WO2008129488A2

WO2008129488A2 - System and method for recalculation of probabilities in decision trees

Info

Publication number: WO2008129488A2
Application number: PCT/IB2008/051495
Authority: WO
Inventors: Paul R. Simons; Stephen M. Pitchers
Original assignee: Koninklijke Philips Electronics N. V.
Priority date: 2007-04-24
Filing date: 2008-04-18
Publication date: 2008-10-30
Also published as: TW200850056A; WO2008129488A3

Abstract

A system and method for determining probabilities in a decision tree (700) includes a processor configure to generate a first hypothesis (Hl) having a first probability (510) of a first device (1) being at a first location (D) based on distances from the first device (1) to two devices (4, 6); generate a second hypothesis (H3) having a second probability (610) for a second device (2) being at a second location (E) based on distances from the second device (2) to the first device (1) and to the two devices (4, 6); and recalculate the first probability (510) to form a recalculated first probability (510') based on distances from the first device (1) to the second device (2) and to the two known devices (4, 6).

Description

System and method for recalculation of probabilities in decision trees

The present systems and methods relate to recalculation of probabilities in decision trees where nodes are automatically assigned to their correct spatial positions within a network, such as a wirelessly controlled lighting array.

A typical wireless lighting array comprises a large number of electrically driven luminaires, which are typically positioned to provide a uniform light distribution, for example. The luminaires within the array are often positioned in a grid or lattice arrangement in the ceiling of a room such that there is uniform spacing between them.

Each of the individual luminaires in such a lighting array is adapted such that it is able to communicate with the other luminaires over a wireless communication network, which is formed by an array of associated communication nodes. Each of the communication nodes in the network is located at the position of its associated luminaire in the lighting array. Hence, the spatial structures of the lighting array and communication network are equivalent.

The communication network provides a means by which the lighting array can be auto-commissioned post-installation. However, the individual nodes in the network are unable to provide their own position information, therefore, it is not known which luminaire is associated with which node. Before the array can be commissioned, the spatial position of each node in the communication network is established via a variety of known methods, including via manual operator input, for example, so that each node can be assigned to the correct luminaire.

The positions of the communication nodes are found by a trilateration process, for example, which is based upon range data provided by the wireless communication network. The range data is provided in the form of range measurements taken between pairs of communication nodes in the wireless network. The calculation of a range between two nodes is derived directly from these range measurements, which are made using known techniques such as using Received Signal Strength Indication (RSSI) or Time-of-Flight information of signal exchanged between various nodes and/or luminaires. In the case of RSSI, the received strength of a radio signal exchanged between a pair of communication nodes is used to calculate the range between them. The strength of the transmitted signal decreases at a rate inversely proportional to the distance traveled and proportional to the wavelength of the signal. Hence, taking the wavelength into account, the distance between the pair of nodes may be calculated from the transmitted signal's attenuation at the receiving node.

In the case of Time-of-Flight measurements, the range between a pair of communication nodes is calculated by measuring the time taken for a radio signal to travel between them. Since radio signals travel at the speed of light, an accurate measure of the time-of-flight between the pair of nodes enables an accurate calculation of the distance between them.

However, these types of range measurement are subject to error and, hence, the derived positions of the communication nodes often do not match exactly to positions on the grid or lattice arrangement on which the luminaires are arranged. There is, therefore, still some uncertainty as to which luminaire is associated with each node.

In order for the wireless lighting array to be successfully commissioned, the communication nodes must be assigned to their correct grid or lattice position, and hence luminaire, in the lighting array. If the communication nodes are assigned to a lattice position which does not correspond to their actual lattice position, the derived spatial structure of the communication network will be incorrect and, and consequently, the lighting array will not function correctly.

In order to resolve such uncertainties in the positions of the communication nodes, the positions derived by trilateration may be compared with a template which defines the lattice positions of the luminaires in the lighting array. By this method, a communication node may be assigned to the closest luminaire to its derived position. Its new position may then be used as a reference point in the trilateration of further communication nodes. In this way, errors in the positions derived by the trilateration process are not accumulated.

However, there is a risk that individual communication nodes will be assigned to the wrong position, i.e., a position which does not correspond to their actual position. In this case, the use of that position to establish the positions of further communication nodes results in the accumulation of large errors. Such errors may become so large that they prevent the overall topology of the lighting array from being established.

Various systems and methods for automatic commissioning of wireless lighting are known, such as described in International Publication Number WO 2006/095317 to Simons, and assigned to Koninklijke Philips Electronics N.V., which is incorporated herein by reference in its entirety, where the system assigns each detected device to a specific position within a building. In particular, building plans are used to help solve the positioning process by providing a template for the positions derived from measuring ranges between devices. Various techniques have also been applied to determine positions of devices from range measurements, as described in International Patent Application Serial Number PCT/IB2007/050707, to Simons et al, filed on March 5, 2007, claiming the benefit of European Patent Application Serial Number 06110706.6, filed on March 6, 2006, (Attorney Docket No. PH004189, ID405269), which are both incorporated herein by reference in their entirety.

