Example: In the long-term navigation of a ship, due to the existence of Schuler oscillation, the undamped inertial navigation system cannot meet the demand. The existence of the random drift of the gyro will cause the oscillation error accumulated over time. The traditional external horizontal damping network can Eliminate the oscillating error, but it will produce overshoot when the damping is switched, and the overshoot is proportional to the difference between the system speed and the external reference speed. The present invention selects the damping based on the time-varying external reference speed error Parameters to achieve higher stability, the implementation process is as attached figure 1 ,Specific steps are as follows:
 Step 1: Analyze the amplitude-frequency characteristics of the constant-speed network and the phase lag-lead network, and complement and match the two networks;
 As attached figure 2 Shown is the error block diagram of the strapdown inertial navigation system single horizontal channel. It can be seen that the main error source of the Schuler loop is the external reference speed error δv r , The accelerometer measurement error Δ and gyroscope drift error ε, the speed error and position error are obtained as:
 Among them, Q(s) is the damping network. Due to the existence of the three major error sources of the Schuler loop and the high-frequency interference signal output by the inertial instrument, the external reference speed error contains high-frequency measurement noise and low-frequency ocean current pollution. The damping network should meet the following characteristics:
 (1) The transfer function of the correction network provides a phase lead in the mid-frequency band to ensure that the characteristic root of the closed-loop characteristic equation of the Schuler damping loop has a negative real part, so that the system is asymptotically stable.
 (2) Under static conditions, The contribution of the constant external reference velocity error to the inertial indication position error and velocity error is zero, while the low-frequency component of the accelerometer measurement error and gyroscope drift error remains unchanged from the undamped state.
 (3) In order to improve the ability to resist high-frequency interference, require So that the Schuler damping circuit has a high-frequency attenuation characteristic above the second order, which can effectively filter the external reference speed and the high-frequency interference signal output by the inertial instrument.
 (4) When encountering strong ocean currents and severe sea conditions, or when navigating the naval vessel, the damping ratio should be reduced in time or even switched to undamped operation to eliminate the adverse effects of excessive external reference speed errors on the inertial indicator parameters.
 Since the constant speed network has the characteristics of suppressing the high-frequency reference speed error, and the phase lag-lead network has high-frequency attenuation characteristics for the gyroscope drift accelerometer error, the two are highly complementary, so consider combining the two networks into complementary Filter, constant speed network Q A (s) and phase lag-advance network Q B (s) is:
 Complementary plan as attached image 3 As shown, the above-mentioned complementary filtering double Schuler loop combination system can be equivalent to a single Schuler loop damping network, that is, Q A (s), Q B (s) Substituted into the position error, the following formula is obtained:
 Based on the complementarity of the two, the following calculations are made:
 δr A (s)×(1-W(s))+δr B (s)×W(s)
 Then get the equivalent series correction network transfer function:
 Among them, W(s) is the second-order low-pass filter, namely
 The reference speed error δv of the constant speed network, the phase lag-lead network and the second-order matching damping network r Compared with the position error characteristics of the accelerometer error Δ, the gyro drift characteristics are similar to the accelerometer error, as shown in Table 1:
 It can be seen from the table that the frequency characteristic of the combined second-order matching network to the high and low frequency reference speed error is not less than 40dB/10deg, and for the accelerometer error and gyro drift, the low frequency has almost no attenuation, that is, the earth periodic oscillation is still exist. However, high frequencies have attenuation characteristics above the second order, which has obvious advantages.
 Step 2: Design an adaptive complementary filter damping network:
 When the strapdown inertial navigation system is switched from the undamped state to the damped state, the overshoot is proportional to the difference δv between the system speed and the external reference speed. Therefore, the single-channel external horizontal damping adaptive control of the system designed in this paper The plan is attached Figure 4 As shown, the adaptive mechanism is added to the inertial navigation system. The difference between the external reference speed measured by the Doppler log and the speed of the inertial navigation system is the input of the adaptive mechanism, and the parameter of the damping network is the adaptive mechanism For output, the adaptive damping system adjusts the damping network parameters in real time according to the external speed error through the adaptive mechanism.
 Step 3: Establish the relationship between the damping parameter and the external reference speed error;
 In order to establish the damping parameters, select the speed error as the objective function of the adaptive mechanism, namely:
 Among them, δv x ,δv y They are the difference between the east and north system speed and the external reference speed. According to the propagation characteristics of strapdown inertial navigation system, the difference between the speed of the system and the external reference speed has a great influence on the damping parameters.
 Because v INS =v+δv INS ,v r =v+δv r ,δv=v r -v INS , Where δv,δv r ,v r ,v INS ,v are the difference between system speed and external reference speed, external reference speed error, external reference speed, system speed and real speed. Since the external reference velocity error measured by the Doppler log is easily affected by the environment, the transmission of the external reference velocity error to the system error needs to pass 1-Q(s), so it can be equivalent to transforming the external reference velocity error to find The optimal damping coefficient method minimizes the objective function. Specific implementation plan: select gyroscope drift and accelerometer error as 0.01°/h, 10 -4 g, and fix one of the damping parameters η = 0.5, and take μ = 1/2η = 0.5, and select the external reference speed error δv according to the overshoot and adjustment time of the platform error angle r The corresponding relationship with the optimal damping ratio ξ is shown in Table 2.
 The fitting curve of the external velocity error and the damping ratio is:
 Step 4: Substitute the adaptive mechanism and the matched high-order damping network into the loop of the inertial navigation system to obtain a new control equation for the inertial navigation solution.
 The damping coefficient ξ is substituted into the damping network according to the above formula, and the size of the damping parameter is selected in real time according to the change of the external speed for adjustment. Get the position control equation (latitude, longitude) of the inertial navigation system:
 Speed control equation (east speed, north speed):
 Platform control equation (x, y, z axis):
 Where Q(s) is a damping network containing a damping parameter with time-varying reference speed error, R M ,R N Is the radius of the earth's meridian circle and the radius of the unitary circle, and Ω is the angular velocity of the earth's rotation. According to the above-mentioned control equation, the inertial navigation solution can be used to eliminate the overshoot of Schuler oscillation and state switching in position error, velocity error and attitude angle error error.
 Implementation process: