios:
[0059] In a factory workshop environment, real-time positioning of parts grasped by a mobile robotic arm requires overcoming environmental factors such as electromagnetic interference and mechanical vibration in the workshop to achieve sub-millimeter positioning accuracy.
[0060] Specific implementation steps:
[0061] Step 1: Build a dynamic measurement network;
[0062] Node deployment:
[0063] Main reference node (Node 1): Installed at a fixed reference position in the workshop (such as the top of the gantry), equipped with a high-precision laser ranging sensor and an environmental perception module (monitoring temperature and electromagnetic noise).
[0064] Auxiliary reference nodes (nodes 2 and 3): deployed on the walls on both sides of the workshop, using ultrasonic sensors, forming a triangular distribution with the main node.
[0065] Environmental Perception:
[0066] Each node collects real-time data through the environmental perception module (such as temperature change ±2°C, electromagnetic interference intensity 0.5mT), and inputs it into the adaptive weight distribution algorithm:
[0067]
[0068] Among them, α = 0.8 (adjustment factor), e i is the node measurement error (for example, when the error of node 2 suddenly increases to 0.3 mm due to electromagnetic interference, its weight is automatically reduced).
[0069] Step 2: Construct the target position estimation error variable;
[0070] Measurement data acquisition:
[0071] The main node and auxiliary node measure the part position synchronously. Assuming the real coordinates of the part are (x, y), the measurement value of each node is:
[0072] Node 1: (x1, y1) = (1000, 800) mm
[0073] Node 2: (x2, y2) = (1200, 750) mm (due to electromagnetic interference, actual error +0.2 mm)
[0074] Node 3: (x3, y3) = (950, 900) mm
[0075] Error calculation:
[0076] The target position estimation error variable is the Euclidean distance deviation between the measured value of each node and the true value.
[0077] Step 3: Kalman filter optimization estimation accuracy;
[0078] Use Kalman filtering to recursively update the estimate:
[0079] Prediction stage: based on the estimated value at the previous moment:
[0080] Correction phase: Using the current measured value z k =(1000,800)mm(master node data), the predicted value is corrected by Kalman gain to obtain the optimal value of the first estimation accuracy function
[0081] Step 4: Design the Master Reference Node Intelligent Measurement Controller
[0082] Neural network optimization: The optimal value of the Kalman filter output is input into the neural network (3-layer fully connected structure, activation function ReLU) to further optimize the estimation accuracy:
[0083] Master node optimal estimation law: Fit nonlinear errors through neural networks and output correction values
[0084] △x=+0.3mm,△y=-0.2mm, and the optimized coordinates are (999.8,799.6)mm.
[0085] Environmental interference compensation law: Based on environmental perception data (such as temperature +2°C), the sensor thermal drift error is compensated (pre-modeled error model: for every 1°C increase in temperature, the laser ranging error is +0.05mm). The corrected coordinates are (1000.0, 800.0) mm.
[0086] Parameter update law: Through online learning (back propagation algorithm), the neural network parameters are updated every 100ms to adapt to changes in the workshop environment.
[0087] Step 5: Build an auxiliary reference node collaborative measurement controller
[0088] Distributed estimator: Auxiliary nodes use the least squares theory to fit the measurement data. For example, nodes 2 and 3 fit the part position using ultrasonic data. The formula is:
[0089]
[0090] The auxiliary estimated value is (1000.1,799.9) mm.
[0091] Dynamic adjustment law: Based on the estimation results of the main node, the auxiliary node automatically adjusts the measurement frequency (for example, when the error of the main node is greater than 0.1mm, the auxiliary node measurement frequency is increased from 10Hz to 20Hz) to ensure network stability.
[0092] Step 6: Collaboratively achieve high-precision positioning;
[0093] Information interaction: The master node and the auxiliary node exchange data in real time through the workshop wireless communication network (such as Wi-Fi6). The master node integrates the weight distribution (W1=0.6, W2=0.2, W3=0.2) and the collaborative estimation results to output the final positioning coordinates (1000.0±0.05, 800.0±0.05) mm, meeting the sub-millimeter accuracy requirements.
[0094] Through the embodiments of the above methods, compared with the traditional three-point measurement method (error ±0.5mm), the error of the present invention is reduced to ±0.05mm through dual optimization of Kalman filtering and neural network. The adaptive weight distribution algorithm of the present invention reduces the influence of the interfered nodes (such as node 2) by 40%, and the environmental compensation law eliminates more than 90% of known interferences (such as temperature and electromagnetic noise). The dynamic adjustment law of the present invention shortens the measurement time from 200ms of the traditional method to 50ms, meeting the real-time control requirements. This embodiment verifies the effectiveness of the present invention in complex industrial environments and provides a reliable solution for the positioning of intelligent equipment.