Probabilistic models have been used to determine position of devices in a wireless network, such described in U.S. Patent Application Publication No. 2005/0128139 to Misikangas, which is incorporated herein by reference in its entirety. Position determination may be achieved using various algorithms, such as one described in an article entitled "An Algorithm for Tracking Multiple Targets" by Donald B. Reid, IEEE Transactions on Automatic Control, volume AC-24, No. 6, pages 843-854, December 1979, used to track moving objects, which is incorporated herein by reference in its entirety. Reid's algorithm has been widely applied to defense systems, particularly for the target-tracking domain. As described in Reid, trees of hypotheses are constructed to represent the possible options for assigning incoming data to existing tracks. Keeping these options open allows the final decision to be delayed until more information is available.

One object of the present systems and methods is to improve known systems and methods of commissioning target devices, such as luminaires, in a network. According to illustrative embodiments, method and system are provided for determining probabilities in a decision tree comprising generating a first hypothesis having a first probability of a first device being at a first location based on distances from the first device to two devices; generating a second hypothesis having a second probability for a second device being at a second location based on distances from the second device to the first device and to the two devices; and recalculating the first probability to form a recalculated first probability based on distances from the first device to the second device and to the two known devices.

Further areas of applicability of the present systems and methods will become apparent from the detailed description provided hereinafter. It should be understood that the detailed description and specific examples, while indicating exemplary embodiments of the systems and methods, are intended for purposes of illustration only and are not intended to limit the scope of the invention.

These and other features, aspects, and advantages of the apparatus, systems and methods of the present invention will become better understood from the following description, appended claims, and accompanying drawing where:

Fig. 1 shows a plan showing network node positions and the target devices according to one illustrative embodiment; and

Fig. 2 shows a block diagram of section of the wireless lighting network shown in Fig. 1 ; Fig. 3 shows a system for automatic commissioning of devices according to an illustrative embodiment;

Fig. 4 shows a processing device according to an illustrative embodiment; and

Figs. 5-10 show examples illustrating recalculation of probabilities according to illustrative embodiments.

The following description of certain exemplary embodiments is merely exemplary in nature and is in no way intended to limit the invention, its applications, or uses. In the following detailed description of embodiments of the present systems and methods, reference is made to the accompanying drawings which form a part hereof, and in which are shown by way of illustration specific embodiments in which the described systems and methods may be practiced. These embodiments are described in sufficient detail to enable those skilled in the art to practice the presently disclosed systems and methods, and it is to be understood that other embodiments may be utilized and that structural and logical changes may be made without departing from the spirit and scope of the present system. The following detailed description is therefore not to be taken in a limiting sense, and the scope of the present system is defined only by the appended claims. The leading digit(s) of the reference numbers in the figures herein typically correspond to the figure number, with the exception that identical components which appear in multiple figures are identified by the same reference numbers. Moreover, for the purpose of clarity, detailed descriptions of well-known devices, circuits, and methods are omitted so as not to obscure the description of the present system.

The present systems and methods use hypothesis trees to represent and resolve the assignment decisions made during the automatic commissioning of target devices in a network, such as luminaires used in a lighting network or system. Decisions trees are used to evaluate problems in which multiple outcomes are possible in order to help determine the most plausible solution. The tree includes a hierarchy of hypotheses, each of which assigns a certain probability to a particular belief. The branch with the highest overall probability represents the best guess at the correct solution. The present systems and methods include techniques to improve the estimation of probability for each hypothesis, which is a crucial in auto-commissioning of target devices, such as luminaires, in a network including a lighting system, for example.

In particular, earlier hypotheses are reviewed in the light of new information that was not available when the hypothesis was first created. The present systems and methods provide improved trilateration, as more data becomes available, leading to better probability calculation, and may be used to reduce the possibility of the correct hypothesis from being eliminated. Further, the present systems and methods correct early stages of decision tree building when information availability is often limited. Thus, significant improvement in results of the completed decision tree is achieved. Further, the present systems and methods are less sensitive to the order in which beliefs are created.

Decision trees are used to represent alternative hypotheses to solve a particular problem. Each hypothesis is assigned a probability indicating the likelihood that a certain belief is correct, such as that a certain device is located at a specified location marked on the building plan, for example. The hypotheses are organized into a tree structure such that the combination of hypotheses along a particular branch of the tree indicates a combined view of a set of assignments of target devices (such as luminaires) to locations.

The likelihood of a particular belief is derived from range data measured from the positions of devices positioned by earlier hypotheses in the tree. Each branch of the tree represents one possible set of assignments of devices to locations. From two known devices used as reference points provided manually via user input or determined via known methods for example, trilateration is used to determine the relative position of an unknown-position third/new or target device from measured distances between the third/new or new target device and each reference point.

Each trilateration operation uses the history of the assignments on its own branch as the starting arrangement to which the new device placement should be added. Each branch constitutes a unique starting arrangement for the trilateration operation. Earlier assignments on that branch are treated as known reference positions for creating a new belief. The range from the device to each of the reference points is used to estimate the position of the new device. The distance between that position and the various locations specified in the building plan is taken into account in determining the likelihood of the new device being at each location specified in the building plan or map. The probability of the parent of each hypothesis is also taken into account when determining the overall probability of each new hypothesis. Once the likelihood of the belief of a particular hypothesis has been estimated, a combined probability is assigned by multiplying this likelihood with the probability of the parent hypothesis. This constitutes feeding information forward from earlier hypotheses to assist in estimating the probability of subsequent hypotheses.

