JP2663265B2 - Navigation device - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION (Industrial application field) The present invention relates to a navigation device for a vehicle, and more particularly, to a satellite-based positioning means for receiving a radio wave from a satellite and recognizing a current position of the vehicle, a geomagnetic field, and a traveling distance. The present invention relates to a navigation device provided with travel history positioning means for detecting a travel history based on the travel history and detecting a current position based on the travel history. (Prior Art) As a car navigation device, for example,
As disclosed in Japanese Patent Application No. 58-70117, there is known an apparatus that displays a current position of a vehicle and a map of its surroundings on a screen of a display device to provide travel guidance. As means for recognizing the current position of a vehicle in such a navigation device, a device utilizing a direction sensor such as a geomagnetic sensor has already been put to practical use. That is, the traveling distance and the direction of the vehicle from a certain reference point are detected by the vehicle speed sensor and the direction sensor, thereby recognizing the current position of the vehicle. Further, it is considered that the azimuth is calculated by detecting the rotation difference between the left and right wheels, the steering angle of the steering wheel, and the like, without using the azimuth sensor. However, in such a conventional current position recognizing means, the current position of the vehicle is calculated by integrating a traveling distance corresponding to a change in azimuth in accordance with traveling from a reference point, that is, from the reference point. Since the current position is measured as a relative position with respect to the reference point based on the traveling history, accuracy decreases due to a measurement error of a traveling distance and an azimuth, and the accuracy decrease increases as the distance from the reference point increases.
The means for measuring the current position based on the running history from such a reference point is referred to as running history positioning means. From the above, it is conceivable that the current position of the vehicle is measured as an absolute position using radio waves emitted from a satellite. For example, the Global Positioning System (hereinafter referred to as GP)
It is conceivable to measure the current position of the vehicle as an absolute position by using S (referred to as S). This GPS can measure the current position of the vehicle with a measurement accuracy of about 30 meters based on radio waves emitted from four artificial satellites (called NAVSTAR) (C / A that is open to the public) Code). In a vehicle using a navigation device equipped with satellite-based positioning means for detecting the current position by such a GPS, for example, a map of a traveling area is displayed on a screen of an in-vehicle CRT or the like, and the satellite usage is displayed on the map. The current position detected by the positioning means is displayed. When the vehicle travels, its current position also moves. Accordingly, this movement needs to be displayed on the screen. For this reason, the navigation device repeatedly receives radio waves from each satellite at predetermined intervals, detects the current position for each reception, and displays the movement of the vehicle on the screen. ing. (Problems to be Solved by the Invention) When the above navigation device is used, the current position of the vehicle can be detected as an absolute position, so that the problem of the accumulated error as in the travel history positioning means is eliminated. The measurement accuracy of the current position using GPS has a variation of about 30 meters, and this variation is often worsened by the position of each satellite and the reception state of radio waves from the satellite. There is a problem that the measurement error of the current position measured by the above is larger than the measurement error of the current position measured by the traveling history positioning means. In particular, since the measurement error by the travel history positioning means is a cumulative error that increases in proportion to the travel distance, when the travel distance from the measurement start point is short, the measurement error by the satellite-based positioning means tends to increase. (Means for Solving the Problems) As described above, when the current position is measured using the satellite-based positioning means, the current position can be grasped as an absolute position. If the reception condition is not good or the mileage is short,
The present invention has been made in view of the problem that the measurement error of the satellite-based positioning means is larger than the measurement error of the travel history positioning means, and therefore, the navigation device according to the present invention uses radio waves from a plurality of satellites. Satellite-based positioning means for receiving the current position of the vehicle and measuring the current position of the vehicle, and traveling history positioning means for measuring the current position based on the traveling history, and displaying the current position measured by these two positioning means on the display means. In the navigation device for displaying, the magnitude of the measurement error of the current position by the satellite-based positioning means and the magnitude of the measurement error by the travel history positioning means are detected, and the smaller of the two measurement errors is measured. Control means for displaying the current position measured by the means on the display means, and the satellite-based positioning means detected by the control means. The magnitude of measurement error in the standing position, characterized in that used for the measurement is obtained is calculated based on the value determined by the geometrical relationship between said plurality of satellites and the vehicle. The magnitude of the measurement error of the current position by the satellite-based