Global positioning system positioning method and computer program product

Abstract

A method of creating a correction function for improving the accuracy of a global positioning system device, the method collecting a plurality of time samples at a plurality of known locations, wherein each time sample consists of global positioning system coordinates and associated satellite data from a plurality of satellites. The satellite data includes or allows for determination of (i) the satellite azimuth and elevation of an associated satellite, (ii) the signal-to-noise ratio of a received signal from the associated satellite; and optionally (iii) the pseudo-range. For each time sample, a respective error between the known location and the corresponding global positioning system coordinates is calculated, and a deep learning / machine learning technique is applied to the plurality of time samples to create an error correction function as a function of the respective global positioning system coordinates and the satellite data.

Description

TECHNICAL FIELD

[0001] The present invention relates to a navigation system and method, particularly for pedestrians. BACKGROUND

[0002] With the advent of smart phones, Global Positioning System (GPS) has become a major navigation method widely used by pedestrians and drivers. Most importantly, pedestrians in urban areas use smart phone GPS instead of traditional paper maps.

[0003] However, mainly in urban areas, pedestrians find it inconvenient, difficult, and sometimes impossible to use GPS due to the low positioning accuracy of mobile phone GPS systems. In addition, pedestrians do not have the orientation data needed for navigation due to the low accuracy of the magnetometer of the mobile phone.

[0004] The main reason for the low accuracy of GPS systems in urban areas is that high-rise buildings obstruct the line of sight of the satellites. In addition, signals from satellites without direct line of sight are reflected by high-rise buildings and are received by the GPS of the pedestrian and misinterpreted, resulting in large errors in the positioning reading. This phenomenon is called "multiple path reflection".

[0005] While multiple path reflection affects both motor vehicles and pedestrians, it is less noticeable in motor vehicles because they constantly move at much higher speeds than pedestrians, the respective satellite visibility constantly and quickly changes, and thus the errors can be smoothed. In addition, since the position of cars and other road vehicles is limited to the road, techniques such as "snap to map" and the use of Inertial Measurement Unit (IMU) data and other information are used. In addition, the direction can be known with high accuracy through GPS motion and velocity.

[0006] This deficiency has become a major problem for companies such as Uber and Lyft, where the success of a driver in picking up a passenger depends largely on the accuracy of the location reported by the passenger's GPS. Drivers and customers can miss each other because the customer is on the other side of the street or at a crossroads.

[0007] Attempts have been made to solve this problem, including 3D modeling of surrounding buildings, ignoring satellites with multiple reflections, phase analysis, and statistical methods. However, to our knowledge, no practical, cost-effective solution has been proposed.

[0008] There is a large body of prior art relating to the positioning of autonomous vehicles, and the optimization of the positioning strategy used by an autonomous vehicle based on the driving environment (e.g. the geographical area in which the autonomous vehicle is travelling, the time of day, the speed of the autonomous vehicle, etc.). In conventional systems, a map database can be used to snap an initial position computed from navigation satellite system data to a physical geographical object, such as a road, so that the final output is displayed by a navigation device. For example, in the manner disclosed in US20110257885, the coarse position provided by a GPS satellite can be significantly improved, enough to guide an autonomous or driven vehicle.

[0009] US20170307761 discloses a method of cooperatively determining positioning errors of satellite-based navigation systems. If the number of receivers is large enough, less accurate receivers (such as smartphones) that are located within a geographical area, whose precise position is unknown, can help produce accurate atmospheric error corrections.

[0010] US20180124572 relates to the use of local correction information in a mobile object network to correct GPS-based position information. If two receivers share the same set of visible satellites (i.e. process received signals from the same set of satellites to derive a positioning solution), the two receivers should experience similar positioning errors. The set of satellites used by a global navigation satellite system / global positioning system (GNSS / GPS) receiver that computes geographical positioning information is dynamic and constantly changing due to several factors.

[0011] US20190147610, published in the name of Uber Technologies, Inc., discloses systems and methods for detecting and tracking objects based on sensor data received from one or more sensors, the sensor data being fed to one or more machine learning models, the one or more machine learning models including one or more first neural networks configured to detect one or more objects based at least in part on the sensor data and one or more second neural networks configured to track the one or more objects through a sequence of sensor data.