The present systems and methods provide for feeding information back in the reverse direction to improve the estimated probability of earlier hypotheses. By using assignments of the child hypotheses as well as parent hypotheses, more reference positions are available than when the earlier hypotheses were created. Among other advantages, this makes the technique less sensitive to the order in which assignments are tackled. Decision trees are used to resolve the positions of wireless devices, for example, using range measurements made between the devices. The range measurements may incorporate large range errors, and the decision tree helps to deal with the resulting uncertainty. The decision tree provides a mechanism of examining all plausible allocations of devices to the locations in the building plan.

Fig. 1 shows a building plan or map including a wireless network 100, for example, with six nodes at known locations A, B, C, D, E and F and six wireless devices, e.g., using the ZigBee™ protocol or other wireless protocols, such as six luminaires 1, 2, 3, 4, 5 and 6. A scan of the wireless network reveals the identities of the wireless devices 1, 2, 3, 4, 5 and 6. The task or auto-commissioning involves determining which identity or target device (e.g., luminaire) 1, 2, 3, 4, 5 and 6 is associated with which location A, B, C, D, E and F of the network, e.g., in a building or any other environment. It should be understood that although luminaires are used as target devices, the present systems and methods are applicable for auto-commissioning of any network and any target devices.

Referring to Fig. 2, a block diagram of a section of the wireless lighting network 100 including electrically driven luminaires 210 and nodes 220, such as the six nodes at location A, B, C, D, E and F, and the six luminaires 1-6 shown in Fig. 1. The nodes 210 and/or luminaires are adapted to communicate with one another through the wireless communication network 100, which comprises wireless communication nodes 220, such as the six nodes at locations A, B, C, D, E and F shown in Fig. 1. Each of the communication nodes 220 comprises, for example, a ZigBee-like radio module, and is associated with one of the electrically driven luminaires 210.

As shown in Fig. 2, the hardware present at each luminaire's position comprises a power supply unit 230, a wireless communication node 220 and a luminaire 210. The power supply unit 230 is adapted to provide electrical power to the communication node(s) 220 and/or to the luminaire(s) 210. The power supply unit(s) 230 may be connected to a mains power supply (e.g., 120V AC, 60Hz or 230V, 50Hz for example) and may comprise electrical components such as transformers for manipulating the mains supply and providing power to the nodes 220 and luminaires 210. The first stage in commissioning the lighting array of the luminaires 210 is to establish the communication network. This is achieved by a network discovery process, which is initiated by all communication nodes 220 upon power-up. Illustratively, every communication node 220 in the network 100 tunes to a control channel and broadcasts an "advertise" message, which contains its node type and a request that all other nodes identify themselves. After a certain time, each other node replies to the message with its identity and functionality. However, the nodes 220 and/or luminaires 210 are typically unable to supply their position information. At this stage, therefore, the spatial structure of the network 100 is unknown. Fig. 3 shows a system 300 for automatic commissioning of devices, such as luminaires 210, including determining the positions of the luminaires in relation to positions of the nodes 220 in an environment, such as a building or the network 100. The system 300 comprises placement algorithm 310 stored in a memory for execution by a processor or CPU 410 shown in Fig. 4. The positions of the nodes 220 in the network 100 may be established with the use of the placement algorithm 310. The placement algorithm 310 is configured to calculate the relative position of each node 220 using range data provided by the wireless communication network 100. The range data is provided in the form of range measurements taken between pairs of communication nodes 220 in the wireless network 100. The calculation of a range between a pair of the six nodes A to F is derived directly from these range measurements, which may be made using techniques like Received Signal Strength Indication (RSSI) or Time-of-Flight information, for example.

The placement algorithm 310 is adapted such that it may be implemented, for example, by a processing device 400 (shown in Fig. 4) such as a laptop computer or PDA which communicates with nodes 220 of the wireless network 100 through a gateway interface 320. The processing device 400 may include the gateway interface 320, and memory for storing the placement algorithm 310, as well as other algorithm and data such as an operating system and the like.

The gateway interface 320 comprises a computer or processor executable program, running on the processor 410 of processing device 400 shown in Fig. 4, which requests and collects data from the communication network 100 through a gateway provided by one of the communication nodes 220. The collected data includes the functionality of each node 220 and range measurements between each pair of nodes 220. The gateway interface 320 continuously monitors the network 100 and is configured to detect if new nodes are added to, or disappear from, the network 100.