positioning means is calculated by multiplying the user equivalent distance difference by a value determined by a geometric relationship between the plurality of satellites used for the measurement and the vehicle. Can be used. Further, as the magnitude of the measurement error of the current position by the traveling history positioning means, a value calculated by multiplying the traveling distance from the measurement start position to the present by a predetermined coefficient for obtaining the accumulated error can be used. (Operation) When the navigation device according to the present invention having the above-described configuration is used, the measurement of the current position by the satellite-based positioning means and the measurement of the current position by the travel history positioning means are both performed. Measuring error calculating means and traveling history measuring error calculating means, by which the measuring errors by the two positioning means are detected, and the control means detects the current position measured by the measuring means having the smaller measuring error and the current position. Is read as a value indicating the current position, thereby improving the measurement accuracy of the current position. Further, the magnitude of the measurement error of the current position by the satellite-based positioning means is calculated based on a value determined by the geometric relationship between the satellite used for measurement and the vehicle, whereby the measurement by the satellite-based positioning means is performed. Compared to the error calculated based on the level of the radio wave from the satellite, the constant radio wave intensity (strength enough to recognize information) is independent of the radio wave intensity and the type of radio wave (digital or analog). If it can be ensured, the error can be calculated. Further, the magnitude of the measurement error of the current position by the satellite-based positioning means is calculated by multiplying the user equivalent distance difference by a value determined by the geometric relationship between the plurality of satellites used for the measurement and the vehicle. Alternatively, the magnitude of the measurement error of the current position by the traveling history positioning means is calculated by multiplying the traveling distance from the measurement start position to the present by a predetermined coefficient for obtaining the accumulated error, whereby the measurement by the positioning means is performed. The magnitude of the error is set to a length corresponding to the measurement error distance, so that the magnitude of the measurement error can be compared more specifically and accurately. Hereinafter, preferred embodiments of the present invention will be described with reference to the drawings. FIG. 1 shows a vehicle navigation device 1 according to the present invention.
FIG. 3 is an overall configuration diagram showing an example. The navigation device includes a GPS receiver 2 for receiving a radio wave from a satellite, a vehicle speed sensor 4a for detecting a vehicle speed, a geomagnetic sensor 4b for detecting terrestrial magnetism, and a current position of the vehicle based on the radio wave received by the GPS receiver 2. Current position recognition means 3 for recognizing the current position and recognizing the current position from the running history based on the signals from the vehicle speed sensor 4a and the geomagnetic sensor 4b, and various signals received from the current position recognition means 3 And a control device 10 for performing signal control. Further, a storage device 5 composed of a compact disk, a ROM or the like storing map information and the like, and an operation device 7 for performing various key operations are connected to the control device 10 via a decoder 6 and an encoder 8, respectively. , A CRT or the like, and a video RAM 15 are connected via a display control device 14. The GPS receiver 2 and the current position recognizing device 3 constitute satellite-based positioning means 1. On the other hand, the vehicle speed sensor 4a, the geomagnetic sensor 4b, and the current position recognizing device 3 calculate a travel history and a current position based on the travel history. The driving history positioning means 9 for recognizing the information is configured. Further, the storage device 5 stores a map or the like in which contents necessary for traveling guidance of vehicles such as roads and buildings are represented. The operation device 7 is a key switch or the like that can be operated by a driver or the like.
The contents displayed in 16 can be switched. The control device 10 includes an arithmetic circuit 12 and an RO connected thereto.
It consists of a microcomputer with M11a, RAM11b,
The arithmetic circuit 12 is connected to the current position recognition device 3 and the like via an interface 13 as shown in the figure. The control device 10 calculates the current position of the vehicle based on the signal from the current position recognition device 3, retrieves a map around the current position from the storage device 5, and displays the current position on the display 16. It is displayed or stored in the video RAM 15. As described above, there are two types of recognition of the current position by the current position recognition device 3: recognition by the satellite-based positioning means 1 and recognition by the traveling history positioning means 9.
The control device 10 includes a satellite-based measurement calculation unit that calculates a measurement error of the current position by the satellite-based positioning unit 1 and a travel history measurement error calculation unit that calculates a measurement error of the current position by the travel history positioning unit 9. By comparing the magnitudes of the two measurement errors, the value of the current position measured by the positioning means having the smaller measurement error is read, and this position is displayed on the display 16. The magnitude of the measurement error by the satellite-based positioning means 1 is determined by a deterioration coefficient GDOP described later.
