FIG. 5, where the two distributions share a common mean and a common standard deviation. As such, the characteristic parameter sent to improve the positioning integrity may include the common mean and the common standard deviation. In yet another aspect of the present disclosure, the error source may be modeled as an asymmetrical paired overbounding model (e.g., a Gaussian distribution), as illustrated in FIG. 6, where a mean of the distribution is offset from zero. As such, the characteristic parameter sent to improve the positioning integrity may include the mean and a standard deviation of the distribution. In yet another aspect of the present disclosure, the error source may be modeled as an asymmetrical paired overbounding model (e.g., two Gaussian distributions), as illustrated in FIG. 7, where the two distributions have their respective means but share a common standard deviation. As such, the characteristic parameter sent to improve the positioning integrity may include the two means and the common standard deviation. In yet another aspect of the present disclosure, the error source may be modeled as an asymmetrical paired overbounding model (e.g., two Gaussian distributions), as illustrated in FIG. 8, where the two distributions have their respective standard deviations but share a common mean. As such, the characteristic parameter sent to improve the positioning integrity may include the two standard deviations and the common mean. In yet another aspect of the present disclosure, the error source may be modeled as an asymmetrical paired overbounding model (e.g., two Gaussian distributions), as illustrated in FIG. 9, where the two distributions have their respective standard deviations and respective means. As such, the characteristic parameter sent to improve the positioning integrity may include the two standard deviations and the two means. For the distribution of error sources or basic distribution Gaussian can be modeled as modeled as Gaussian distribution or other distribution having relation with Gaussian distribution, such as truncated Gaussian distribution or a table based on the distribution.

Embodiment 2

In various embodiments, the error source can be associated with one or more timing-related errors/measurements. In an example where the characteristic parameters (e.g., one or more means, and/or one or more standard deviations) modeling the error source are sent for an LMF-based positioning (e.g., measuring the PRS), the error source can include at least one of: a Reference Signal Time Difference (RSTD) measurement, a Relative Time of Arrival (RTOA) measurement, a UE Rx-Tx time difference measurement, a gNB Rx-TX time difference measurement, or an inter-TRP synchronization. Specifically, the RSTD measurement may be an error source for DL-TDOA, the RTOA measurement may be an error source for UL-TDOA, the UE Rx-Tx time difference measurement may be an error source for Multi-RTT, the gNB Rx-Tx time difference measurement may be an error source for Multi-RTT, and the inter-TRP synchronization may be an error source for UL-TDOA. In an example where the characteristic parameters (e.g., one or more means, and/or one or more standard deviations) modeling the error source are sent for a UE-based positioning (e.g., measuring the SRS), the error source can include an inter-TRP synchronization. Specifically, the inter-TRP synchronization may be an error source for DL-TDOA.

However, it should be understood that the error source may be associated with any of various other timing-related errors/measurements, while remaining within the scope of the present disclosure. Below is a list illustrating some examples of such other timing-related errors/measurements.

Timing-Related Error Source:
Sources of Error for Timing-Based Positioning Methods;

- TRP/UE measurements errors (e.g., ToA, Rx-Tx timing difference);
- Error in assistance data (e.g., TRP location, Inter-TRP synchronization errors (e.g., RTD));
- TRP/UE Timing error;
- RSTD measurement is an error source for DL-TDOA;
- RTOA measurement is an error source for UL-TDOA;
- UE Rx-Tx time difference measurement is an error source for Multi-RTT;
- gNB Rx-Tx time difference measurement is an error source for Multi-RTT;
- TEG-related timing error from timing related measurement error (e.g., RTOA, RSTD, UE/gNB Rx-Tx time difference);
- the measurement error is considered for each ToA or for the reported RSTD value; and
- inter-TRP synchronization.

More Detail Grouped Error Sources:

- The above timing-related error source in LOS case;
- The above timing-related error source in NLOS case;
- The above timing-related error source in LOS&NLOS case; and
- The above timing-related error source in grouped scenario.

In various embodiments, the characteristic parameters (e.g., one or more means, and/or one or more standard deviations) can be associated with an Information Element (IE), “TimingQuality” or “MeasurementQuality.” Specifically, the characteristic parameters can be defined through a plural number of measurements on the IE (TimingQuality/MeasurementQuality). For example, the IE NR-TimingQuality defines the quality of a timing measurement value for DL-TDOA and Multi-RTT measurement on the UE side, and the IE MeasurementQuality defines the quality of timing value for UL-TDOA and Multi-RTT measurement one the TRP side in terms of meter.

