Height integrated navigation method and system for low-altitude sea-skimming aircraft
By combining a third-order combined filtering system of a radio altimeter and a vertical accelerometer, the problem of inaccurate altitude measurement for low-altitude sea-skimming aircraft was solved, achieving high-precision and stable altitude control and ensuring the safety of the aircraft and the reliability of mission execution.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- BEIJING ZHONGKE AEROSPACE TECH CO LTD
- Filing Date
- 2025-12-30
- Publication Date
- 2026-04-10
AI Technical Summary
When existing aircraft fly at low altitudes over the sea, their altitude measurement accuracy is not high, and they are easily affected by electromagnetic echoes from the sea surface and the fluctuations of waves, resulting in unstable altitude control and the risk of collision or crashing into the sea.
A third-order combined system was formed by combining a radio altimeter and a vertical accelerometer with a third-order combined filter processor. The radio altimeter signal damped the altitude divergence of the inertial system. By utilizing the short-term accuracy of inertial measurement and the long-term stability of the radio altimeter signal, a third-order combined filter system was designed.
It achieves high-precision and high-stability altitude control for aircraft when skimming the sea at low altitudes, possesses adaptive characteristics and anti-interference capabilities, and ensures flight safety.
Smart Images
Figure CN121829520A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of aircraft, and more specifically, to a height-integrated navigation method and system for low-altitude sea-skimming aircraft. Background Technology
[0002] In the field of modern aviation and aircraft technology, low-altitude sea-skimming flight is one of the key capabilities for achieving complex missions and efficient navigation. When flying in airspace close to the sea surface, aircraft can make full use of surface features and environmental conditions, effectively improving their stealth and mission reliability. In this process, accurate perception and stable control of flight altitude are core technical aspects for ensuring flight safety and achieving predetermined flight profiles. Flying too low will directly lead to collisions or crashing into the sea, while flying too high will weaken the inherent advantages of low-altitude flight. Therefore, aircraft flying low over the sea require high-precision altitude measurement above the sea surface. However, this environment presents two major challenges: First, the electromagnetic echo from the sea surface is composed of target scattering, sea surface scattering, and multiple scatterings between the two, requiring the aircraft to have strong clutter suppression capabilities; second, wave fluctuations can cause instability in the altitude measurement reference, directly affecting the accuracy of altitude measurement. Currently, aircraft altitude control mainly uses a GNSS+IMU combined filtering scheme, supplemented by a radio altimeter. Each system has its limitations. Radio altimeters are susceptible to interference from sea waves, which can lead to erroneous responses in the altitude control system (risk of wave fluctuations). GNSS altitude signals are susceptible to interference from the multipath effect on the sea surface. Altitude signals output by vertical accelerometers are not affected by sea waves, but the results of such pure inertial altitude measurements will diverge over time.
[0003] Therefore, how to provide a method that can generate a high-precision and high-stability height estimate has become an urgent problem to be solved in this field. Summary of the Invention
[0004] To address the aforementioned problems, this application proposes an altitude-integrated navigation system for low-altitude sea-skimming aircraft, comprising: a radio altimeter, a vertical accelerometer, and a combined altitude filter processor; the radio altimeter is used to measure the actual radio altitude of the aircraft; the vertical accelerometer is used to measure the vertical acceleration of the aircraft; the combined altitude filter processor is connected to the radio altimeter and the vertical accelerometer respectively, and is used to output a combined altitude, a combined vertical velocity, and a combined vertical acceleration based on the actual radio altitude and the vertical acceleration of the aircraft.
[0005] The altitude combination navigation system for low-altitude sea-skimming aircraft described above includes a third-order combination system formed by a third-order radio altitude and inertial altitude combination filter circuit, wherein the combined altitude filter processor employs a third-order combination system.
[0006] As described above, the altitude-integrated navigation system for low-altitude sea-skimming aircraft includes a third-order integrated system that processes the measured value h* of the aircraft's actual radio altitude as measured by the radio altimeter into a first-order inertial element to obtain the radio altimeter-measured altitude h. b .