[0012] In summary, the prior art teaches techniques for correcting satellite errors and recognizes that error corrections associated with a satellite serving multiple receivers in the same geographic area will apply to all receivers in that area. The prior art also discloses collating data from a large number of vehicles traversing a geographic area and using data received therefrom to improve maps that allow autonomous vehicles to safely navigate the same roads. The prior art also addresses the need for self-driving taxis to locate stationary passengers and provides navigation techniques for moving pedestrians, recognizing that traditional correction methods applied to vehicles do not always apply to pedestrians. The prior art discusses the use of deep learning and neural networks to improve map data.

[0013] However, the art does not appear to suggest processing a large number of GPS positioning errors by applying deep learning / machine learning techniques to a plurality of time samples to create a respective correction function for a plurality of known locations as a function of respective GPS coordinates and satellite data.

[0014] Nor does the art suggest using error correction data associated with satellites within a geographic area to make corresponding or derivative corrections to GPS navigation systems for pedestrians carrying mobile devices such as smartphones. SUMMARY

[0015] It is therefore an object of the present invention to provide a method that addresses this need.

[0016] This object is achieved according to the present invention by a two-part process. The first part is a learning method that creates an error correction function for improving the accuracy of GPS devices within a region of interest, while the second part provides a method for using the error correction function that has been determined to improve the accuracy of GPS coordinates received within the region of interest. In the context of the specification and the appended claims, the term "GPS device" is used to refer to any device having a built-in GPS module. The GPS device is typically a smartphone, but can also be any other suitable device configured for GPS positioning.

[0017] Thus, in a first aspect of the present invention, the present invention provides a method of creating a correction function for improving the accuracy of a Global Positioning System (GPS) device, the method comprising:

[0018] collecting a plurality of time samples at a plurality of known locations, wherein each time sample consists of GPS coordinates and associated satellite data from a plurality of satellites, wherein the satellite data includes or is sufficient to determine (i) an azimuth and an elevation of an associated satellite, and (ii) a signal-to-noise ratio of a received signal from the associated satellite;

[0019] for each time sample, calculating a respective error between the known position and the corresponding GPS coordinates; and

[0020] by applying a deep learning / machine learning technique to the plurality of time samples to create an error correction function as a function of the respective GPS coordinates and the satellite data.

[0021] In a second aspect of the application, the application provides a method for improving the accuracy of GPS coordinates within a region of interest, wherein an error correction function for the region of interest has been obtained, the method comprising:

[0022] inputting the GPS coordinates and associated satellite data into the correction function to obtain a position with improved accuracy.

[0023] The two processes are independent of each other. In particular, while the second process cannot be implemented until an error correction function for the desired region of interest has been derived, once the error correction function exists, the second process can be implemented in an independent manner. In this case, the two processes are executed sequentially. However, they can also be executed simultaneously, with the learning process being executed at the same time as the second aspect, either for a different region of interest, or by continually collecting new data and applying the deep learning technique to an ever-expanding data set to refine the error correction function.

[0024] In some embodiments, the plurality of time samples is obtained by collecting the GPS coordinates and associated satellite data obtained by on-board GPS devices and enhanced accuracy positioning of motor vehicles travelling in an extended urban area, each of the time samples consisting of the GPS coordinates and associated satellite data obtained by the on-board GPS devices and enhanced accuracy positioning.

[0025] In concept, the principle of the present invention is to repeat the above method for a plurality of locations within a desired geographical area over time, so as to obtain a plurality of time samples for each location. GPS coordinates are the coordinates of a GPS device obtained typically by triangulating between three or more satellites and represent a coarse location, for which the present invention is used to improve the accuracy. GPS data is determined from a plurality of satellite signals comprising the time of each satellite transmitted signal. The GPS device records the time of receipt of the signal, the difference between the time of transmission and receipt reflects the time of flight between the satellite and the GPS device, which when multiplied by the speed of light yields the pseudo-range between the satellite and the receiver. Since the GPS device's clock is not as accurate as the high precision atomic clocks of the satellites, this is referred to as a "pseudo-range". Therefore, at least four satellites are required to solve the coarse positioning problem of the GPS device in a known manner. The resulting data is stored in a database and analyzed to derive a function for each coarse location which when applied to the GPS coordinates and using the satellite data obtained for the coarse location, corrects the GPS coordinates and yields a more accurate location. The accuracy can be improved by an order of magnitude, such that if the coarse location is correct to within 30 meters, the location corrected by the present invention will be accurate to within 3 meters. It is understood that in practice, it can not be possible to map every coordinate in space. However, it is assumed that over time, a sufficient number of points in close proximity to each other are mapped, so that the error correction function calculated is equally applicable to the location of any point in space which deviates slightly from the mapped points.

[0026] It is understood that each time sample can be comprised of different GPS coordinates and different satellite data. This means that different GPS coordinates with different associated satellite data can be related to the same corrected location. The derivation of the error correction function is such that it will give the same corrected location regardless of which set of GPS coordinates and associated satellite data are applied.

[0027] The GPS coordinates and associated satellite data and positioning errors of a plurality of points within the area of interest are stored in a database for subsequent processing. In some embodiments, the database is based on data collected by a crowdsourcing application such as Waze TMThe data collected by navigation systems of vehicles is compiled. In any case, such systems collect coarse locations, i.e. relevant GPS coordinates, from the vehicle GPS device and transmit enhanced location data to the vehicle. Thus, the only additional information needed is the satellite data corresponding to each satellite from which the signal of each coarse location is obtained. Of course, said information is known to the on-board GPS, which can be collected from the on-board GPS and used to compile the database and derive the correction function of the present application. In use, the coarse location received from the GPS device is fed into the database together with the satellite data and the enhanced location coordinates. This database is used to derive the correction function using deep learning techniques.

[0028] Even if the pedestrian carries a smartphone with a built-in GPS device, the pedestrian can at most obtain a coarse location using the Waze TM navigation system, as described above. This is because navigation systems apply a higher precision to vehicles, which can only travel along prescribed paths, and cannot be applied to pedestrians who can freely wander around. Furthermore, as described above, the errors caused by multipath reflections have a greater impact on pedestrian devices in urban areas, which are stationary or travel slower than motor vehicles. However, according to the present application, since the correction function is based on and applied to coarse locations, it can equally be applied to the GPS device in a pedestrian smartphone to derive a more accurate location. Likewise, RADAR, LIDAR and other enhancement technologies being developed by Advanced Driver Assistance Systems (ADAS) can also be used to determine enhanced positioning accuracy. The correction function can be downloaded to the pedestrian's smartphone from a remote server in communication with the pedestrian's GPS device; or, if there is sufficient memory, it can be stored in the pedestrian's GPS device.

[0029] The error correction function receives as input a vector composed of a coarse location corresponding to a GPS coordinate and relevant satellite data from which the GPS coordinate is obtained, and produces as output a true location. BRIEF DESCRIPTION OF DRAWINGS

[0030] For the purposes of understanding the present application and to see how it can be put into practice, the embodiments will now be described by way of non-limiting example only with reference to the accompanying drawings, in which:

[0031] Figure 1 is a diagram of a system according to the present application;

[0032] Figure 2A plurality of time samples collected and stored by vehicles at random over time for a region of interest, which can be used to generate a database according to embodiments of the present application, are schematically shown; and

[0033] Figure 3 is a flowchart showing the main operations performed by a method for improving the passenger / driver experience according to embodiments of the present application. DETAILED DESCRIPTION

[0034] Figure 1 is an illustration of a system 10 according to one embodiment of the present application. System 10 shows a pedestrian 11 holding a smartphone 12 in a region of interest, smartphone 12 having a built-in GPS module that receives GPS data from at least three satellites 13, 13' and 13" and uses triangulation to calculate a coarse location in a known manner. In this specification and the appended claims, we refer to the coarse location as the GPS coordinates of the GPS device. Vehicles 14, 14' that randomly drive through the region of interest will likewise receive GPS data from the satellites and determine a coarse location for each vehicle. However, these vehicles are equipped with WAZE TM , SATNAV TM and similar navigation systems, and similar devices that improve the accuracy of the GPS coordinates so as to know the correct or true location of the vehicle. For the sake of clarity, "true" or "correct" does not mean that the corrected location is absolutely accurate, but rather much more accurate than the coarse location based on coordinates alone. Anyone who has used WAZE TM and similar navigation systems knows that they are instructed to turn left at the next intersection, and when they are in front of the intersection, they are instructed to "turn left". It is this level of accuracy that makes navigation systems so reliable and friendly.

