## 1. Introduction

[2] The Wide Area Augmentation System (WAAS) is designed to provide reliable differential GPS corrections for aircraft navigation [*RTCA*, 1996]. In the absence of selective availability, the largest source of positioning error is the carrier phase advance and pseudorange group delay caused by the ionosphere. Since WAAS user measurements generally do not coincide with reference station measurements, it is necessary to rely on ionospheric correlation to infer the state of the ionosphere in regions sampled by the user. In WAAS, vertical ionospheric delays are modeled at regularly spaced intervals in geographic latitude and longitude, i.e., at ionospheric grid points (IGPs). The broadcast bound on the error at each of these points is designated the grid ionospheric vertical error (GIVE). A critical integrity requirement of WAAS is that the broadcast GIVE at each IGP bounds the residual error with a very high degree of confidence. Specifically, the probability of broadcasting hazardously misleading information (HMI) must not exceed 10^{−7} per approach at any point in the service volume under the worst foreseeable conditions. Here hazardously misleading information refers to a broadcast GIVE that fails to bound the actual error, and foreseeable conditions include any event that is regular, common, or strongly correlated with observed parameters (by definition, unforeseeable conditions must be extremely rare, not adhering to any predictable pattern).

[3] The threat posed by the ionosphere manifests itself in three ways: (1) instantaneous residual errors due to mismodeling of the ionosphere at the IGPs; (2) residual errors that arise when interpolating IGP delays to a user position; and (3) residual errors that grow over the life span of the broadcast message.

[4] The broadcast GIVE must protect the user from each of these threats. The rate, in both space and time, at which neighboring measurements of ionospheric delay become decorrelated is a critical component in the calculation of the WAAS GIVE. Irregularities in the ionosphere represent a threat to the accuracy of the confidence bounds describing the integrity of the broadcast corrections [*Hansen et al.*, 2000a, 2000b; *Lejeune et al.*, 2001].

[5] Under nominal quiet-time conditions, a planar fit of slant delay measurements projected to vertical provides estimates of the local vertical delay that are of sufficient accuracy for WAAS operation. When the ionosphere is disturbed, the residual error associated with the planar fit increases, indicating that delay estimates based on this fit are less reliable. Consequently, the confidence bounds must be increased or the fit declared unusable. As long as the fit residuals accurately reflect the degree of disturbance of the ionosphere, the integrity of the corrections should remain high. Since fits are performed at finite intervals, however, it is possible that significant growth in the degree of disturbance could occur between fit evaluations. In this case the fit residuals no longer accurately reflect the true ionospheric state as encountered by the user.

[6] The WAAS GIVE is based, in part, on the uncertainty in the vertical ionospheric delay as modeled by the planar fit. In the first phase of WAAS implementation, this uncertainty is conservatively assumed to be a constant (35 cm) independent of both measurement elevation angle and distance from the IGP. Subsequent implementations of WAAS that have higher performance requirements will demand a reduction in the magnitude of the GIVE broadcast under nominal conditions. Achieving this reduction will require a better understanding of the decorrelation of ionospheric delay, in both space and time.

[7] In this paper we focus on the temporal decorrelation of the ionospheric delay. The objective is to establish a methodology for assessing the risk to the WAAS user of sudden increases in the level of ionospheric disturbance. Our means of risk assessment relies on defining *P*_{D}, the probability that a WAAS user will sample a region of the ionosphere during the onset of a significant disturbance. An upper bound on *P*_{HMI}, the probability of broadcasting HMI, is shown to depend linearly upon *P*_{D}. We have determined a limiting upper bound on *P*_{D} of 4 × 10^{−7}, which falls well within the margin needed to meet WAAS integrity requirements.

[8] In section 2 we derive an upper bound on *P*_{HMI} and examine its dependence on *P*_{D}. In section 3 we review the WAAS model for ionospheric delay and related algorithms. We provide in section 4 a precise definition of *P*_{D}, upon which a quantitative evaluation can be based. Section 5 describes our method for estimating an upper bound on *P*_{D}. Section 6 presents an iterative method for calculating σ_{decorr}, the standard deviation of the local vertical total electron content of the ionosphere relative to a planar approximation. In section 7 we discuss the manner in which observational data have been processed. Section 8 reports the results of our analysis, and conclusions are presented in section 9.