(Geomwtrical Dilution Of Precision), and the magnitude of the measurement error by the travel history positioning means 9 is a value proportional to the travel distance. Therefore, the magnitude can be determined by multiplying the travel distance by a ratio generated as an accumulated error. Here, the satellite-based positioning means 1 will be described first. The satellite-based positioning means 1 comprises, for example, 18 to 21 GPS control units, for example, as shown schematically in FIG. 2, which are controlled by, for example, four ground antennas 1b in which a terrestrial main control station 1a is appropriately distributed. Of the satellites within the receivable area (field of view)
It constitutes a GPS user part that measures the current position of the vehicle based on radio waves transmitted from the individual satellites S1 to S4. Incidentally, the measurement accuracy of the satellite-based positioning means 1 is such that the positioning accuracy is reduced by the position of the satellite, the perturbation of the satellite, the state of the ionosphere, etc., or the positioning cannot be performed locally for a very short time. For example, obstacles on the ground, such as traveling in a tunnel, make it difficult to receive necessary radio waves,
Or become impossible. The degree of the decrease in the positioning accuracy in the satellite-based positioning means 1 varies depending on the deterioration coefficient and the electric field strength. That is, the deterioration coefficient is a value determined by the geometric relationship between the satellite used and the vehicle at the time of positioning, and as the deterioration coefficient increases, the positioning error increases and the positioning accuracy decreases. Other factors that lower the positioning accuracy appear as a reduction in the electric field strength. When the deterioration coefficient increases or the electric field intensity decreases, the positioning error increases. This deterioration factor is obtained from the satellite's position data at the time of positioning, which is transmitted from each satellite based on the satellite tracking result of the ground antenna 1b and the reception data of the ground monitoring station 1c, etc. And the electric field strength can be detected by the strength of the radio wave received from the satellite. However, when a radio wave is transmitted as a digital signal, the measurement error does not depend on the magnitude of the electric field strength as long as the electric field strength can be maintained at a constant level. The principle of positioning by GPS is as follows. If there is a clock that is completely synchronized with the transmission point and the reception point of the radio wave, and the transmission signal is controlled by that clock, measuring the reception timing at the reception point will determine the propagation time of the radio wave between the transmission and reception points By multiplying it by the speed of light, the distance between the transmitting and receiving points can be obtained. Now, as shown in FIG. 4, the user's field of view (receivable area) is 3
There are satellites S1, S2, S3, and each satellite S1, S2, S3
Are transmitting distance measurement signals by clocks synchronized with each other. If the reception time of these signals is measured at the receiving point P, the distance between each satellite S1, S2, S3 and the receiving point P is obtained, and the receiving point P is the intersection of three spherical surfaces centering on each satellite S1, S2, S3. Can be obtained as However, synchronizing the clock at the receiving point P with that at the transmitting point is not only technically problematic but also disadvantageous in reducing the cost of the receiver. This problem is solved by increasing the number of satellites receiving the signal by one more. FIG. 3 shows this two-dimensionally for easy understanding. If the clock at the receiving point is later than the clock of each satellite by Δtu, the radius of the three measured circles is larger than the actual one by Δtuc (c is the speed of light) and intersects at one point. The three power circles no longer intersect (solid line diagram). If the value of Δtuc is adjusted so that these three circles intersect at one point, Δtu can be obtained simultaneously with the position of the receiving point P. In GPS, satellite i
The measured value of a distance different from the true distance Ri by Δtuc is called a pseudo distance. The pseudorange Ri for the satellite i is represented by Ri = Ri + cΔtai + c (Δtu−Δtsvi). Here, Δtai is the delay time of radio waves in the ionosphere and the troposphere, and Δtsvi is the time offset of the clock of satellite i. Instead of synchronizing each other, the atomic clocks on the satellite measure their offset values, make predictions, and use Δtsvi
In a form that can calculate the value of and transmit it from the satellite.
For three-dimensional positioning, four unknowns, ie, three position coordinates and Δtu can be solved using four pseudorange measurements for four satellites with i = 1 to 4. Similarly, using the Doppler frequency of the signal from the satellite, that is, the measured value of the pseudorange change rate, the three-dimensional velocity of the user can be measured. When determining the position of the user based on the position of the satellite, the user must know the position of the satellite that changes every moment and the state of the clock on the satellite, and these data are also described later. Broadcast from satellite. Each satellite is equipped with a receiving circuit (not shown) for receiving radio waves transmitted from the main control station 1a via the ground antenna 1b and a transmitting circuit 20 shown in FIG. This transmission circuit 20
Is a reference frequency oscillating circuit 21 that outputs a reference frequency signal of, for example, 10.23 MHz, and forms the L1 carrier (1575.42 MHz) as the _first carrier by multiplying the frequency of the reference frequency signal to be output by 154 times. And a multiplier 23 for multiplying the frequency of the reference frequency signal by 120 to form an L2 carrier (1227.6 MHz) as a _second carrier. Further, the transmitting circuit 20 includes a clock forming circuit 24 that forms a clock signal having a predetermined cycle from the reference frequency signal,
A code generation circuit 25 for forming two types of code signals called a P code and a C / A code as ranging signals from the reference frequency signal and this clock signal, and the position of the satellite, which is timing-controlled by the clock signal and changes every moment. And a computer 26 for outputting data relating to the state of the clock on the satellite. The P code is a highly accurate secret code that can be used only by users who have been specifically recognized as military, and is superimposed on data output from the computer 26.
It is a long code transmitted in the form of orthogonal modulation of both the L ₁ and L ₂ carriers, with a repetition rate of 10.23 Mbit / s and a length of one week. The C / A code is a code that is used for coarse positioning (standard positioning) and capturing of a P code, and that is open to the public. The C / A code signal, after being superimposed with the data output from the computer 26, is transmitted in the form of modulating the L _1, L ₂ both carriers, at a repetition rate of 1.023Mbit / s, the length
It is repeated every 1,023 bits, that is, every 1 ms. Note that the C / A code generation circuit is composed of, for example, a Gold code generation circuit using two 10-stage shift registers. The data output from the computer 26 is measured and predicted by a control unit on the ground, stored in a storage circuit (not shown) of the satellite, and sequentially read. These data are transmitted at a predetermined timing at a transmission speed of, for example, 50 bit / s. The data includes telemeter language, handover language, ionospheric correction parameters, delay correction for one frequency receiver, age of clock correction data, reference clock for clock correction, GPS system time, age of orbit prediction, and orbital elements. For the reference time of the trajectory, the average perihelion angle at the orbital element reference time, the eccentricity, the square root of the major radius, the ascending intersection of right ascension, the orbital inclination angle, the perigee argument, the perturbation of the ascending intersection, the correction of the average movement, the inclination angle correction The data includes parameters, correction items for orbit disturbance, satellite identification numbers, reference times of data subframes, satellite health conditions, and the like. In addition, it predicts the period during which the user's receiver can receive the signals of each satellite, selects the combination of satellites that provides the highest positioning accuracy from the satellites in the field of view, and captures the signals from the satellite as soon as possible. The calendar (al
manac) data is also included. The above control part consists of the main control station 1a and ground antennas arranged at a plurality of (four or more planned) fixed points on the ground.
1b, and a plurality of (four or more planned) fixed points on the ground are provided as monitor stations 1c. The main control station 1a tracks the satellite via the terrestrial antenna 1b, predicts the clock on the satellite and the orbit of the satellite based on the result, and stores the data for putting them into the memory of the satellite so as to broadcast them from the satellite. It is a manned facility equipped with a large computer and a series of operation control consoles, which are provided to transmit and receive other telemeters and commands required for satellite control. The monitor station 1c is a receiver of a signal from a satellite,
An unmanned station equipped with an atomic clock and a meteorological instrument for calculating tropospheric delay. As shown in FIG. 1, the satellite-based positioning means 1, which is a user part, measures the current position of the vehicle from the GPS receiver 2 that receives a signal of a required satellite and the received signal, and corresponds to the current position. A current position recognition device 3 for outputting a position signal. In addition, as shown in FIG.
