CN110662164A - Wireless sensor network accurate positioning algorithm based on E-RSSI - Google Patents

Wireless sensor network accurate positioning algorithm based on E-RSSI Download PDF

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CN110662164A
CN110662164A CN201910912423.3A CN201910912423A CN110662164A CN 110662164 A CN110662164 A CN 110662164A CN 201910912423 A CN201910912423 A CN 201910912423A CN 110662164 A CN110662164 A CN 110662164A
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nodes
beacon
rssi
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乔建华
张雪英
高巨帅
胡远
张兵
侯筠
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Taiyuan University of Science and Technology
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
    • H04W4/02—Services making use of location information
    • H04W4/023—Services making use of location information using mutual or relative location information between multiple location based services [LBS] targets or of distance thresholds
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S11/00—Systems for determining distance or velocity not using reflection or reradiation
    • G01S11/02—Systems for determining distance or velocity not using reflection or reradiation using radio waves
    • G01S11/06—Systems for determining distance or velocity not using reflection or reradiation using radio waves using intensity measurements
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W64/00—Locating users or terminals or network equipment for network management purposes, e.g. mobility management
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W84/00—Network topologies
    • H04W84/18—Self-organising networks, e.g. ad-hoc networks or sensor networks

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Abstract

The invention discloses an E-RSSI-based wireless sensor network accurate positioning algorithm, which comprises the following steps: (1) determining a communication radius, a propagation model and three neighbor beacon nodes; (2) converting the signal strength indication received by the beacon node into the distance from an unknown node to the beacon node; (3) calculating coordinates of unknown nodes by trilateration
Figure 100004_DEST_PATH_IMAGE002
(ii) a (4) For other unknown nodes with beacon nodes less than three within the communication radius, using the node positioned in the step (3) as a new beacon node to position other unknown nodes; (5) repeating the above stepsAnd (4) accurately positioning all nodes in the sensor network. The E-RSSI-based wireless sensor network accurate positioning algorithm provided by the invention is not limited by the number of the initially set beacon nodes, and all nodes in the same network range with connectivity can be positioned as long as the number of the beacon nodes which can enable the algorithm to run is met no matter what the initially set beacon node ratio is.

Description

Wireless sensor network accurate positioning algorithm based on E-RSSI
Technical Field
The invention relates to the technical field of network positioning algorithms, in particular to an E-RSSI-based wireless sensor network accurate positioning algorithm.
Background
The development of wireless communication, microelectronics and computer technology enables low-energy-consumption multipurpose sensors to be widely applied in various fields, a Wireless Sensor Network (WSN) is composed of a large number of sensor nodes which are low in price and small in size, the sensor nodes are placed in a monitored range and are self-organized into a multi-hop system by utilizing wireless communication, the WSN can sense and acquire data in the monitored range and send the data to monitoring personnel, the task of the sensing technology is to acquire the data, the task of the communication technology is to send the data, the task of the computer technology is to analyze and process the data, and the following problems can be encountered when the data are acquired in a real application environment: inaccurate positioning, overlarge information acquisition area, influence of obstacles on transmission precision and the like.
The node position information of the wireless sensor network is important for monitoring activities of the sensor network, the sensor node must know the geographical position information of the sensor node, the transmitted data is meaningful, and the positioning information is used for reporting the place where the event occurs, tracking the target in real time, monitoring the action route of the target, predicting the advancing track of the target and the like.
In general, if nodes in a wireless sensor network are equipped with a Global Positioning System (GPS), it is possible to determine their own position within a few meters of accuracy, but in practical cases, it is inappropriate to use GPS in a WSN involving several nodes, the first reason being that GPS receivers are expensive and the configuration of GPS at each node increases the cost of network deployment, and the second reason being that using GPS at each node is not an energy-saving method, because these networks have energy limitations, GPS is not suitable for indoor environments, and environmental factors such as large buildings can affect the performance of GPS.