[0007] The altitude-integrated navigation system for low-altitude sea-skimming aircraft described above involves obtaining the measured altitude h by performing first-order inertial processing on the actual measurements from the radio altimeter. b , will h b The combined altitude h of the third-order combined system output radio / inertial system ib After comparison, a height error signal is generated. The height error signal is then passed through the system feedback gain K1 and K2 to obtain the vertical acceleration and vertical velocity correction signals.
[0008] The altitude-integrated navigation system for low-altitude sea-skimming aircraft described above includes a third-order integrated system that further comprises a system feedback gain K3. The altitude error signal, after passing through the system feedback gain K3, outputs a value used to correct the integrated vertical acceleration a. ib This is to eliminate the constant zero-point error of the vertical accelerometer.
[0009] The altitude-integrated navigation system for low-altitude sea-skimming vehicles described above, wherein the closed-loop transfer function of the third-order integrated system in the s-domain is expressed as:
[0010]
[0011] h ib (s) represents the group height, a z (s) represents the vertical acceleration, h b (s) indicates the altitude measured by the radio altimeter.
[0012] The altitude-integrated navigation system for low-altitude sea-skimming vehicles described above further includes a third-order integrated system whose closed-loop transfer function determines the system's closed-loop transfer function, expressed as:
[0013] s 3 +K1s 2 +K2s+K3=0
[0014] The altitude-integrated navigation system for low-altitude sea-skimming vehicles described above further includes: constructing a Routh table based on the system's characteristic equations; obtaining the parameter conditions for system stability through the Routh table; and the system stability conditions are as follows:
[0015]
[0016] A method for altitude-integrated navigation for low-altitude sea-skimming aircraft includes the following steps: acquiring the actual radio altitude of the aircraft measured by a radio altimeter and the vertical acceleration measured by a vertical accelerometer; and outputting a combined altitude, a combined vertical velocity, and a combined vertical acceleration based on the actual radio altitude and the vertical acceleration of the aircraft.
[0017] The altitude-integrated navigation method for low-altitude sea-skimming aircraft described above, wherein outputting combined altitude, combined vertical velocity, and combined vertical acceleration based on the measured actual altitude and the aircraft's vertical acceleration includes the following sub-steps: performing first-order inertial processing on the measured actual altitude and comparing it with the combined altitude output by the system to determine an altitude error signal; determining a correction signal based on the altitude error signal and the system feedback gain; and correcting the vertical acceleration and vertical velocity based on the correction signal to obtain the combined altitude, combined vertical acceleration, and combined vertical velocity.
[0018] This application has the following beneficial effects:
[0019] (1) The altitude combination navigation system for low-altitude sea-skimming aircraft proposed in this application addresses the altitude control problem of low-altitude sea-skimming aircraft by fusing data from radio altimeters and accelerometers and designing a third-order altitude filtering system. It uses radio altitude signals to dampen the altitude divergence of the inertial system, combining the complementary advantages of short-term high accuracy of accelerometers and long-term stability of altimeters.
[0020] (2) The third-order combined system designed in this application utilizes the high short-term accuracy of inertial measurement to compensate for sea wave noise interference from the radio altimeter, while simultaneously using the long-term stability of the radio altimeter signal to suppress the divergence of inertial altitude over time. It exhibits good adaptive characteristics, anti-interference capability, and long-term stability. Low-pass filtered altimeter data provides a long-term reference to correct the integral divergence of the accelerometer. At the same time, the smoothing characteristics of inertial altitude are used to filter out noise in the altimeter data. The fusion of these two methods yields a combined altitude signal that satisfies both high accuracy and stability. Attached Figure Description
[0021] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this application. For those skilled in the art, other drawings can be obtained based on these drawings.
[0022] Figure 1 This is a schematic diagram of the internal structure of an altitude-integrated navigation system for a low-altitude sea-skimming aircraft, provided according to an embodiment of this application.
[0023] Figure 2This is a schematic diagram of the combined height filtering processor provided in an embodiment of this application;
[0024] Figure 3 This is a Bode plot of the combined height filtering processor provided in the embodiments of this application;
[0025] Figure 4 This is a schematic flowchart of an altitude-integrated navigation method for low-altitude sea-skimming aircraft provided according to an embodiment of this application. Detailed Implementation
[0026] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.