Further, these IEs are used to represent the deviation of the real distance from the estimation between a UE and a TRP. Basically, the candidate values of standard deviation of the error source model for integrity can be based on the candidate values of the above IEs, where the measurement uncertainty range is timing Quality Value*timingQualityResolution. Based on the uncertainty range timing Quality Value*timingQualityResolution, the standard deviation is (timing Quality Value*timingQualityResolution)/n, and the parameter n could be one, two, three and others values. Specially, when n is equal to one, the standard deviation is timing Quality Value*timing QualityResolution. And if n is equal to 3 which may be based on empirical, the standard deviation is (timingQuality Value*timingQualityResolution)/3.

If without thinking the unit/resolution timing QualityResolution in the formula, the standard deviation can be defined as follows:

- (timingQuality Value)/n, and the parameter n could be one, two, three and others values. Specifically, when n is equal to one, the standard deviation is timingQuality Value. And if n is equal to 3 which may be based on empirical, the standard deviation is (timingQuality Value)/3.

For the maximum uncertainty values with different resolutions can be {3.1 m, 31 m, 310 m, 930 m}, i.e., 31*timingQualityResolution. Based on the uncertainty value range, the maximum standard deviation of the timing error source model may be presented as follows:

${std}_{\max} = round (\frac{31}{n})$

For example, if based on empirical values, n is equal to 3. The standard deviation std could be one of the list {0,1,2, . . . 10}. Considering the resolution timing QualityResolution, the standard deviation std could be one of the list {0,1,2, . . . 10} *timingQualityResolution. And the max standard deviation could be (31/n)*timingQualityResolution. If n is 3, the max standard deviation is 10*timingQualityResolution. The character ‘*’ means multiplication.

For another example, for the Inter-TRP synchronization error, all above schemes is suitable. Inter-TRP synchronization error is normal distribution.

$Std value : {0, 1, 2, \dots {std}_{\max}}, where$

${std}_{\max} = round (\frac{31}{n}), and n = 3 or other values$

$Resolution : [mdot 1, mdot 5, m 1, m 5, m 10, m 20, m 30, \dots}$

As mentioned above, the inter-TRP synchronization may be an error source for the UE-based positioning methods and for UE-assisted DL-TDOA method for LMF-based positioning integrity mode. For UE-based positioning methods, the IE NR-RTD-Info is used by the location server to provide time synchronization information between a reference TRP and a list of neighboring TRPs. Because the inter-TRP synchronization is signaled by higher layer parameter NR-RTD-Info as follows, and the error is reflected by the synchronization uncertainty, i.e. rtd-RefQuality or rtd-Quality, hence, the similar distribution for timing measurement error can be used. At least, Gaussian/normal distribution should be supported.

For another example, for the AdditionalPathList, which is used by the target device to provide information about additional paths in association to the TOA measurements associated to NR positioning in the form of a relative time difference and a quality value. The additional path nr-RelativeTimeDifference is the detected path timing relative to the detected path timing used for the TOA value, and each additional path can be associated with a quality value nr-PathQuality/NR-TimingQuality.

The parameter(s) of the distribution of the error source is related with the PathQuality. And the std parameter is as following:

$Std value : {0, 1, 2, \dots {std}_{\max}}, where$

${std}_{\max} = round (\frac{31}{n}), and n = 3 or other values$

$Resolution : [mdot 1, mdot 5, m 1, m 5, m 10, m 20, m 30, \dots}$

Embodiment 3

In various embodiments, the error source can be associated with one or more location-related errors/measurements. In an example, the error source includes a TRP or an ARP location. Specifically, the TRP/ARP location may be an error source for DL-TDOA/DL-AOD and UL-AOA positioning methods. In various embodiments, the characteristic parameters (e.g., one or more means, and/or one or more standard deviations) can be associated with an Information Element (IE), “LocationUncertainty,” or its sub-IE, e.g., “horizontalUncertainty,” “horizontalConfidence,” “verticalUncertainty,” and “verticalConfidence.” Specifically, the characteristic parameters can be defined through a plural number of measurements on the IE (LocationUncertainty) or its sub-IE (horizontalUncertainty, horizontalConfidence, verticalUncertainty, and/or verticalConfidence).