[0095] In summary, the present invention improves the measurement accuracy, efficiency, and robustness of the system in complex environments by introducing an environmental perception module and a distributed collaborative algorithm, while reducing the computational cost, making it suitable for multi-scenario intelligent measurement tasks.
Claims
1. An intelligent measurement and positioning method based on the principle of three-point measurement, characterized in that: The following steps are involved: Step 1: Construct a dynamic measurement network consisting of three reference nodes, including a main reference node and two auxiliary reference nodes, numbered 1, 2, and 3, and monitor external interference factors in real time through an environmental perception module; Step 2: Construct the target position estimation error variable based on the measurement data of the dynamic measurement network and each reference node; Step 3: Based on the target position estimation error variable, a Kalman filter algorithm is used to construct a virtual measurement model to obtain the optimal value of the first estimation accuracy function of the target position; Step 4: Processing the optimal value of the first estimation accuracy function based on a deep learning method combined with a neural network, and designing an intelligent measurement controller of the master reference node, wherein the control law used by the intelligent measurement controller of the master reference node includes a master node optimal estimation law, an environmental interference compensation law, and a master node parameter update law; Step 5: Based on the distributed collaborative algorithm, according to the optimal value of the first estimation accuracy function and in combination with least squares theory and neural network, a collaborative measurement controller of the auxiliary reference node is constructed, wherein the collaborative measurement controller of the auxiliary reference node includes a distributed estimator and a dynamic adjustment law; Step 6: Based on the intelligent measurement controller of the primary reference node and the collaborative measurement controller of the auxiliary reference node, high-precision intelligent measurement and positioning of the target position are achieved.
2. The intelligent measurement and positioning method based on the three-point measurement principle according to claim 1 is characterized in that: The environment perception module is used to collect data on external interference factors and dynamically adjust the measurement contribution of each reference node through an adaptive weight allocation algorithm. The expression of the adaptive weight allocation algorithm is: Among them, w i represents the weight of the i-th reference node, e i represents the measurement error of the i-th reference node, α is the adjustment factor, and e j represents the measurement error of the jth reference node.
3. The intelligent measurement and positioning method based on the three-point measurement principle according to claim 1 is characterized in that: The expression of the Kalman filter algorithm is: in, represents the estimated target position at the kth moment, Represents the position value predicted based on the previous moment, K k is the Kalman gain, z k is the measurement value at the current moment, and H is the observation matrix.
4. The intelligent measurement and positioning method based on the three-point measurement principle according to claim 1 is characterized in that: The intelligent measurement controller of the master reference node further optimizes the optimal value of the first estimation accuracy function output by the Kalman filter algorithm through a neural network to improve the estimation accuracy.
5. The intelligent measurement and positioning method based on the three-point measurement principle according to claim 1 is characterized in that: The environmental interference compensation law compensates the measurement results according to the data collected by the environmental perception module to eliminate the influence of external interference.
6. The intelligent measurement and positioning method based on the three-point measurement principle according to claim 1 is characterized in that: The master node parameter update law continuously optimizes the parameters of the neural network through online learning to adapt to changes in the environment.
7. The intelligent measurement and positioning method based on the three-point measurement principle according to claim 1 is characterized in that: The distributed estimator in the cooperative measurement controller of the auxiliary reference node fits the measurement data through the least squares theory to improve the measurement accuracy.
8. The intelligent measurement and positioning method based on the three-point measurement principle according to claim 1 is characterized in that: The dynamic adjustment law in the cooperative measurement controller of the auxiliary reference node dynamically adjusts the measurement strategy of the auxiliary reference node according to the estimation result of the main reference node to ensure the overall stability of the measurement network.
9. The intelligent measurement and positioning method based on the three-point measurement principle according to claim 1 is characterized in that: The primary reference node and the auxiliary reference node exchange information via a communication link to achieve cooperative working capability of the measurement network.
10. The intelligent measurement and positioning method based on the three-point measurement principle according to claim 1, characterized in that: The dynamic measurement network achieves efficient and accurate target position measurement and positioning in complex environments through an adaptive weight allocation algorithm and a distributed collaborative algorithm.