[0027] This application proposes a height-integrated navigation method and system for low-altitude sea-skimming aircraft. When the aircraft is flying at normal altitude, it primarily relies on GNSS+IMU combined altitude filtering, supplemented by radio radar altitude measurement and vertical accelerometer altitude measurement. However, during low-altitude sea-skimming flight, the accuracy of the GNSS altitude signal decreases due to interference from the sea surface multipath effect in ultra-low altitude environments, at which point the altitude is primarily determined by a combination of radio radar altitude measurement and vertical accelerometer altitude measurement. This complementary approach achieves high-precision altitude determination for the aircraft. Simultaneously, the high short-term accuracy of inertial measurement effectively compensates for sea wave noise interference from the radio altimeter; and the long-term stability of the radio altitude signal suppresses the divergence of inertial altitude over time. This mechanism ensures that the aircraft's altitude control system possesses excellent adaptive characteristics, anti-interference capabilities, and long-term stability during low-altitude sea-skimming flight.
[0028] Example 1
[0029] like Figure 1 As shown, this embodiment provides an altitude-integrated navigation system for low-altitude sea-skimming aircraft, including a radio altimeter, a vertical accelerometer, and an integrated altitude filter processor.
[0030] The radio altimeter is used to measure the actual radio altitude of the aircraft.
[0031] Vertical accelerometers are used to measure the vertical acceleration of aircraft.
[0032] The combined altitude filter processor is connected to the radio altimeter and the vertical accelerometer, respectively, and is used to output the combined altitude, combined vertical velocity, and combined vertical acceleration based on the actual radio altitude and vertical acceleration of the aircraft.
[0033] Among them, such as Figure 2 As shown, the combined altitude filter processor uses a third-order combined system formed by a third-order radio altitude and inertial altitude combined filter loop. The radio altitude signal is used to dampen the altitude divergence of the inertial system, which can eliminate the influence of accelerometer zero-point error on the output.
[0034] The actual radio altitude measurement h of the aircraft * Inevitably, a certain amount of high-frequency measurement noise will be mixed in. After passing through a first-order inertial element to filter out the high-frequency noise and retain the low-frequency signal, the height h measured by the radio altimeter is obtained. b .
[0035] Vertical acceleration a z The acceleration is obtained through calculation based on the three-axis acceleration measured by the IMU. The specific calculation process is as follows: The acceleration value output by the IMU is for the local system, while the vertical acceleration needs to be obtained from the navigation system acceleration. Based on the attitude angles [φ,θ,ψ] (roll, pitch, heading), the coordinate transformation matrix of the navigation system (East-North-Sky) is calculated using a 312 rotation sequence to transform to the local system (Right-Front-Up).
[0036] The acceleration a of this system is expressed using the coordinate transformation matrix. b Converted to navigation system acceleration a n :
[0037]
[0038] in,
[0039] The vertical acceleration component, including gravitational acceleration, measured by the inertial navigation system is:
[0040] a U =
[001] ·a n
[0041] To obtain the vertical acceleration, we need to subtract the gravitational acceleration g, and then obtain:
[0042] a z =a U -g
[0043] Measure altitude h using a radio altimeter b The combined altitude h of the third-order combined system output radio / inertial system ib After comparison, a height error signal is generated. This signal provides a correction signal for the calculation of vertical acceleration and vertical velocity through gains K2 and K1, ensuring that the inertial height output does not diverge over time.
[0044] in Figure 2 The system operates simultaneously through three parallel channels, including the integral at the system feedback gain K1 to form the vertical velocity v. z The corrected signal is integrated at the system feedback gain K2 to form the vertical acceleration a. z The correction signal is integrated at the feedback gain K3 to eliminate the influence of the accelerometer's zero-position error on the system's steady-state error.