Existing network location algorithms are mainly divided into ranging-based algorithms, such as trilateration, and non-ranging-based algorithms, including centroid algorithm, bounding box algorithm, GirdScan, APIT algorithm, etc., in WSN, nodes can determine their geographical location by using external assisted location or self-location techniques, in such networks most nodes are static and can determine their location at the initialization stage of the network. In WSNs, trilateration and triangulation methods are more common, which use relative measurements of 3 or 4 beacon nodes to calculate node location information, and other methods are bounding box algorithms, multidimensional scaling and hop-count based methods.
There will be one receiver per sensor node and this receiver can be used to measure the distance between any two nodes, and the distance calculation is based on two types, the first being based on the Received Signal Strength Indication (RSSI) and the other being based on the number of hops.
RSSI is an indication of the received signal strength, and when a signal is transmitted through the medium, the signal energy of the radio is reduced. The attenuation of its intensity is proportional to the square of the propagation distance. Therefore, the receiver can estimate the distance between itself and the signal transmitting end through the signal strength of the receiving end and the signal source end. The relationship between the distance and the received power can be determined by
Figure DEST_PATH_IMAGE001
To obtain wherein
Figure 641371DEST_PATH_IMAGE002
Is the power of the received signal, k depends on the frequency and the transmission power, k = PT-PL(d0) D is the distance between the receiver and the sender, and n is the attenuation exponent.
The biggest limitations of trilateration based on RSSI ranging techniques are the overall node density problem and the beacon node occupancy. The problem of overall node density is well understood in that each sensor node has its own communication range beyond which it cannot associate, and increasing node density decreases the distance between any two nodes, thus increasing density increases the number of nodes located. The trilateration method utilizes 3 beacons to locate, so that the beacon ratio is improved, the locating efficiency is improved, meanwhile, the algorithm measures other unknown nodes by the beacons, and once no 3 beacons exist near the unknown nodes, part of the unknown nodes cannot be located. In summary, for a wireless sensor network with a certain beacon node ratio, the RSSI method has a small positioning error, but the number of nodes that are not positioned is larger.
The results of comparing the positioning error and the number of unset nodes of the RSSI algorithm with other positioning algorithms Mds-map algorithm, bounding box algorithm, centroid algorithm, Grid Scan algorithm, DV-Hop algorithm, amophorus algorithm and APIT algorithm under the condition of different total node densities and different beacon node ratios are shown in fig. 1 and fig. 2, and it can be seen that:
(1) trilateration based on RSSI ranging techniques has a location error that is infinitely close to 0 regardless of changes in total node density or beacon fraction. It can be found that although the algorithm can accurately locate the unknown node, a large number of nodes cannot be located, and the total number of the nodes cannot be located decreases with the increase of the total node density and the proportion of the beacon nodes, and finally all the nodes can be located. It can be considered as a highly accurate positioning algorithm.
(2) The Mds-map algorithm is such that when its density is greater than or equal to 200 total nodes, its positioning error is small no matter what proportion of its beacon nodes are. And when the density is 100 total nodes, the positioning error is smaller when the beacon node accounts for a ratio of 0.3. And the algorithm can locate all nodes within the monitored range. When the density reaches 200 total nodes, the algorithm can be regarded as an algorithm with high positioning precision. But the algorithm is more complex.
(3) The bounding box algorithm generally looks like that as the total node density is increased, the positioning accuracy of the algorithm is gradually improved, and the algorithm is influenced less by different beacon nodes. The most effective method for improving the positioning accuracy of the algorithm is to improve the total node density in the monitored range. And nodes which cannot be located exist in almost any state, and the number of the nodes which cannot be located in the algorithm is gradually increased along with the increase of the beacon node ratio under the same total node density. The algorithm is dependent on the proportion of the beacon nodes, and the capacity of locating the nodes can be improved by increasing the beacon node ratio.
(4) The centroid algorithm achieves the best effect when the beacon node ratio is 0.5 in 200 total node density, and then the number of the summary points or the positioning error of the beacon node ratio is increased to be maintained at most about 0.22. But requires a high total number of nodes and beacon occupancy.
(5) The Grid Scan algorithm achieves the best effect of the algorithm when the beacon node occupancy is 0.6 at 300 total node densities. But in consideration of the cost problem, the positioning error of the algorithm is not much different from the optimal positioning error of the algorithm when the beacon node occupation ratio of 200 total nodes is 0.5, and the algorithm has better effect than the centroid algorithm. But the algorithm will have partially unseen nodes at 100 total node density and the algorithm will be able to locate all nodes as the total node density increases.