[0035] The navigation systems in the vehicles use auxiliary data to improve the accuracy of the coarse location based on satellite data alone, for example, based on a pre-compiled accurate map, and allow correction of the location of the vehicle using known techniques such as snap to map.

[0036] Likewise, RADAR, LIDAR and other enhancement technologies that are being developed by Advanced Driver Assistance Systems (ADAS) can also be used to determine enhanced positioning accuracy.

[0037] Although only two vehicles are shown in the figure, it is understood that in reality, thousands of vehicles are travelling along the routes on the map, e.g. highways, roads, streets, or even off-road, which are accurately mapped and accessible by the vehicle navigation system, either because map data has been pre-loaded, or because they have access to map data online, typically over the Internet 15. The satellite data received by the vehicle navigation system includes or allows determination of the satellite azimuth and elevation angle of each relevant satellite, the signal-to-noise ratio (SNR) of the received signal from the relevant satellite, and optionally other data, such as the pseudo-range (PR).

[0038] The present invention is based on the collection and storage in a time sample database consisting of coarse positions, satellite data and true positions, and the derivation of an error correction function by deep learning from the compilation over time of motor vehicle traffic moving along the mapped routes in the area of interest in which the GPS device is located. To this end, the present invention comprises two different phases, which will now be described.

[0039] Data collection and learning:

[0040] The main operations to be performed by the first flow are now described. A number of GPS errors for a number of specific known positions are collected over time under a variety of different satellite and environmental conditions, which encompass a large number of positioning errors and satellite data.

[0041] Although it is theoretically possible to collect the data by manually mapping the positions in more or less the same way as the original ordnance survey maps were compiled, in order to quickly and automatically obtain sufficient data in an extended area, data can be collected over time from motor vehicles travelling in the desired area. Figure 2 A number of time samples randomly obtained by motor vehicles passing through a number of known positions in the area of interest are schematically shown, each known position collecting a number of time samples over a significant period of time in the area of interest. Thus, by way of simple illustration, it shows three positions x1, x2 and x3 through which vehicles pass randomly, and the coarse GPS positions, satellite data and enhanced positions are transmitted to the database server. It can be seen that, in the given time segment, six vehicles marked v 11 …v 61 pass through position x1, seven vehicles marked v 12 …v 72 pass through position x2, and five vehicles marked v 13 …v 53 pass through position x3. Although not important, it can be seen that Figure 2It is noted that for each known location, the actual time of each sample can vary greatly. The GPS navigation system in the vehicle is constantly receiving coarse GPS positions and satellite data and deriving enhanced positions. Likewise, although the vehicle has discrete markers, this is for clarity. In reality, any given vehicle will pass through multiple locations, so not all vehicles reaching three discrete locations xi, x2, and x3 are different. In fact, a vehicle can also pass through the same known point more than once, for example, on the way there and on the way back, or due to the same vehicle repeatedly driving in subsequent time periods. The information collected includes coarse GPS positions, satellite status data, and true positions. This allows the localization error to be determined. Since most motor vehicles today have GPS navigation systems, motor vehicles cover most urban areas, so data can be collected over time for a large area of interest. Thus, various data corresponding to a large number of locations in a large urban area are collected, including coarse and corrected positions, localization errors, and related satellite data. These data are used as input to derive an error correction function using deep learning techniques. The error correction function is configured to receive a vector consisting of coarse positions corresponding to GPS coordinates and related satellite data (as input) and produce true positions (as output). As more vehicles pass through known points within the area of interest, their data can be collected and stored, allowing the error correction function to be further refined over time.

[0042] Estimating GPS deviation using deep neural networks (DNN)

[0043] We assume that at a given point at a known location (x, y, z), we get an estimated position (x', y', z') produced by a GPS system. The deviation between the true position and the position produced by the GPS (x-x', y-y', z-z') is called the GPS deviation (GPS-deviation). The task we consider is to estimate the GPS deviation in order to correct the position produced by the GPS system and obtain the correct position as accurately as possible.