[0045] Considering the aircraft's very low altitude while skimming the sea, we can ignore the change in gravitational acceleration with altitude. Therefore, for... Figure 2 The simplified state-space model of the third-order combinatorial system shown is as follows:
[0046]
[0047] Among them, h b To measure altitude with a radio altimeter; a z h is the vertical acceleration. ib v ib a ib These are the height, vertical velocity, and vertical acceleration of the combined filter system, respectively. These represent the vertical velocity, vertical acceleration, and vertical jerk of the combined filter system, respectively. The model above shows that by appropriately selecting parameters K1, K2, and K3, an altimeter system with steady-state error and dynamic performance meeting the requirements for sea-skimming flight can be obtained.
[0048] After determining the execution principle of the third-order combined system, it is also necessary to conduct a theoretical analysis of the system stability and theoretically prove that the third-order combined system can work stably.
[0049] The theoretical analysis of system stability includes:
[0050] Determine the closed-loop transfer function of the system;
[0051] Determine the system characteristic equation based on the closed-loop transfer function;
[0052] Construct the Routh table based on the system's characteristic equation;
[0053] The parameters that stabilize the system are obtained through the Routh table;
[0054] After obtaining the parameters that make the system stable, the system parameters are designed.
[0055] The closed-loop transfer function of the system in the s-domain is as follows:
[0056]
[0057] By examining the closed-loop transfer function, we can see that the input a z (s) and hb How do changes in (s) affect the final output h? ib (s).
[0058] The first term on the right-hand side of the equation indicates the vertical acceleration a. z (s) for the combined height h ib The influence of (s) indicates that the numerator of the first term has only one differential operator, which means that the constant zero bias of the vertical acceleration does not affect the combined height in steady state, i.e., the system has a suppressive effect on the constant zero bias. This is because if the vertical acceleration has a constant zero bias Δa, its Laplace transform is... s in the molecule and input The s-phase cancels out, according to the final value theorem s·h ib (s) makes the steady-state error zero. This indicates that the constant input s in the numerator has been completely filtered out through the differentiation operation. The second term on the right indicates the altitude h of the altimeter. b (s) for the combined height h ib The steady-state error of (s) is also 0, meaning that the combined height eventually converges to the altimeter measurement.
[0059] The equation extracted from the denominator of the closed-loop transfer function is the characteristic equation of the system, s 3 +K1s 2 +K2s+K3=0.
[0060] The Routh table is constructed as follows:
[0061]
[0062] According to the Routh criterion, if all coefficients in the first column of the Routh table are positive, then the conditions for system stability are as follows:
[0063]
[0064] Further analysis of the system reveals that the aircraft's true altitude is equal to the second integral of its acceleration, as shown in the following equation:
[0065]
[0066] The altitude measured by the radio altimeter is as follows:
[0067]
[0068] Where τ is the time delay constant of the infinite electric altimeter.
[0069] The vertical velocity is:
[0070]
[0071] The design of system parameters includes the design of the system gain value.
[0072] Based on the Routh criterion, the necessary and sufficient condition for the stability of a third-order system is: K1>0, K3>0. For a strongly stable system with a phase margin (PM) > 60°, the following conditions must be met at the crossover frequency:
[0073] PM = 180° + ∠G(jw) c >60°
[0074] Among them, ∠G(jw c ) represents the open-loop transfer function at the crossover frequency ω. c The phase at that point must satisfy:
[0075] ∠G(jw c -120°
[0076] Since a third-order combined system has three poles, and system stability requires all poles to be in the negative half-plane, the poles are configured as two low-damped second-order conjugate dominant poles. And a real pole (-a) far from the imaginary axis.
[0077] Therefore, let the damping ratio ζ≈0.5 and the natural frequency w n =1 rad / s, then the two poles are:
[0078] p 1,2 = -0.5 ± 0.866j
[0079] Next, choose real poles, setting p3 = -5, far from the imaginary axis to reduce their influence. Therefore, the characteristic polynomial can be constructed:
[0080] D(s) = (s+5)(s) 2 +s+1)=s 3 +6s 2 +6s+5
[0081] Therefore, we obtain: K1 = 6, K2 = 6, K3 = 5. Substituting these values into the equations confirms that the Routh criterion meets the stability condition.