Referring to Fig. 4, the hardware of the processing device 400 includes a processor such as central processing unit (CPU) 410 for executing the placement algorithm 310 and for managing and controlling the operation of the computer 400. The CPU 410 is connected to a number of devices via a bus 420, the devices including a storage device, for example a hard disk drive 430, and memory devices including ROM 440 and RAM 450 for storing application algorithm and data for execution and processing by the CPU 410. The computer hardware further includes a network card 450, which provides means for interfacing to the communication network 100, and a display 460, which allows a user to monitor the operation of the computer 400. Of course any other input/output device may also be provided, such as a keyboard, mouse etc. The computer 400 is configured to communicate with the gateway via a serial or Ethernet cable, for example. However, the computer 400 may communicate with the gateway wirelessly.

In a further embodiment, the placement algorithm 310 is adapted such that it may be implemented by computer hardware which is integrated into the wireless communication network 100. Such hardware may be, for example, part of the communication nodes 220 and/or the luminaires 210, for example.

In commissioning the lighting array or network, the processor 410 of the computer 400 requests and receives range data from the wireless communication network 100 through the gateway provided by one of the communication nodes 220. The computer 400 then uses the range data to implement the placement algorithm 310. Figs. 5-10 illustrate the method by which the placement algorithm 310 uses range measurements to derive the positions of the four luminaires 1, 2, 3, 5 in the network 100, starting with known positions of luminaires 4 and 6, provided manually by a system operator or user, for example, or determined via any other means.

For the purposes of the illustrative example using six luminaires 1, 2, 3, 4, 5 and 6, and six network nodes at locations A, B, C, D, E and F, it is assumed that luminaires 4 and 6 are already known to be in locations A and B, respectively, which may be determined by known methods, including via manual input from the system user, for example, as well as using the methods described in International Patent Application Serial Number PCT/IB2007/050707, for example. The processor 410 when executing the placement algorithm 310 may then use range measurements from these reference positions A and B to determine the most likely identities of the devices 1, 2, 3 and 5, in the remaining positions C, D, E and F. As is well known, transceivers and detectors of the nodes 220 and/or luminaires 210 communicate with other and exchange signals, from which distances may be determined, such as using RSSI or Time-of-Flight information. Fig. 5 shows the first level of a decision tree 500 and hypothesis Hl and H2, having probabilities as indicated by reference numerals 510, 520, respectively, showing circles 530, 540 having radii representing distance or range data as measured, e.g., via RSSI or Time-of-Flight methods. One circle 530 is generated, e.g., from measured range data between location-unknown device 1 and location-known or first reference device 4. The circle 530 has a center at the node located at position A, where the location-known luminaire 4 is also located, and a radius which is equal to the measured distance between the luminaire 4 (or node A) and the location-unknown luminaire 1 , whose position or location within the network or building plan, map or lighting array, is being determined. Luminaire 1 is selected from among other luminaires of unknown or yet to be determined positions, since it is the closest luminaire to the two reference luminaires or target devices 4, 6 of known locations (namely, located at locations A and B, respectively). This closeness of the luminaire 1 to at least one of the two reference luminaires 4, 6 may also be determined using RSSI or Time-of-Flight methods, for example. Once the position of the luminaire 1 is determined, then the next closest luminaire to at least one of the three position-known luminaires 1, 4, 6 is selected for determination of the position of this next closest luminaire. The other circle 540 (generated from distance or range measurement between location-unknown device 1 and location-known or reference device 6) has a center at the node located at position B, where the reference luminaire 6 is also located, and a radius which is equal to the measured distance between the reference luminaire 6 (or node B) and the closest luminaire 1 whose position is to be determined. Initial range or distance measurements are performed between the first position-known device 4 and position-unknown devices and/or range measurements between the second position-known device 6 and the position-unknown devices. From such closeness measurements, the closest position-unknown device to at least one of the two position-known devices 4, 6 is selected for its position determination, namely, luminaire 1 in the illustrative example shown in Fig. 5.

As shown in Fig. 5, the initial range measurements indicate that target device or luminaire 1 is the closest to known reference points 4 and 6 so it is selected to be placed next. Further range measurements are made between the position-unknown device 1 and the first position-known device 4, and between the position-unknown device 1 and the second position-known device 6. The two range circles 530, 540 produce an intersection point 550 of the two range circles 530, 540, as shown in Fig. 5. This intersection point 550 is compared with the four locations C, D, E, and F that have not yet been assigned a target device. For the sake of clarity only the closest two target or possible locations D and E for location-unknown device 1 are illustrated. Further, the tree is routinely pruned to prevent the unnecessary expansion of hypotheses with a very low probability. Hypothesis Hl represents the assignment of device 1 to location D, and hypothesis H2 represents the assignment of device 1 to location E.

The likelihood or probability of each hypothesis Hl, H2 is calculated based on the distance from the intersection point 550 to the target locations D or E. As shown in Fig. 5, the decision tree 500 has two outcomes, possibilities or branches 560, 570 representing hypothesis Hl (having probability 510) and hypothesis H2 (having probability 520). Since the intersection point 550 is closer to location D than to location E, then the first branch 560, representing hypothesis Hl (having probability 510), is allocated a higher likelihood or probability, namely, 0.75, which is higher than the probability of 0.25 for hypothesis H2 (having probability 520) associated with the second branch 570 of the decision tree 500. Fig. 6 shows the next level of the decision tree 600, which considers the assignment of device 2. Four new possible outcomes or hypotheses H3, H4, H5, H6 (having calculated probabilities 610, 620, 630, 640, respectively,) are created, namely, two child hypotheses H3, H4 created from the first branch 560 from parent hypothesis Hl (having probability 510) and two child hypotheses H5, H6 created from the second branch 570 starting from parent hypothesis H2 (having probability 520). Three reference points are now available, namely the three position-known devices 1, 4, 6, thus enabling three range circles 650, 655, 660 to be drawn to produce an intersection point 665, for hypotheses H3, H4.