The IE, LocationUncertainty, can be used to determine the characteristic parameters of the distribution for ARP/TRP location error integrity calculation. The TRP/ARP location may be an error source for DL-TDOA/DL-AOD and UL-AOA positioning methods. The TRP/ARP location indicates the coordinates of the transmission/antenna reference points for a set of TRPs. Since TRP/ARP location indicates the coordinates of the transmission/antenna reference points for a set of TRPs, that the TRP/ARP location error can be modeled as a normal distribution for the horizontal and the vertical domain, respectively. Alternatively, the model of TRP/ARP location error distribution can be modeled as a uniform distribution, where the range of uniform distribution is [0, horizontalUncertainty] and [0, verticalUncertainty] for horizontal and vertical domain, respectively.

In an example where the TRP/ARP location (the error source) is modeled as a Gaussian distribution, the characteristic parameters are related to the measurement result(s) of confidence and/or uncertainty. For example, the standard deviation of the Gaussian distribution is related to the measurement result(s) of confidence and/or uncertainty. If there is “no information” for confidence, the standard deviation is related with uncertainty. The confidence can be horizontalConfidence and/or verticalConfidence and/or a joint function horizontalConfidence and verticalConfidence. The uncertainty can be horizontalUncertainty and/or verticalUncertainty and/or a joint function horizontalUncertainty and verticalUncertainty.

Scheme 1: The characteristic parameter is the same level as the measurement/error.

For example, the std can computed from the existing LocationUncertainty reporting where it is either LMF reporting to UE for UE based positioning or TRP reporting to LMF. The extra signaling for TRP location error of positioning integrity is not needed.

Alternatively,

The parameter(s) std signaling for TRP location error of positioning integrity is needed.

For example, the association between the characteristic parameter and the IE (and/or its sub-IE) can be defined as follows:

$δ = \frac{1}{\sqrt{2}} \frac{a}{\erf^{1} (P)},$

where erf¹(·) is an inverse error function, P is a confidence value (including horizontalConfidence and/or verticalConfidence), a is an Uncertainty value (including horizontalUncertainty and/or verticalUncertainty).

Take the example of horizontal location, the reasoning process is following:

The a is horizontalUncertainty. The result of integral computation of f(x) should be equal to P, where P is a constant (Determine value) from horizontalConfidence. Hence, the following equations are satisfied.

$\int_{- a}^{a} f (x) dx = \int_{- a}^{a} \frac{1}{\sqrt{2 π} δ} e^{- \frac{x^{2}}{2 δ^{2}} dx = P},$

$\int_{0}^{a} \frac{1}{\sqrt{2 π} δ} e^{- \frac{x^{2}}{2 δ^{2}} dx = 2 P},$

$(1 + \erf (\frac{x}{δ \sqrt{2}})) \int_{0}^{a} = 2 P,$

$\erf (\frac{a}{δ \sqrt{2}}) = P,$

$\frac{a}{δ \sqrt{2}} = \erf^{- 1} (P) .$

So the standard deviation δ is

$δ = \frac{1}{\sqrt{2}} \frac{a}{\erf^{- 1} (P)},$

where erf¹(·) is the inverse error function.

For another example, the association between the characteristic parameter and the IE (and/or its sub-IE) can be defined as follows:

- Std value: {0, 1,2, . . . std_max}, where

${std}_{\max} = round (\frac{255}{n}),$

and n=3 or other values for the horizon domain and the vertical domain, respectively.

Scheme 2: The characteristic parameter is the higher level than the measurement/error. That means there are more than one measurement/error results for the IE of characteristic parameter(s).

For example, the association between the characteristic parameter and the IE (and/or its sub-IE) can be defined as follows: The error distribution parameters of TRP location is per TRP-LocationInfoElement IE in the NR-TRP-LocationInfo

Alternatively,

The error distribution parameters of TRP location is per LocationInfoPerFreqLayer IE in the NR-TRP-LocationInfo

Alternatively,

The error distribution parameters of TRP location is per TRP-LocationInfo IE.

Alternatively,

The error distribution parameters of TRP location is higher level than TRP-LocationInfo IE.