[0082] in Figure 3Perform open-loop frequency response characteristic analysis on the Bode plot of the system. The gain margin (GM) and phase margin (PM) of the system are important indicators in the stability analysis of the control system. The gain margin measures how many dB the gain can be increased without causing the system to become unstable when the phase reaches -180°. The phase margin reflects how much phase lag the system can tolerate at cross-frequency points before becoming unstable. Generally, system stability requires both GM and PM to be greater than 0, but strong system stability requires GM > 10 and PM > 60°. Figure 2 The figure shows the open-loop frequency response of the system when K1=6, K2=6, and K3=5. The gain margin is positive infinity, and the phase margin is 142 degrees, far exceeding the strong stability threshold. This proves that the system does not have the risk of instability due to increased gain and has extremely strong phase lag tolerance. The system gain design is effective.
[0083] Example 2
[0084] like Figure 4 As shown, this embodiment provides an altitude-integrated navigation method for low-altitude sea-skimming aircraft, specifically including the following steps:
[0085] Step S1: Obtain the actual height measured by the radio altimeter and the vertical acceleration measured by the vertical accelerometer;
[0086] Step S2: Based on the measured actual altitude and the aircraft's vertical acceleration, output the combined altitude, combined vertical velocity, and combined vertical acceleration.
[0087] Step S2 includes the following sub-steps:
[0088] Step S21: After performing first-order inertial processing on the measured actual height, compare it with the combined height output by the system to determine the height error signal.
[0089] Step S22: Determine the correction signal based on the altitude error signal and the system feedback gain.
[0090] Step S23: Correct the vertical acceleration and vertical velocity according to the correction signal to obtain the combined height, combined vertical acceleration and combined vertical velocity.
[0091] This application also provides a computer storage medium storing computer instructions, which, when invoked, are used to execute the altitude-integrated navigation method for low-altitude sea-skimming aircraft.
[0092] The embodiments disclosed in this invention provide a computer-readable storage medium storing computer program instructions that, when executed on a computer, cause the computer to perform the aforementioned altitude-integrated navigation method for a low-altitude sea-skimming aircraft.
[0093] This invention provides a processor for processing the aforementioned altitude-integrated navigation method for low-altitude sea-skimming aircraft.
[0094] In this embodiment of the invention, the processor can be an integrated circuit chip with signal processing capabilities. The processor can be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.
[0095] The various methods, steps, and logic diagrams disclosed in the embodiments of this invention can be implemented or executed. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the methods disclosed in the embodiments of this invention can be directly implemented by a hardware decoding processor, or implemented by a combination of hardware and software modules in the decoding processor. The software modules can reside in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. The processor reads information from the storage medium and, in conjunction with its hardware, completes the steps of the above methods.
[0096] The storage medium can be memory, such as volatile memory or non-volatile memory, or may include both volatile and non-volatile memory.
[0097] Non-volatile memory can be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. Volatile memory can be random access memory (RAM), which is used as an external cache. By way of example, but not limitation, many forms of RAM are available, such as Static Random Access Memory (SRAM), Dynamic Random Access Memory (DRAM), Synchronous DRAM (SDRAM), Double Data Rate Synchronous DRAM (DDRSDRAM), Enhanced Synchronous DRAM (ESDRAM), Synchlink DRAM (SLDRAM), and Direct Rambus RAM (DRRAM).
[0098] This application has the following beneficial effects:
[0099] (1) The altitude combination navigation system for low-altitude sea-skimming aircraft proposed in this application addresses the altitude control problem of low-altitude sea-skimming aircraft by fusing data from radio altimeters and accelerometers and designing a third-order altitude filtering system. It uses radio altitude signals to dampen the altitude divergence of the inertial system, combining the complementary advantages of short-term high accuracy of accelerometers and long-term stability of altimeters.
[0100] (2) The third-order combined system designed in this application utilizes the high short-term accuracy of inertial measurement to compensate for sea wave noise interference from the radio altimeter, while simultaneously using the long-term stability of the radio altimeter signal to suppress the divergence of inertial altitude over time. It exhibits good adaptive characteristics, anti-interference capability, and long-term stability. Low-pass filtered altimeter data provides a long-term reference to correct the integral divergence of the accelerometer. At the same time, the smoothing characteristics of inertial altitude are used to filter out noise in the altimeter data. The fusion of these two methods yields a combined altitude signal that satisfies both high accuracy and stability.