(6) The DV-Hop algorithm achieves the best effect of the algorithm when the 300 total node density beacon node proportion is 0.5, and the algorithm has the only advantage that all nodes in the monitored range can be located, but the algorithm has larger location error compared with other algorithms.
(7) The Amorphous algorithm achieves the best results of the algorithm at a 400 total node density beacon ratio of 0.2, but its positioning error is still large, similar to the dv-hop algorithm.
(8) The APIT algorithm works best when the 400 total node density beacon node fraction is 0.4, but the algorithm is the one with the largest positioning error among the several algorithms, and at the same time, the algorithm is similar to the RSSI ranging based trilateration in the number of nodes that can not be positioned, but is far less accurate than the RSSI ranging trilateration positioning.
Through the analysis, the trilateration method based on the RSSI ranging technology has the highest positioning accuracy, and meanwhile, the algorithm is slightly influenced by the terrain, but a large number of nodes which cannot be positioned exist in the algorithm.
Disclosure of Invention
The invention aims to provide an E-RSSI-based wireless sensor network accurate positioning algorithm aiming at the problems that the RSSI algorithm is high in positioning accuracy but a large number of undetermined nodes are provided.
In order to achieve the purpose, the invention adopts the following technical scheme:
an E-RSSI-based wireless sensor network accurate positioning algorithm comprises the following steps:
(1) determining communication radius, propagation model and three neighbor beacon nodes A
Figure DEST_PATH_IMAGE003
、B
Figure 760637DEST_PATH_IMAGE004
And C
Figure DEST_PATH_IMAGE005
Unknown node D;
(2) respectively calculating the distance from the unknown node to the beacon node A according to the Received Signal Strength Indicator (RSSI) of the beacon node A, B, C
Figure 950310DEST_PATH_IMAGE006
Distance to beacon node B
Figure DEST_PATH_IMAGE007
And distance to beacon node C
Figure 974766DEST_PATH_IMAGE008
；
Wherein, PR(d) The unit is dBm for the received signal power; p (d)0) Distance d for wireless transceiver nodes0When m is reached, the unit of the intensity value of the received signal of the receiving node is dBm; n is a path loss exponent; d is the distance between the transmitting end and the receiving end. P (d)0)=PT-PL(d0),PTFor transmitting signal power, PL (d)0) Is a reference distance d0Loss path power. For certain scenarios and node positions, PTAnd PL (d)0) Is determined. d0Can be set to be 1m, P (d) when the distance between the transmitting and receiving nodes is 1m can be measured0) And a signal strength indicator value P received by each beacon nodeR(d) The distance from each beacon node to the unknown node can be obtained.
The path loss index n can take the value of 2 ~ 4, and in order to improve the accuracy of the environmental experience value and reduce the conversion accuracy from the RSSI value to the distance, the parameter n can be obtained by measuring the RSSI value of the beacon node1And A2Receiving to fixed node A0Has a mean value of the signal intensity of P1And P2Beacon node A1And A2To a fixed node A0A distance of d1And d2Then according to
Figure 540877DEST_PATH_IMAGE010
And also
Figure DEST_PATH_IMAGE011
Then, then
Figure 530961DEST_PATH_IMAGE012
。
(3) Let the coordinates of the unknown node D be
Figure DEST_PATH_IMAGE013
Then A is
Figure 891535DEST_PATH_IMAGE003
、B
Figure 278654DEST_PATH_IMAGE004
、C
Figure 648455DEST_PATH_IMAGE014
、D
Figure 476734DEST_PATH_IMAGE013
、、
Figure 882625DEST_PATH_IMAGE007
And
Figure 56117DEST_PATH_IMAGE008
the following relationship exists between:
Figure DEST_PATH_IMAGE015
；
(4) the coordinate of D can be solved through the formula in the step (3)
Figure 253749DEST_PATH_IMAGE013
Comprises the following steps:
Figure 221705DEST_PATH_IMAGE016
；
(5) for unknown nodes E with beacon nodes less than three in the communication radius, taking the node D positioned in the step (4) as a new beacon node to position the unknown nodes E;
(6) and (3) repeating the step (1), the step (2), the step (3), the step (4) and the step (5) for multiple times, so that accurate positioning of all nodes in the wireless sensor network with connectivity in the monitoring area can be realized.