The scheme 1 and/or scheme 2 can be also applied to other erroe sources. The specific signaling name could be different.

For example:

For the TRP/ARP location error distribution is modeled as normal distribution. The std can be calculated based on the existing parameter LocationUncertainty including uncertainty value and confidence value.

- The std value δ should make

$\int_{- a}^{a} \frac{1}{\sqrt{2 π} δ} e^{- \frac{x^{2}}{2 δ^{2}} dx = P}, and δ = \frac{1}{\sqrt{2}} \frac{a}{\erf^{- 1} (P)},$

where P is the mean (or other statistical method) of some confidence values, a is the mean (or other statistical method) of some Uncertainty values, and erf¹(·) is the inverse error function.

Alternatively,

For example:

TRP ARP location error distribution is modeled as normal distribution. The std can be calculated based on the existing parameter Location Uncertainty including uncertainty value and confidence value.

- One std value δ should make

$\int_{- a}^{a} \frac{1}{\sqrt{2 π} δ} e^{- \frac{x^{2}}{2 δ^{2}} dx = P}, and δ = \frac{1}{\sqrt{2}} \frac{a}{\erf^{- 1} (P)},$

where P is the confidence value, a is the Uncertainty value, and erf¹(·) is the inverse error function.

At last the (report) signaling std_last for overbounding model is based on at last one (/more than one) std value.

Such as the last signaling contain the std_last is the mean (or other statistical method) of a series of (or a group of) stds.

Embodiment 4

In various embodiments, In various embodiments, the error source can be associated with one or more angle-related errors/measurements. In an example, the error source includes at least one of: an Angle of Arrival (AoA) measurement, an AoA in Line-of-Sight (LCS), a Zenith Angle of Arrival (ZoA) in LCS, an AoA in Global Coordinate System (GCS), a ZoA in GCS, an AoA in LOS, an AoA in Non-Line-of-Sight (NLOS), or an AoA in LOS and NLOS. In various embodiments, the characteristic parameters (e.g., one or more means, and/or one or more standard deviations) can be associated with an Information Element (IE), “Angle Measurement Quality.” Specifically, the characteristic parameters can be defined through a plural number of measurements on the IE (Angle Measurement Quality).

For example, the association between the characteristic parameter and the IE can be defined as follows. Candidate values of the standard deviation can be determined based on a value range of the IE, Angle Measurement Quality. A measurement uncertainty range is Azimuth Quality/Zenith Quality*Resolution, so the maximum uncertainty value is 255*Resolution. Accordingly, the maximum value of the standard deviation is defined as follows:

${std}_{\max} = round (\frac{255}{n}),$

- and
  
  the range of the standard deviation is defined as follows:
- P Std value: {0,1,2, . . . std_max}, where n=3, with Resolution: {0.1 deg, . . . }.

Embodiment 5

Considering whether the distribution parameters of the UE measurement should be associated with each TRP (pair), or with each measurement report. There are several methods as following:

Case1:

All RSTD measurements within a TRP pair (i.e., a same NR-DL-TDOA-MeasElement LPP message) should be associated with one set of error distribution parameters. Error source of Rx-Tx time different measurement should have the same principle with RSTD measurement that, all the Rx-Tx time difference measurements within a TRP (i.e., a same NR-Multi-RTT-MeasElement LPP message) should be associated with one set of error distribution parameters. Similarly, all the DL-PRS RSRPP of the first path or the DL-PRS RSRP for LMF-based DL-AoD within a TRP (i.e., a same NR-DL-AoD-MeasElement LPP message) should be associated with one set of error distribution parameters.

Case 2:

All RSTD measurements containing in a same measurement report (i.e., a same NR-DL-TDOA-ProvideLocationInformation LPP message) should be associated with one set of error distribution parameters. Error source of Rx-Tx time different measurement should have the same principle with RSTD measurement that, all Rx-Tx time difference measurements containing in a same measurement report (i.e., a same NR-Multi-RTT-ProvideLocationInformation LPP message) should be associated with one set of error distribution parameters. Similarly, all the DL-PRS RSRPP of the first path or the DL-PRS RSRP for LMF-based DL-AoD containing in a same measurement report (i.e., a same NR-DL-AoD-ProvideLocationInformation LPP message) should be associated with one set of error distribution parameters.

