## 1. Introduction

[2] Accurate determination of HF and low-VHF propagation characteristics for purposes like direction finding or analyzing signal penetration likelihoods requires an accurate determination of the ionospheric electron density distribution in three dimensions. Vertical and oblique HF sounding is certainly useful in this regard, but sounders are often not available in the region of interest or they may be too geographically sparse to get a good representation of the ionosphere over a broad region. GPS receivers are both relatively inexpensive and fairly ubiquitous, and since the total electron content (TEC) of the ionosphere between a GPS satellite transmitter and a ground receiver can be determined from the GPS two-frequency signals, GPS presents a potentially powerful tool for determining the state of the ionosphere when insufficient sounding data are available.

[3] We are developing a capability for inverting the data recorded by an array of GPS receivers, vertical sounders, and electron density sensors to recover the three-dimensional electron density distribution of the ionosphere in the region pierced by the GPS lines of sight. Since each GPS receiver typically views from four to six GPS satellites and since it is possible to have many GPS receivers in a region of interest, many intersecting lines of sight can be formed. On each line of sight, TEC can be determined to some accuracy. Obtaining the three-dimensional electron density distribution that best reproduces these many (intersecting) TEC data requires inverse processing. We concentrate on building a robust algorithm for regional real-time monitoring of the three-dimensional ionosphere using only the computational power of a personal computer. The system should be capable of processing raw data from an arbitrary number of GPS receivers, vertical sounders, and in situ electron density sensors available in the area of interest. The area of interest may be of the order of several thousand kilometers in diameter, while horizontal spatial resolution may be of the order or less than 50 km.

[4] The task of reconstructing the three-dimensional electron density from multisensor data has been addressed by a number of researchers, notably by *Mitchell and Spencer* [2003] and *Bust et al.* [2004]. Our approach stems from the inversion technique previously developed by our group within the CREDO project [*Fridman*, 1998; *Fridman and Nickisch*, 2001]. This system utilized conventional sounding data (both vertical and oblique) in addition to relative TEC data from a number of Transit receivers and demonstrated robust performance and flexibility in assimilating data from diverse sensors. The effort reported here is to extend our methodology to solve the task of inverting TEC data from GPS receivers combined with vertical sounding data.

[5] We apply the Tikhonov regularization technique and the residual principle combined with a Newton algorithm to solve the full three-dimensional inverse problem. This approach may be interpreted as finding the most reasonable distribution of electron density that agrees with all available measurements within errors of measurements. The algorithm is described in section 2. Performance of the algorithm is discussed in section 3.