[0044] This task can be accomplished by standard methods of training a Deep Neural Network (DNN). One example of training a DNN for this task can be based on He, K, Zhang, X, Ren, S, Sun, J. 2015 "Deep Residual Learning for Image Recognition" arXiv: 1512.03385 (He et al.) as follows. The network input is a vector of parameters produced by the GPS system (GPS data), including satellite positions, signal strengths, time of measurement, and other possible parameters. Such data is collected multiple times for each given location. The DNN output is an estimate of the bias, for example, represented as a probability distribution over a set of biases. The training is done using a loss function, for example, the cross entropy between the known biases and the estimated biases produced by the DNN. One possible state-of-the-art architecture for this task can be a ResNet DNN (as described by He et al.) with sufficient depth, using standard training procedures, for example, splitting the data into training and test sets, searching for a good learning rate, using batch normalization, and so on. In order to obtain sufficient amount of data to train the network, the training process can use data from multiple different locations, multiple times. It is worth noting that although the method described by He et al. is applied to images, it is equally applicable to the general architecture of the present application.

[0045] Correction:

[0046] The correction model is used to correct the GPS error of any point, as a function of the satellite data (as defined above). Thus, in use, a navigation system or application in a GPS device such as a smartphone within a region of interest receives the coarse GPS position and the associated satellite data, obtains the correction function and applies it to the coarse GPS coordinates in order to derive the corrected position.

[0047] Application

[0048] Deriving a person's orientation using a handheld digital map device

[0049] While digital maps greatly simplify navigation for pedestrians, the need for a pedestrian to correctly orient the map remains a common shortcoming. In a traditional printed map, the user identifies his or her position on the map, identifies landmarks (such as streets), and then aligns the landmarks on the map with the landmarks in the real scene in order to correctly align the map with the real scene. Smartphones attempt to do this using inertial magnetic units (IMUs) that attempt to align an internal magnetometer used as a compass with true north so that a user standing in a known location knows whether to turn left or right, or move forward or backward.

[0050] In practice, as is well known to tourists trying to navigate an unfamiliar place, this is not reliable, and it is common for a user to realize that he or she has taken a wrong turn only after walking for some time and encountering a landmark (such as a street shown on the map) in the opposite direction. This also applies to navigation software that provides voice instructions.

[0051] In one application, the present invention uses a smartphone with an integral camera to image a scene with identifiable landmarks, and points the camera of the smartphone at the landmark. When correctly aligned, an application in the smartphone will be manually initiated by the user to find the landmark in an image of Street View. This enables the smartphone application to determine the position of the landmark, and since the position of the user corresponds to the position of the smartphone, the application is able to determine the azimuth of the landmark relative to the user's position.

[0052] Thus, in the case where the user device is a smartphone with a built-in GPS device, a software application stored in the smartphone determines the direction by the following process:

[0053] i. determining the position of the smartphone using the GPS device;

[0054] ii. pointing a line-of-sight unit with an IMU at one specific object in the real scene;

[0055] iii. identifying an image of the object on an image of Street View displayed on the screen of the smartphone;

[0056] iv. extracting the position of the object from a database of Street View;

[0057] v. calculating the azimuth of the object relative to the position of the smartphone to allow a user holding the smartphone to position himself in space relative to the object.

[0058] Note that "Street View" is the name of a proprietary program of Google, Inc. Since Google, Inc. has invested a great deal of money in the development of Street View, and it is readily available, the present invention prefers to use Google's Street View. However, any digital map database

[0059] Any digital map database that resolves landmarks to street level is available, and therefore in the full text of the appended claims, the term "Street View" is not intended to limit the scope of the claims to Google's Street View map, but to any digital map database with similar functionality.

[0060] Improving the experience of the driver / passenger

[0061] In one embodiment, the present invention can be used to allow a passenger waiting at a street corner or other location to communicate an accurate location to a taxi driver equipped with a navigation system that can achieve an enhanced positioning so that the taxi driver knows exactly where to meet the passenger. Typically, the passenger uses his own mobile device to obtain his own location and then communicates it to the taxi driver. But for the reasons set out above, the location obtained by the passenger's mobile device is prone to error. Thus, even if the taxi arrives at a location close to the passenger, the taxi driver can not be able to identify the passenger. In practice, this is usually resolved by the driver calling the passenger or vice versa and providing appropriate directions. But this is both inconvenient and time consuming and is not feasible when the taxi is an autonomous vehicle.

