This paper focuses on the cubature Kalman filters (CKFs) for the nonlinear dynamic systems with additive process and measurement noise. As is well known, the heart of the CKF is the third-degree spherical—radial cubature rule which makes it possible to compute the integrals encountered in nonlinear filtering problems. However, the rule not only requires computing the integration over an n-dimensional spherical region, but also combines the spherical cubature rule with the radial rule, thereby making it difficult to construct higher-degree CKFs. Moreover, the cubature formula used to construct the CKF has some drawbacks in computation. To address these issues, we present a more general class of the CKFs, which completely abandons the spherical—radial cubature rule. It can be shown that the conventional CKF is a special case of the proposed algorithm. The paper also includes a fifth-degree extension of the CKF. Two target tracking problems are used to verify the proposed algorithm. The results of both experiments demonstrate that the higher-degree CKF outperforms the conventional nonlinear filters in terms of accuracy.

The strength of the GPS signal on the earth's surface averages-160 dBw. While many GPS receivers leave large space for signal dynamics, enough power space is left for the GPS signals to be spoofed. Spoofing is completely different from jamming. The objective of jamming is to simply interrupt the availability of the signal in space at the receiver. The effect is to cause the signal at the receiver to be corrupted so that no valid GPS signal can be decoded by the receiver. The goal of spoofing, on the other hand, is to provide the receiver with a misleading signal, fooling the receiver to use fake signals in space for positioning calculations. The receiver will produce a misleading position solution. While the GPS P-code is heavily encrypted and thus, is hard to spoof. The civilian GPS signal, is easy to spoof because the signal structure, the spread spectrum codes, and modulation methods are open to the public. The stability and predictability of GPS L1 signal are good, because: the frequencies, initial phase and C/A code for each level of modulation are stable, without frequency hopping which is frequently used in military radio communications.

The ionospheric total electron content (TEC) is an important ionospheric parameters, Research of it has important significance on communication, radar, spaceflight, GNSS and other domains. Traditional short-term forecast model of ionospheric TEC uses single model so as to affects the prediction precision. A combination model based on seasonal model and ARMA model was put forward to overcome the shortages of traditional model. The TEC data of IGS in 2013 is used to analyze the two models. Prediction result shows the precision of combination model is superior to the traditional model.