[0101] Although the examples referred to in the present application are described for illustrative purposes only and not for limiting the scope of the application, changes, additions and / or deletions to the implementation may be made without departing from the scope of the application.
[0102] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.
Claims
1. A high-altitude integrated navigation system for low-altitude sea-skimming aircraft, characterized in that, include: Radio altimeter, vertical accelerometer, and combined altitude filter processor; A radio altimeter is used to measure the actual radio altitude of an aircraft. Vertical accelerometer, used to measure the vertical acceleration of an aircraft; The combined altitude filter processor is connected to the radio altimeter and the vertical accelerometer, respectively, and is used to output the combined altitude, combined vertical velocity, and combined vertical acceleration based on the actual radio altitude and vertical acceleration of the aircraft.
2. The altitude-integrated navigation system for low-altitude sea-skimming aircraft as described in claim 1, characterized in that, The combined altitude filter processor employs a third-order combined system formed by a third-order radio altitude and inertial altitude combined filter loop.
3. The altitude-integrated navigation system for low-altitude sea-skimming aircraft as described in claim 2, characterized in that, The third-order integrated system includes the measurement value h of the aircraft's actual radio altitude as measured by the radio altimeter. * After processing with a first-order inertial element, the altitude h measured by the radio altimeter is obtained. b .
4. The altitude-integrated navigation system for low-altitude sea-skimming aircraft as described in claim 3, characterized in that, The measured height h is obtained by performing first-order inertial processing on the actual measurement value from the radio altimeter. b , will h b The combined altitude h of the third-order combined system output radio / inertial system ib After comparison, a height error signal is generated. The height error signal is then passed through the system feedback gain K1 and K2 to obtain the vertical acceleration and vertical velocity correction signals.
5. The altitude-integrated navigation system for low-altitude sea-skimming aircraft as described in claim 4, characterized in that, The third-order combined system also includes a system feedback gain K3. After the height error signal passes through the system feedback gain K3, it outputs a value used to correct the combined vertical acceleration a. ib This is to eliminate the constant zero-point error of the vertical accelerometer.
6. The altitude-integrated navigation system for low-altitude sea-skimming aircraft as described in claim 5, characterized in that, The closed-loop transfer function of a third-order combined system in the s-domain is expressed as: h ib (s) represents the group height, a z (s) represents the vertical acceleration, h b (s) indicates the altitude measured by the radio altimeter.
7. The altitude-integrated navigation system for low-altitude sea-skimming aircraft as described in claim 6, characterized in that, It also includes the fact that the closed-loop transfer function of a third-order combined system determines the closed-loop transfer function of the system, expressed as: s 3 +K1s 2 +K2s+K3=0 8. The altitude-integrated navigation system for low-altitude sea-skimming aircraft as described in claim 7, characterized in that, It also includes, Construct the Routh table based on the system's characteristic equation; The parameters that stabilize the system are obtained through the Routh table; The conditions for system stability are as follows:
9. A height-integrated navigation method for low-altitude sea-skimming aircraft, characterized in that, Includes the following steps: Acquire the actual radio altitude of the aircraft as measured by the radio altimeter and the vertical acceleration as measured by the vertical accelerometer; Based on the aircraft's actual radio altitude and vertical acceleration, output the combined altitude, combined vertical velocity, and combined vertical acceleration.
10. The altitude-integrated navigation method for low-altitude sea-skimming aircraft as described in claim 9, characterized in that, Based on the measured actual altitude and the aircraft's vertical acceleration, the output of combined altitude, combined vertical velocity, and combined vertical acceleration includes the following sub-steps: The measured actual height is processed by first-order inertial processing and compared with the combined height output by the system to determine the height error signal; The correction signal is determined based on the altitude error signal and the system feedback gain; The vertical acceleration and vertical velocity are corrected based on the correction signal to obtain the combined height, combined vertical acceleration, and combined vertical velocity.