Includes a crystal oscillator 38 that outputs a reference frequency signal that is an overall timing control signal, and a clock oscillation circuit 39 that forms a clock signal that controls the operation timing of the signal processing unit 37 from the reference frequency signal, GP
Antenna 31 and preamplifier 3 connected in front of S receiver 2
2 and a bandpass filter 33. The GPS receiver 2 includes a frequency synthesizing circuit 61 for generating a signal having the same pattern as the data relating to the carrier wave of the satellite transmitter 20, the position of the satellite, and the state of the clock on the satellite based on the reference frequency signal oscillated by the crystal oscillator 38. A clock signal output from the clock oscillation circuit 39, a code generation circuit 62 for forming a code signal having the same pattern as the distance measurement signal, and a signal output from the frequency synthesis circuit 61 and the code signal generation circuit 62 on the satellite. And a data and carrier detector 63 for correlation detection of data and carrier waves of the orbit of the clock and the satellite, and a code clock detector 64 for correlation detection of the ranging signal by a code signal output by the code generation circuit 62. I have. Further, the signal processing means
37 is controlled in timing by the clock signal output from the clock oscillation circuit 39. Fig. 5 shows a GP with one receiving channel.
Although an S receiver 2 is shown, two receiving channels are provided, a first receiving channel is dedicated to sequentially switching reception of signals from four satellites in the field of view, and a second receiving channel is dedicated to each satellite. Eliminate positioning interruptions due to sequential stoppage of acquisition of data from satellites on the first reception channel, for example, to acquire broadcast data from satellites and to preliminarily capture signals from satellites to be received next Is possible. In the case of a 5-channel receiver, simultaneous continuous tracking of four satellites is performed on four channels, and in parallel with this, preliminary acquisition of the next satellite is performed on another one channel, and switching of the satellite used is instantaneous. It is possible to do. By the way, in GPS, all the errors involved in the above pseudo distance measurement are converted into distances, and the user equivalent distance difference (User Equ
ivalent Range Error.UERE).
The cause of the UERE and the nominal value of the size for each cause in the P-code are as shown in Table 1 below. U in C / A code
It is thought that both the ionospheric error and the receiver error of the ERE are several times larger. The positioning error value (positioning accuracy) of GPS can be obtained simply by multiplying this UERE by the deterioration coefficient GDOP. In the C / A code, the positioning accuracy is nominally 40 m (50%) in terms of the radius for probability error (CEP). . In addition, as shown in FIG. 1, the traveling history positioning means 9
The vehicle includes a vehicle speed sensor 4a, a geomagnetic sensor (magnetic compass) 4b, and a current position recognizing device 3 that measures the current position of the vehicle from the outputs thereof and outputs a position signal corresponding to the current position to the control device 10. A known speed sensor or the like is used as the vehicle speed sensor 4a, and the traveling distance is calculated by integrating the vehicle speed by the sensor 4a, and the traveling distance is accumulated in accordance with a change in the traveling direction detected by the geomagnetic sensor 4b. By doing so, it is possible to obtain a running history, thereby calculating a running route from the reference point and measuring the current position. Since such a running history positioning means 9 is already well known, a detailed description thereof will be omitted. The operation of recognizing the current position by the navigation device having the satellite-based positioning means 1 and the travel history positioning means 9 described above will be described with reference to the flowchart shown in FIG. 6 and the explanatory diagram of FIG. In this operation, first, at step 71, the current position Pd (Xd, Yd) is measured by the traveling history positioning means 9. Next, a predetermined coefficient for calculating an accumulated error in the travel distance L from the reference position (measurement start position) Po (Xo, Yo) at which the measurement by the travel history positioning means 9 is started to the present (this value is determined by the accuracy of the distance sensor, etc.) (Determined value) to determine the magnitude of the measurement error ΔLd. This measurement error ΔLd represents the maximum error between the measured current position Pd and the actual current position.If a circle with a radius ΔLd is drawn around Pd, the actual current position will be located within this circle . Next, in step 73, it is determined whether or not the radio wave from the satellite is being received. If the radio wave is being received, the current position Pg (X