Furthermore, the wireless sensor network accurate positioning algorithm based on the E-RSSI disclosed by the invention is simulated through MATLAB.
Further, the communication Model set in the MATLAB simulation process is one of a Regular Model, a DOI Model, a Logarithmic engagement Model, and an RIM Model.
The invention has the beneficial effects that: the accurate positioning algorithm of the wireless sensor network based on the E-RSSI, disclosed by the invention, takes the positioned unknown nodes as new beacon nodes to position other unknown nodes which are not positioned, so that the number of the beacon nodes is saved, except the beacon nodes which are initially set, the other unknown nodes are new beacon nodes as long as being positioned, the occupation ratio of the beacon nodes can possibly reach 100%, which means that all the nodes can be accurately positioned, meanwhile, the algorithm is not limited by the number of the initially set beacon nodes, and the same effect can be achieved as long as the number of the beacon nodes which can enable the algorithm to run is given enough no matter what the occupation ratio of the initially set beacon nodes is.
Drawings
Fig. 1 is a positioning error map of each algorithm under different total node densities and different beacon ratios.
Fig. 2 is a graph of the number of nodes that cannot be located by each algorithm at different densities and beacon ratios.
FIG. 3 is a node distribution plot of a 0.2 beacon node ratio over 100 nodes in a MATLAB simulation.
Fig. 4 is a graph of RSSI positioning effect of 100 nodes 0.2 beacon node ratio in MATLAB simulation.
Fig. 5 is a graph of the E-RSSI positioning effect of a 0.2 beacon node ratio for 100 nodes in a MATLAB simulation.
FIG. 6 is a node distribution plot of a 0.4 beacon node ratio over 100 nodes in a MATLAB simulation.
Fig. 7 is a graph of RSSI positioning effect of 100 nodes 0.4 beacon node ratio in MATLAB simulation.
FIG. 8 is a graph of the E-RSSI positioning effect of a 0.4 beacon node ratio for 100 nodes in a MATLAB simulation.
Fig. 9 is a graph of RSSI positioning effect of 100 nodes 0.4 beacon nodes in MATLAB simulation compared to type C region.
Fig. 10 is a graph of the E-RSSI positioning effect of 100 nodes 0.4 beacon nodes in MATLAB simulation compared to type C region.
Fig. 11 is a graph of RSSI positioning effect of 121 nodes 0.4 beacon nodes in MATLAB simulation versus a grid-type area.
Fig. 12 is a graph of the E-RSSI positioning effect of 121 nodes 0.4 beacon nodes in MATLAB simulation versus a grid-type area.
Fig. 13 is a graph of RSSI positioning effect of 100 nodes 0.4 beacon nodes in a grid type C region in MATLAB simulation.
Fig. 14 is a graph of the E-RSSI positioning effect of 100 nodes 0.4 beacon nodes in MATLAB simulation compared to grid type C area.
Fig. 15 is an overall comparison graph of the RSSI algorithm and the E-RSSI algorithm failing to locate the number of nodes.
Detailed Description
The following examples are presented to enable those skilled in the art to more fully understand the present invention and are not intended to limit the invention in any way.