Embodiment 6

For DL assistance data, TRP location is only for UE-based positioning integrity mode (UE based DL-TDOA and UE based DL-AoD), and inter-TRP synchronization is for UE-based and LMF-based positioning integrity mode (UE based DL-TDOA and LMF based DL-TDOA).

TRP location as an error source means the error of wrong TRP location relative to the real TRP location obeys a distribution. The TRP's location may not be stable when time varies, for example at one time TRP location is at point A, and at another time the TRP location is at point B (in which point A and point B are very close), so its TRP location shift (error) should form a distribution (a normal distribution or uniform distribution) and this distribution should be an attribute of the TRP.

TRP synchronization as an error source means the error of wrong TRP synchronization relative to the real TRP synchronization obeys a distribution. The synchronization between two TRPs may not be stable when time varies, for example at one time TRP synchronization value between two TRPs is A, and at another time TRP synchronization value between the same two TRPs is B (in which value A and value B are very close), so its TRP synchronization shift (error) should form a distribution (a normal distribution or uniform distribution) and this distribution should be an attribute of the TRP pair.

Since they are both TRP-specific assistance data, the error distribution parameters of these two error sources should be configured per TRP in the DL assistance data, similar as A-GNSS design which is per satellite per GNSS. To be specific, the error distribution parameter of TRP location should be configured per TRP-LocationInfoElement in the NR-TRP-LocationInfo, and the error distribution parameter of inter-TRP synchronization should be configured per ReferenceTRP-RTD-Info in NR-RTD-Info.

Support to configure the error distribution parameters of TRP location per TRP-LocationInfoElement IE in the NR-TRP-LocationInfo.

Support to configure the error distribution parameters of inter-TRP synchronization per ReferenceTRP-RTD-Info IE in the NR-RTD-Info.

Embodiment 7

For UL/UL+DL positioning (UL-TDOA, UL-AoA and multi-RTT), TRPs measure the SRS and perform measurement result, then each gNB gathers TRPs measurements and reports to LMF. There may be error sources existing at TRP/gNB side, for example TRP measurement error. Thus, NG-RAN nodes to report error distribution parameters for TRP measurement error along with TRP measurement report should be supportted. As the agreement indicated above, the error source of RTOA measurement, gNB Rx-Tx time difference measurement and angle of arrival measurement should have their corresponding error bound. Similar as DL measurements, since each TRP only reports one measurement for each measurement type, the error distribution parameters of RTOA measurement, gNB Rx-Tx time difference measurement and angle of arrival should be associated with multiple TRP's measurements, to be specific, associated with each MEASUREMENT RESPONSE message or MEASUREMENT REPORT message.

Embodiment 8

TRP location is provided per TRP in NRPPa message; ARP location is configured per TRP since one TRP can associate multiple ARPs, and inter-TRP synchronization is indicated as SFN Initialisation Time in the IE TRP information. Similar to the DL assistance data, the error source of ARP location and inter-TRP synchronization can have their corresponding error distribution parameters, and the error distribution parameters of these two error sources can be configured per TRP information.

Embodiment 9

FIG. 12 illustrates a flow diagram of a method 1200 for improving positioning with modeling one or more error sources. The method 1200 may be implemented using any one or more of the components and devices detailed herein in conjunction with FIGS. 1-11 (e.g., FIG. 3). In overview, the method 1200 may be performed by a core network entity (e.g., LMF), in some embodiments. Additional, fewer, or different operations may be performed in the method 1200 depending on the embodiment. At least one aspect of the operations is directed to a system, method, apparatus, or a computer-readable medium.

For example, the method 1200 can include sending, by a core network entity to a first wireless communication entity, a message including measurement and/or assistance data for positioning, in which the assistance data includes no or one or more characteristic parameters associated with a model of an error source. The characteristic parameters can include one or more means and/or one or more standard deviations of a model of the error source, as discussed above. The error source can be associated with one or more timing-related errors/measurements, one or more location-related errors/measurements, or one or more angle-related errors/measurements. For example, the first wireless communication entity can be a UE. As such, the message may be sent concurrently with, or subsequently to a base station (e.g., TRP) sending another message to the LMF that includes various measurement results such as, for example, a measurement result on a UL reference signal for positioning (e.g., a Sounding Reference Signal).