The first circle 650 represents the range area from device 2/location E to device 4/location A; the second circle 655 represents the range area from device 2/location E to device 6/location B; and the third circle 660 represents the range area from device 2/location E to device I/location D. That is, the first circle 650 has a center at device 4/location A and a radius being the measured distance between device 2 (and/or node at location E) and device 4 (and/or node at location A), e.g., via RSSI and/or Time-of-Flight measured data from signals exchanged between device 2/location E and device 4/location A; the second circle 655 has a center at device 6/location B and a radius being the measured distance between device 2/location E and device 6/location B; the third circle 660 has a center at device I/location D and a radius being the measured distance between device 2/location E and device I/location D. The three circles intersect at various locations. An average intersection point or position 665 is determined by averaging the positions derived from the best set of intersections, as described in International Patent Application Serial Number PCT/IB2006/054921, filed on December 18, 2006, claiming the benefit of European Patent Application Serial Number 05112465.9, to Pitchers et ah, entitled "A Method and Apparatus for Determining the Location of Nodes in a Wireless Network" filed on December 20, 2005, (Attorney Docket No. PH003798, IDs 405346, 406150), which are both incorporated herein by reference in their entirety.

Three other circles 670, 675, 680 are generated similarly for hypotheses H5, H6 and have an estimated position 685, where the location of device 1 is assumed to be at node E, instead of node D for hypotheses H3, H4. Illustratively, the fourth circle 670 has a center at device 4/location A and a radius being the measured distance between device 4/location A and device 2/location F; the fifth circle 675 has a center at device 6/location B and a radius being the measured distance between device 6/location B and device 2/location F; the sixth circle 680 has a center at device I/location E and a radius being the measured distance between device I/location E and device 2/location F. As seen from Fig. 6, the intersection point 665, 685 depend upon the parent hypothesis because each branch 560, 570 specifies a different starting position or parent hypothesis Hl, H2. In particular, hypotheses H3, H4 (having probabilities 610, 620) have hypothesis Hl (having probabilities 510 of 0.75) as the parent, which assumes (with a likelihood or probability of 0.75) that device 1 is at location D (I=D for branch 560), where the three circles 650, 655, 660 have an estimated position 665. Further, hypotheses H5, H6 (having probabilities 630, 640) have hypothesis H2 (having probabilities 520 of 0.25) as the parent, assuming (with a probability of 0.25) that device 1 is at location E (I=E for branch 570), where the three circles 670, 675, 680 have an estimated position 685.

Again, the likelihood or probability 610, 620, 630, 640 of each of the four child hypotheses H3, H4, H5, H6 is proportional to or based on the distances from the intersection point 665, 685 to the target locations. Additionally, an overall or combined probability is assigned by multiplying this likelihood of the particular branch or child by the probability of the parent hypothesis. As shown in Fig. 6, the overall probability of branches 560, 690 related to the likelihood of device 2 being located at position E, where device 1 is at location D (I=D and 2=E) is 0.5; the overall probability of branches 560, 692 (I=D and 2=F) is 0.24; the overall probability of branches 570, 694 (I=E and 2=D) is 0.05; and the overall probability of branches 570, 696 (I=E and 2=F) is 0.21.

Hypothesis H3 (having probability 610) has the highest overall probability of 0.50 as it inherits a good probability (of 0.75) from hypothesis Hl (having probability 510), and yields a close intersection point 665 to target location E (hypothesis H3), which is closer than the distance from the intersection point 665 to the target location F of hypothesis H4, where it is hypothesized or assumed that the device 2 is at location F. Accordingly, luminaire 1 is assigned to location D and luminaire 2 is assigned to location E since hypothesis H3 has the highest probability 610 as compared to the other probabilities 620, 630, 640 at the same tree level, i.e., the second level of the decision tree 600. Of course, if desired, hypothesis H3 may be chosen if its probability exceeds a predetermined value, which may depend on the number of branches at the particular tree level. For example, in the case of the second level of the decision tree 600 having four branches, the predetermined level may be 1/4, so the branch(es) or hypothesis having a probability of greater than 1/4 or 0.25 is selected as providing the correct assignment of luminaires to nodes or locations. Similarly, branches or hypotheses may be pruned or discarded having a probability of less than predetermined level, which may be fixed such as 0.1 , or may depend on the number of branches, such as one divided by a multiple (e.g., 5 times) of the number of branches, e.g., l/(4x5)=l/20 or 0.05 for the second level of the decision tree 600 having four branches.