An E-RSSI-based wireless sensor network accurate positioning algorithm comprises the following steps:
(1) determining communication radius, propagation model and three neighbor beacon nodes A
Figure 317837DEST_PATH_IMAGE003
、B
Figure 29441DEST_PATH_IMAGE004
And C
Figure 832312DEST_PATH_IMAGE005
Unknown node D;
(2) respectively calculating the distance from the unknown node to the beacon node A according to the Received Signal Strength Indicator (RSSI) of the beacon node A, B, C
Figure 971169DEST_PATH_IMAGE006
Distance to beacon node B
Figure 554597DEST_PATH_IMAGE007
And distance to beacon node C
Figure 804313DEST_PATH_IMAGE008
：
Figure 789587DEST_PATH_IMAGE009
Wherein, PR(d) The unit is dBm for the received signal power; p (d)0) Distance d for wireless transceiver nodes0When m is reached, the unit of the intensity value of the received signal of the receiving node is dBm; n is a path loss exponent; d is the distance between the transmitting end and the receiving end. P (d)0)=PT-PL(d0),PTFor transmitting signal power, PL (d)0) Is a reference distance d0Loss path power. For certain scenarios and node positions, PTAnd PL (d)0) Is determined. d0Can be set to be 1m, P (d) when the distance between the transmitting and receiving nodes is 1m can be measured0) And a signal strength indicator value P received by each beacon nodeR(d) The distance from each beacon node to the unknown node can be obtained.
The path loss index n can take the value of 2 ~ 4, and in order to improve the accuracy of the environmental experience value and reduce the conversion accuracy from the RSSI value to the distance, the parameter n can be obtained by measuring the RSSI value of the beacon node1And A2Receiving to fixed node A0Has a mean value of the signal intensity of P1And P2Beacon node A1And A2To a fixed node A0A distance of d1And d2Then according to
Figure 787761DEST_PATH_IMAGE010
And also
Figure 858485DEST_PATH_IMAGE011
Then, then
Figure 911892DEST_PATH_IMAGE012
。
(3) Let the coordinates of the unknown node D beThen A is
Figure 170015DEST_PATH_IMAGE003
、B
Figure 462456DEST_PATH_IMAGE004
、C
Figure 319553DEST_PATH_IMAGE014
、D
Figure 13840DEST_PATH_IMAGE013
、
Figure 665401DEST_PATH_IMAGE006
、
Figure 897668DEST_PATH_IMAGE007
And
Figure 292877DEST_PATH_IMAGE008
the following relationship exists between:
；
(4) the coordinate of D can be solved through the formula in the step (3)
Figure 929712DEST_PATH_IMAGE013
Comprises the following steps:
Figure 196745DEST_PATH_IMAGE016
；
(5) for unknown nodes E with beacon nodes less than three in the communication radius, taking the node D positioned in the step (4) as a new beacon node to position the unknown nodes E;
(6) and (3) repeating the step (1), the step (2), the step (3), the step (4) and the step (5) for multiple times, so that accurate positioning of all nodes in the wireless sensor network with connectivity in the monitoring area can be realized.
In the preferred embodiment, the wireless sensor network accurate positioning algorithm based on the E-RSSI disclosed by the invention is simulated through MATLAB.
In this preferred embodiment, the communication Model set in the MATLAB simulation process is one of a Regular Model, a DOI Model, a Logarithmic engagement Model, and an RIM Model.
In the design of an application system, a CC2530 chip can be adopted, and an RSS module is contained in the CC2530 chip, so that an RSSI value can be directly obtained, and the application is convenient.
As can be seen from fig. 1 and fig. 2, the RSSI algorithm has a smaller positioning error but the number of undetermined nodes is the highest compared with other 7 positioning algorithms such as Mds-map algorithm, DV-Hop algorithm and the like under the conditions of different total node densities and different beacon node ratios.
As can be seen by comparing fig. 3, fig. 4 and fig. 5, under the condition of 100 total nodes and 0.2 beacon node ratio, the original algorithm has 57 unknown nodes which cannot be located, the location error is 3.0495e-15, and the algorithm improved by the application has 1 unknown node which cannot be located, the location error is 1.5545e-14, so that it can be seen that the improved algorithm can locate all nodes in the monitored area at the 0.2 beacon node ratio, and the location accuracy is slightly lower than that of the original algorithm, but is very accurate and far exceeds that of other algorithms.
As can be seen by comparing fig. 6, fig. 7 and fig. 8, under the condition of 100 total nodes and 0.4 beacon node ratio, there are 14 unknown nodes which cannot be located by using the original algorithm and the location error is 1.8901e-15, and there are 3 unknown nodes which cannot be located by using the improved algorithm of the present application and the location error is 2.0059e-15, so that it can be seen that the improved algorithm can locate all the nodes in the monitored area at 0.4 beacon node ratio, and the location accuracy is slightly lower than that of the original algorithm, but is very accurate and far better than that of other algorithms.
