## 1 Introduction
The concept of minimising the load of gusts with the use of the Doppler LIDAR [7] sensor is based on the measurement of atmospheric disturbances before they reach the aircraft wings and exert further loads on construction. It is worth noticing that the above-mentioned warning systems provide the information about dangerous phenomena to aircrews so that adequate escape and avoiding manoeuvres can be executed. The analysis of the functioning of the automatic control systems as well as aircrew opinions suggests that a more accurate gust measurement system in challenging conditions would be useful, but in conditions not yet precluding the continuation of approach or exercising wind shear escape manoeuvres [11]. One of means of protecting aircraft against the adverse and severe impact of gusts are procedures described in the aircraft flight manual. Procedures often assume during flight at a cruising altitude that the auto-throttle system needs to be reloaded or disabled to prevent exceeding the maximum allowed speed regardless of previously set limitations [12]. Hence, during the gusts, both precision and reaction time are insufficient. Thus, a question is if it is possible that in gusty conditions, the autopilot might get disconnected, although the system remains stabilized on the correct glide path. Despite the fact that auto-throttle is not required for flights in reduced vertical separation minima (RVSM) airspace or for automatic landing used in ILS CAT II, the sudden disconnection of the system is an additional element of surprise, which contributes to the safety of operation. Based on analysis of on-board measurement systems of the aircraft and taking into consideration increasing reactive capabilities of direct measurements, it was observed that the auto-throttle input signal, which refers to the airspeed, comes from the air data inertial reference unit (ADIRU) left and right. Every ADIRU consists of two subsystems: air data reference (ADR) and inertial reference (IR) [12; 13]. The IR subsystem is based on three laser gyroscopes and three accelerometers, providing the data about: attitude, heading, present position, and acceleration. Airspeed information comes from the ADR and is based on pressure measurements characterised by a relatively long delay. The commonly used techniques for on-board estimation of wind speed and direction result from the analysis of TAS and GS velocity vectors [3; 14]. In order to reduce delays in the wind parameter estimation process and exclude the influence of airplane control on the obtained result, inertial measurements and flight dynamics are also taken into account [15; 16; 17]. A gust of the same intensity acting on a small airplane or an unmanned aerial vehicle (UAV) [18; 19; 20] has a different impact on its accelerations than acting on an airplane which weigh a dozen tons [21]. Massive airplanes' responses are slower and more delayed in time. In our work, for the purpose of estimating headwind gusts, it was decided to take into account the complex reaction of the aircraft in the longitudinal mode of motion. The main assumption of the presented method is a quick change of the pitch rate and pitch rate acceleration resulting from the headwind gust. Unfortunately, these parameters are also extremely affected by the operation of the control system (thrust change, and especially the elevator deflection). However, taking into account the model of the longitudinal motion of the aircraft in the estimation process allows for the compensation of this effect. The original contribution of this work is the integration of dependencies resulting from the linear mathematical model of longitudinal motion of the aircraft (taking into account the impact of headwind and vertical gusts on aircraft dynamics) with the classical method estimating wind parameters. The work was carried out assuming the practical availability of all signals required for estimation.