For improved hypothesis tree generation, the present systems and methods include an additional step that improves the calculation of probabilities, by re- evaluating previous levels of hypotheses. As each created child hypotheses represents an assignment of a device to a position, the re-evaluation may also use the child hypotheses to provide additional reference positions. Fig. 7 revisits the calculation of probabilities of hypotheses Hl and H2, after hypotheses H3, H4, H5 and H6 have been created where their overall probabilities 610, 620, 630, 640 are 0.50, 0.24, 0.05 and 0.21, as shown in Fig. 6. As shown in Fig.7, and by comparison to Fig. 5, additional range measurements shown as circles 710, 720, 730, 740 are now generated and available for use in reevaluating a hypotheses (e.g., hypothesis Hl shown in Fig. 5) and recalculating its probability using its child hypotheses (e.g., hypothesis H3 shown in Fig. 6 as the child of hypothesis Hl). Referring to Fig. 7, each branch of the decision tree 700 is treated separately as, in general, each hypothesis may have many offspring. For example, when recalculating the probability 510 of hypothesis Hl, child hypothesis H3' (having probability 610') will give a different arrangement of reference positions to that of child hypothesis H4' (having probability 620'). Calculating the new likelihood separately ensures that the overall probability of the entire branch reflects its own unique set of beliefs.

As shown in Fig. 7, recalculating the probability 610' for hypothesis H3' includes generating a new circle 710 having a center at device 2 located at position E and a radius which is equal to the measured distance between the device 2 (and/or node E) and the device 1 (and/or node D). The intersections of this circle 710 with previously generated circles 530, 540 (as described in connection with Fig. 5), as well as other intersections of the three circles 530, 540, 710 are evaluated. Intersections that have a low probability, i.e., are far away from possible nodes or locations (e.g., location D) of device 1 are pruned or discarded, and an average intersection point 750 is determined from the remaining intersections near the possible location D, for example, to provide improved trilateration. The distance from the intersection point 750 of the three generated circles 530, 540, 710 to device 1 (position D) is less than the distance from the intersection point 550 to device 1 (position D) shown in Fig. 5. Thus, the recalculated probability 510' of device 1 being at position D (i.e., hypothesis Hl') is greater than the probability 510 of 0.75 for hypothesis Hl, resulting in a larger overall probability 610' for hypothesis H3' of 0.57 (as shown in Fig. 7) which is greater than previously calculated overall probability 610 of 0.50 for hypothesis H3, as shown in Fig. 6. Accordingly, it is more likely that the correct position of device 1 is location D and the correct position of device 2 is location E. That is, once the recalculated probabilities are factored in to the overall probability for each branch, it should be noted that the overall trilateration result for hypothesis H3' has improved, increasing its overall likelihood 610' to 0.57 as shown in Fig. 7 (from 0.5 shown in Fig. 6). Similarly, probabilities 620', 630', 640' are recalculated to yield 0.24, 0.02 and 0.21 for the other three hypotheses H4', H5', H6', respectively, via similar trilateration, using the additional circles 720, 730 ,740 in combination with circles 530, 540.

As shown in Fig. 7, the trilateration results 620', 640' for hypothesis H4' and H6' remains virtually unchanged at 0.24, and 0.21, respectively (as compared to probabilities 620, 640 shown in Fig. 6). Hypothesis H5' inherits a worse trilateration result from hypothesis H2' reducing its probability 630' to just 0.02 as shown in Fig.7 (from the probability 630 of 0.05 shown in Fig 6.). The recalculation indicates that hypothesis H3' is the most internally consistent set of assignments, namely, device 1 at location D, device 2 at location E, while devices 4 and 6 are at locations A and B, respectively. As shown in Fig. 7, the worst trilateration 755 is for hypothesis H2', where it is assumed that device 2 is located at position D and device 1 is located at position E. This re-evaluation technique may be applied as each new level of created hypotheses, constantly feeding back information to improve the parent hypotheses for every hypothesis in the tree. In fact, it is the probabilities of these leaf or child hypotheses H3, H4, H5 and H6 that are most significant. It is not in actually necessary to modify the probabilities of intermediate hypotheses, provided the overall total probability is independently recalculated along each branch of the decision tree. By postponing the re-evaluation until the tree has been fully completed, the amount of processing time can be greatly reduced. However, it may be beneficial to re-evaluate every few levels during the construction of the tree in order to make better pruning decisions, which depends on good estimates of probability. Thus, the better the probability estimates, the more likely that proper pruning is performed. Accordingly, it is desirable to recalculate probability before pruning.

It may seem that this example causes only subtle changes to the probabilities, but this technique can be applied when many levels of hypotheses have been built. The ability to feed backwards not just one reference point, as in the example given, but a number of reference points improves the reliability of the trilateration further. Also subtle changes in probability when calculated over a number of levels may cause more dramatic changes, as the revised probabilities are fed back up the hypothesis structure from parent to child until they reach the top level.

Figs. 8-10 show another example of triangulation to determine device location in a network, i.e., to assign devices 1 to 10 (shown in Fig. 10) to nodes or locations A to J, shown in the array 800 Fig. 8.