As can be seen from comparison of fig. 9, fig. 10, fig. 11, fig. 12, fig. 13, and fig. 14, the improved algorithm of the present application is still applicable to the C-type region, the grid-type region, and the grid C-type region, and the effect in the C-type region is better than that in the grid region.
Those skilled in the art will appreciate that the above embodiments are merely exemplary embodiments and that various changes, substitutions, and alterations can be made without departing from the spirit and scope of the invention.

Claims (3)

1. An E-RSSI-based wireless sensor network accurate positioning algorithm is characterized by comprising the following steps:
(1) determining communication radius, propagation model and three neighbor beacon nodes A
Figure DEST_PATH_IMAGE002
、B
Figure DEST_PATH_IMAGE004
And C
Figure DEST_PATH_IMAGE006
Unknown node D;
(2) respectively calculating the distance from the unknown node to the beacon node A according to the Received Signal Strength Indicator (RSSI) of the beacon node A, B, C
Figure DEST_PATH_IMAGE008
Distance to beacon node B
Figure DEST_PATH_IMAGE010
And distance to beacon node C
Figure DEST_PATH_IMAGE012
:
Wherein, PR(d) The unit is dBm for the received signal power; p (d)0) Distance d for wireless transceiver nodes0When m is reached, the unit of the intensity value of the received signal of the receiving node is dBm; n is a path loss exponent; d is the distance between the transmitting end and the receiving end. P (d)0)=PT-PL(d0),PTFor transmitting signal power, PL (d)0) Is a reference distance d0Loss path power. For certain scenarios and node positions, PTAnd PL (d)0) Is determined. d0Can be set to be 1m, P (d) when the distance between the transmitting and receiving nodes is 1m can be measured0) And a signal strength indicator value P received by each beacon nodeR(d) The distance from each beacon node to the unknown node can be calculated;
the path loss index n can take the value of 2 ~ 4, and in order to improve the accuracy of the environmental experience value and reduce the conversion accuracy from the RSSI value to the distance, the parameter n can be obtained by measuring the RSSI value of the beacon node1And A2Receiving to fixed node A0Has a mean value of the signal intensity of P1And P2Beacon node A1And A2To a fixed node A0A distance of d1And d2Then according to
Figure DEST_PATH_IMAGE016
And also
Figure DEST_PATH_IMAGE018
Then, then
Figure DEST_PATH_IMAGE020
。
(3) Let the coordinates of the unknown node D be
Figure DEST_PATH_IMAGE022
Then A is
Figure 134701DEST_PATH_IMAGE002
、B
Figure 51841DEST_PATH_IMAGE004
、C、D
Figure 831579DEST_PATH_IMAGE022
、、
Figure 228111DEST_PATH_IMAGE010
And
Figure 50573DEST_PATH_IMAGE012
the following relationship exists between:
Figure DEST_PATH_IMAGE026
；
(4) the coordinate of D can be solved through the formula in the step (3)Comprises the following steps:
；
(5) for unknown nodes E with beacon nodes less than three in the communication radius, taking the node D positioned in the step (4) as a new beacon node to position the unknown nodes E;
(6) and (3) repeating the step (1), the step (2), the step (3), the step (4) and the step (5) for multiple times, so that accurate positioning of all nodes in the wireless sensor network with connectivity in the monitoring area can be realized.
2. The accurate positioning algorithm for the wireless sensor network based on the E-RSSI according to the claim 1, characterized in that the accurate positioning algorithm for the wireless sensor network based on the E-RSSI disclosed by the invention is simulated by MATLAB. In the design of an application system, a CC2530 chip can be adopted, and an RSS module is contained in the CC2530 chip, so that an RSSI value can be directly obtained, and the application is convenient.
3. The accurate positioning algorithm for the wireless sensor network based on the E-RSSI as claimed in claim 2, wherein the communication Model set in the MATLAB simulation process is one of Regular Model, DOI Model, logarithmication Model and RIM Model. The Logarithmic engagement Model requires no parameters, the DOI Model requires parameters, both are irregular models, and the RIM Model is a very irregular Model.
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