[0062] The present invention provides a remedy because when the taxi arrives within a pick-up distance of the passenger, it can be assumed that the GPS positioning error corresponding to the location of the taxi also applies to the passenger and can therefore be used to correct the passenger's GPS positioning. Thus, the taxi driver receives from the passenger a coarse GPS location and his satellite data, and when the satellite data received from the passenger matches the satellite data of the taxi, the correction is applied, enabling him to locate the accurate position of the passenger without the need for verbal instructions.

[0063] More generally, this aspect of the present invention provides a method of locating a first entity by a second entity, the first and second entities carrying first and second GPS devices respectively, the second entity having a navigation system that provides an enhanced accuracy positioning of the second entity based on the GPS coordinates of the second GPS device. Figure 3 is a flowchart showing the main operations in such a method performed by the second entity:

[0064] i. receiving respective GPS coordinates and associated satellite data of the first GPS device, wherein the satellite data comprises or allows to determine (i) the satellite azimuth and elevation of one associated satellite, (ii) the signal-to-noise ratio of the received signal from the associated satellite, and (iii) optionally, other data, such as pseudo-range;

[0065] ii. comparing the respective satellite data of both GPS devices when the second GPS device is in proximity to the first GPS device;

[0066] iii. determining an offest between the GPS coordinates of the second GPS device and the enhanced accuracy positioning of the second entity when the respective satellite data of both GPS devices substantially match;

[0067] and

[0068] iv. applying the offest to the GPS coordinates of the first GPS device to better estimate the correct position of the first GPS device.

[0069] In particular, it should be noted that features described with reference to one or more embodiments are described by way of example and not by way of limitation. Thus, optional features described with reference to some embodiments are presumed to be equally applicable to all other embodiments unless otherwise stated or unless a particular combination is obviously not allowed.

[0070] It is also to be understood that the system according to the present application can be a suitably programmed computer. Likewise, the present application encompasses a computer program which can be read by a computer for carrying out the method of the present application. The present application further encompasses a machine-readable storage which indeed contains a program of instructions which can be executed by a machine for carrying out the method of the present application. While the computer is typically the processing unit in a mobile phone, it is not limited thereto. It can be any other handheld or head-mounted device. Handheld refers to a device which is held in the hand in normal mode of use.

Claims

1. A method for creating a correction function, the correction function being used to improve the accuracy of a Global Positioning System (GPS) device, the method comprising: Multiple time samples are collected at multiple known locations, each time sample consisting of GPS coordinates and associated satellite data from multiple satellites, wherein the satellite data includes or allows determination of (i) the azimuth and elevation angles of an associated satellite, and (ii) the signal-to-noise ratio of the received signals from the associated satellites; For each time sample, calculate the respective error between the known location and the corresponding GPS coordinates; and Deep learning / machine learning techniques are applied to the multiple time samples to create error correction functions, which serve as functions of the respective GPS coordinates and satellite data.

2. The method of claim 1, wherein the error correction function is created by collecting multiple time samples from a motor vehicle traveling in an extended urban area and equipped with an onboard GPS device and enhanced precision positioning, each of the multiple time samples consisting of GPS coordinates obtained by the onboard GPS device and enhanced precision positioning, and associated satellite data.

3. The method of claim 1, wherein the satellite data includes or allows for the determination of (iii) pseudorange.

4. A method for improving the accuracy of Global Positioning System (GPS) coordinates within a region of interest, comprising obtaining an error correction function for the region of interest using a GPS device according to claim 1, wherein the method for improving the accuracy of GPS coordinates within the region of interest comprises: The GPS coordinates and associated satellite data are input into the correction function to obtain a position with improved accuracy.

5. The method of claim 4, wherein the error correction function is stored on the global positioning system device.

6. The method of claim 4, wherein the error correction function is downloaded to the GPS device from a remote server communicating with the GPS device.

7. A method for improving positioning using a handheld smartphone with an integrated Global Positioning System (GPS) device, the method comprising: The location of the smartphone is determined by the global positioning system device using the method of any one of claims 4 to 6; Point the line-of-sight unit with an inertial measurement unit to the exact object in the region of interest; Identify the image of the object on the street view image displayed on the smartphone screen; Extract the location of the object from the street view database; Calculate the azimuth angle of the object relative to the smartphone to allow the user holding the smartphone to locate themselves in space relative to the object.

8. A computer program product having a memory storing program instructions, which, when run on a processor of the global positioning system device, execute the method according to any one of claims 4 to 6.

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