Fig. 9 shows a typical triangulation result 900 as the decision tree is constructed. Device 5 is considered as a plausible assignment for location E, but as the assignments for locations F to J have yet to be established. Consequently, the triangulation result shown by averaged intersection points 910, 920 has a poor geometry, as indicated by two possible positions 910, 920 for Device 5, where one average intersection point or position 910 is close to location E, while the other average intersection point 920 is close to location F. Thus, a typical triangulation without re- evaluation leads to a rather low triangulation result, even though one of the assignments, namely, assignment of device 5 to locations E is in fact the correct one. Fig. 10 shows the mapping 1000 which takes into account re-evaluating the intersection points once the remaining positions have been placed by child hypotheses. The use of the new information has expanded the set of reference positions for trilateration, improving the geometry and therefore improving the reliability of the probability calculation. In particular, both possible outcomes or intersection points 1010, 1020 for Device 5 are at the correct location, namely, location E. During construction of the hypothesis tree, re-evaluation provides accurate estimates of probability reduce the chances of the correct solution being pruned. Re-evaluation at the completion of the tree provides the most accurate probabilities when determining the most plausible solution. The present systems and methods for re-evaluating outcomes by feeding information back in reverse to improve the estimated probability of earlier hypotheses may be applied wherever decisions need to be made in the face of uncertainty. The re- evaluation technique may significantly improve the estimation of probability for each alternative solution.

It should be understood that the various components of the re-evaluation system, such as the various nodes, target devices, processor 410, memories 440, 450, hard disk 430, various circuit cards such as the network card 450 and display 460 shown in Fig. 4, for example, may be interconnected through any type of bus, for example, or operationally coupled to each other by any type of link, including wired or wireless link(s), for example. Further, the processor 410, memories 440, 450, and hard disk 430 may be centralized or distributed among the various system components where, for example, each target device may have its own controller or processor and memory.

Of course, as it would be apparent to one skilled in the art of communication in view of the present description, various elements may be included in the system or network components for communication, such as transmitters, receivers, or transceivers, antennas, modulators, demodulators, converters, duplexers, filters, multiplexers etc. The communication or links among the various system components may be by any means, such as wired or wireless for example. The system elements may be separate or integrated together, such as with the processor. As is well-known, the processor executes instructions stored in the memory, for example, which may also store other data, such as predetermined or programmable settings related to system control. Various modifications may also be provided as recognized by those skilled in the art in view of the description herein. The operation acts of the present methods are particularly suited to be carried out by a computer software program. The computer software program, for example, may contain modules corresponding to the individual steps or acts of the methods. The application data and other data are received by the controller or processor for configuring it to perform operation acts in accordance with the present systems and methods. Such software, application data as well as other data may of course be embodied in a computer-readable medium, such as an integrated chip, a peripheral device or memory, such as the memory or other memory coupled to the processor of the controller or light module.

The computer-readable medium and/or memory may be any recordable medium (e.g., RAM, ROM, removable memory, CD-ROM, hard drives, DVD, floppy disks or memory cards) or may be a transmission medium (e.g., a network comprising fiber-optics, the world- wide web, cables, and/or a wireless channel using, for example, time-division multiple access, code-division multiple access, or other wireless communication systems). Any medium known or developed that can store information suitable for use with a computer system may be used as the computer-readable medium and/or memory.

Additional memories may also be used. The computer-readable medium, the memory, and/or any other memories may be long-term, short-term, or a combination of long- and-short term memories. These memories configure the processor/controller to implement the methods, operational acts, and functions disclosed herein. The memories may be distributed or local and the processor, where additional processors may be provided, may be distributed or singular. The memories may be implemented as electrical, magnetic or optical memory, or any combination of these or other types of storage devices. Moreover, the term "memory" should be construed broadly enough to encompass any information able to be read from or written to an address in the addressable space accessed by a processor. With this definition, information on a network, such as the Internet, is still within or part of the memory, for instance, because the processor may retrieve the information from the network.

The processors and the memories may be any type of processor/controller and memory. The processor may be capable of performing the various described operations and executing instructions stored in the memory. The processor may be an application- specific or general-use integrated circuit(s). Further, the processor may be a dedicated processor for performing in accordance with the present system or may be a general-purpose processor wherein only one of many functions operates for performing in accordance with the present system. The processor may operate utilizing a program portion, multiple program segments, or may be a hardware device utilizing a dedicated or multi-purpose integrated circuit. Finally, the above-discussion is intended to be merely illustrative of the present system and should not be construed as limiting the appended claims to any particular embodiment or group of embodiments. Thus, while the present system has been described in particular detail with reference to specific exemplary embodiments thereof, it should also be appreciated that numerous modifications and alternative embodiments may be devised by those having ordinary skill in the art without departing from the broader and intended spirit and scope of the present system as set forth in the claims that follow. The specification and drawings are accordingly to be regarded in an illustrative manner and are not intended to limit the scope of the appended claims.