g, Yg). At the same time, the magnitude ΔLg of the measurement error of the current measurement position by the satellite-based positioning means 1 is calculated. As described above, the measurement error ΔLg is calculated by multiplying the user equivalent distance difference (UERE) by the deterioration coefficient (GDOP). Thereafter, the process proceeds to step 74, where the magnitude of the measurement error ΔLd obtained by the traveling history positioning means 9 obtained as described above is compared with the magnitude of the measurement error ΔLg by the satellite-based positioning means 1. If ΔLd> ΔLg, the measured value Pg (Xg, Yg) obtained by the satellite-based positioning means is read as the current position in step 75 and displayed on the display 16 as the current position. It is stored as a reference position Po (Xo, Yo) for the current position measurement by the positioning means 9. On the other hand, if it is detected in step 73 that the radio wave from the satellite is not received, the process proceeds to step 76, and the value Pd (Xd, Yd) measured by the traveling history positioning means 9 in step 71 is set as the current position. After reading, this position is displayed on the display 16. If a radio wave is received from the satellite, but it is determined in step 74 that ΔLd ≦ ΔLg, the process proceeds to step 76, where the measured value Pd by the travel history positioning means 9 is read as the current position. (Effects of the Invention) As described above, according to the present invention, the measurement of the current position by the satellite-based positioning means and the measurement of the current position by the travel history positioning means are performed at the same time. Driving history measurement error calculating means,
These are used to detect the measurement error by the two positioning means, and the control means reads the current position measured by the positioning means with the smaller measurement error as a value indicating the current position. Among the positioning means, the current position measured by the means having the higher measurement accuracy at that time is displayed, and the recognition accuracy of the current position can be improved. Further, since the magnitude of the measurement error of the current position by the satellite-based positioning means is calculated based on a value determined by the geometric relationship between the satellite used for measurement and the vehicle, the measurement error of the satellite-based positioning means is calculated. A certain level of radio wave intensity (strength enough to recognize information) is ensured, irrespective of the radio wave intensity and the type of radio wave (digital or analog), as compared with those obtained based on the radio wave level from the satellite If possible, it is possible to calculate the error. Further, the magnitude of the measurement error of the current position by the satellite-based positioning means is calculated by multiplying the user equivalent distance difference by a value determined by the geometric relationship between the plurality of satellites used for the measurement and the vehicle. Alternatively, if the magnitude of the measurement error of the current position by the traveling history positioning means is calculated by multiplying the traveling distance from the measurement start position to the present by a predetermined coefficient for obtaining the accumulated error, the measurement by the positioning means can be performed. The magnitude of the error can be a length corresponding to the measurement error distance, so that the magnitude of the measurement error can be compared more specifically and accurately.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is an overall configuration diagram showing an example of a navigation device according to the present invention, FIG. 2 is a perspective view showing an outline of GPS, and FIG. 3 is an explanatory diagram of the principle of GPS positioning. FIG. 4 is a block diagram of a satellite transmission circuit, FIG. 5 is a block diagram of satellite-based positioning means, FIG. 6 is a flowchart showing an operation of recognizing a current position by the navigation device according to the present invention, FIG. FIG. 4 is an explanatory diagram for explaining an operation of recognizing the current position. 1 ... satellite-based positioning means, 1a ... main control station 1b ... terrestrial antenna, 1c ... monitor station 2 ... GPS receiver, 4a ... vehicle speed sensor 4b ... geomagnetic sensor, 9 ... travel history positioning means 10 Control device 16 Display 20 Transmitter circuit

Claims (1)

(57) [Claims] Satellite-based positioning means for receiving the radio waves from a plurality of satellites to measure the current position of the vehicle; and traveling history positioning means for measuring the current position based on the traveling history.
A navigation device for displaying the current position measured by the two positioning means on the display means, detecting a magnitude of a measurement error of the current position by the satellite-based positioning means and a magnitude of a measurement error by the traveling history positioning means, A control unit for displaying, on the display unit, the current position measured by the positioning unit having the smaller size of the measurement errors, the magnitude of the measurement error of the current position by the satellite-based positioning unit detected by the control unit; Is calculated based on a value determined by a geometric relationship between the plurality of satellites and the vehicle used for measurement. 2. The magnitude of the measurement error of the current position by the satellite-based positioning means is calculated by multiplying the user equivalent distance difference by a value determined by the geometric relationship between the plurality of satellites used for the measurement and the vehicle. The navigation device according to claim 1, wherein 3. The magnitude of the measurement error of the current position by the travel history positioning means is calculated by multiplying the travel distance from the measurement start position to the present by a predetermined coefficient for obtaining an accumulated error. 2. The navigation device according to 2.