In interpreting the appended claims, it should be understood that: a) the word "comprising" does not exclude the presence of other elements or acts than those listed in a given claim; b) the word "a" or "an" preceding an element does not exclude the presence of a plurality of such elements; c) any reference signs in the claims do not limit their scope; d) several "means" may be represented by the same or different item or hardware or software implemented structure or function; e) any of the disclosed elements may be comprised of hardware portions (e.g., including discrete and integrated electronic circuitry), software portions (e.g., computer programming), and any combination thereof; f) hardware portions may be comprised of one or both of analog and digital portions; g) any of the disclosed devices or portions thereof may be combined together or separated into further portions unless specifically stated otherwise; and h) no specific sequence of acts or steps is intended to be required unless specifically indicated.

Claims

CLAIMS:

1. A method for determining probabilities in a decision tree (700) comprising the acts of: generating a first hypothesis (Hl) having a first probability (510) of a first device (1) being at a first location (D) based on distances from the first device (1) to two devices (4, 6); generating a second hypothesis (H3) having a second probability (610) for a second device (2) being at a second location (E) based on distances from the second device (2) to the first device (1) and to the two devices (4, 6); and recalculating the first probability (510) to form a recalculated first probability (510') based on distances from the first device (1) to the second device (2) and to the two known devices (4, 6).

2. The method of claim 1 , further comprising the acts of: generating a combined probability (610') for the second device (2) by combining the recalculated first probability (510') with the second probability (610); and assigning the second device (2) to the second position (E) if the combined probability (610') is greater than at least one of a predetermined value and another combined probability of the second device (2) being at another position.

3. The method of claim 1, further comprising the acts of: generating a first circle (530) having a center at a third location of a third device (4) of the two devices (4, 6) and a radius being a distance from the first device (1) to the third device (4); generating a second circle (540) having a center at a fourth location of a fourth device (6) of the two devices (4, 6) and a radius being a distance from the first device (1) to the fourth device (6); wherein the first probability (510) is related to a distance from an intersection point (550) of the first circle (530) and the second circle (540) to the first location (D).

4. The method of claim 1, further comprising the acts of: measuring distances from at least one of the two devices (4, 6) to other devices; and selecting the first device (1) for location determination, wherein the first device (1) is a closest device to the two devices (4, 6).

5. A system for automatic commissioning of devices, comprising a processor (410) configured to: generate a first hypothesis (Hl) having a first probability (510) of a first device (1) being at a first location (D) based on distances from the first device (1) to two devices (4, 6); generate a second hypothesis (H3) having a second probability (610) for a second device (2) being at a second location (E) based on distances from the second device (2) to the first device (1) and to the two devices (4, 6); and recalculate the first probability (510) to form a recalculated first probability (510') based on distances from the first device (1) to the second device (2) and to the two known devices (4, 6).

6. The system of claim 5, wherein the processor is further configured to: generate a combined probability (610') for the second device (2) by combining the recalculated first probability (510') with the second probability (610); and assign the second device (2) to the second position (E) if the combined probability (610') is greater than at least one of a predetermined value and another combined probability of the second device (2) being at another position.

7. The system of claim 5, wherein the processor is further configured to: generate a first circle (530) having a center at a third location of a third device (4) of the two devices (4, 6) and a radius being a distance from the first device (1) to the third device (4); and generate a second circle (540) having a center at a fourth location of a fourth device (6) of the two devices (4, 6) and a radius being a distance from the first device (1) to the fourth device (6); wherein the first probability (510) is related to a distance from an intersection point (550) of the first circle (530) and the second circle (540) to the first location (D).

8. The system of claim 5, wherein the processor is further configured to: measure distances from at least one of the two devices (4, 6) to other devices; and select the first device (1) for location determination, wherein the first device (1) is a closest device to the two devices (4, 6).

9. A computer readable storage medium comprising a program product operative to cause a processor to: generate a first hypothesis (Hl) having a first probability (510) of a first device (1) being at a first location (D) based on distances from the first device (1) to two devices (4, 6); generate a second hypothesis (H3) having a second probability (610) for a second device (2) being at a second location (E) based on distances from the second device (2) to the first device (1) and to the two devices (4, 6); and recalculate the first probability (510) to form a recalculated first probability (510') based on distances from the first device (1) to the second device (2) and to the two known devices (4, 6).

10. The computer readable storage medium of claim 9, wherein the processor is further configured to: generate a combined probability (610') for the second device (2) by combing the recalculated first probability (510') with the second probability (610); and assign the second device (2) to the second position (E) if the combined probability (610') is greater than at least one of a predetermined value and another combined probability of the second device (2) being at another position.

11. The computer readable storage medium of claim 9, wherein the processor is further configured to: generate a first circle (530) having a center at a third location of a third device (4) of the two devices (4, 6) and a radius being a distance from the first device (1) to the third device (4); and generate a second circle (540) having a center at a fourth location of a fourth device (6) of the two devices (4, 6) and a radius being a distance from the first device (1) to the fourth device (6); wherein the first probability (510) is related to a distance from an intersection point (550) of the first circle (530) and the second circle (540) to the first location (D).

12. The computer readable storage medium of claim 9, wherein the processor is further configured to: measure distances from at least one of the two devices (4, 6) to other devices; and select the first device (1) for location determination, wherein the first device (1) is a closest device to the two devices (4, 6).